Quantum energy inequalities in two dimensions

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The_electronic_properties_of_graphene

The electronic properties of grapheneA.H.Castro NetoDepartment of Physics,Boston University,590Commonwealth Avenue,Boston,Massachusetts02215,USAF.GuineaInstituto de Ciencia de Materiales de Madrid,CSIC,Cantoblanco,E-28049Madrid,SpainN.M.R.PeresCenter of Physics and Department of Physics,Universidade do Minho,P-4710-057,Braga,PortugalK.S.Novoselov and A.K.GeimDepartment of Physics and Astronomy,University of Manchester,Manchester,M139PL,United Kingdom͑Published14January2009͒This article reviews the basic theoretical aspects of graphene,a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations.The Dirac electrons can be controlled by application of external electric and magneticﬁelds,or by altering sample geometry and/or topology.The Dirac electrons behave in unusual ways in tunneling,conﬁnement,and the integer quantum Hall effect.The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers.Edge͑surface͒states in graphene depend on the edge termination͑zigzag or armchair͒and affect the physical properties of nanoribbons.Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties.The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.DOI:10.1103/RevModPhys.81.109PACS number͑s͒:81.05.Uw,73.20.Ϫr,03.65.Pm,82.45.MpCONTENTSI.Introduction110II.Elementary Electronic Properties of Graphene112A.Single layer:Tight-binding approach1121.Cyclotron mass1132.Density of states114B.Dirac fermions1141.Chiral tunneling and Klein paradox1152.Conﬁnement and Zitterbewegung117C.Bilayer graphene:Tight-binding approach118D.Epitaxial graphene119E.Graphene stacks1201.Electronic structure of bulk graphite121F.Surface states in graphene122G.Surface states in graphene stacks124H.The spectrum of graphene nanoribbons1241.Zigzag nanoribbons1252.Armchair nanoribbons126I.Dirac fermions in a magneticﬁeld126J.The anomalous integer quantum Hall effect128 K.Tight-binding model in a magneticﬁeld128 ndau levels in graphene stacks130 M.Diamagnetism130 N.Spin-orbit coupling131 III.Flexural Phonons,Elasticity,and Crumpling132 IV.Disorder in Graphene134A.Ripples135B.Topological lattice defects136C.Impurity states137D.Localized states near edges,cracks,and voids137E.Self-doping138F.Vector potential and gaugeﬁeld disorder1391.Gaugeﬁeld induced by curvature1402.Elastic strain1403.Random gaugeﬁelds141G.Coupling to magnetic impurities141H.Weak and strong localization142I.Transport near the Dirac point143J.Boltzmann equation description of dc transport indoped graphene144 K.Magnetotransport and universal conductivity1451.The full self-consistent Born approximation͑FSBA͒146 V.Many-Body Effects148A.Electron-phonon interactions148B.Electron-electron interactions1501.Screening in graphene stacks152C.Short-range interactions1521.Bilayer graphene:Exchange1532.Bilayer graphene:Short-range interactions154D.Interactions in high magneticﬁelds154VI.Conclusions154 Acknowledgments155 References155REVIEWS OF MODERN PHYSICS,VOLUME81,JANUARY–MARCH20090034-6861/2009/81͑1͒/109͑54͒©2009The American Physical Society109I.INTRODUCTIONCarbon is the materia prima for life and the basis of all organic chemistry.Because of the ﬂexibility of its bond-ing,carbon-based systems show an unlimited number of different structures with an equally large variety of physical properties.These physical properties are,in great part,the result of the dimensionality of these structures.Among systems with only carbon atoms,graphene—a two-dimensional ͑2D ͒allotrope of carbon—plays an important role since it is the basis