Phase diagram of a class of spin-triplet ferromagnetic superconductors
化工专业英语练习题 参考答案
练习一参考答案1将下列句子或段落翻译成英语1)A process is any operation or series of operations that causes a physical or chemical change in asubstance or a mixture of substances .The material that enters a process is referred to as input or feed the process,and that which leaves is called output or product.2)As a chemical engineer,you might be called on to design individual process units (such as reactors,distillation columns,heat exchangers),supervise the operation of a process,or modify a process design to accommodate a change in the feed or in the desired product characteristics.As a rule,to any of these things you must know the amounts,compositions,and conditions of the materials that enter and leave each process unit,and if you are working with an existing units,you must be able to measure enough of these quantities to verify that the process is doing what it was designed to do.3)Founded in 1839from a small production firm for pharmaceutical products,B.Braun has grown steadilyinto a multinational company dealing with medical products,medical technology,pharmaceutical and biotechnology.2将下列句子或段落翻译成汉语1）包括的一系列操作，如混合、蒸发、过滤，无论产物是什么，这些操作都基本同，从而导致了单元操作的概念。
A New Quantum Liquid of Spin-Charge Separation in the Doped-Mott System A Model for Monolay
Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033
We study the triangular t-J model with multiple spin exchange interactions using exact diagonalization of small clusters, as a model of monolayer liquid 3He. It is found that a new quantum liquid state is realized due to the competition between ferromagnetic two-spin and antiferromagnetic four-spin exchange interactions. This new quantum liquid shows spin-charge separation. This gives an interpretation of the anomalous heat capacity recently observed in monolayer liquid 3He adsorbed on a graphite.
why such a spin-charge separation is realized in this system.
In this letter, we present a theoretical justification of the spin-charge separation in the doped-Mott region of monolayer liquid 3He. First an effective model is intro-
chapter4-phase diagrams相图双语
Chapter Outline
4.1 Definition and basic concepts 4.2 Binary alloy phase diagram 4.3 Isomorphous phase diagram 4.4 Eutectic phase diagram 4.5 Peritectic phase diagram 4.6 Intermetallic Compounds
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4.2 Binary alloy phase diagram
constant pressure (fixed parameter). Three independent variables: T, P, compositions The binary eutectic phase diagram explains the chemical behavior of two immiscible (unmixable) crystals from a completely miscible (mixable) melt.
3、mark critical points, and connect start and finish points of sodification 4、label various phase regions
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1085
Tie lines and phase compositions for a Cu-40% Ni alloy at several temperatures
09.Phase.diagrams
Phase Diag
• Examples:
Co = 35 wt% Ni At T A : Only Liquid (L) W L = 100 wt%, W α = 0 At T D : Only Solid ( α ) W L = 0, W α = 100 wt% At T B : Both α and L
§ 9.4 Microstructure
-Microstructure is characterized by number of phases, their proportions, and the manner in which they are distributed. -The microstructure is affected by alloying elements, alloy concentration, heat treatment, temperature, etc.
- Every pure material is a phase. - In the previous example, sugar-water solution is one phase, & sugar solid is another phase. - Two phases are different in physical or chemical properties, but it is not necessary for all to be different.
Engr Mater: 09 4
Phase Diag
§9.7 Binary Isomorphous Systems
• An isomorphous system refers to the complete liquid and solid solubility of the two components. • Definitions of liquidus line and solidus line • Reading the phase diagram: - melting temperature of elements - range of melting of solid solutions. - phases present - composition of these phases - fraction of each phase Cu-Ni system
The Phase Diagram of Strongly-Interacting Matter
a r X i v :0801.4256v 1 [h e p -p h ] 28 J a n 2008The Phase Diagram of Strongly-Interacting MatterP.Braun-Munzinger 1,2and J.Wambach 1,21Gesellschaft f¨u r Schwerionenforschung mbH,Planckstr,1,D64291Darmstadt,Germany 2Technical University Darmstadt,Schlossgartenstr.9,D64287Darmstadt,GermanyA fundamental question of physics is what ultimately happens to matter as it is heated or com-pressed.In the realm of very high temperature and density the fundamental degrees of freedom of the strong interaction,quarks and gluons,come into play and a transition from matter consisting of confined baryons and mesons to a state with ’liberated’quarks and gluons is expected.The study of the possible phases of strongly-interacting matter is at the focus of many research activi-ties worldwide.In this article we discuss physical aspects of the phase diagram,its relation to the evolution of the early universe as well as the inner core of neutron stars.We also summarize recent progress in the experimental study of hadronic or quark-gluon matter under extreme conditions with ultrarelativistic nucleus-nucleus collisions.PACS numbers:21.60.Cs,24.60.Lz,21.10.Hw,24.60.KyContentsI.Introduction1II.Strongly-Interacting Matter under ExtremeConditions2A.Quantum Chromodynamics 2B.Models of the phase diagram 4III.Results from Lattice QCD6IV.Experiments with heavy ions8A.Opaque fireballs and the ideal liquid scenario 8B.Hadro-Chemistry9C.Medium modifications of vector mesons 11D.Quarkonia-messengers of deconfinement 14V.Phases at high baryon densities16A.Color Superconductivity 16VI.Summary and Conclusions17Acknowledgments 18References18I.INTRODUCTIONMatter that surrounds us comes in a variety of phases,which can be transformed into each other by a change of external conditions such as temperature,pressure,com-position etc.Transitions from one phase to another are often accompanied by drastic changes in the physical properties of a material,such as its elastic properties,light transmission or electrical conductivity.A good ex-ample is water,whose phases are (partly)accessible to everyday experience.Changes in external pressure and temperature result in a rich phase diagram which,be-sides the familiar liquid and gaseous phases,features a variety of solid (ice)phases in which the H 20molecules arrange themselves in spatial lattices of certain symme-tries (Fig.1).Twelve of such crystalline (ice)phases are known at present.In addition,three amorphous (glass)phasesFIG.1The phase diagram of H 20(Chaplin,2007).Besides the liquid and gaseous phase a variety of crystalline and amor-phous phases occur.Of special importance in the context of strongly-interacting matter is the critical endpoint between the vapor and liquid phase.have been identified.Famous points in the phase dia-gram are the triple point where the solid-liquid-and gas phases coexist and the critical endpoint at which there is no distinction between the liquid and gas phase.This is the endpoint of a line of first-order liquid-gas transitions and is of second order.Under sufficient heating water and,for that matter any other substance,goes over into a new state,a ’plasma’,consisting of ions and free electrons.This transition is mediated by molecular or atomic collisions.It is continuous 1and hence not a phase transition in the strict thermodynamic sense.On the other hand,the2plasma exhibits new collective phenomena such as screen-ing and ’plasma oscillations’(Mrowczynski and Thoma,2007).Plasma states can alsobeinduced byhighcompression,whereelectronsare delocalizedfrom their orbitals and form a conducting ’degenerate’quantum plasma.In contrast to a hot plasma there exists in this case a true phase transition,the ’metal-insulator’transition (Gebhard,1997;Mott,1968).A good exam-ple are white dwarfs,stars at the end of their evolution which are stabilized by the degeneracy pressure of free electrons (Chandrasekhar,1931;Shapiro and Teukolsky,1983).One may ask what ultimately happens when matter is heated and compressed.This is not a purely academic question but is of relevance for the early stages of the universe as we go backwards in time in the cosmic evolu-tion.Also,the properties of dense matter are important for our understanding of the composition and properties of the inner core of neutron stars,the densest cosmic objects.Here,the main players are no longer forces of electromagnetic origin but the strong interaction,which is responsible for the binding of protons and neutrons into nuclei and of quarks and gluons into hadrons.In the Standard Model of particles physics the strong in-teraction is described in the framework of a relativistic quantum field theory called Quantum Chromodynamics (QCD),where point-like quarks and gluons are the ele-mentary constituents.The question of the fate of matter at very high tem-perature was first addressed by Hagedorn in a seminal paper in 1965(Hagedorn,1965)and later elaborated by Frautschi (Frautschi,1971).The analysis was based on the (pre-QCD)’bootstrap model’in which strongly-interacting particles (hadrons)were viewed as composite ’resonances’of lighter hadrons.A natural consequence of this model is the exponential growth in the density of mass statesρ(M h )∝M −5/2he M h /T H.(1)This is well verified by summing up the hadronic states listed by the Particle Data Group (Yao et al.,2006).A fit to the data yields T H ∼160−180MeV.It is then easy to see that logarithm of the partition function of such a ’resonance gas’ln ZRG(T )=iln Z RG i +κ∞m 0dM h ρ(M h )M 3/2h e −M h /T(2)and,hence,all thermodynamic quantities diverge when T =T H ,which implies that matter cannot be heated be-yond this limiting ’Hagedorn temperature’.Here,ln Z i is the logarithm of the partition function for all well iso-lated particles with mass m i .Above a certain mass m 0all particles start to overlap and from that point on the sum is converted into an integral over the mass density ρ(m )and all particles can be treated in Boltzmann ap-proximation.For the present argument the explicit valueof the constant κis immaterial.The energy that is sup-plied is used entirely for the production of new particles.This is of course at variance with our present understand-ing of the big bang in which the temperature is set by the Planck scale T ∼M Planck =2In all formulas below we use ¯h =c =13This term was coined by Edward Shuryak (Shuryak,1978a)3of electrons with photons is given byL QED=−14G aµνGµνa+¯qγµ(i∂µ−g sλa4Quarks form a fundamental representation of the Lie group SU(3).which now includes a non-linear term.Its form is en-tirely dictated by the gauge group(which is now SU(3) rather than U(1))through its’structure constants’f abc5. The group structure is also reflected in the quark-gluon coupling through the’Gell-Mann’matricesλa which are the analog of the SU(2)Pauli matrices.The more elab-orate group structure renders QCD much more compli-cated than QED even at the classical level of Maxwell’s equations.6In any relativisticfield theory the vacuum itself be-haves,due to quantumfluctuations,like a polarizable medium.In QED the photon,although uncharged, can create virtual electron-positron pairs,causing partial screening of the charge of a test electron.This implies that the dielectric constant of the QED vacuum obeys7ǫ0>1.On the other hand,because of Lorentz invari-ance,ǫ0µ0=1,i.e.the magnetic permeabilityµ0is smaller than one.Thus the QED vacuum behaves like a diamagnetic medium.In QCD,however,the gluons carry color charge as well as spin.In addition to vir-tual quark-antiquark pairs,which screen a color charge and thus would make the vacuum diamagnetic,the self-interaction of gluons can cause a color magnetization of the vacuum and make it paramagnetic.This effect ac-tually overcomes the diamagnetic contribution from¯q q pairs such thatµc0>1.The situation is somewhat simi-lar to the paramagnetism of the electron gas,where the intrinsic spin alignment of electrons overwhelms the dia-magnetism of orbital motion.Sinceµc0>1it follows thatǫc0<1,so that the color-electric interaction be-tween charged objects becomes stronger as their separa-tion grows(’infrared slavery’).In this sense the QCD vac-uum is an’antiscreening’medium.As the distance r→0, on the other hand,µc0andǫc0→1,and the interaction be-comes weaker(’asymptotic freedom’).This gives rise to a pronounced variation(’running’)of the strong’fine struc-ture constant’αs=g2s/4πwith(space-time)distance or momentum transfer Q.Its mathematical form to lead-ing order was worked out in1973by Gross and Wilczeck and independently by Politzer(Gross and Wilczek,1973; Politzer,1973)and yieldsαs(Q2)=12π5Gauge groups other than U(1)wherefirst discussed by Yang and Mills in1954(Yang and Mills,1954)in the context of SU(2)and the correspondingfield theories are therefore called’Yang-Mills theories’.Since the generators of SU(N)do not commute such theories are also called’non-abelian’.6For instance,the wave equation for the vector potentials A aµis non-linear and its solutions in Euclidean space-time include solitons called’instantons’.7Provided the distance r is large enough so that the virtual cloud around the test charge is not penetrated.This distance is ex-tremely small.scale parameter.As indicated in Fig.2the running ofαs8The situation is analogous to the case of a cavity in a perfectconductor(superconductor)withµ=0,ǫ=∞except that therole ofµandǫare interchanged.baryons or quark-antiquark pairs for mesons and impos-ing appropriate boundary conditions on the quark wavefunctions to prevent leakage of color currents across theboundary,B can be determined from afit to knownhadron masses.For the quark-hadron transition the MIT-Bag modelprovides the following picture:when matter is heated,nuclei eventually dissolve into protons and neutrons(nu-cleons).At the same time light hadrons(preferentiallypions)are created thermally,which increasinglyfill thespace between the nucleons.Because of theirfinitespatial extent the pions and other thermally producedhadrons begin to overlap with each other and with thebags of the original nucleons such that a network of zoneswith quarks,antiquarks and gluons is formed.At a cer-tain critical temperature T c these zonesfill the entire vol-ume in a’percolation’transition.This new state of mat-ter is the quark-gluon plasma(QGP).The vacuum be-comes trivial and the elementary constituents are weaklyinteracting sinceµc0=ǫc0=1everywhere.There is,how-ever,a fundamental difference to ordinary electromag-netic plasmas in which the transition is caused by ioniza-tion and therefore gradual.Because of confinement therecan be no liberation of quarks and radiation of gluonsbelow the critical temperature.Thus a relatively sharptransition is expected.A similar picture emerges whenmatter is strongly compressed.In this case the nucleonsoverlap at a critical number density n c and form a colddegenerate QGP consisting mostly of quarks.This statecould be realized in the inner core of neutron stars andits properties will be discussed later.In the MIT-Bag model thermodynamic quantities suchas energy density and pressure can be calculated as afunction of temperature and quark chemical potential9µqand the phase transition is inferred via the Gibbs con-struction of the phase boundary.Under the simplifyingassumption of a free gas of massless quarks,antiquarksand gluons in the QGP atfixed T andµq one obtains thepressurep QGP(T,µq)=37π22π2−B.