for the understanding of the electronic properties in other allotropes.Graphene is made out of carbon atoms ar-ranged on a honeycomb structure made out of hexagons ͑see Fig.1͒,and can be thought of as composed of ben-zene rings stripped out from their hydrogen atoms ͑Pauling,1972͒.Fullerenes ͑Andreoni,2000͒are mol-ecules where carbon atoms are arranged spherically,and hence,from the physical point of view,are zero-dimensional objects with discrete energy states.Fullerenes can be obtained from graphene with the in-troduction of pentagons ͑that create positive curvature defects ͒,and hence,fullerenes can be thought as wrapped-up graphene.Carbon nanotubes ͑Saito et al.,1998;Charlier et al.,2007͒are obtained by rolling graphene along a given direction and reconnecting the carbon bonds.Hence carbon nanotubes have only hexa-gons and can be thought of as one-dimensional ͑1D ͒ob-jects.Graphite,a three dimensional ͑3D ͒allotrope of carbon,became widely known after the invention of the pencil in 1564͑Petroski,1989͒,and its usefulness as an instrument for writing comes from the fact that graphite is made out of stacks of graphene layers that are weakly coupled by van der Waals forces.Hence,when one presses a pencil against a sheet of paper,one is actually producing graphene stacks and,somewhere among them,there could be individual graphene layers.Al-though graphene is the mother for all these different allotropes and has been presumably produced every time someone writes with a pencil,it was only isolated 440years after its invention ͑Novoselov et al.,2004͒.The reason is that,ﬁrst,no one actually expected graphene to exist in the free state and,second,even with the ben-eﬁt of hindsight,no experimental tools existed to search for one-atom-thick ﬂakes among the pencil debris cov-ering macroscopic areas ͑Geim and MacDonald,2007͒.Graphene was eventually spotted due to the subtle op-tical effect it creates on top of a chosen SiO 2substrate ͑Novoselov et al.,2004͒that allows its observation with an ordinary optical microscope ͑Abergel et al.,2007;Blake et al.,2007;Casiraghi et al.,2007͒.Hence,graphene is relatively straightforward to make,but not so easy to ﬁnd.The structural ﬂexibility of graphene is reﬂected in its electronic properties.The sp 2hybridization between one s orbital and two p orbitals leads to a trigonal planar structure with a formation of a ␴bond between carbon atoms that are separated by 1.42Å.The ␴band is re-sponsible for the robustness of the lattice structure in all allotropes.Due to the Pauli principle,these bands have a ﬁlled shell and,hence,form a deep valence band.The unaffected p orbital,which is perpendicular to the pla-nar structure,can bind covalently with neighboring car-bon atoms,leading to the formation of a ␲band.Since each p orbital has one extra electron,the ␲band is half ﬁlled.Half-ﬁlled bands in transition elements have played an important role in the physics of strongly correlated systems since,due to their strong tight-binding charac-ter,the Coulomb energies are large,leading to strong collective effects,magnetism,and insulating behavior due to correlation gaps or Mottness ͑Phillips,2006͒.In fact,Linus Pauling proposed in the 1950s that,on the basis of the electronic properties of benzene,graphene should be a resonant valence bond ͑RVB ͒structure ͑Pauling,1972͒.RVB states have become popular in the literature of transition-metal oxides,and particularly in studies of cuprate-oxide superconductors ͑Maple,1998͒.This point of view should be contrasted with contempo-raneous band-structure studies of graphene ͑Wallace,1947͒that found it to be a semimetal with unusual lin-early dispersing electronic excitations called Dirac elec-trons.While most current experimental data in graphene support the band structure point of view,the role of electron-electron interactions in graphene is a subject of intense research.It was P .R.Wallace in 1946who ﬁrst wrote on the band structure of graphene and showed the unusual semimetallic behavior in this material ͑Wallace,1947͒.At that time,the thought of a purely 2D structure was not reality and Wallace’s studies of graphene served him as a starting point to study graphite,an important mate-rial for nuclear reactors in the post–World War II era.During the following years,the study of graphite culmi-nated with the Slonczewski-Weiss-McClure ͑SWM ͒band structure of graphite,which provided a description of the electronic properties in this material ͑McClure,1957;Slonczewski and Weiss,1958͒and was successful in de-scribing the experimental data ͑Boyle and Nozières 1958;McClure,1958;Spry and Scherer,1960;Soule et al.,1964;Williamson et al.,1965;Dillon et al.,1977͒.From 1957to 1968,the assignment of the electron and hole states within the SWM model were oppositetoFIG.1.͑Color online ͒Graphene ͑top left ͒is a honeycomb lattice of carbon atoms.Graphite ͑top right ͒can be viewed as a stack of graphene layers.Carbon nanotubes are rolled-up cylinders of graphene ͑bottom left ͒.Fullerenes ͑C 60͒are mol-ecules consisting of wrapped graphene by the introduction of pentagons on the hexagonal lattice.From Castro Neto et al.,2006a .110Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009what is accepted today.In1968,Schroeder et al.͑Schroeder et al.,1968͒established the currently ac-cepted location of electron and hole pockets͑McClure, 1971͒.The SWM model has been revisited in recent years because of its inability to describe the van der Waals–like interactions between graphene planes,a problem that requires the understanding of many-body effects that go beyond the band-structure description ͑Rydberg et al.,2003͒.These issues,however,do not arise in the context of a single graphene crystal but they show up when graphene layers are stacked on top of each other,as in the case,for instance,of the bilayer graphene.Stacking can change the electronic properties considerably and the layering structure can be used in order to control the electronic properties.One of the most interesting aspects of the graphene problem is that its low-energy excitations are massless, chiral,Dirac fermions.In neutral graphene,the chemical potential crosses exactly the Dirac point.This particular dispersion,that is only valid at low energies,mimics the physics of quantum electrodynamics͑QED͒for massless fermions except for the fact that in graphene the Dirac fermions move with a speed v F,which is300times smaller than the speed of light c.Hence,many of the unusual properties of QED can show up in graphene but at much smaller speeds͑Castro Neto et al.,2006a; Katsnelson et al.,2006;Katsnelson and Novoselov, 2007͒.Dirac fermions behave in unusual ways when compared to ordinary electrons if subjected to magnetic ﬁelds,leading to new physical phenomena͑Gusynin and Sharapov,2005;Peres,Guinea,and Castro Neto,2006a͒such as the anomalous integer quantum Hall effect ͑IQHE͒measured experimentally͑Novoselov,Geim, Morozov,et al.,2005a;Zhang et al.,2005͒.Besides being qualitatively different from the IQHE observed in Si and GaAlAs͑heterostructures͒devices͑Stone,1992͒, the IQHE in graphene can be observed at room tem-perature because of the large cyclotron energies for “relativistic”electrons͑Novoselov et al.,2007͒.In fact, the