(9)To the factor37=16+21,16gluonic(8×2),12quark(3×2×2)and12antiquark degrees of freedom contribute.For quarks an additional factor of7/8accounts for thedifferences in Bose-Einstein and Fermi-Dirac statistics.The temperature dependence of the pressure follows aStefan-Boltzmann law,in analogy to the black-body ra-diation of massless photons.The properties of the physi-cal vacuum are included by the bag constant B,which is a measure for the energy density of the vacuum.By con-struction,the quark-hadron transition in the MIT bag model is offirst order,implying that the phase boundary is obtained by the requirement that at constant chemi-cal potential the pressure of the QGP is equal to that in the hadronic phase.For the latter the equation of state (EoS)of hadronic matter is needed.Taking for simplic-ity a gas of massless pions with pπ(T,µq)=(3π2/90)T4, a simple phase diagram emerges in which the hadronic phase is separated from the QGP by afirst-order transi-tion line.Taking for the bag constant the original MIT fit to hadronic masses,B=57.5MeV/fm3one obtains T c∼100MeV atµq=0andµc∼300MeV at vanishing temperature(Buballa,2005).These results have a number of problems.On the one hand,the transition temperature is too small,as we know in the mean time.We will come back to this in the next section.On the other hand at3µq=µb∼M N(mass of the nucleon M N=939MeV),where homogeneous nu-clear matter consisting of interacting protons and neu-trons is formed,a cold QGP is energetically almost de-generate with normal nuclear matter.Both problems are, however,merely of quantitative nature and can be cir-cumvented by raising the value of B.More serious is the fact that,at largeµq,a gas of nucleons because of its color neutrality is always energetically preferred to the QGP. The biggest problem is,however,that QCD has a number of other symmetries besides local gauge symmetry which it shares with QED.Most notable in the present context is chiral symmetry,which is exact in the limit of vanishing quark masses.For physical up and down quark masses of only a few MeV this limit is well satisfied10.Exact chiral symmetry implies that only quarks with the same helicity or’chirality’interact11,i.e.the left-handed and right-handed world completely decouple.This means in particular that physical states of opposite parity must be degenerate in mass.Similar to a ferromagnet,where rotational symmetry is spontaneously broken at low temperatures through spin alignment,also the chiral symmetry of the strong inter-action is spontaneously broken in the QCD vacuum as a result of the strong increase ofαs at small momenta (Fig.2).Empirical evidence is the absence of parity doublets in the mass spectrum of hadrons.Since mass-less quarksflip their helicity at the bag boundary the MIT-Bag model massively violates chiral symmetry.For100%0%FIG.3Fraction of the effective quark mass generated dy-namically (light-grey)as compared to that from the Higgs mechanism in the electro-weak sector of the Standard Model (dark grey).QCD vacuum.In QCD,mesons emerge as bound states of quark-antiquark pairs with constituent mass.Because of spon-taneous chiral symmetry breaking there appears,how-ever,a peculiarity that is known from condensed matter physics and was first noted by J.Goldstone (Goldstone,1961).For vanishing (bare)quark mass there must be a massless excitation of the vacuum,known as the ’Gold-stone mode’.Such highly collective modes occur e.g.in spin systems.The ferromagnetic ground state has a spon-taneous alignment of all spins.A spin wave of infinite wavelength (λ→∞,k →0)corresponds to a simulta-neous rotation of all spins,which costs no energy 12.In strong interaction physics with two flavors this mode is identified with the pion.The fact that pions are not ex-actly massless is related to the finite bare mass of the up and down quarks.Nevertheless the pion mass with ∼140MeV is significantly smaller than that of the ρ-or the ωmeson (∼800MeV ∼2M q ).In the 1980’s and 1990’s the NJL model was used ex-tensively in theoretical studies of the phase diagram.Since it incorporates spontaneous symmetry breaking and the ensuing mass generation one can address ques-tions of chiral symmetry restoration with increasing T and µq and the corresponding medium modifications of hadron masses.The quark-antiquark condensate ¯q q serves as an order parameter for chiral symmetry break-ing,analogous to the spontaneous magnetization in a spin system.Similar to the Curie-Weiss transition,the order parameter vanishes at a critical temperature T c in the chiral limit.This is the point where chiral symmetry is restored and the quarks become massless 13.Figure 4displays a prediction for the evolution of the chiral con-densate with temperature and quark-chemical potential for physical up and down quark masses obtained in mean-7 and the statistical mechanics of a system with temper-ature T=1/τ.With this method of’lattice QCD’thepartition function of the grand canonical ensembleZ(V,T,µq)= D[A,q]e 1/T0dτ V d3x(L QCD−µq q†q)(11)can be evaluated stochastically via Monte Carlo samplingoffield configurations14.From the partition function,thethermodynamic state functions such as energy densityand pressure can be determined asε≡EV ∂ln Z V;p=T∂ln Z14For vanishingµq the integration measure is always positive defi-nite.This is no longer true forfiniteµq due to the fermion’sign problem’to the QGP.The critical energy densityǫ(T c)is700±300 MeV/fm3which is roughly5times higher than the en-ergy density in the center of a heavy nucleus like208P b. At the same time the chiral condensate ¯q q =∂p/∂m q diminishes rapidly near T c signalling therestoration of broken chiral symmetry.As indicated in Fig.5a sys-tematic discrepancy of about15%between the calcu-lated energy density(and pressure)and the free gas Stefan-Boltzmann limit is observed for T>2T c.Al-though this is roughly consistent with thefirst-order cor-rection from perturbation theory,the perturbation series is poorly convergent and resummation techniques have to be employed(Blaizot et al.,2006)for a quantitative understanding of the high-temperature EoS.The ab-initio numericalfindings support the simple model results for the existence of a QGP transition dis-cussed above.In this connection it should be mentioned, however,that most lattice calculations still have to use unrealistically large values for the light quark masses and rather small space-time volumes.With anticipated high-performance computers in the range of hundreds of Ter-aflop/s these calculations will be improved in the near future.Ultimately they will also provide definite answers concerning the nature of the transition.Among others, this is of importance for primordial nucleosynthesis,i.e. the formation of light elements,such as deuterium,he-lium and lithium.In a stronglyfirst-order quark-hadron transition bubbles form due to statisticalfluctuations, leading to significant spatial inhomogeneities.These would influence the local proton-to-neutron ratios,pro-viding inhomogeneous initial conditions for nucleosyn-thesis(Boyanovsky et al.,2006).Other consequences would be the generation of magneticfields,gravitational waves and the enhanced probability of black-hole forma-tion(Boyanovsky et al.,2006).At present,indications are that forµq=0,relevant for the early universe,the transition is a’cross over’,i.e. not a true phase transition in the thermodynamic sense (Aoki et al.,2006a).Near T c the state functions change smoothly but rapidly as in hot electromagnetic plasmas. For most of the experimental observables to be discussed below this subtlety is,however,of minor relevance.A cross over would wash out large spatialfluctuations and hence rule out inhomogeneous cosmic scenarios.Very recent studies(Aoki et al.,2006b;Cheng et al.,2006)in-dicate that the exact value of the transition temperature is still poorly known.In fact,these investigations have yielded values for T c in the range150-190MeV.This is in part due to difficulties with the necessary extrapola-tion to the thermodynamic(infinite volume)limit and in part due to the general difficulty in providing an absolute scale for the lattice calculations.Progress in this difficult area is expected with simulations on much larger lattices at the next generation computer facilities.While atµq=0the lattice results are relatively pre-cise,the ab-initio evaluation of the phase boundary in the(T,µq)-plane(Fig.4)poses major numerical dif-ficulties.This is basically related to the Fermi-Dirac8statistics of the quarks and is known in many-body physics as the ’fermion-sign problem’.For the integral (11)this implies that the integrand becomes an oscilla-tory function and hence Monte-Carlo sampling methods cease to work.Only recently new methods have been developed (Allton et al.,2003;Fodor and Katz,2002;de Forcrand and Philipsen,2002;Philipsen,2006)to go into the region of finite µq .What can be expected?Considering the phase bound-ary as a line of (nearly)constant energy density,the bag model (Braun-Munzinger and Stachel,1996a)pre-dicts that the critical temperature decreases with increas-ing µq .By construction the bag model describes a first-order phase transition for all chemical potentials.For large values of µq and low temperatures there are indi-cations from various QCD-inspired model studies,chiefly the NJL model (see Fig.4),that the (chiral)phase tran-sition is indeed first order.On the other hand,the lat-tice results discussed above seem to indicate that at very small µq the transition is a cross over.This would im-ply that there is a critical endpoint in the phase dia-gram,where the line of first-order transitions ends in a second-order transition (as in the liquid-gas transition of water).In analogy to the static magnetic suscepti-bility χM =∂M/∂H in a spin system one can define a ’chiral susceptibility’as the derivative of the in-medium chiral condensate ¯q q T,µq wrt the bare quark mass m q or equivalently as the second derivative of the pressure,χm =∂ ¯q q T,µq /∂m q =∂2p/∂m 2q .Here the quark mass m q plays the role of the external magnetic field H .In the Curie-Weiss transition χM diverges.The same should happen with χm at the CEP.On the other hand lat-tice studies and model calculations indicate that also the quark number susceptibility χn =∂n q /∂µq =∂2p/∂µ2q diverges.This implies that in the vicinity of the CEP the matter becomes very easy to compress since the isother-mal compressibility is given by κT =χn /n 2q .It is con-jectured that the critical behavior of strongly-interacting matter lies in the same universality class as the liquid-gas transition of water (Stephanov,2004).The exper-imental identification of a CEP and its location in the (T,µq )plane would be a major milestone in the study of the phase diagram.Although very difficult,there are several theoretical as well experimental efforts un-derway (Proceedings of Science,2006)to identify signals for such a point.For a recent critical discussion concern-ing the existence of a CEP in the QCD phase diagram see (Philipsen,2007).IV.EXPERIMENTS WITH HEAVY IONSThe phase diagram of strongly-interacting matter can be accessed experimentally in nucleus-nucleus collisions at ultrarelativistic energy,i.e.energies/nucleon in the center of mass (c.m.)frame that significantly ex-ceed the rest mass of a nucleon in the colliding nu-clei.After first intensive experimental programs at theBrookhaven Alternating GradientSynchrotron (AGS)and the CERN Super Proton Synchrotron (SPS)the ef-fort is at present concentrated at the Relativistic Heavy-Ion Collider (RHIC)at Brookhaven.A new era of ex-perimental quark matter research will begin in 2008with the start of the experimental program at the CERN Large Hadron Collider (LHC).Here we will not attempt to give an overview over the experimental status in this field (for recent reviews see (Braun-Munzinger and Stachel,2007;Gyulassy and McLerran,2005))but concentrate on a few areas which in our view have direct bearing on the phase diagram.Before doing so we will,however,briefly sketch two of the key results from RHIC,which have led to the discovery that quark-gluon matter in the vicinity of the phase boundary behaves more like an ideal liquid rather than a weakly-interacting plasma.A.Opaque fireballs and the ideal liquid scenarioAt RHIC,Au-Au collisions are investigated at c.m.energies of 200GeV per nucleon pair.In such colli-sions a hot fireball is created,which subsequently cools and expands until it thermally freezes out 15and free-streaming hadrons reach the detector.The spectroscopy of these hadrons (and the much rarer photons,elec-trons and muons)allow conclusions about the state of the matter inside the fireball,such as its temperature and density.The four experiments at RHIC have re-cently summarized their results (Adams et al.,2005b;Adcox et al.,2005;Arsene et al.,2005;Back et al.,2005).For a complete overview see also the proceedings of the two recent quark matter con-ferences (Proc.Quark-Matter 2005Conference,2006;Proc.Quark-Matter 2006Conference,2007).9FIG.6Geometry in the plane perpendicular to the beam di-rection of thefireball in a nucleus-nucleus collision with large impact parameter.The producedfireball has such a high density and tem-perature that apparently all partons(quarks and glu-ons)reach equilibrium very rapidly(over a time scale of less than1fm/c).Initially,the collision zone is highly anisotropic with an almond-like shape,at least for colli-sions with not too small impact parameter.The situa-tion is schematically described in Fig.6.In this equili-brated,anisotropic volume large pressure gradients exist, which determine and drive the hydrodynamic evolution of thefireball.Indeed,early observations at RHIC con-firmed that the data on theflow pattern of the mat-ter follow closely the predictions(Huovinen et al.,2001; Kolb and Heinz,2004;Teaney et al.,2002)based on the laws of ideal relativistic hydrodynamics.By Fourier anal-ysis of the distribution in azimuthal angleΦ(see Fig.6) of the momenta of produced particles the Fourier coef-ficient v2= cos(2Φ) can be determined as a function of the particles transverse momentum p t.These distri-butions can be used to determine the anisotropy of the fireball’s shape and are compared,in Fig.7for various particle species,to the predictions from hydrodynamical calculations.The observed close agreement between data and predictions,in particular concerning the mass or-dering of theflow coefficients,implies that thefireball flows collectively like an liquid with negligible shear vis-cosityη.Similar phenomena were also observed in ultra-cold atomic gases of fermions in the limit of very large scattering lengths,where it was possible,by measuring ηthroughflow data,to establish that the system is in a strongly coupled state(O’Hara et al.,2002).The appli-cation of such techniques are currently also discussed for quark-gluon matter.This liquid-likefireball is dense enough that even quarks and gluons of high momentum(jets)cannot leave without strong rescattering in the medium.This’jet quenching’manifests itself in a strong suppression(by about a factor of5)of hadrons with large momenta transverse to the beam axis compared to expectations from a superposition of binary nucleon-nucleon collisions. The interpretation is that a parton which eventually turns into a hadron must suffer a large energy loss while traversing the hot and dense collision zone.To make matters quantitative one defines the suppression factor R AA as the ratio of the number of events at a given transverse momentum p t in Au-Au collisions to that in proton-proton collisions,scaled to the Au-Au system by the number of collisions such that,in the absence of parton energy loss,R AA=1.Corresponding data are presented in Fig.8.The strong suppression observed by the PHENIX and,in fact,all RHIC collaborations (Adams et al.,2005b;Adcox et al.,2005;Arsene et al., 2005;Back et al.,2005)demonstrates the opaqueness of thefireball even for high momentum partons while pho-tons which do not participate in strong interactions can leave thefireball unscathed.Theoretical analysis ofthese FIG.7The Fourier coefficient v2for pions,kaons,protons andΛbaryons(with masses of140,495,940and1115MeV, respectively)emitted with transverse momentum p t in semi-central Au-Au collisions at RHIC.The data are from the STAR collaboration(Adams et al.,2005a).The lines cor-respond to predictions(Huovinen et al.,2001)from hydro-dynamical calculations with an equation of state based on weakly interacting quarks and gluons.data(Gyulassy and McLerran,2005;Vitev,2006)pro-vides evidence,albeit indirectly,for energy densities ex-ceeding10GeV/fm3in the center of thefireball.There is even evidence for the presence of Mach cone-like shock waves(Casalderrey-Solana et al.,2005;Stoecker,2005) caused by supersonic partons traversing the QGP.Ap-parently both elastic parton-parton collisions as well as gluon radiation contribute to the energy loss but it is fair to say that the details of this mechanism are currently not well understood.The situation is concisely summa-rized in(Gyulassy and McLerran,2005).B.Hadro-ChemistryIn ideal hydrodynamics no entropy is generated dur-ing the expansion and cooling of thefireball,i.e.the system evolves through the phase diagram(essentially) along isentropes,starting in the QGP phase.This can be experimentally verified through the production of a variety of mesons and baryons.The analysis of particle production data at AGS,SPS and RHIC en-ergies has clearly demonstrated(Andronic et al.,2006; Becattini et al.,2004;Braun-Munzinger et al.,2004a) that the measurements can understood to a high ac-curacy by a statistical ansatz,in which all hadrons are produced from a thermally and chemically equilibrated state.This hadro-chemical equilibrium is achieved dur-ing or shortly after the phase transition and leads to abundances of the measured hadron species that can be described by Bose-Einstein or Fermi-Dirac distributions n j=g j。
【精品】科技英语4低通滤波器原文和翻译
【关键字】精品Words and Expressionsintegrator n. 积分器amplitude n. 幅值slope n 斜率denominator n. 分母impedance n 阻抗inductor n. 电感capacitor n 电容cascade n. 串联passband n 通带ringing n. 振铃damping n. 阻尼，衰减conjugate adj. 共轭的stage v. 成为low-pass filters 低通滤波器building block 模块linear ramp 线性斜坡log/log coordinates 对数/对数坐标Bode plot 伯德图transfer function 传递函数complex-frequency variable 复变量complex frequency plane 复平面real component 实部frequency response 频率响应complex function 复变函数Laplace transform 拉普拉斯变换real part 实部imaginary part 虚部angular frequency 角频率frequency response 频率响应transient response 瞬态响应decaying-exponential response 衰减指数响应step function input 阶跃（函数）输入time constant 时间常数first-order filters 一阶滤波器second-order low-pass filters 二阶低通滤波器passive circuit 无源电路active circuit 有源电路characteristic frequency 特征频率quality factor n. 品质因子，品质因数circular path 圆弧路径complex conjugate pairs 共轭复数对switched-capacitor 开关电容negative-real half of the complex plane 复平面负半平面Unit 4 Low-pass FiltersFirst-Order FiltersAn integrator (Figure 2. la) is the simplest filter mathematically, and it forms the building block for most modern integrated filters. Consider what we know intuitively about an integrator. If you apply a DC signal at the input (i.e., zero frequency), the output will describe a linear ramp that grows in amplitude until limited by the power supplies. Ignoring that limitation, the response of an integrator at zero frequency is infinite, which means that it has a pole at zero frequency. (A pole exists at any frequency for which the transfer function's value becomes infinite.)（为什么为极点，为什么低通？）Figure A simple RC integratorWe also know that the integrator's gain diminishes with increasing frequency and that at high frequencies the output voltage becomes virtually zero. Gain is inversely proportional to frequency, so it has a slope of -1 when plotted on log/log coordinates (i.e., -20dB/decade on a Bode plot, Figure 2. 1b).Figure 2.1 b A Bode plot of a simple integratorYou can easily derive the transfer function asWhere s is the complex-frequency variable and is 1/RC. If we think of s as frequency, this formula confirms the intuitive feeling that gain is inversely proportional to frequency.The next most complex filter is the simple low-pass RC type (Figure 2. 2a). Its characteristic (transfer function) isWhen, the function reduces to , i.e., 1. When s tends to infinity, the function tends to zero, so this is a low-pass filter. When, the denominator is zero and the function's value is infinite, indicating a pole in the complex frequency plane. The magnitude of the transfer function is plotted against s in Figure 2. 2b, where the real component of s () is toward us and the positive imaginary part () is toward the right. The pole at - is evident. Amplitude is shown logarithmically to emphasize the function's form. For both the integrator and the RC low-pass filter, frequency response tends to zero at infinite frequency; that is, there is a zero at. This single zero surrounds the complex plane.But how does the complex function in s relate to the circuit's response to actual frequencies? When analyzing the response of a circuit to AC signals, we use the expression for impedance of an inductor and for that of a capacitor. When analyzing transient response using Laplace transforms, we use sL and 1/sC for the impedance of these elements. The similarity is apparent immediately. The in AC analysis is in fact the imaginary part of s, which, as mentioned earlier, is composed of a real part and an imaginary part.If we replace s by in any equation so far, we have the circuit's response to an angular frequency. In the complex plot in Figure 2.2b, and hence along the positive j axis. Thus, the function's value along this axis is the frequency response of the filter. We have sliced the function along the axis and emphasized the RC low-pass filter's frequency-response curve by adding a heavy line for function values along the positive j axis. The more familiar Bode plot (Figure 2.2c) looks different in form only because the frequency isexpressed logarithmically.（根据图翻译这两句话）Figure 2.2a A simple RC low-pass filterWhile the complex frequency's imaginary part () helps describe a response to AC signals, the real part() helps describe a circuit's transient response. Looking at Figure 2.2b, we can therefore say something about the RC low-pass filter's response as compared to that of the integrator. The low-pass filter's transient response is more stable, because its pole is in the negative-real half of the complex plane. That is, the low-pass filter makes a decaying-exponential response to a step-function input; the integrator makes an infinite response. For the low-pass filter, pole positions further down the axis mean a higher, a shorter time constant, and therefore a quicker transient response. Conversely, a pole closer to the j axis causes a longer transient response.So far, we have related the mathematical transfer functions of some simple circuits to their associated poles and zeroes in the complex-frequency plane . From these functions, we have derived the circuit ’s frequency response (and hence its Bode plot) and also its transient response. Because both the integrator and the RC filter have only one s in the denominator of their transfer functions, they each have only one pole. That is, they are first-order filters .Figure 2.2b The complex function of an RC low-pass filterFigure 2.2c A Bode plot of a low-pass filterHowever, as we can see from Figure 2.1b, the first-order filter does not provide a very selective frequency response. To tailor a filter more closely to our needs , we must move on to higher orders. From now on, we will describe the transfer function using f(s) rather than the cumbersome IN OUT V V . Second-Order Low-Pass FiltersA second-order filter has 2s in the denominator and two poles in the complex plane. You can obtain such a response by using inductance and capacitance in a passive circuit or by creating an active circuit of resistors, capacitors, and amplifiers. Consider the passive LC filter in Figure 2.3a, for instance. We can show that its transfer function has the formand if we defineLC /120=ωand R L Q /0ω=,then where 0ωis the filter's characteristic frequency and Q is the quality factor (lower R means higher Q).Figure 2.3a An RLC low-pass filterThe poles occur at s values for which the denominator becomes zero; that is,when 0/2002=++ωωQ s s . We can solve this equation by remembering that the roots of 02=++c bx ax are given byIn this case, a = 1, b 0ω=, and 20ω=c .The term (ac b 42-) equals ()4/1220-Q ω, so if Q isless than 0.5 then both roots are real and lie on the negative-real axis. The circuit's behavior is much like that of two first order RC filters in cascade . This case isn't very interesting, so we'll consider only the case where Q > 0.5, which means ()ac b 42-is negative and the roots are complex.Figure 2.3b A pole-zero diagram of an RLC low-pass filterThe real part is therefore a b 2/-, which is Q 2/0ω-, and common to both roots. The roots' imaginary parts will be equal and opposite in signs. Calculating the position of the roots in the complex plane, we find that they lie at a distance of0ωfrom the origin, as shown in Figure 2.3b. Varying 0ω, changes the poles' distance from the origin. Decreasing the Q moves the poles toward each other, whereas increasing the Q moves the poles in a semicircle away from each other and toward the ωj axis. When Q = 0.5, the poles meet at 0ω-on the negative-real axis. In this case, the corresponding circuit is equivalent to two cascaded first-order filters.Now let's examine the second-order function's frequency response and see how it varies with Q. As before, Figure 2.4a shows the function as a curved surface, depicted in the three-dimensional space formed by the complex plane and a vertical magnitude vector . Q =0.707, and you can see immediately that the response is a low-pass filter.The effect of increasing the Q is to move the poles in a circular path toward the ωj axis. Figure2.4b shows the case where Q = 2. Because the poles are closer to the ωj axis, they have a greater effect on the frequency response, causing a peak at the high end of the passband .Figure 2.4a The complex function of a second-order low-pass filter (Q = 0.707)Figure 2.4b The complex function of a second-order low-pass filter (Q = 2)There is also an effect on the filter's transient response. Because the poles' negative-real part is smaller, an input step function will cause ringing at the filter output. Lower values of Q result in less ringing, because the damping is greater. On the other hand, if Q becomes infinite, the poles reach the ωj axis, causing an infinite frequency response (instability and continuous oscillation) at 0ωω=. In the LCR circuit in Figure 2.3a, this condition would be impossible unless R=0. For filters that contain amplifiers, however, the condition is possible and must be considered in the design process.A second-order filter provides the variables 0ωand Q, which allow us to place poles wherever we want in the complex plane. These poles must, however, occur as complex conjugate pairs , in which the real parts are equal and the imaginary parts have opposite signs. This flexibility in pole placement is a powerful tool and one that makes the second-order stage a useful component in many switched-capacitor filters. As in the first-order case, the second-order low-pass transfer function tends to zero as frequency tends to infinity. The second-order function decreases twice as fast, however, because of the 2s factor in the denominator. The result is a double zero （零点） at infinity. 低通滤波器一阶滤波器从数学公式上讲，积分器（见图2.1a ）是最简单的滤波器；它是构成大多数现代滤波器的基本模块。
Twist Grain Boundary Phases
298
H.-S. Kitzerow
Hale Waihona Puke (a)(b) Figure 10.1. (a) Structure of a phase which shows a local smectic order and a helical director ®eld at the same time, as proposed by Pollmann [21] and Mu È ller (from [20]). (b) Structure of the TGBA phase proposed by Renn and Lubensky. In addition to the structural features displayed in (a), the grain boundaries and the screw dislocations are shown. Characteristic lengths: d smectic layer spacing, lb thickness of the smectic slabs, ld distance between neighboring screw dislocations, and p pitch of the director ®eld (reprinted from [125]). (c) Smectic layers of two neighboring blocks above (solid lines) and below the drawing plane (dashed lines), and screw dislocations (vertical tubes) between the two blocks. The relation between the layer spacing d and the distance of the defect lines ld is given by (10.1).
BinaryPhaseDiagrams：二元相图
Binary Phase DiagramsPurposeTo construct a liquid/vapor temperature-composition (T-X) phase diagram for a binary mixture of cyclohexane and ethanol.TheoryBinary mixtures of two volatile liquids exhibit a range of boiling behavior from ideal, with a simple continuous change in boiling point with composition, to nonideal, showing the presence of an azeotrope and either a maximum or minimum boiling point. In this experiment, the properties of a binary mixture of cyclohexane and methanol will be investigated by studying the change in boiling point with composition. You will construct a boiling point diagram and identify any nonideal behavior in the system.For ideal mixtures of liquids, the composition of the vapor phase is always richer in the component with the higher vapor pressure. According to Raoult's Law, the vapor pressure of component A is given byp A =xApA* [1]where x A is the mole fraction of A in solution and pA∗ is the vapor pressure of pure A. Actual vapor pressures can be greater or less than those predicted by Raoult's Law, indicating negative and positive deviations from ideality. In some cases, the deviations are large enough to produce maxima or minima in the boiling point and vapor pressure curves. At the maximum or minimum, the compositions of the liquid and vapor phases are the same, but the system is not a pure substance. This results in an azeotrope, a mixture which boils with constant composition.A distillation will not be able to completely separate the two components. Either the distillate or the residue will eventually reach the azeotropic composition and no further separation will occur.Simple distillation can be used to obtain a boiling point diagram so long as some method exists to analyze both the distillate and the residue. In practice, several mixtures of differing composition of the two liquids are distilled and samples of both the distillate and residue are taken. The temperature (boiling point) of each distillation is recorded and the composition of both the distillate and residue is determined. The analysis method should provide a measurement which changes significantly and continuously over the entire range of concentration, from one pure liquid to the other pure liquid. In many cases, the refractive index provides a suitable measure of concentration. A calibration curve must be obtained using known mixtures. The refractive index of an unknown mixture is then measured and the composition obtained using the calibration curve.ProcedureCalibration Curve1. Make up 5 mL each of 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 percent by volume ethanol solutions using volumetric pipets.2. Measure the refractive index for each of these solutions.3. Convert the percent volume concentrations into mole fraction.4. Construct a plot of mole fraction versus index of refraction.DistillationA simple distillation setup similar to that shown below is used. A two- or three-necked roundbottom flask should be used. This equipment should be in a hood.Have several Pasteur pipets available for taking samples of the distillate and residue. Also prepare twenty sample vials labeled V1 to V10 and L1 to L10 as discussed below. The vials marked V (for vapor) will be used to collect the distillate (the condensed vapor phase) and the vials marked L will be used to collect the residue (the liquid phase). Graduated cylinders should be used for measuring the pure liquids for the distillation.1. Place 75 mL of ethanol and 25 mL of cyclohexane in the distillation flask. Start thedistillation with an Erlenmeyer flask or beaker as your receiving vessel and continue until about 5 mL of distillate is collected and then discard. Now collect 5 more mL into sample vial V1. Record the temperature during this collection period. Turn off the heater and allow the boiling to stop, then transfer about 2 mL of the distillate into vial L1. Make sure that you cap the vials and record their refractive index soon thereafter.Repeat the process four more times, adding 25 mL of cyclohexane to the distillation flask each time.2. Start over with a mixture containing 95 mL of cyclohexane and 5 mL of ethanol. Distill andcollect samples of the distillate and residue as in part 1, labeling them V6 and L6,respectively. Repeat four more times adding 10 mL of ethanol to the distillation flask each time.3. During the lab period, using the second distillation apparatus, the boiling points for pureethanol and pure cyclohexane should be obtained. Also, record the atmospheric pressure. CalculationsUsing the distillation data and your calibration curve, plot the temperatures against the mole fraction of ethanol for both the liquid and vapor phases on the same plot. Make sure the data from the pure liquid distillations are included. Draw (this means do not perform a fit in excel, why?) two smooth curves, one through the liquid data (residue) and one through the vapor data (distillate).From your plot determine the azeotropic composition (as mass fraction and mole fraction) and the azeotropic temperature. Compare to a literature value.Questions1. What type of deviation from ideality (if any) does this system show? Rationalize thisbehavior in terms of the intermolecular forces expected for this system.2. How could one separate the components in an azeotrope? One of the most importantazeotropes is that formed in the ethanol-water system. Find the composition of thisazeotrope (use the literature) and also find a method for "breaking" this azeotrope. It must be possible since we can buy 100% ethanol and 100% water!3. Use the literature to find a binary mixture whose azeotropic mole fraction is roughly 0.504. A similar experiment can be conducted to obtain a solid/liquid temperature-compositionphase diagram. For solid/liquid systems, eutectics may form rather than azeotropes as is the case for liquid/vapor systems. Discuss the similarity between a eutectic and an azeotrope.。
材料导论中英文讲稿 (14)
Phase diagramHello everybody, welcome to my class. Today, we will talk about phase diagram and Gibbs phase rule, as well as how to calculate the corresponding proportion of liquid phase and solid phase.译文：大家好，欢迎来到我的课程。
今天，我们将讨论相图，吉布斯相律，以及如何计算液相和固相的相对含量。
First of all, let’s introduce the definition of phase. Phase is defined as a homogeneous part or aggregation of material. This homogenous part is distinguished from another part due to difference in structure, composition, or both. The different structures form an interface to difference in structure and composition. （这里要注意相的概念，相是指在结构和组成方面与其它部分不同的均匀体。
）译文：我们首先学习相的定义。
相是指在一种材料中，结构、组成，或两者同时不同于其他部分的均匀体或聚集体部分。
不同部分间形成界面，也就是相与相之间的分界面。
Some solid materials have the capability of changing their crystal structure under the varying conditions of pressure and temperature, causing an ability of phase-change.译文：一些固体材料随着压力和温度条件的改变而发生结晶结构变化，具有相变的能力。
2d NMR
In the first period, called the preparation time, the sample is excited by one or more pulses. The resulting magnetization is allowed to evolve for the first time period, t1. Then another period follows, called the mixing time, which consists of a further pulse or pulses. After the mixing period the signal is recorded as a function of the second time variable, t2. This sequence of events is called a pulse sequence and the exact nature of the preparation and mixing periods determines the information found in the spectrum. It is important to realize that the signal is not recorded during the time t1, but only during the time t2 at the end of the sequence. The data is recorded at regularly spaced intervals in both t1 and t2. The two-dimensional signal is recorded in the following way. First, t1 is set to zero, the pulse sequence is executed and the resulting free induction decay recorded. Then the nuclear spins are allowed to return to equilibrium. t1 is then set to ∆1, the sampling interval in t1, the sequence is repeated and a free induction decay is recorded and stored separately from the first. Again the spins are allowed to equilibrate, t1 is set to 2 ∆1, the pulse sequence repeated and a free induction decay recorded and stored. The whole process is repeated again for t1 = 3∆1, 4 ∆1 and so on until sufficient data is recorded, typically 50 to 500 increments of t1. Thus recording a two-dimensional data set involves repeating a pulse sequence for increasing values of t1 and recording a free induction decay as a function of t2 for each value of t1. 7.1.2 Interpretation of peaks in a two-dimensional spectrum Within the general framework outlined in the previous section it is now possible to interpret the appearance of a peak in a two-dimensional spectrum at particular frequency co-ordinates.