anomalous IQHE is the trademark of Dirac fermion behavior.Another interesting feature of Dirac fermions is their insensitivity to external electrostatic potentials due to the so-called Klein paradox,that is,the fact that Dirac fermions can be transmitted with probability1through a classically forbidden region͑Calogeracos and Dombey, 1999;Itzykson and Zuber,2006͒.In fact,Dirac fermions behave in an unusual way in the presence of conﬁning potentials,leading to the phenomenon of Zitter-bewegung,or jittery motion of the wave function͑Itzyk-son and Zuber,2006͒.In graphene,these electrostatic potentials can be easily generated by disorder.Since dis-order is unavoidable in any material,there has been a great deal of interest in trying to understand how disor-der affects the physics of electrons in graphene and its transport properties.In fact,under certain conditions, Dirac fermions are immune to localization effects ob-served in ordinary electrons͑Lee and Ramakrishnan, 1985͒and it has been established experimentally that electrons can propagate without scattering over large distances of the order of micrometers in graphene͑No-voselov et al.,2004͒.The sources of disorder in graphene are many and can vary from ordinary effects commonly found in semiconductors,such as ionized impurities in the Si substrate,to adatoms and various molecules ad-sorbed in the graphene surface,to more unusual defects such as ripples associated with the soft structure of graphene͑Meyer,Geim,Katsnelson,Novoselov,Booth, et al.,2007a͒.In fact,graphene is unique in the sense that it shares properties of soft membranes͑Nelson et al.,2004͒and at the same time it behaves in a metallic way,so that the Dirac fermions propagate on a locally curved space.Here analogies with problems of quantum gravity become apparent͑Fauser et al.,2007͒.The soft-ness of graphene is related with the fact that it has out-of-plane vibrational modes͑phonons͒that cannot be found in3D solids.Theseﬂexural modes,responsible for the bending properties of graphene,also account for the lack of long range structural order in soft mem-branes leading to the phenomenon of crumpling͑Nelson et al.,2004͒.Nevertheless,the presence of a substrate or scaffolds that hold graphene in place can stabilize a cer-tain degree of order in graphene but leaves behind the so-called ripples͑which can be viewed as frozenﬂexural modes͒.It was realized early on that graphene should also present unusual mesoscopic effects͑Peres,Castro Neto, and Guinea,2006a;Katsnelson,2007a͒.These effects have their origin in the boundary conditions required for the wave functions in mesoscopic samples with various types of edges graphene can have͑Nakada et al.,1996; Wakabayashi et al.,1999;Peres,Guinea,and Castro Neto,2006a;Akhmerov and Beenakker,2008͒.The most studied edges,zigzag and armchair,have drastically different electronic properties.Zigzag edges can sustain edge͑surface͒states and resonances that are not present in the armchair case.Moreover,when coupled to con-ducting leads,the boundary conditions for a graphene ribbon strongly affect its conductance,and the chiral Dirac nature of fermions in graphene can be used for applications where one can control the valleyﬂavor of the electrons besides its charge,the so-called valleytron-ics͑Rycerz et al.,2007͒.Furthermore,when supercon-ducting contacts are attached to graphene,they lead to the development of supercurrentﬂow and Andreev pro-cesses characteristic of the superconducting proximity effect͑Heersche et al.,2007͒.The fact that Cooper pairs can propagate so well in graphene attests to the robust electronic