Phase diagram as a function of temperature and magnetic field for magnetic semiconductors
Degenerate antiferromagnetic semiconductors are obtained by strongly doping antiferromagnetic semiconductors (e.g., europium chalcogenides or lanthanium manganites). Over a concentration range of doping impurities, the ground state of these compounds will be a mixture of antiferromagnetic (AF) and ferromagnetic (FM) phases [1, 2, 3]. Starting from a pure compound and doping, we find that the ground state at T = H = 0 is AF and non-conducting up to some conduction electron concentration driven by impurities, nd , from which the homogeneous state turns out to be unstable against phase separation. The ground state becomes then inhomogeneous with a simply connected AF phase and a multiply connected FM phase. The exact geometry of the multiply connected phase is of fractal nature. On increasing doping, a geometric transition takes place in which the topology of the sample changes due to percolation of the FM phase. Now, the ground state corresponds to a multiply connected AF phase and a simply connected FM one. The doping concentration at which this transition occurs is denoted by nT . At this point an important change in the conductivity is expected, the material becomes a conductor. On a further increase of doping, a certain concentration, nu , exits at which this phase-separated state starts to be unstable and the sample becomes again homogeneous but now FM. The physical reason for having a phase-separated state in an antiferromagnetic semiconductor at T = H = 0 is the dependence of the energy of the charge carriers that appear on doping on the magnetic order of the lattice. The charge carrier energy is lower if they move in a FM region. Therefore, by interaction with the spin system in the lattice, they are able to change its magnetic order, creating FM micro-regions and become trapped in them. In a degenerate magnetic semiconductor this is a cooperative phenomenon: a number of electrons are self-trapped
美国GMP指南(英文)
GUIDELINE FORGOOD MANUFACTURING PRACTICESINSPECTIONSPAN AMERICAN NETWORK FOR DRUG REGULATORY HARMONIZATION WORKING GROUP ON GOOD MANUFACTURING PRACTICESMEMBERS*Justina Molzon*, Associate Director for International Programs, FDA/USA. Group CoordinatorArgentina: Carlos Chiale; Rodolfo Mocchetto*, Coordinator INAME/ANMATBrazil: Antonio Bezerra, Suzana Avila*, Inspección y Control de Medicamentos, ANVISACanada: France Dasereau, Stephen McCaul; Louise Jodoin*, Inspection Unit, Health CanadaChile: Magadalena Reyes*, Inspector GMP. Instituto de Salud Pública (ISP) Guatemala: Esmeralda Villagran; José Luis Aguilar; Norma de Pinto*, Jefe Monitoreo y Vigilancia de Medicamentos, Ministerio de SaludMexico: Rosa María Morales, Suleta García*, COFEPRISVenezuela: Elsa Castejón*, Asesora Dirección de Drogas y Cosméticos, Ministerio de Salud.ALIFAR: Miguel Maito, Gerente Laboratorios Farmacéuticos Argentina; Marisela Benaim*, CIFAR, VenezuelaFIFARMA, Marco Vega, QA/QC Manager, Lilly; Carmen Araujo, Laboratorios Elmor, Marisela Poot,* GSK Regulatory DirectorResource Persons:Rebecca Rodríguez, National Expert Drugs Investigator. FDA/USAMillie Barber, International Programa Manger, FDA/USASecretariatRosario D’Alessio, PAHO/WHOJuana M. De Rodriguez, PAHO-GuatemalaMiguel A. Lopez, PAHO-Venezuela*Current membersINTRODUCTIONThis Guideline for Good Manufacturing Practices Inspection for the pharmaceuticalindustry was prepared by the Working Group on Good Manufacturing Practices (WG/GMP), inMay 2003. The Guideline addresses the requirements of the WHO Technical Report onGood Manufacturing Practices # 32 and the particular considerations of all members of thegroup.The WG/GMP proposed a plan for Guideline validation, to the Steering Committee of thePan-American Network for Drug Regulatory Harmonization, which was approved and was developed in two parts:1. The Guideline was implementation in a pilot phase at volunteering pharmaceuticalindustry plants. PAHO/WHO Consultants, Drug Regulatory Officers and people from thepharmaceutical industry conducted the pilot implementation at several plants in differentcountries of the Americas Region. The guideline was later revised according to theircomments and suggestions regarding the contents and usefulness.2. The Guideline was published in the PAHO/WHO web page to promote participation anddiscussion by institutions and professional experts in this topic. This gave all those whowere interested, the opportunity to send suggestions, comments, or to simply give theiropinion. The Guideline remained in the web page since June 2004 in order to receivecomments and others input.Associations like (ALIFAR and FIFARMA) and countries (Argentina, Guatemala andVenezuela) also sent their comments.The GMP Working Group reviewed and analyzed all the comments received and preparedthis revised version of the Regional Guideline of GMP Inspection for the Americas, which is submitted for consideration to the IV Pan American Conference on Drug Regulatory Harmonization.Some of the advantages of the Guideline are:1. The guideline will help to establish the standards for GMP inspections;2. It will be more comprehensive than what is in place in the economic blocks (countries)and will send the message that countries need to work as a community to meetestablished standards; and therefore, improve the quality of pharmaceutical products;3. It will serve as a work model necessary for common criteria;4. It should not be used as a check list, but it should show principles important toconsider in association with an inspection;5. It can be used as a training document for GMP inspections; and6. It will be helpful to countries in educating inspectors with unified criteria.TABLE OF CONTENTSCHAPTER 1 (5)ADMINISTRATION AND GENERAL INFORMATION (5)CHAPTER 2 (8)PERSONNEL (8)CHAPTER 3 (10)PREMISES (10)GENERAL CONDITIONS (10)ANCILLARY AREAS (11)MAINTENANCE (12)CHAPTER 4 (13)WATER SYSTEMS (13)POTABLE WATER (13)PURIFIED WATER (14)WATER FOR INJECTION (17)CHAPTER 5 (21)STORAGE AREAS (21)CHAPTER 6 (29)RETURNED PRODUCTS (29)CHAPTER 7 (30)PRODUCTS RECALL (30)CHAPTER 8 (31)DOCUMENTATION (31)CHAPTER 9 (40)SAMPLING AREA (40)CHAPTER 10 (41)WEIGHING AREA (41)WEIGHING AREA (42)WEIGHING AREA (43)CHAPTER 11 (44)PRODUCTION (44)NON-STERILE PRODUCTS (44)PRODUCTION (53)SEGREGATED PHARMACEUTICAL PRODUCTS (53)PRODUCTION (54)STERILE PRODUCTS (54)CHAPTER 12 (68)QUALITY CONTROL (68)CHAPTER 13 (78)QUALITY ASSURANCE (78)CHAPTER 14 (83)VALIDATION (83)CHAPTER 1REF:ADMINISTRATION AND GENERAL INFORMATIONWHO 321 What is the company's name?________________________________________________________________________2 What is the company's legal address?_______________________________________________________________________3 What is the manufacturing site’s address?______________________________________________________________________4 Does the company have authorization, according to the regulations of each country, at other address(es)(warehouses, quality control laboratory, etc.) which are under the company’s responsibility?If "YES", indicate which companies and provide their addresses._______________________________________________________________________________________________________________________________________________________________________________________________________________5 Is there evidence of registration of the qualified person responsible by the Regulatory Authority?____________________________________________________________________________________________________________________________________________6 Is the qualified person responsible, according to company's organization chart, present at the time of theinspection?YESPROVIDE INFORMATION REGARDING THIS PERSON (WHO RECEIVES THE INSPECTION)________________________________________________________________________________________________________________________________________NO7 Is there evidence of a license to operate issued by the Regulatory Authority?Indicate all authorized activities.______________________________________________________________________________________________________________________________________REF:ADMINISTRATION AND GENERAL INFORMATIONWHO 328 Does the company develop exclusively those production and quality control activities properly authorizedby the Regulatory Authority?YESNO9 Does the company manufacture dietary supplements?YESNO10 Does the company manufacture cosmetic products?YESNO11 Does the company manufacture veterinary products?YESNO12 Does the company manufacture reagents for “in vitro” diagnostic use?YESNO13 Does the company manufacture reagents for “in vivo” diagnostic use?YESNO14 Does the company manufacture other products not indicated above?YESIf “YES” indicate below__________________________________________________________________________________________________________________________________NO15 Does the company manufacture products with beta-lactam active ingredients (penicillins /cephalosporins)?YESIf "YES", indicate in which pharmaceutical dosage form__________________________________________________________________________________________________________________________________NO16 Does the company manufacture products with cytostatic / cytotoxic active ingredients?YESIf "YES", indicate in which pharmaceutical dosage form__________________________________________________________________________________________________________________________________NO17 Does the company manufacture products with hormone active ingredients?YESIf "YES", indicate in which pharmaceutical dosage form__________________________________________________________________________________________________________________________________NOREF:WHO 32ADMINISTRATION AND GENERAL INFORMATION17.1 Does the company manufacture products with corticosteroids active ingredients?YESIf "YES", indicate in which pharmaceutical dosage form__________________________________________________________________________________________________________________________________NO18 Does the company manufacture products with active ingredients from biological origin?YESIf "YES", indicate in which pharmaceutical dosage form__________________________________________________________________________________________________________________________________NO19 Does the company manufacture products with active ingredients from biotechnological origin?YESIf "YES", indicate in which pharmaceutical dosage form__________________________________________________________________________________________________________________________________NO20 Is there a list available of current licensed products? Attach the listYESNO21 Is there a list available of marketed products? Attach the listYESNO21.1 Do all marketed products and its pharmaceutical presentations have current (valid) license?YESNO22 Are the updated building schematics approved by the Regulatory Authority shown, if required?YESNO23 Section 8. Does the company have contract production activities? YESNO24Section 8 Is there documentation certifying registration/authorization of the third party contracted by the Regulatory Authority?YESNO25 Section 8.15 Is there batch documentation issued by the third party in charge of production? YESNO26 Section 8 Does the company act as a third party producer? YESNO27 Sections 8.1, 8.3, 8.12 and8.13 If the company produces by or for third parties, are there contracts that link the parties? YESNOCHAPTER 2PERSONNELREF:WHO 32YES NO1 Sections 10.1, 10.4, 10.11,10.23. Are there Standard Operating Procedures (SOP) related to personnel, including professional qualification, training?2Section 10.3.Is there an updated organization chart of the company? Attach copy3 Section 10.3 Is there a description of the responsibilities and functions of production and quality control personnel?4 Section 10.6. Are the responsibilities of production and quality control personnel independent of each other?5 Section 10.7. Are there trained personnel for the supervision of production and quality control activities?6 Section 10.12. Is there a program for training new employees on GMP, including specific training appropriate to the duties assigned to them?6.1 Section 10.4,10.12. Is there a program for continuous training on GMP for all staff, including specific training appropriate to the duties assigned to them?6.2Section 10.12Are records kept?7 Section 10.15,10.23 Is there a SOP dealing with the use of proper clothing for other persons who enter production areas (technical service/maintenance, cleaning personnel, quality control inspectors, quality assurance inspectors, and visitors)?8 Section 10.23 Are there visible written instructions and/or diagrams for the right use of clothing in the change rooms and other areas where they are required?9 Section 10.16 Are the personnel required to undergo a medical examination prior to being employed (including sensitivity test to beta-lactam substances, if required)?10Section 10.1Are the personnel subject to periodic medical examinations, at least once a year?10.1Sections 10.18,10.19.Are the personnel required to report health problems?11 Section 10.16,10.18 Is there a procedure to prevent any person who has an apparent illness from entering areas in which they may adversely affect the quality of the product or affect their own health?12 Section 10.22 Is smoking, eating, drinking and chewing prohibited in production, storage and laboratory areas?REF:WHO 32PERSONNEL YES NO13Section 10.17Are the personnel instructed to wash their hands before entering production areas?13.1 Section 10.17 Are there signs posted outlining mandatory hand washing before exiting, in change rooms and washrooms?14Section 10.21.Are the personnel using the appropriate uniform for the specified area?12.1Section 11.12.Are the uniforms clean and in good condition?CHAPTER 3PREMISESGENERAL CONDITIONSREF:WHO 32YES NO1Section11.1Is the building exterior in good conditions?2 Section 11.2. Are there any sources of environmental contamination in the area surrounding the building?2.1Section11.2.If "YES", are protective measures undertaken?3 Section 11.2. Are the free and non-productive areas belonging to the company in good clean and orderly conditions?4 Section 11.2. Are the roads leading to the building tarred and/or built so that dust from the road is not a source of contamination inside the plant?5 Section 11.6 Is there any protection against the entry of rodents, insects, birds and other animals?6Section14.46(f)Is there a written pest control program with its respective records?7Section14.46(f)Is there a SOP for pest control?7.1 Does the SOP indicate the substances used for pest control?7.2 Does the Regulatory Authority authorize the used substances?8 Section 4.1 Does the SOP ensure the avoidance of contamination of starting materials, packaging materials, in process-products and finished products with rodenticides and/or fumigant agents?9 Sections 11.1;11.2and 11.21 Is the flow of personnel and materials such that they prevent product contamination?10 Are corridors free of in-transit materials?11 Sections 11.5 and 11.26 Are air conditioning and/or ventilation systems for each area in accordance with the operation to be carried out?WHO 32GENERAL CONDITIONSYES NO12Section11.5.Are visible electric installations in good conditions?13 Section 12.4. Are water, gases, electricity, steam, compressed air and other gas pipelines identified?14 Does the company comply with the national legislation on fire control andprevention?15 Sections 13.38 13.39 Are there SOPs for waste classification and treatment? Are they followed (or complied with)?16Sections13.38 and13.39Is waste treatment undertaken in the premises?16.1 Sections 13.38 and 13.39 If "YES", is there a specific area for waste treatment, completely separated from manufacturing areas?REF:WHO 32 ANCILLARY AREAS YES NO 1Section11.8.Are there general change rooms in the plant?2 Section 11.8. Are toilets, change rooms and showers separated from manufacturing areas?Are they of easy access, and in good condition with respect to cleanliness, sanitation, order and conservation?Are they adequate for the number of users?3 Section 11.7 Are the dining room, social areas and cafeteria (rest and snacks) separated from production areas?4 Sections 10.21 and 10.23. Are plant staffs (temporary and permanent) provided with proper working clothes for each area, including protective coverings to avoid direct contact with products and to protect themselves?5 Are there SOP’s for washing uniforms separately depending on the type of area(sterile, non sterile, maintenance, special products)?6 Is there a laundry area for uniforms which is separate from production areas?7 If an outside laundry facility is used, are personnel and the person responsibleinstructed about the corresponding SOP?7.1 Are there instruction records?WHO 32 ANCILLARY AREAS YES NO7.2 Is this outside laundry facility periodically audited?7.3 Are there audit records?REF:WHO 32 MAINTENANCE YES NO 8Section11.9.Are the maintenance areas physically separated from production areas?9 Is there a SOP of the use, cleaning and maintenance of different servicegenerated equipment?10 Are there preventive maintenance programs for equipment and critical supportsystems?Are performance records for this preventive maintenance program kept?11 Sections 18.18 and 12.11 Is equipment identified as out-of-service or in reparation identified as such? Are they removed from production areas as soon as possible?12 Section 14.46 (c) Is there a preventive maintenance program for the premises?Are there performance records for this preventive maintenance program?13Section14.47 (c)Are records of the usage of critical equipment showed?14 Section 12.1 Is there a preventive maintenance program for quality control equipment? Is there a performance record for this preventive maintenance program?REF:WHO 32 GENERAL SERVICES YES NO15Section15.11Is there a pure steam generator, if necessary?16Section15.11Is there a compressed air generator free of oil, if necessary?17 Sections 15.17Is there an electricity generator for the maintenance of critical systems and processes to be used in case of problems with the electricity supply occur?18Section11.2Are the system generators for different services separated from production areas?19 Do they use gases that will be in direct contact with products?19.1 Are gas piping and valves in good conditions and are they dedicated for each gas?CHAPTER 4 WATER SYSTEMSREF: WHO 32POTABLE WATERYes No NA What is the source of water used in the company?Public Network?Artesian Well, semiartesian well?1Others?2 If necessary, is any treatment for making water potable undertaken before the water isstored?2.1 Does the selected treatment assure potability, according to each country’s requirements?3 Are the system schematics shown?Are the distribution network layouts shown?Are the sampling points shown?4 Does the company have water tanks?4.1 What materials is the water tanks made of?5 Are the cleaning and disinfecting procedures for water and cistern tanks documented?Does the procedure include a justifiable frequency and sampling points?5.1 Are performance records shown?6 Are physicochemical tests of potable water undertaken?Are physicochemical tests of potable water recorded?Indicate frequency7 Is potable water used as a source of purified water or water for injection production?8 Is microbiological control of potable water undertaken?Is microbiological control of potable water recorded?Indicate frequency9 Is potable water used for the initial washing of equipment and tools?10 Is the visible piping used for the transportation of potable water maintained in goodconditions?WHO 32 POTABLE WATER Yes No NA11 Is there a preventive maintenance program that includes the potable water system?Is there a performance record for this preventive maintenance program?REF:WHO 32 PURIFIED WATER Yes No NA1 Is the purified water used, produced by the company?Which is the system used to obtain purified water?Ionic exchange resins?Reverse Osmosis?Distillation?2Others (specify which)?3 Section 17.33 Are the system schematics shown?Are the distribution network layouts shown? Are the sampling points shown?4Section17.33What is the production capacity in liters/hour?4.1 What is the average consumption?5Section14.35Are there written procedures for the operation of the system?7Section17.33Is the purified water stored?7.1 What is the reservoir capacity?7.2 Is the reservoir constructed of sanitary type material?8 If purified water remains stored longer than 24 hours, is there any treatment to preventmicrobiological contamination?8.1Section17.33Does the selected treatment prevent microbiological contamination?9 Are the pipes and valves used to distribute purified water made of sanitary material?10Section15.21Are the visible piping used in water distribution maintained in good conditions?11Sections15.2117.42Is the distribution system of purified water sanitized?WHO 32 PURIFIED WATER Yes No NA 11.1 Is there a SOP for the sanitation of purified water storage and distribution system?11.2 What is the sanitation method used?11.3 In the case of an open distribution system that is not used in 24 hours or more, issanitation undertaken the day before its use?11.4 Are records kept?11.5 In the case of chemical sanitation, are sanitizing agent residues tested?11.6 Arethererecords?12 Is there any type of filter in the distribution system?12.1 In the case that filters exist, are they sanitized?12.2 Are the filter sanitation records shown?12.3 Are the filter replacement records shown?12.4 In the case of open distribution system not used in 24 hours or more, is sanitation donethe day before its use?13 Is any other system, to reduce bacterial burden from purified water, used in thedistribution system?Which type?14 Is the purified water used as a raw material to manufacture non-parenteral products?15 Is the purified water used for washing production equipment and utensils?15.1 Is the purified water used for the final rinse of the equipment used in the manufacture ofnon-parenteral products?15.2 Is the purified water used for the final rinse of the equipment used in the manufacture ofnon-parenteral products?16 Is a non-continuous purified water production system used?16.1 Section 17.42 Does each batch or production day release, by Quality control, undergo physicochemical test established official pharmacopoeias or by alternative validated methods?16.2Section17.42Are microbiological controls undertaken on the day of use?16.3 Is an action limit established?16.4 Is the action limit no more than 100 cfu / mL?WHO 32 PURIFIED WATER Yes No NA 16.5 When the action limit is exceeded, is an investigation always undertaken to ensurequality of the batches of products made with such water?16.6 Is the documentation shown?17 Is a continuous system of purified water production used?17.1Section17.42Is there a continuous monitoring of the quality of the purified water?17.2 Is there an automatic system to prevent use of the purified water, if this is out ofspecifications?17.3 If there is an automatic system, is this checked to verify that it is functioning properly?17.4 Are physicochemical analyses undertaken daily or with an established frequencyaccording to the procedures established by current editions of official pharmacopoeias orby alternative validated methods?17.5 Are microbiological analysis undertaken on the days of use or with an establishedfrequency which is properly validated?17.6 Is an action limit established?17.7 Is the action limit no more than 100 cfu / mL?17.8 When the action limit is exceeded, is an investigation always undertaken to ensurequality of the batches of product made with that water?17.9 Is the documentation shown?18Section17.42Are the sampling points rotated to cover all points of use?19 Is there a SOP for sampling?20 If the water that feeds the system is chlorinated, is there a system to remove thechlorine?21 Are ionic exchange resins used?21.1 Section 17.42 Is there a SOP that considers the criteria to follow for the regeneration of resins and the frequency of regeneration?21.2Section17.42Are records kept?22 Are there SOPs for the sanitation of the purified water system?22.1 What is the sanitation system used?WHO 32 PURIFIED WATER Yes No NA 22.2 What is the sanitation frequency?22.3 Are records kept?23 Is there a preventive maintenance program that includes the components of the purifiedwater system?23.1 Are records kept?REF:WHO 32 WATER FOR INJECTION Yes No NA1 Which treatment system is used to get Water for Injection?2 Section 17.33Are system schematics shown?Are distribution network layouts shown? Are sampling points shown?3Section14.35Are there written procedures for the operation of the system?4Section17.33What is the production capacity in liters/hour?4.1 What is the average consumption?5 If a reverse osmosis system is used:5.1 Is a two-steps system or double osmosis system used on line?5.2 Is the water that feeds the system pre-treated?5.3 What is the pre-treatment system?5.4 Is the system sanitized?5.4.1 What is the sanitation frequency?5.4.2 Are records kept?5.5 In case that chemical sanitation is undertaken, are sanitizing agent residuesinvestigated?5.5.1 Are records kept?6 If distillation is used:6.1 Is the water that feeds the system pre-treated?WHO 32 WATER FOR INJECTION Yes No NA6.2 Which is the pre-treatment system?____________________________________________________________________________________________________________________________7 Is there a storage tank for the Water used for injection?7.1 Is the tank made of sanitary material?7.2 What is its capacity?7.3 Does it have a hydrophobic vent absolute filter?7.4 Are periodic integrity tests undertaken?7.5 Are records kept?8 Are pipes used in the distribution of Water for Injection up to the point of use?8.1 Are pipes made of sanitary material?8.2 Is there any type of heat exchanger in the system?8.3 If “YES", are there guarantees that the heat exchanger is not a source of contamination?9 Is there a SOP for the sanitation of the water storage and distribution system?9.1 What is the sanitation method used?9.2 What is the sanitation frequency?9.3 Are records kept?9.4 In case of chemical sanitation, is the existence of sanitizing agent residues investigated?9.5 Are records kept?9.6 If sanitation is thermal, is it undertaken periodically by a fluent steam circulation?9.7 Are records kept?10 Section 17.33 If water is not used the same day of its production, is the water maintained above 80 °C or below 4º and with constant recirculation through a loop up to points of use?11 If recirculation is below 4o C, ¿are additional precautions taken to prevent access ofmicrobial contaminants and its proliferation?WHO 32 WATER FOR INJECTION Yes No NA 11.1 What are those precautions?________________________________________________________________________________________________________________________________________________________________________________________11.2 Do the storage and recirculation of the water at this temperature ensure its qualityaccording to its use?12 If the water is produced by reverse osmosis, is there any system to maintain its quality?13 If the company manufactures parenteral products, does it use water for injections as araw material?14 If the company manufactures parenteral products, does it use water for injections for thefinal rinse of equipments and components used in manufacturing?15 Is a non-continuous and non-recirculated production system of Water for injection used?15.1 If this is the case: is water used only during the day of its production?15.2 Is water disposed at end of the day of its production?15.3 Is each batch released by Quality control by physicochemical and bacterial endotoxinstests according to the procedures established by current editions of officialpharmacopoeias or by alternative methods validated?15.4 Are microbiological tests of each batch undertaken?15.5 Is an action limit established?15.6 Is action limit no more than 10 cfu /100mL ?15.7 When the action limit is exceeded, is an investigation of the system always undertaken?15.8 Is the investigation report shown?15.9 Are measures undertaken?15.10 What measures are undertaken?16 Is there a continuous system of for the production of water for injections used?Is there a continuous monitoring of the water quality?16.1Section17.4216.2 Is there an automatic system to prevent the use of the water for injections, if it is out ofspecifications?。
专八英语阅读
英语专业八级考试TEM-8阅读理解练习册（1）(英语专业2012级)UNIT 1Text AEvery minute of every day, what ecologist生态学家James Carlton calls a global ―conveyor belt‖, redistributes ocean organisms生物.It’s planetwide biological disruption生物的破坏that scientists have barely begun to understand.Dr. Carlton —an oceanographer at Williams College in Williamstown,Mass.—explains that, at any given moment, ―There are several thousand marine species traveling… in the ballast water of ships.‖ These creatures move from coastal waters where they fit into the local web of life to places where some of them could tear that web apart. This is the larger dimension of the infamous无耻的，邪恶的invasion of fish-destroying, pipe-clogging zebra mussels有斑马纹的贻贝.Such voracious贪婪的invaders at least make their presence known. What concerns Carlton and his fellow marine ecologists is the lack of knowledge about the hundreds of alien invaders that quietly enter coastal waters around the world every day. Many of them probably just die out. Some benignly亲切地，仁慈地—or even beneficially — join the local scene. But some will make trouble.In one sense, this is an old story. Organisms have ridden ships for centuries. They have clung to hulls and come along with cargo. What’s new is the scale and speed of the migrations made possible by the massive volume of ship-ballast water压载水— taken in to provide ship stability—continuously moving around the world…Ships load up with ballast water and its inhabitants in coastal waters of one port and dump the ballast in another port that may be thousands of kilometers away. A single load can run to hundreds of gallons. Some larger ships take on as much as 40 million gallons. The creatures that come along tend to be in their larva free-floating stage. When discharged排出in alien waters they can mature into crabs, jellyfish水母, slugs鼻涕虫，蛞蝓, and many other forms.Since the problem involves coastal species, simply banning ballast dumps in coastal waters would, in theory, solve it. Coastal organisms in ballast water that is flushed into midocean would not survive. Such a ban has worked for North American Inland Waterway. But it would be hard to enforce it worldwide. Heating ballast water or straining it should also halt the species spread. But before any such worldwide regulations were imposed, scientists would need a clearer view of what is going on.The continuous shuffling洗牌of marine organisms has changed the biology of the sea on a global scale. It can have devastating effects as in the case of the American comb jellyfish that recently invaded the Black Sea. It has destroyed that sea’s anchovy鳀鱼fishery by eating anchovy eggs. It may soon spread to western and northern European waters.The maritime nations that created the biological ―conveyor belt‖ should support a coordinated international effort to find out what is going on and what should be done about it. (456 words)1.According to Dr. Carlton, ocean organism‟s are_______.A.being moved to new environmentsB.destroying the planetC.succumbing to the zebra musselD.developing alien characteristics2.Oceanographers海洋学家are concerned because_________.A.their knowledge of this phenomenon is limitedB.they believe the oceans are dyingC.they fear an invasion from outer-spaceD.they have identified thousands of alien webs3.According to marine ecologists, transplanted marinespecies____________.A.may upset the ecosystems of coastal watersB.are all compatible with one anotherC.can only survive in their home watersD.sometimes disrupt shipping lanes4.The identified cause of the problem is_______.A.the rapidity with which larvae matureB. a common practice of the shipping industryC. a centuries old speciesD.the world wide movement of ocean currents5.The article suggests that a solution to the problem__________.A.is unlikely to be identifiedB.must precede further researchC.is hypothetically假设地，假想地easyD.will limit global shippingText BNew …Endangered‟ List Targets Many US RiversIt is hard to think of a major natural resource or pollution issue in North America today that does not affect rivers.Farm chemical runoff残渣, industrial waste, urban storm sewers, sewage treatment, mining, logging, grazing放牧,military bases, residential and business development, hydropower水力发电,loss of wetlands. The list goes on.Legislation like the Clean Water Act and Wild and Scenic Rivers Act have provided some protection, but threats continue.The Environmental Protection Agency (EPA) reported yesterday that an assessment of 642,000 miles of rivers and streams showed 34 percent in less than good condition. In a major study of the Clean Water Act, the Natural Resources Defense Council last fall reported that poison runoff impairs损害more than 125,000 miles of rivers.More recently, the NRDC and Izaak Walton League warned that pollution and loss of wetlands—made worse by last year’s flooding—is degrading恶化the Mississippi River ecosystem.On Tuesday, the conservation group保护组织American Rivers issued its annual list of 10 ―endangered‖ and 20 ―threatened‖ rivers in 32 states, the District of Colombia, and Canada.At the top of the list is the Clarks Fork of the Yellowstone River, whereCanadian mining firms plan to build a 74-acre英亩reservoir水库，蓄水池as part of a gold mine less than three miles from Yellowstone National Park. The reservoir would hold the runoff from the sulfuric acid 硫酸used to extract gold from crushed rock.―In the event this tailings pond failed, the impact to th e greater Yellowstone ecosystem would be cataclysmic大变动的，灾难性的and the damage irreversible不可逆转的.‖ Sen. Max Baucus of Montana, chairman of the Environment and Public Works Committee, wrote to Noranda Minerals Inc., an owner of the ― New World Mine‖.Last fall, an EPA official expressed concern about the mine and its potential impact, especially the plastic-lined storage reservoir. ― I am unaware of any studies evaluating how a tailings pond尾矿池，残渣池could be maintained to ensure its structural integrity forev er,‖ said Stephen Hoffman, chief of the EPA’s Mining Waste Section. ―It is my opinion that underwater disposal of tailings at New World may present a potentially significant threat to human health and the environment.‖The results of an environmental-impact statement, now being drafted by the Forest Service and Montana Department of State Lands, could determine the mine’s future…In its recent proposal to reauthorize the Clean Water Act, the Clinton administration noted ―dramatically improved water quality since 1972,‖ when the act was passed. But it also reported that 30 percent of riverscontinue to be degraded, mainly by silt泥沙and nutrients from farm and urban runoff, combined sewer overflows, and municipal sewage城市污水. Bottom sediments沉积物are contaminated污染in more than 1,000 waterways, the administration reported in releasing its proposal in January. Between 60 and 80 percent of riparian corridors (riverbank lands) have been degraded.As with endangered species and their habitats in forests and deserts, the complexity of ecosystems is seen in rivers and the effects of development----beyond the obvious threats of industrial pollution, municipal waste, and in-stream diversions改道to slake消除the thirst of new communities in dry regions like the Southwes t…While there are many political hurdles障碍ahead, reauthorization of the Clean Water Act this year holds promise for US rivers. Rep. Norm Mineta of California, who chairs the House Committee overseeing the bill, calls it ―probably the most important env ironmental legislation this Congress will enact.‖ (553 words)6.According to the passage, the Clean Water Act______.A.has been ineffectiveB.will definitely be renewedC.has never been evaluatedD.was enacted some 30 years ago7.“Endangered” rivers are _________.A.catalogued annuallyB.less polluted than ―threatened rivers‖C.caused by floodingD.adjacent to large cities8.The “cataclysmic” event referred to in paragraph eight would be__________.A. fortuitous偶然的，意外的B. adventitious外加的，偶然的C. catastrophicD. precarious不稳定的，危险的9. The owners of the New World Mine appear to be______.A. ecologically aware of the impact of miningB. determined to construct a safe tailings pondC. indifferent to the concerns voiced by the EPAD. willing to relocate operations10. The passage conveys the impression that_______.A. Canadians are disinterested in natural resourcesB. private and public environmental groups aboundC. river banks are erodingD. the majority of US rivers are in poor conditionText CA classic series of experiments to determine the effects ofoverpopulation on communities of rats was reported in February of 1962 in an article in Scientific American. The experiments were conducted by a psychologist, John B. Calhoun and his associates. In each of these experiments, an equal number of male and female adult rats were placed in an enclosure and given an adequate supply of food, water, and other necessities. The rat populations were allowed to increase. Calhoun knew from experience approximately how many rats could live in the enclosures without experiencing stress due to overcrowding. He allowed the population to increase to approximately twice this number. Then he stabilized the population by removing offspring that were not dependent on their mothers. He and his associates then carefully observed and recorded behavior in these overpopulated communities. At the end of their experiments, Calhoun and his associates were able to conclude that overcrowding causes a breakdown in the normal social relationships among rats, a kind of social disease. The rats in the experiments did not follow the same patterns of behavior as rats would in a community without overcrowding.The females in the rat population were the most seriously affected by the high population density: They showed deviant异常的maternal behavior; they did not behave as mother rats normally do. In fact, many of the pups幼兽，幼崽, as rat babies are called, died as a result of poor maternal care. For example, mothers sometimes abandoned their pups,and, without their mothers' care, the pups died. Under normal conditions, a mother rat would not leave her pups alone to die. However, the experiments verified that in overpopulated communities, mother rats do not behave normally. Their behavior may be considered pathologically 病理上，病理学地diseased.The dominant males in the rat population were the least affected by overpopulation. Each of these strong males claimed an area of the enclosure as his own. Therefore, these individuals did not experience the overcrowding in the same way as the other rats did. The fact that the dominant males had adequate space in which to live may explain why they were not as seriously affected by overpopulation as the other rats. However, dominant males did behave pathologically at times. Their antisocial behavior consisted of attacks on weaker male,female, and immature rats. This deviant behavior showed that even though the dominant males had enough living space, they too were affected by the general overcrowding in the enclosure.Non-dominant males in the experimental rat communities also exhibited deviant social behavior. Some withdrew completely; they moved very little and ate and drank at times when the other rats were sleeping in order to avoid contact with them. Other non-dominant males were hyperactive; they were much more active than is normal, chasing other rats and fighting each other. This segment of the rat population, likeall the other parts, was affected by the overpopulation.The behavior of the non-dominant males and of the other components of the rat population has parallels in human behavior. People in densely populated areas exhibit deviant behavior similar to that of the rats in Calhoun's experiments. In large urban areas such as New York City, London, Mexican City, and Cairo, there are abandoned children. There are cruel, powerful individuals, both men and women. There are also people who withdraw and people who become hyperactive. The quantity of other forms of social pathology such as murder, rape, and robbery also frequently occur in densely populated human communities. Is the principal cause of these disorders overpopulation? Calhoun’s experiments suggest that it might be. In any case, social scientists and city planners have been influenced by the results of this series of experiments.11. Paragraph l is organized according to__________.A. reasonsB. descriptionC. examplesD. definition12．Calhoun stabilized the rat population_________.A. when it was double the number that could live in the enclosure without stressB. by removing young ratsC. at a constant number of adult rats in the enclosureD. all of the above are correct13.W hich of the following inferences CANNOT be made from theinformation inPara. 