coherence in this material.In fact,quantum interference phenomena such as weak localization,uni-versal conductanceﬂuctuations͑Morozov et al.,2006͒, and the Aharonov-Bohm effect in graphene rings have already been observed experimentally͑Recher et al., 2007;Russo,2007͒.The ballistic electronic propagation in graphene can be used forﬁeld-effect devices such as p-n͑Cheianov and Fal’ko,2006;Cheianov,Fal’ko,and Altshuler,2007;Huard et al.,2007;Lemme et al.,2007; Tworzydlo et al.,2007;Williams et al.,2007;Fogler, Glazman,Novikov,et al.,2008;Zhang and Fogler,2008͒and p-n-p͑Ossipov et al.,2007͒junctions,and as“neu-111Castro Neto et al.:The electronic properties of graphene Rev.Mod.Phys.,V ol.81,No.1,January–March2009trino”billiards ͑Berry and Modragon,1987;Miao et al.,2007͒.It has also been suggested that Coulomb interac-tions are considerably enhanced in smaller geometries,such as graphene quantum dots ͑Milton Pereira et al.,2007͒,leading to unusual Coulomb blockade effects ͑Geim and Novoselov,2007͒and perhaps to magnetic phenomena such as the Kondo effect.The transport properties of graphene allow for their use in a plethora of applications ranging from single molecule detection ͑Schedin et al.,2007;Wehling et al.,2008͒to spin injec-tion ͑Cho et al.,2007;Hill et al.,2007;Ohishi et al.,2007;Tombros et al.,2007͒.Because of its unusual structural and electronic ﬂex-ibility,graphene can be tailored chemically and/or struc-turally in many different ways:deposition of metal at-oms ͑Calandra and Mauri,2007;Uchoa et al.,2008͒or molecules ͑Schedin et al.,2007;Leenaerts et al.,2008;Wehling et al.,2008͒on top;intercalation ͓as done in graphite intercalated compounds ͑Dresselhaus et al.,1983;Tanuma and Kamimura,1985;Dresselhaus and Dresselhaus,2002͔͒;incorporation of nitrogen and/or boron in its structure ͑Martins et al.,2007;Peres,Klironomos,Tsai,et al.,2007͓͒in analogy with what has been done in nanotubes ͑Stephan et al.,1994͔͒;and using different substrates that modify the electronic structure ͑Calizo et al.,2007;Giovannetti et al.,2007;Varchon et al.,2007;Zhou et al.,2007;Das et al.,2008;Faugeras et al.,2008͒.The control of graphene properties can be extended in new directions allowing for the creation of graphene-based systems with magnetic and supercon-ducting properties ͑Uchoa and Castro Neto,2007͒that are unique in their 2D properties.Although the graphene ﬁeld is still in its infancy,the scientiﬁc and technological possibilities of this new material seem to be unlimited.The understanding and control of this ma-terial’s properties can open doors for a new frontier in electronics.As the current status of the experiment and potential applications have recently been reviewed ͑Geim and Novoselov,2007͒,in this paper we concen-trate on the theory and more technical aspects of elec-tronic properties with this exciting new material.II.ELEMENTARY ELECTRONIC PROPERTIES OF GRAPHENEA.Single layer:Tight-binding approachGraphene is made out of carbon atoms arranged in hexagonal structure,as shown in Fig.2.The structure can be seen as a triangular lattice with a basis of two atoms per unit cell.The lattice vectors can be written asa 1=a 2͑3,ͱ3͒,a 2=a2͑3,−ͱ3͒,͑1͒where a Ϸ1.42Åis the carbon-carbon distance.Thereciprocal-lattice vectors are given byb 1=2␲3a͑1,ͱ3͒,b 2=2␲3a͑1,−ͱ3͒.͑2͒Of particular importance for the physics of graphene are the two points K and K Јat the corners of the graphene Brillouin zone ͑BZ ͒.These are named Dirac points for reasons that will become clear later.Their positions in momentum space are given byK =ͩ2␲3a ,2␲3ͱ3aͪ,K Ј=ͩ2␲3a ,−2␲3ͱ3aͪ.