1?A. Calhoun's experiment is still considered important today.B. Overpopulation causes pathological behavior in rat populations.C. Stress does not occur in rat communities unless there is overcrowding.D. Calhoun had experimented with rats before.14. Which of the following behavior didn‟t happen in this experiment?A. All the male rats exhibited pathological behavior.B. Mother rats abandoned their pups.C. Female rats showed deviant maternal behavior.D. Mother rats left their rat babies alone.15. The main idea of the paragraph three is that __________.A. dominant males had adequate living spaceB. dominant males were not as seriously affected by overcrowding as the otherratsC. dominant males attacked weaker ratsD. the strongest males are always able to adapt to bad conditionsText DThe first mention of slavery in the statutes法令，法规of the English colonies of North America does not occur until after 1660—some forty years after the importation of the first Black people. Lest we think that existed in fact before it did in law, Oscar and Mary Handlin assure us, that the status of B lack people down to the 1660’s was that of servants. A critique批判of the Handlins’ interpretation of why legal slavery did not appear until the 1660’s suggests that assumptions about the relation between slavery and racial prejudice should be reexamined, and that explanation for the different treatment of Black slaves in North and South America should be expanded.The Handlins explain the appearance of legal slavery by arguing that, during the 1660’s, the position of white servants was improving relative to that of black servants. Thus, the Handlins contend, Black and White servants, heretofore treated alike, each attained a different status. There are, however, important objections to this argument. First, the Handlins cannot adequately demonstrate that t he White servant’s position was improving, during and after the 1660’s; several acts of the Maryland and Virginia legislatures indicate otherwise. Another flaw in the Handlins’ interpretation is their assumption that prior to the establishment of legal slavery there was no discrimination against Black people. It is true that before the 1660’s Black people were rarely called slaves. But this shouldnot overshadow evidence from the 1630’s on that points to racial discrimination without using the term slavery. Such discrimination sometimes stopped short of lifetime servitude or inherited status—the two attributes of true slavery—yet in other cases it included both. The Handlins’ argument excludes the real possibility that Black people in the English colonies were never treated as the equals of White people.The possibility has important ramifications后果，影响.If from the outset Black people were discriminated against, then legal slavery should be viewed as a reflection and an extension of racial prejudice rather than, as many historians including the Handlins have argued, the cause of prejudice. In addition, the existence of discrimination before the advent of legal slavery offers a further explanation for the harsher treatment of Black slaves in North than in South America. Freyre and Tannenbaum have rightly argued that the lack of certain traditions in North America—such as a Roman conception of slavery and a Roman Catholic emphasis on equality— explains why the treatment of Black slaves was more severe there than in the Spanish and Portuguese colonies of South America. But this cannot be the whole explanation since it is merely negative, based only on a lack of something. A more compelling令人信服的explanation is that the early and sometimes extreme racial discrimination in the English colonies helped determine the particular nature of the slavery that followed. (462 words)16. Which of the following is the most logical inference to be drawn from the passage about the effects of “several acts of the Maryland and Virginia legislatures” (Para.2) passed during and after the 1660‟s?A. The acts negatively affected the pre-1660’s position of Black as wellas of White servants.B. The acts had the effect of impairing rather than improving theposition of White servants relative to what it had been before the 1660’s.C. The acts had a different effect on the position of white servants thandid many of the acts passed during this time by the legislatures of other colonies.D. The acts, at the very least, caused the position of White servants toremain no better than it had been before the 1660’s.17. With which of the following statements regarding the status ofBlack people in the English colonies of North America before the 1660‟s would the author be LEAST likely to agree?A. Although black people were not legally considered to be slaves,they were often called slaves.B. Although subject to some discrimination, black people had a higherlegal status than they did after the 1660’s.C. Although sometimes subject to lifetime servitude, black peoplewere not legally considered to be slaves.D. Although often not treated the same as White people, black people,like many white people, possessed the legal status of servants.18. According to the passage, the Handlins have argued which of thefollowing about the relationship between racial prejudice and the institution of legal slavery in the English colonies of North America?A. Racial prejudice and the institution of slavery arose simultaneously.B. Racial prejudice most often the form of the imposition of inheritedstatus, one of the attributes of slavery.C. The source of racial prejudice was the institution of slavery.D. Because of the influence of the Roman Catholic Church, racialprejudice sometimes did not result in slavery.19. The passage suggests that the existence of a Roman conception ofslavery in Spanish and Portuguese colonies had the effect of _________.A. extending rather than causing racial prejudice in these coloniesB. hastening the legalization of slavery in these colonies.C. mitigating some of the conditions of slavery for black people in these coloniesD. delaying the introduction of slavery into the English colonies20. The author considers the explanation put forward by Freyre andTannenbaum for the treatment accorded B lack slaves in the English colonies of North America to be _____________.A. ambitious but misguidedB. valid有根据的but limitedC. popular but suspectD. anachronistic过时的，时代错误的and controversialUNIT 2Text AThe sea lay like an unbroken mirror all around the pine-girt, lonely shores of Orr’s Island. Tall, kingly spruce s wore their regal王室的crowns of cones high in air, sparkling with diamonds of clear exuded gum流出的树胶; vast old hemlocks铁杉of primeval原始的growth stood darkling in their forest shadows, their branches hung with long hoary moss久远的青苔;while feathery larches羽毛般的落叶松,turned to brilliant gold by autumn frosts, lighted up the darker shadows of the evergreens. It was one of those hazy朦胧的, calm, dissolving days of Indian summer, when everything is so quiet that the fainest kiss of the wave on the beach can be heard, and white clouds seem to faint into the blue of the sky, and soft swathing一长条bands of violet vapor make all earth look dreamy, and give to the sharp, clear-cut outlines of the northern landscape all those mysteries of light and shade which impart such tenderness to Italian scenery.The funeral was over,--- the tread鞋底的花纹/ 踏of many feet, bearing the heavy burden of two broken lives, had been to the lonely graveyard, and had come back again,--- each footstep lighter and more unconstrained不受拘束的as each one went his way from the great old tragedy of Death to the common cheerful of Life.The solemn black clock stood swaying with its eternal ―tick-tock, tick-tock,‖ in the kitchen of the brown house on Orr’s Island. There was there that sense of a stillness that can be felt,---such as settles down on a dwelling住处when any of its inmates have passed through its doors for the last time, to go whence they shall not return. The best room was shut up and darkened, with only so much light as could fall through a little heart-shaped hole in the window-shutter,---for except on solemn visits, or prayer-meetings or weddings, or funerals, that room formed no part of the daily family scenery.The kitchen was clean and ample, hearth灶台, and oven on one side, and rows of old-fashioned splint-bottomed chairs against the wall. A table scoured to snowy whiteness, and a little work-stand whereon lay the Bible, the Missionary Herald, and the Weekly Christian Mirror, before named, formed the principal furniture. One feature, however, must not be forgotten, ---a great sea-chest水手用的储物箱,which had been the companion of Zephaniah through all the countries of the earth. Old, and battered破旧的，磨损的, and unsightly难看的it looked, yet report said that there was good store within which men for the most part respect more than anything else; and, indeed it proved often when a deed of grace was to be done--- when a woman was suddenly made a widow in a coast gale大风，狂风, or a fishing-smack小渔船was run down in the fogs off the banks, leaving in some neighboring cottage a family of orphans,---in all such cases, the opening of this sea-chest was an event of good omen 预兆to the bereaved丧亲者;for Zephaniah had a large heart and a large hand, and was apt有…的倾向to take it out full of silver dollars when once it went in. So the ark of the covenant约柜could not have been looked on with more reverence崇敬than the neighbours usually showed to Captain Pennel’s sea-chest.1. The author describes Orr‟s Island in a(n)______way.A.emotionally appealing, imaginativeB.rational, logically preciseC.factually detailed, objectiveD.vague, uncertain2.According to the passage, the “best room”_____.A.has its many windows boarded upB.has had the furniture removedC.is used only on formal and ceremonious occasionsD.is the busiest room in the house3.From the description of the kitchen we can infer that thehouse belongs to people who_____.A.never have guestsB.like modern appliancesC.are probably religiousD.dislike housework4.The passage implies that_______.A.few people attended the funeralB.fishing is a secure vocationC.the island is densely populatedD.the house belonged to the deceased5.From the description of Zephaniah we can see thathe_________.A.was physically a very big manB.preferred the lonely life of a sailorC.always stayed at homeD.was frugal and saved a lotText BBasic to any understanding of Canada in the 20 years after the Second World War is the country' s impressive population growth. For every three Canadians in 1945, there were over five in 1966. In September 1966 Canada's population passed the 20 million mark. Most of this surging growth came from natural increase. The depression of the 1930s and the war had held back marriages, and the catching-up process began after 1945. The baby boom continued through the decade of the 1950s, producing a population increase of nearly fifteen percent in the five years from 1951 to 1956. This rate of increase had been exceeded only once before in Canada's history, in the decade before 1911 when the prairies were being settled. Undoubtedly, the good economic conditions of the 1950s supported a growth in the population, but the expansion also derived from a trend toward earlier marriages and an increase in the average size of families; In 1957 the Canadian birth rate stood at 28 per thousand, one of the highest in the world. After the peak year of 1957, thebirth rate in Canada began to decline. It continued falling until in 1966 it stood at the lowest level in 25 years. Partly this decline reflected the low level of births during the depression and the war, but it was also caused by changes in Canadian society. Young people were staying at school longer, more women were working; young married couples were buying automobiles or houses before starting families; rising living standards were cutting down the size of families. It appeared that Canada was once more falling in step with the trend toward smaller families that had occurred all through theWestern world since the time of the Industrial Revolution. Although the growth in Canada’s population had slowed down by 1966 (the cent), another increase in the first half of the 1960s was only nine percent), another large population wave was coming over the horizon. It would be composed of the children of the children who were born during the period of the high birth rate prior to 1957.6. What does the passage mainly discuss?A. Educational changes in Canadian society.B. Canada during the Second World War.C. Population trends in postwar Canada.D. Standards of living in Canada.7. According to the passage, when did Canada's baby boom begin?A. In the decade after 1911.B. After 1945.C. During the depression of the 1930s.D. In 1966.8. The author suggests that in Canada during the 1950s____________.A. the urban population decreased rapidlyB. fewer people marriedC. economic conditions were poorD. the birth rate was very high9. When was the birth rate in Canada at its lowest postwar level?A. 1966.B. 1957.C. 1956.D. 1951.10. The author mentions all of the following as causes of declines inpopulation growth after 1957 EXCEPT_________________.A. people being better educatedB. people getting married earlierC. better standards of livingD. couples buying houses11.I t can be inferred from the passage that before the IndustrialRevolution_______________.A. families were largerB. population statistics were unreliableC. the population grew steadilyD. economic conditions were badText CI was just a boy when my father brought me to Harlem for the first time, almost 50 years ago. We stayed at the hotel Theresa, a grand brick structure at 125th Street and Seventh avenue. Once, in the hotel restaurant, my father pointed out Joe Louis. He even got Mr. Brown, the hotel manager, to introduce me to him, a bit punchy强力的but still champ焦急as fast as I was concerned.Much has changed since then. Business and real estate are booming. Some say a new renaissance is under way. Others decry责难what they see as outside forces running roughshod肆意践踏over the old Harlem. New York meant Harlem to me, and as a young man I visited it whenever I could. But many of my old haunts are gone. The Theresa shut down in 1966. National chains that once ignored Harlem now anticipate yuppie money and want pieces of this prime Manhattan real estate. So here I am on a hot August afternoon, sitting in a Starbucks that two years ago opened a block away from the Theresa, snatching抓取，攫取at memories between sips of high-priced coffee. I am about to open up a piece of the old Harlem---the New York Amsterdam News---when a tourist。
The Refractive Index of Curved Spacetime the Fate of Causality in QED
a r X i v :0707.2303v 2 [h e p -t h ] 29 O c t 2007Preprint typeset in JHEP style -HYPER VERSIONTimothy J.Hollowood and Graham M.Shore Department of Physics,University of Wales Swansea,Swansea,SA28PP,UK.E-mail:t.hollowood@,g.m.shore@ Abstract:It has been known for a long time that vacuum polarization in QED leads to a superluminal low-frequency phase velocity for light propagating in curved spacetime.Assuming the validity of the Kramers-Kronig dispersion relation,this would imply a superluminal wavefront velocity and the violation of causality.Here,we calculate for the first time the full frequency dependence of the refractive index using world-line sigma model techniques together with the Penrose plane wave limit of spacetime in the neighbourhood of a null geodesic.We find that the high-frequency limit of the phase velocity (i.e.the wavefront velocity)is always equal to c andcausality is assured.However,the Kramers-Kronig dispersion relation is violated due to a non-analyticity of the refractive index in the upper-half complex plane,whose origin may be traced to the generic focusing property of null geodesic congruences and the existence of conjugate points.This puts into question the issue of micro-causality,i.e.the vanishing of commutators of field operators at spacelike separated points,in local quantum field theory in curved spacetime.1.IntroductionQuantumfield theory in curved spacetime is by now a well-understood subject.How-ever,there remain a number of intriguing puzzles which hint at deeper conceptual implications for quantum gravity itself.The best known is of course Hawking radia-tion and the issue of entropy and holography in quantum black hole physics.A less well-known effect is the discovery by Drummond and Hathrell[1]that vacuum po-larization in QED can induce a superluminal phase velocity for photons propagating in a non-dynamical,curved spacetime.The essential idea is illustrated in Figure1. Due to vacuum polarization,the photon may be pictured as an electron-positron pair, characterized by a length scaleλc=m−1,the Compton wavelength of the electron. When the curvature scale becomes comparable toλc,the photon dispersion relation is modified.The remarkable feature,however,is that this modification can induce a superluminal1low-frequency phase velocity,i.e.the photon momentum becomes spacelike.Figure1:Photons propagating in curved spacetime feel the curvature in the neighbourhood of their geodesic because they can become virtual e+e−pairs.Atfirst,it appears that this must be incompatible with causality.However, as discussed in refs.[2–4],the relation of causality with the“speed of light”is far more subtle.For our purposes,we may provisionally consider causality to be the requirement that no signal may travel faster than the fundamental constant c defining local Lorentz invariance.More precisely,we require that the wavefront velocity v wf, defined as the speed of propagation of a sharp-fronted wave pulse,should be less than,or equal to,c.Importantly,it may be shown[2,4,5]that v wf=v ph(∞),the high-frequency limit of the phase velocity.In other words,causality is safe even if the low-frequency2phase velocity v ph(0)is superluminal provided the high-frequency limit does not exceed c.This appears to remove the potential paradox associated with a superluminal v ph(0).However,a crucial constraint is imposed by the Kramers-Kronig dispersion relation3(see,e.g.ref.[6],chpt.10.8)for the refractive index,viz.Re n(∞)−Re n(0)=−2ωIm n(ω).(1.1)where Re n(ω)=1/v ph(ω).The positivity of Im n(ω),which is true for an absorptive medium and is more generally a consequence of unitarity in QFT,then implies that Re n(∞)<Re n(0),i.e.v ph(∞)>v ph(0).So,given the validity of the KK dispersion relation,a superluminal v ph(0)would imply a superluminal wavefront velocity v wf= v ph(∞)with the consequent violation of causality.We are therefore left with three main options[4],each of which would have dramatic consequences for our established ideas about quantumfield theory: Option(1)The wavefront speed of light v wf>1and the physical lightcones lie outside the geometric null cones of the curved spacetime,inapparent violation of causality.It should be noted,however,that while this would certainly violate causality for theories in Minkowski spacetime,it could still be possible for causality to be preserved in curved spacetime if the effective metric characterizing the physical light cones defined by v wf nevertheless allow the existence of a global timelike Killing vectorfield. This possible loophole exploits the general relativity notion of“stable causality”[8,9] and is discussed further in ref.[2].Option(2)Curved spacetime may behave as an optical medium ex-hibiting gain,i.e.Im n(ω)<0.This possibility was explored in the context ofΛ-systems in atomic physics in ref.[4], where laser-atom interactions can induce gain,giving rise to a negative Im n(ω)and superluminal low-frequency phase velocities while preserving v wf=1and the KKdispersion relation.However,the problem in extending this idea to QFT is that the optical theorem,itself a consequence of unitarity,identifies the imaginary part of forward scattering amplitudes with the total cross section.Here,Im n(ω)should be proportional to the cross section for e+e−pair creation and therefore positive.A negative Im n(ω)would appear to violate unitarity.Option(3)The Kramers-Kronig dispersion relation(1.1)is itself vio-lated.Note,however,that this relation only relies on the analyticity ofn(ω)in the upper-half plane,which is usually considered to be a directconsequence of an apparently fundamental axiom of local quantumfieldtheory,viz.micro-causality.Micro-causality in QFT is the requirement that the expectation value of the com-mutator offield operators 0|[A(x),A(y)]|0 vanishes when x and y are spacelike separated.While this appears to be a clear statement of what we would understand by causality at the quantum level,in fact its primary rˆo le in conventional QFT is as a necessary condition for Lorentz invariance of the S-matrix(see e.g.ref.[6], chpts.5.1,3.5).Since QFT in curved spacetime is only locally,and not globally, Lorentz invariant,it is just possible there is a loophole here allowing violation of micro-causality in curved spacetime QFT.Despite these various caveats,unitarity,micro-causality,the identification of light cones with geometric null cones and causality itself are all such fundamental elements of local relativistic QFT that any one of these options would represent a major surprise and pose a severe challenge to established wisdom.Nonetheless,it appears that at least one has to be true.To understand how QED in curved spacetime is reconciled with causality,it is therefore necessary to perform an explicit calculation to determine the full frequency dependence of the refractive index n(ω)in curved spacetime.This is the technical problem which we solve in this paper.The remarkable result is that QED chooses option(3),viz.analyticity is violated in curved spacetime.Wefind that in the high-frequency limit,the phase velocity always approaches c,so we determine v wf= 1.Moreover,we are able to confirm that where the background gravitationalfield induces pair creation,γ→e+e−,Im n(ω)is indeed positive as required by unitarity. However,the refractive index n(ω)is not analytic in the upper half-plane,and the KK dispersion relation is modified accordingly.One might think that this implies a violation of microcausality,however,there is a caveat in this line of argument which requires a more ambitious off-shell calculation to settle definitively[7].–3–In order to establish this result,we have had to apply radically new techniques to the analysis of the vacuum polarization for QED in curved spacetime.The original Drummond-Hathrell analysis was based on the low-energy,O(R/m2)effective action for QED in a curved background,L=−1m2 aRFµνFµν+bRµνFµλFνλ+cRµνλρFµνFλρ +···.(1.2) derived using conventional heat-kernel or proper-time techniques(see,for example, [10–14].A geometric optics,or eikonal,analysis applied to this action determines the low-frequency limit of the phase velocity.Depending on the spacetime,the photon trajectory and its polarization,v ph(0)may be superluminal[1,15,16].In subsequent work,the expansion of the effective action to all orders in derivatives,but still at O(R/m2),was evaluated and applied to the photon dispersion relation[11,12,17, 18].However,as emphasized already in refs.[2,3,18],the derivative expansion is inadequate tofind the high-frequency behaviour of the phase velocity.The reason is that the frequencyωappears in the on-shell vacuum polarization tensor only in the dimensionless ratioω2R/m4.The high-frequency limit depends non-perturbatively on this parameter4and so is not accessible to an expansion truncated atfirst order in R/m2.In this paper,we instead use the world-line formalism which can be traced back to Feynman and Schwinger[19,20],and which has been extensively developed in recent years into a powerful tool for computing Green functions in QFT via path integrals for an appropriate1-dim world-line sigma model.(For a review,see e.g.ref.[21].) The power of this technique in the present context is that it enables us to calculate the QED vacuum polarization non-perturbatively in the frequency parameterω2R/m4 using saddle-point techniques.Moreover,the world-line sigma model provides an extremely geometric interpretation of the calculation of the quantum corrections to the vacuum polarization.In particular,we are able to give a very direct interpretation of the origin of the Kramers-Kronig violating poles in n(ω)in terms of the general relativistic theory of null congruences and the relation of geodesic focusing to the Weyl and Ricci curvatures via the Raychoudhuri equations.A further key insight is that to leading order in R/m2,but still exact inω2R/m4, the relevant tidal effects of the curvature on photon propagation are encoded in thef(ωm2Penrose plane-wave limit[22,23]of the spacetime expanded about the original null geodesic traced by the photon.This is a huge simplification,since it reduces the problem of studying photon propagation in an arbitrary background to the much more tractable case of a plane wave.In fact,the Penrose limit is ideally suited to this physical problem.As shown in ref.[24],where the relation with null Fermi normal coordinates is explained,it can be extended into a systematic expansion in a scaling parameter which for our problem is identified as R/m2.The Penrose expansion therefore provides us with a systematic way to go beyond leading order in curvature.The paper is organized as follows.In Section2,we introduce the world-line formalism and set up the geometric sigma model and eikonal approximation.The relation of the Penrose limit to the R/m2expansion is then explained in detail, complemented by a power-counting analysis in the appendix.The geometry of null congruences is introduced in Section3,together with the simplified symmetric plane wave background in which we perform our detailed calculation of the refractive index. This calculation,which is the heart of the paper,is presented in Section4.The interpretation of the result for the refractive index is given in Section5,where we plot the frequency dependence of n(ω)and prove that asymptotically v ph(ω)→1. We also explain exactly how the existence of conjugate points in a null congruence leads to zero modes in the sigma model partition function,which in turn produces the KK-violating poles in n(ω)in the upper half-plane.The implications for micro-causality are described in Section6.Finally,in Section7we make some further remarks on the generality of our results for arbitrary background spacetimes before summarizing our conclusions in Section8.2.The World-Line FormalismFigure2:The loop xµ(τ)with insertions of photon vertex operators atτ1andτ2.–5–In the world-line formalism for scalar QED5the1-loop vacuum polarization is given byΠ1-loop=αT3 T0dτ1dτ2Z V∗ω,ε1[x(τ1)]Vω,ε2[x(τ2)] .(2.1)The loop with the photon insertions is illustrated in Figure(2).The expectation value is calculated in the one-dimensional world-line sigma model involving periodic fields xµ(τ)=xµ(τ+T)with an actionS= T0dτ 15Since all the conceptual issues we address are the same for scalars and spinors,for simplicity we perform explicit calculations for scalar QED in this paper.The generalization of the world-line formalism to spinor QED is straightforward and involves the addition of a further,Grassmann,field in the path integral.For ease of language,we still use the terms electron and positron to describe the scalar particles.6This will require some appropriate iǫprescription.In particular,the T integration contour should lie just below the real axis to ensure that the integral converges at infinity.7In general,one has to introduce ghostfields to take account of the non-trivial measure for the fields, [dxµ(τ)of geometric optics where Aµ(x)is approximated by a rapidly varying exponential times a much more slowly varying polarization.Systematically,we haveAµ(x)= εµ(x)+ω−1Bµ(x)+··· e iωΘ(x).(2.4) We will need the expressions for the leading order piecesΘandε.This will necessitate solving the on-shell conditions to thefirst two non-trivial orders in the expansion in R1/2/ω.To leading order,the wave-vector kµ=ωℓµ,whereℓµ=∂µΘis a null vector (or more properly a null1-form)satisfying the eikonal equation,ℓ·ℓ≡gµν∂µΘ∂νΘ=0.(2.5) A solution of the eikonal equation determines a family or congruence of null geodesics in the following way.9The contravariant vectorfieldℓµ(x)=∂µΘ(x),(2.6) is the tangent vector to the null geodesic in the congruence passing through the point xµ.In the particle interpretation,kµ=ωℓµis the momentum of a photon travelling along the geodesic through that particular point.It will turn out that the behaviour of the congruence will have a crucial rˆo le to play in the resulting behaviour of the refractive index.The general relativistic theory of null congruences is considered in detail in Section3.Now we turn to the polarization vector.To leading order in the WKB approxima-tion,this is simply orthogonal toℓ,i.e.ε·ℓ=0.Notice that this does not determine the overall normalization ofε,the scalar amplitude,which will be a space-dependent function in general.It is useful to splitεµ=Aˆεµ,whereˆεµis unit normalized.At the next order,the WKB approximation requires thatˆεµis parallel transported along the geodesics:ℓ·Dˆεµ=0.(2.7) The remaining part,the scalar amplitude A,satisfies1ℓ·D log A=−εµD·ℓ.(2.9)2Since the polarization vector is defined up to an additive amount of k,there are two linearly independent polarizationsεi(x),i=1,2.Since there are two polarization states,the one-loop vacuum polarization is ac-tually a2×2matrixΠ1-loop ij =αT3 T0dτ1dτ2Z× εi[x(τ1)]·˙x(τ1)e−iωΘ[x(τ1)]εj[x(τ2)]·˙x(τ2)e iωΘ[x(τ2)] .(2.10)In order for this to be properly defined we must specify how to deal with the zero mode of xµ(τ)in the world-line sigma model.Two distinct–but ultimately equiv-alent–methods for dealing with the zero mode have been proposed in the litera-ture[25–29].In thefirst,the position of one particular point on the loop is defined as the zero mode,while in the other,the“string inspired”definition,the zero mode is defined as the average position of the loop:xµ0=1Now notice that the exponential pieces of the vertex operators in(2.1)act as source terms and so the complete action including these ism2S=−T+can always be brought into the formds2=2du dΘ−C(u,Θ,Y a)dΘ2−2C a(u,Θ,Y b)dY a dΘ−C ab(u,Θ,Y c)dY a dY b.(2.14) It is manifest that dΘis a null1-form.The null congruence has a simple description as the curves(u,Θ0,Y a0)forfixed values of the transverse coordinates(Θ0,Y a0).The geodesicγis the particular member(u,0,0,0).It should not be surprising that the Rosen coordinates are singular at the caustics of the congruence.These are points where members of the congruence intersect and will be described in detail in the next section.With the form(2.14)of the metric,onefinds that the classical equations of motion of the sigma model action(2.13)have a solution with Y a=Θ=0whereu(τ)satisfies¨u=−2ωTm2δ(τ).(2.15)More general solutions with constant but non-vanishing(Θ,Y a)are ruled out by the constraint(2.12).The solution of(2.15)is˜u(τ)=−u0+ 2ωT(1−ξ)τ/m20≤τ≤ξ2ωTξ(1−τ)/m2ξ≤τ≤1.(2.16)where the constantu0=ωTξ(1−ξ)/m2(2.17) ensures that the constraint(2.12)is satisfied.The solution describes a loop which is squashed down onto the geodesicγas illustrated in Figure(3).The electron and positron have to move with different world-line velocities in order to accommodate the fact that in generalξis not equal to1Now that we have defined the Rosen coordinates and found the classical saddle-point solution,we are in a position to set up the perturbative expansion.The idea is to scale the transverse coordinatesΘand Y i in order to remove the factor of m2/T in front of the action.The affine coordinate u,on the other hand,will be left alone since the classical solution˜u(τ)is by definition of zeroth order in perturbation theory. The appropriate scalings are precisely those needed to define the Penrose limit[22]–in particular we closely follow the discussion in[23].The Penrose limit involvesfirst a boost(u,Θ,Y a)−→(λ−1u,λΘ,Y a),(2.18) whereλ=T1/2/m,and then a uniform re-scaling of the coordinates(u,Θ,Y a)−→(λu,λΘ,λY a).(2.19) As argued above,it is important that the null coordinate along the geodesic u is not affected by the combination of the boost and re-scaling;indeed,overall(u,Θ,Y a)−→(u,λ2Θ,λY a).(2.20) After these re-scalings,the sigma model action(2.13)becomesS=−T+1m2Θ(ξ)+ωT4 10dτ 2˙u˙Θ−C ab(u,0,0)˙Y a˙Y b −ωT m2Θ(0)+···.(2.22) The leading order piece is precisely the Penrose limit of the original metric in Rosen coordinates.Notice that we must keep the source terms because the combination ωT/m2,or more precisely the dimensionless ratioωR1/2/m2,can be large.However, there is a further simplifying feature:once we have shifted the“field”about the clas-sical solution u(τ)→˜u(τ)+u(τ),it is clear that there are no Feynman graphs with-out externalΘlines that involve the vertices∂n u C ab(˜u,0,0)u n˙Y a˙Y b,n≥1;hence, we can simply replace C ab(˜u+u,0,0)consistently with the background expression C ab(˜u,0,0).This means that the resulting sigma model is Gaussian to leading order in R/m2:S(2)=14 10dτC ab(˜u,0,0)˙Y a˙Y b,(2.23)wherefinally we have dropped the˙u˙Θpiece since it is just the same as inflat space and the functional integral is normalized relative toflat space.This means that all the non-trivial curvature dependence lies in the Y a subspace transverse to the geodesic.10It turns out that the Rosen coordinates are actually not the most convenient co-ordinates with which to perform explicit calculations.For this,we prefer Brinkmann coordinates(u,v,y i).To define these,wefirst introduce a“zweibein”in the subspace of the Y a:C ab(u)=δij E i a(u)E j b(u),(2.24) with inverse E a i.This quantity is subject to the condition thatΩij≡dE iadE ia2E a j.(2.29)du2We have introduced these coordinates at the level of the Penrose limit.However, they have a more general definition for an arbitrary metric and geodesic.They are in fact Fermi normal coordinates.These are“normal”in the same sense as the more common Riemann normal coordinates,but in this case they are associated to the geodesic curveγrather than to a single point.This description of Brinkmann coordinates as Fermi normal coordinates and their relation to Rosen coordinates and the Penrose limit is described in detail in ref.[24].In particular,this reference givestheλexpansion of the metric in null Fermi normal coordinates to O(λ2).To O(λ) this isds2=2du dv−R iuju y i y j du2−dy i2+λ −2R uiuv y i v du2−43R uiuj;k y i y j y k du2 +O(λ2),(2.30)which is consistent with(2.28)since R iuju=−h ij for a plane wave.It is worth pointing out that Brinkmann coordinates,unlike Rosen coordinates,are not singular at the caustics of the null congruence.One can say that Fermi normal coordinates (Brinkmann coordinates)are naturally associated to a single geodesicγwhereas Rosen coordinates are naturally associated to a congruence containingγ.In Brinkmann coordinates,the Gaussian action(2.23)for the transverse coordi-nates becomesS(2)=−12m2Ωij y i y j τ=ξ−ωTexplicitly.In doing so,we discover many surprising features of the dispersion relation that will hold in general.The symmetric plane wave metric is given in Brinkmann coordinates by(2.28), with the restriction that h ij is independent of u.This metric is locally symmetric in the sense that the Riemann tensor is covariantly constant,DλRµνρσ=0,and can be realized as a homogeneous space G/H with isometry group G.12With no loss of generality,we can choose a basis for the transverse coordinates in which h ij is diagonal:h ij y i y j=σ21(y1)2+σ22(y2)2.(3.1) The sign of these coefficients plays a crucial role,so we allow theσi themselves to be purely real or purely imaginary.For a general plane-wave metric,the only non-vanishing components of the Rie-mann tensor(up to symmetries)areR uiuj=−h ij(u).(3.2) So for the symmetric plane wave,we have simplyR uu=σ21+σ22,(3.3)R uiui=−σ2iand for the Weyl tensor,1C uiui=−σ2i+12Notice that,contrary to the implication in ref.[4,18],the condition that the Riemann tensor is covariantly constant only implies that the spacetime is locally symmetric,and not necessarily maximally symmetric[13,23].A maximally symmetric space has Rµνρσ=1plane wave background,then explain how the key features are described in the gen-eral theory of null congruences.The geodesic equations for the symmetric plane wave(2.28),(3.1)are:¨u=0,¨v+2˙u2i=1σ2i y i˙y i=0,¨y i+˙u2σ2i y i=0.(3.5)We can therefore take u itself to be the affine parameter and,with the appropriate choice of boundary conditions,define the null congruence in the neighbourhood of, and including,γas:v=Θ−122i=1σi tan(σi u+a i)y i2.(3.9)The tangent vector to the congruence,defined asℓµ=gµν∂νΘ,is therefore ℓ=∂u+1The polarization vectors are orthogonal to this tangent vector,ℓ·εi=0,and are further constrained by(2.9).Solving(2.7)for the normalized polarization(one-form) yields13ˆεi=dy i+σi tan(σi u+a i)y i du.(3.11) The scalar amplitude A is determined by the parallel transport equation(2.8),from which we readilyfind(normalizing so that A(0)=1)A=2i=1 cos(σi u+a i)(3.12)The null congruence in the symmetric plane wave background displays a number of features which play a crucial role in the analysis of the refractive index.They are best exhibited by considering the Raychoudhuri equation,which expresses the behaviour of the congruence in terms of the optical scalars,viz.the expansionˆθ, shearˆσand twistˆω.These are defined in terms of the covariant derivative of the tangent vector as[30]:ˆθ=1112Rµνℓµℓν,Ψ0=Cµρνσℓµℓνmρmσ.14As demonstrated in refs.[31],the effectof vacuum polarization on low-frequency photon propagation is also governed by the two curvature scalarsΦ00andΨ0.Indeed,many interesting results such as the polarization sum rule and horizon theorem[31,32]are due directly to special properties ofΦ00andΨ0.As we now show,they also play a key rˆo le in the world-line formalism in determining the nature of the full dispersion relation.√2R uu=1 2(C u1u1−C u2u2)=1By its definition as a gradientfield,it is clear that D[µℓν]=0so the null con-gruence is twist-freeˆω=0.The remaining Raychoudhuri equations can then be rewritten as∂u(ˆθ+ˆσ)=−(ˆθ+ˆσ)2−Φ00−|Ψ0|,∂u(ˆθ−ˆσ)=−(ˆθ−ˆσ)2−Φ00+|Ψ0|.(3.15) The effect of expansion and shear is easily visualized by the effect on a circular cross-section of the null congruence as the affine parameter u is varied:the expansionˆθgives a uniform expansion whereas the shearˆσproduces a squashing with expansion along one transverse axis and compression along the other.The combinationsˆθ±ˆσtherefore describe the focusing or defocusing of the null rays in the two orthogonal transverse axes.We can therefore divide the symmetric plane wave spacetimes into two classes, depending on the signs ofΦ00±|Ψ0|.A Type I spacetime,whereΦ00±|Ψ0|are both positive,has focusing in both directions,whereas Type II,whereΦ00±Ψ0 have opposite signs,has one focusing and one defocusing direction.Note,however, that there is no“Type III”with both directions defocusing,since the null-energy condition requiresΦ00≥0.For the symmetric plane wave,the focusing or defocusing of the geodesics is controlled byeq.(3.6),y i=Y i cos(σi u+a i).Type I therefore corresponds toσ1and σ2both real,whereas in Type II,σ1is real andσ2is pure imaginary.The behaviour of the congruence in these two cases is illustrated in Figure(4).1y21y2Figure4:(a)Type I null congruence with the special choiceσ1=σ2and a1=a2so that the caustics in both directions coincide as focal points.(b)Type II null congruence showing one focusing and one defocusing direction.To see this explicitly in terms of the Raychoudhuri equations,notefirst that the curvature scalarsΦ00−|Ψ0|=σ21,Φ00+|Ψ0|=σ22are simply the eigenvalues of h ij.The optical scalars areˆθ=−12 σ1tan(σ1u+a1)−σ2tan(σ2u+a2) (3.16)and we easily verify∂uˆθ=ˆθ2−ˆσ2−12(σ21−σ22).(3.17)It is clear that provided the geodesics are complete,those in a focusing direction will eventually cross.In the symmetric plane wave example,with y i=Y i cos(σi u+ a i),these“caustics”occur when the affine parameterσi u=π(n+115This does not necessarily mean that the conjugate points are joined by more than one actual geodesic,only that an infinitesimal deformation ofγter we shall see that the existence of conjugate points relies on the existence of zero modes of a linear problem.Conversely,the existence of a geodesic other thanγjoining p and q does not necessarily mean that p and q are conjugate[8,33].16Whether these deformed geodesics become actual geodesics is the question as to whether they lift from the Penrose limit to the full metric.4.World-line Calculation of the Refractive IndexIn this section,we calculate the vacuum polarization and refractive index explicitly for a symmetric plane wave.As we mentioned at the end of Section 2,the explicit calculations are best performed in Brinkmann coordinates.We will need the expres-sions for Θand εi for the symmetric plane wave background:these are in eqs.(3.9),(3.11)and (3.12).From these,we have the following explicit expression for the vertex operator 17V ω,εi [x µ(τ)]= ˙y i +σi tan(σi ˜u +a i )˙˜u y i 2 j =1 cos(σj ˜u +a j )×exp iω v +1410dτ ˙y i 2−˙˜u 2σ2i yi 2 −ωT σi −det g [x (τ)]which can be exponenti-ated by introducing appropriate ghosts [25–29].However,in Brinkmann coordinatesafter the re-scaling (2.27),det g =−1+O (λ)and so to leading order in R/m 2the determinant factor is simply 1and so plays no rˆo le.The same conclusion would not be true in Rosen coordinates.The y i fluctuations satisfy the eigenvalue equation¨y i+˙˜u 2σ2i y i −2ωT σi 17Notice that at leading order in R/m 2we are at liberty to replace u (τ)by its classical value ˜u (τ).The argument is identical to the one given in Section 2.。
2 Fermi Liquids and Luttinger Liquids
10
Heinz J. Schulz et al.