͑3͒The three nearest-neighbor vectors in real space are given by␦1=a 2͑1,ͱ3͒␦2=a 2͑1,−ͱ3͒␦3=−a ͑1,0͒͑4͒while the six second-nearest neighbors are located at ␦1Ј=±a 1,␦2Ј=±a 2,␦3Ј=±͑a 2−a 1͒.The tight-binding Hamiltonian for electrons in graphene considering that electrons can hop to both nearest-and next-nearest-neighbor atoms has the form ͑we use units such that ប=1͒H =−t͚͗i ,j ͘,␴͑a ␴,i †b ␴,j +H.c.͒−t Ј͚͗͗i ,j ͘͘,␴͑a ␴,i †a ␴,j +b ␴,i †b ␴,j +H.c.͒,͑5͒where a i ,␴͑a i ,␴†͒annihilates ͑creates ͒an electron with spin ␴͑␴=↑,↓͒on site R i on sublattice A ͑an equiva-lent deﬁnition is used for sublattice B ͒,t ͑Ϸ2.8eV ͒is the nearest-neighbor hopping energy ͑hopping between dif-ferent sublattices ͒,and t Јis the next nearest-neighbor hopping energy 1͑hopping in the same sublattice ͒.The energy bands derived from this Hamiltonian have the form ͑Wallace,1947͒E ±͑k ͒=±t ͱ3+f ͑k ͒−t Јf ͑k ͒,1The value of t Јis not well known but ab initio calculations ͑Reich et al.,2002͒ﬁnd 0.02t Շt ЈՇ0.2t depending on the tight-binding parametrization.These calculations also include the effect of a third-nearest-neighbors hopping,which has a value of around 0.07eV.A tight-binding ﬁt to cyclotron resonance experiments ͑Deacon et al.,2007͒ﬁnds t ЈϷ0.1eV.FIG.2.͑Color online ͒Honeycomb lattice and its Brillouin zone.Left:lattice structure of graphene,made out of two in-terpenetrating triangular lattices ͑a 1and a 2are the lattice unit vectors,and ␦i ,i =1,2,3are the nearest-neighbor vectors ͒.Right:corresponding Brillouin zone.The Dirac cones are lo-cated at the K and K Јpoints.112Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009f ͑k ͒=2cos ͑ͱ3k y a ͒+4cosͩͱ32k y a ͪcosͩ32k x a ͪ,͑6͒where the plus sign applies to the upper ͑␲*͒and the minus sign the lower ͑␲͒band.It is clear from Eq.͑6͒that the spectrum is symmetric around zero energy if t Ј=0.For ﬁnite values of t Ј,the electron-hole symmetry is broken and the ␲and ␲*bands become asymmetric.In Fig.3,we show the full band structure of graphene with both t and t Ј.In the same ﬁgure,we also show a zoom in of the band structure close to one of the Dirac points ͑at the K or K Јpoint in the BZ ͒.This dispersion can be obtained by expanding the full band structure,Eq.͑6͒,close to the K ͑or K Ј͒vector,Eq.͑3͒,as k =K +q ,with ͉q ͉Ӷ͉K ͉͑Wallace,1947͒,E ±͑q ͒Ϸ±vF ͉q ͉+O ͓͑q /K ͒2͔,͑7͒where q is the momentum measured relatively to the Dirac points and v F is the Fermi velocity,given by v F =3ta /2,with a value v F Ӎ1ϫ106m/s.This result was ﬁrst obtained by Wallace ͑1947͒.The most striking difference between this result and the usual case,⑀͑q ͒=q 2/͑2m ͒,where m is the electron mass,is that the Fermi velocity in Eq.͑7͒does not de-pend on the energy or momentum:in the usual case we have v =k /m =ͱ2E /m and hence the velocity changes substantially with energy.The expansion of the spectrum around the Dirac point including t Јup to second order in q /K is given byE ±͑q ͒Ӎ3t Ј±vF ͉q ͉−ͩ9t Јa 24±3ta 28sin ͑3␪q ͉͒ͪq ͉2,͑8͒where␪q =arctanͩq x q yͪ͑9͒is the angle in momentum space.Hence,the presence of t Јshifts in energy the position of the Dirac point and breaks electron-hole symmetry.Note that up to order ͑q /K ͒2the dispersion depends on the direction in mo-mentum space and has a threefold symmetry.This is the so-called trigonal warping of the electronic spectrum ͑Ando et al.,1998,Dresselhaus and Dresselhaus,2002͒.1.Cyclotron massThe energy dispersion ͑7͒resembles the energy of ul-trarelativistic particles;these particles are quantum me-chanically described by the massless Dirac equation ͑see Sec.II.B for more on this analogy ͒.An immediate con-sequence of this massless Dirac-like dispersion is a cy-clotron mass that depends on the electronic density as its square root ͑Novoselov,Geim,Morozov,et al.,2005;Zhang et al.,2005͒.The cyclotron mass is deﬁned,within the semiclassical approximation ͑Ashcroft and Mermin,1976͒,asm *=12␲ͫץA ͑E ͒ץEͬE =E F,͑10͒with A ͑E ͒the area in k space enclosed by the orbit andgiven byA ͑E ͒=␲q ͑E ͒2=␲E 2v F2.