Subsequently, I will first briefly discuss the case of a noninteracting manyfermion system (the Fermi gas), and then turn to Landau’s theory of the interacting case (the liquid), first from a phenomenological point of view, and then microscopically. A much more detailed and complete exposition of these subjects can be found in the literature [5–9]. 2.2.1 The Fermi Gas
2
Fermi Liquids and Luttinger Liquids
Heinz J. Schulz, Gianaurelio Cuniberti, and Pierbiagio Pieri
2.1
Introduction
In these lecture notes, corresponding roughly to lectures given at the summer school in Chia Laguna, Italy, in September 1997, an attempt is made to present the physics of three-dimensional interacting fermion systems (very roughly) and that of their one-dimensional counterparts, the so-called Luttinger liquids (in some more detail). These subjects play a crucial role in a number of currently highly active areas of research: high temperature and organic superconductors, quantum phase transitions, correlated fermion systems, quantum wires, the quantum Hall effect, low-dimensional magnetism, and probably some others. Some understanding of this physics thus certainly should be useful in a variety of areas, and it is hoped that these notes will be helpful in this. As the subject of these lectures was quite similar to those delivered at Les Houches, some overlap in the notes [1] was unavoidable. However, a number of improvements have been made, for example a discussion of the “Klein factors” occurring in the bosonization of one-dimensional fermions, and new material added, mainly concerning spin chains and coupled Luttinger liquids. Some attempt has been made to keep references up to date, but this certainly has not always been successful, so we apologize in advance for any omissions (but then, these are lecture notes, not a review article).
PhaseDiagram
Example: Cu-Ni phase diagram (only for slow cooling conditions) Liquidus line: the line connecting Ts at which liquid starts to solidify under equilibrium conditions Solidus: the temperature at which the last of the liquid phase solidifies Between liquidus and solidus: P =2
Chapter 8
8
53 wt% Ni – 47 wt% Cu at 1300oC
P=1 F=3–P=2
P=2;F=3–P=1
• contains both liquid and solid phases ⇒ neither of these phases can have average composition 53 wt% Ni – 47 wt% Cu • draw a tie line at 1300oC ⇒ from the graph: composition of liquid phase wL = 45% and solid phase wS = 58% at 1300oC
F is # of degrees of freedom or variance P is # of phases C is # of components Component is the minimum # of species necessary to define the composition of the system H2O C=1 (i) P=1, F=2; (ii) P=2, F=1; (iii) P=3, F=0
Spin - or, actually Spin and Quantum Statistics
S´ eminaire Poincar´ e
SPIN OR, ACTUALLY: SPIN AND QUANTUM STATISTICS∗
arXiv:0801.2724v3 [math-ph] 29 Feb 2008
J¨ urg Fr¨ ohlich Theoretical Physics ´ † ETH Z¨ urich and IHES
Abstract. The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli’s theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value ge = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of ge are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics, relevant in the theory of the quantum Hall effect, are described.
Ch.6 Exercises for phase diagram
Exercises for phase diagram1. For alloys of two hypothetical metals A and B, there exist an α, A-rich phase and a β, B-rich phase. From the mass fractions of both phases for two different alloys provided in the table below, (which are at the same temperature), determine the composition of the phase boundary (or solubility limit) for both α and β phases at this temperature.Alloy Composition Fractionα PhaseFractionβ Phase60 wt% A-40 wt% B 0.57 0.4330 wt% A-70 wt% B 0.14 0.862. Construct the hypothetical phase diagram for metals A and B between temperatures of 600ºC and 1000ºC given the following information:• The melting temperature of metal A is 940ºC.• The solubility of B in A is negligible at all temperatures.• The melting temperature of metal B is 830ºC.• The maximum solubility of A in B is 12 wt% A, which occurs at 700ºC.• At 600ºC, the solubility of A in B is 8 wt% A.• One eutectic（共晶）occurs at 700ºC, and 75 wt% B–25 wt% A.• A second eutectic occurs at 730ºC, and 60 wt% B–40 wt% A.• A third eutectic occurs at 755ºC and 40 wt% B–60 wt% A.• One congruent （无成分变化）melting point occurs at 780ºC and 51 wt% B–49 wt% A.• A second congruent melting point occurs at 755ºC and 67 wt% B–33 wt% A.• The intermetallic compound （金属间化合物）AB exists at 51 wt% B–49 wt% A.• The intermetallic compound AB2exists at 67 wt% B–33 wt% A.3. Consider 1.0 kg of austenite（奥氏体）containing 1.15 wt% C, cooled to below 725ºC (998 K).(a) What is the proeutectoid（先共析） phase?(b) How many kilograms each of total ferrite（铁素体） and cementite（渗碳体） form?(c) How many kilograms each of pearlite（珠光体）and the proeutectoid phase form?(d) Schematically sketch the cooling curve and label the resulting microstructure.4. Compute the maximum mass fraction of proeutectoid cementite possible for a hypereutectoid（过共析） iron–carbon alloy.。
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a r X i v :c o n d -m a t /0305585v 1 [c o n d -m a t .s u p r -c o n ] 26 M a y 2003Phase diagram of a class of spin-triplet ferromagnetic superconductors D.V.Shopova ∗and D.I.Uzunov CPCM Laboratory,G.Nadjakov Institute of Solid State Physics,Bulgarian Academy of Sciences,BG-1784Sofia,Bulgaria.∗Corresponding author:sho@issp.bas.bg Key words :superconductivity,ferromagnetism,phase diagram,order parameter profile.PACS :74.20.De,74.20.Rp Abstract We investigate thermodynamic phases,including the phase of coexistence of superconductivity and ferromagnetism,the possible phase transitions of first and second order,and the shape of the phase diagram in mean-field approximation for a phenomenological model of spin-triplet ferromagnetic superconductors.The results are discussed in view of application to metallic ferromagnets as UGe 2,ZrZn 2,URhGe,and Fe.Recently,the coexistence of ferromagnetism and superconductivity was discovered in the metallic compounds UGe 2[1,2,3],ZrZn 2[4],URhGe [5]and also in Fe [6]in experiments at low temperatures and high pressure.In contrast to other superconducting materials,in these metals the phase transition temperature to the ferromagnetic state is higher than the phase transition temperature to the superconducting state.Moreover,it seems that the superconductivity in the metallic compounds mentioned above always coexists with the ferromagnetic order and is enhanced by the latter.In these systems the superconduc-tivity seems to arise from the same electrons that create the band magnetism,and is most naturally understood as a triplet rather than spin-singlet pairing phenomenon [7,8,9].The same unconventional superconductivity has been suggested [1]as a possible outcome of the interpretation of experiments in Fe [6].Note,that both vortex and Meissner su-perconductivity phases [6]are found in the high-pressure crystal modification of Fe which has a hexagonal close-packed lattice.In this hexagonal lattice the strong ferromagnetism of the usual bcc iron crystal probably disappears [10].Recently,the phenomenological theory that explains coexistence of ferromagnetism and unconventional spin-triplet superconductivity of Landau-Ginzburg type was developed[11,12].The possible low-order coupling between the superconducting and ferromagnetic order parameters is derived on the basis of general symmetry group arguments and several important features of the superconducting vortex state in the ferromagnetic phase of unconventional ferromagnetic superconductors are established [11,12].In this letter we shall use the approach presented in Refs.[11,12]to investigate the con-ditions for the occurrence of the Meissner phase and to demonstrate that the presence of ferromagnetic order enhances the p -wave superconductivity.For this aim we shall es-tablish the phase diagram corresponding to model ferromagnetic superconductors in a zero external magnetic field.We shall also show that the phase transition to the super-conducting state in ferromagnetic superconductors can be either of first or second order depending on the particular substance.We confirm the predictions made in Refs.[11,12]about the symmetry of the ordered phases.Our investigation is based on the mean-field approximation [13]as well as on familiar results about the possible phases in nonmagnetic superconductors with triplet (p -wave)Cooper pairs [7,14,15].We shall neglect all anisotropies,usually given by the respective additional Landau invariants and gradient terms [8,9]in the Ginzburg-Landau free energy of unconventional superconductors.The reasons is that the inclusion of crystal anisotropy is related with lengthy formulae and a multivariant analysis which will obscure our main aims and results.Let us emphasize that the present results should be valid in the same or modified form when the crystal anisotropy is properly taken into account.We have to mention also that there is a formal similarity between the phase diagram obtained in our investigation and the phase diagram of certain improper ferroelectrics [16,17].Following Refs.[11,12]we consider the Ginzburg-Landau free energy F = d 3xf (ψ,M ),where f =22|ψ|4+a f M 2+βH[11,12]rather than fromfluctuations ofψ(this effect is extremely small and can be safely ignored).Note,that thefirst term in(1)still persists for H=0because of the diamagnetic effect created by of magnetization M= B/4π>0.As we shall investigate the conditions for the occurrence of the Meissner phase whereψis uniform,the spatial dependence ofψand,hence,thefirst term in r.h.s.of(1)will be neglected(see also a brief discussion at the end of this paper).In case of a strong easy axis type of magnetic anisotropy,as is in UGe2[1],the overall complexity of mean-field analysis of the free energy(1)can be avoided by performing an Ising-like description: M=(0,0,M),where M=±|M|is the magnetization along the“z-axis.”Further,because of the equivalence of the two physical states(±M)the thermodynamic analysis can be performed within the“gauge”M≥0.But this stage of consideration can also be achieved without the help of crystal anisotropy arguments. When the magnetic order has a continuous symmetry one may take advantage of the symmetry of model(1)and avoid the consideration of equivalent thermodynamic states that occur as a result of the respective symmetry breaking at the phase transition point but have no effect on thermodynamics of the system.In the isotropic system one may again choose a gauge,in which the magnetization vector has the same direction as z-axis (| M|=M z≡M)and this will not influence the generality of thermodynamic analysis. With the help of convenient notations,ϕj=b1/4ψj,ϕj=φj exp(θj),M=β1/4M,γ=γ0/(b2β)1/4,r=a s/√β,and neglecting thefirst term in(1)the free energybecomesf=r|φ|2+12M4+2γMφ1φ2sinθ,(2)whereφ2=(φ21+φ22+φ23),andθ=(θ2−θ1).The possible(stable,metastable and unstable)phases are given in Table1together with the respective existence and stability conditions.The stability conditions define the do-main of the phase diagram where the respective phase is either stable or metastable[13]. The normal(disordered)phase,denoted in Table1by N always exists(for all tempera-tures T≥0)but is stable for t>0,r>0.The superconductivity phase denoted in Table 1by SC1is unstable.The same is valid for the phase of coexistence of ferromagnetism and superconductivity denoted in Table1by CO2.The N-phase,the ferromagnetic phase (FM),the superconducting phases(SC1-3)and two of the phases of coexistence(CO1-3) are generic phases because they appear also in the decoupled case(γ≡0).When the Mψ–coupling is not present,the phases SC1-3are identical and represented by the order parameterϕwhere the componentsϕj participate on equal footing.The asterisk attached to the stability condition of“the second superconductivity phase”,(SC2),indicates that our analysis is insufficient to determine whether this phase corresponds to a minimum of the free energy.As we shall see later the phase SC2,as well as the other two purely superconducting phases and the coexistence phase CO1,have no chance to become stable forγ=0.This is so,because the non-generic phase of coexistence of superconductivity and ferromagnetism(FS in Table1),which does not exist forγ=0is stable and has a lower free energy in their domain of stability.TABLE1.Phases and their existence and stability properties(k=0,±1,...).order parameter stability domainφj=M=0t>0,r>0φj=0,M2=−t r>0,r2>γ2tφ1=M=0,φ2=−r unstableφ2=−r,θ=πk,M=0(t>0)∗φ1=φ2=M=0,φ23=−r r<0,t>0φ1=φ2=0,φ23=−r,M2=−t r<0,t<0φ1=0,φ2=−r,θ=θ2=πk,M2=−t unstable2φ21=2φ22=φ2=−r+γM,φ3=03M2>(−t+γ2/2)We have outlined the domain in the(t,r)plane where the FS phase exists and is a minimum of the free energy.For r<0the third-degree algebraic equation for M(see Table 1)and the existence and stability conditions are satisfied for any M≥0provided t≥γ2. For t<γ2the condition M≥M0have to be fulfilled,here the value M0=(−t+γ2/2)1/2 of M is obtained from r(M0)=0.Thus for r=0the N-phase is stable for t≥γ2/2,on the other hand FS is stable for t≤γ2/2.For r>0,the requirement for the stability of FS leads to the inequalitiesmax r3)and M0should be the positive solution of the third-degree equation of state from Table1;M m>0gives a maximum of the function r(M).The further analysis leads to the existence and stability domain of FS below the line AB given by circles(see Fig.1).In Fig.1the curve of circles starts from the point A with coordinates(γ2/2,0)and touches two other(solid and dotted)curves at the point B with coordinates(−γ2/4,γ2/2).Line of circles represents the function r(M m)≡r m(t)wherer m(t)=43γ γ2|t|.The inequality r<r m(t)is a condition for the stability of FS,whereas the inequality r≤r e(t)for(−t)≥γ2/4is a condition for the existence of FS as a solution of the respective equation of state.This existence condition for FS has been obtained fromγM>r(see Table1).In the region on the left of the point B in Fig.1,the FS phase satisfies the existence conditionγM>r only below the dotted line.In the domain confined between the lines of circles and the dotted line on the left of the point B the stability condition for FS is satisfied but the existence condition is broken.The inequality r≥r e(t)is the stability condition of FM for0≤(−t)≤γ2/4.For(−t)>γ2/4the FM phase is stable for all r≥r e(t).Figure1:The phase diagram in the plane(t,r)with two tricritical points(A and B)and a triple point C;γ=1.2.In the region confined by the line of circles AB,the dotted line for0<(−t)<γ2/4,and the t−axis,the phases N,FS and FM have an overlap of stability domains.The same problem exists for FS and the SC phases in the second quadrant and for the phases FS and CO1in the third quadrant of the plane(t,r).The comparison of the respective free energies for r<0shows that the stable phase is FS whereas the other phases are metastable within their domains of stability.The part of the t-axis given by r=0and t>γ2/2is a phase transition line of second order which describes the N-FS transition.The same transition for0<t<γ2/2is represented by the solid line AC which is the equilibrium transition line of afirst order phase transition.This equilibrium transition curve is given by the function1r eq(t)=√2r eq (0)=γ2/4]the phases N,FM,and FS coexist.For t <0the straight liner ∗eq (t )=γ2|t |).On the dotted line of the second order FM-FS transition the equilibrium value of M is equal to that of the FMphase (M eq =2+ T ∗ς)T ∗,(9)where ς=βα2s /4bα2f .This means that the second order FM-FS transition should disap-pear for sufficiently large Mψ–coupling.Such a condition does not exist for the first order transitions FM-FS and N-FS.Taking into account the first term in the free energy(1)should lead to a depression of the equilibrium transition temperature.As the magnetization increases with the decrease of the temperature,the vortex state should occur at temperatures which are lower than the equilibrium temperature T eq of the homogeneous (Meissner)state.For example,the critical temperature (˜T c )corresponding to the inhomogeneous (vortex)phase of FS-type has been evaluated [12]to be lower than the critical temperature (8):(T c −˜T c )=4πµB M /αs (µB =|e | /2mc -Bohr magneton).For J ≫µB ,we have T c ≈˜Tc .Finally,let us emphasize that a more reliable description of these phenomena,in particular,of the thermodynamic behaviour of the FS phase at relatively large values of M can be performed if an additional term of type M 2|ψ|2is included in the model (1).Acknowledgments:DIU thanks the hospitality of MPI-PKS-Dresden.Financial sup-port through Scenet(Parma)and collaborative project with JINR-Dubna is also acknowl-edged.References[1]S.S.Saxena,P.Agarwal,K.Ahilan,F.M.Grosche,R.K.W.Haselwimmer,M.J.Steiner,E.Pugh,I.R.Walker,S.R.Julian,P.Monthoux,G.G.Lonzarich,A.Huxley.I.Sheikin,D.Braithwaite,and 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