͑11͒Using Eq.͑11͒in Eq.͑10͒,one obtainsm *=E Fv F2=k Fv F.͑12͒The electronic density n is related to the Fermi momen-tum k F as k F2/␲=n ͑with contributions from the two Dirac points K and K Јand spin included ͒,which leads tom *=ͱ␲v Fͱn .͑13͒Fitting Eq.͑13͒to the experimental data ͑see Fig.4͒provides an estimation for the Fermi velocity andtheFIG.3.͑Color online ͒Electronic dispersion in the honeycomb lattice.Left:energy spectrum ͑in units of t ͒for ﬁnite values of t and t Ј,with t =2.7eV and t Ј=−0.2t .Right:zoom in of the energy bands close to one of the Diracpoints.FIG.4.͑Color online ͒Cyclotron mass of charge carriers in graphene as a function of their concentration n .Positive and negative n correspond to electrons and holes,respectively.Symbols are the experimental data extracted from the tem-perature dependence of the SdH oscillations;solid curves are the best ﬁt by Eq.͑13͒.m 0is the free-electron mass.Adapted from Novoselov,Geim,Morozov,et al.,2005.113Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009hopping parameter as v F Ϸ106ms −1and t Ϸ3eV,respec-tively.Experimental observation of the ͱn dependence on the cyclotron mass provides evidence for the exis-tence of massless Dirac quasiparticles in graphene ͑No-voselov,Geim,Morozov,et al.,2005;Zhang et al.,2005;Deacon et al.,2007;Jiang,Henriksen,Tung,et al.,2007͒—the usual parabolic ͑Schrödinger ͒dispersion im-plies a constant cyclotron mass.2.Density of statesThe density of states per unit cell,derived from Eq.͑5͒,is given in Fig.5for both t Ј=0and t Ј 0,showing in both cases semimetallic behavior ͑Wallace,1947;Bena and Kivelson,2005͒.For t Ј=0,it is possible to derive an analytical expression for the density of states per unit cell,which has the form ͑Hobson and Nierenberg,1953͒␳͑E ͒=4␲2͉E ͉t 21ͱZ 0F ͩ␲2,ͱZ 1Z 0ͪ,Z 0=Άͩ1+ͯE t ͯͪ2−͓͑E /t ͒2−1͔24,−t ഛE ഛt4ͯE t ͯ,−3t ഛE ഛ−t ∨t ഛE ഛ3t ,Z 1=Ά4ͯE t ͯ,−t ഛE ഛtͩ1+ͯE tͯͪ2−͓͑E /t ͒2−1͔24,−3t ഛE ഛ−t ∨t ഛE ഛ3t ,͑14͒where F ͑␲/2,x ͒is the complete elliptic integral of theﬁrst kind.Close to the Dirac point,the dispersion is ap-proximated by Eq.͑7͒and the density of states per unit cell is given by ͑with a degeneracy of 4included ͒␳͑E ͒=2A c ␲͉E ͉v F2,͑15͒where A c is the unit cell area given by A c =3ͱ3a 2/2.It is worth noting that the density of states for graphene is different from the density of states of carbon nanotubes ͑Saito et al.,1992a ,1992b ͒.The latter shows 1/ͱE singu-larities due to the 1D nature of their electronic spec-trum,which occurs due to the quantization of the mo-mentum in the direction perpendicular to the tube axis.From this perspective,graphene nanoribbons,which also have momentum quantization perpendicular to the ribbon length,have properties similar to carbon nano-tubes.B.Dirac fermionsWe consider the Hamiltonian ͑5͒with t Ј=0and theFourier transform of the electron operators,a n =1ͱN c͚ke −i k ·R na ͑k ͒,͑16͒where N c is the number of unit ing this transfor-mation,we write the ﬁeld a n as a sum of two terms,coming from expanding the Fourier sum around K Јand K .This produces an approximation for the representa-tion of the ﬁeld a n as a sum of two new ﬁelds,written asa n Ӎe −i K ·R n a 1,n +e −i K Ј·R n a 2,n ,b n Ӎe −i K ·R n b 1,n +e −i K Ј·R n b 2,n ,͑17͒ρ(ε)ε/tρ(ε)ε/tFIG.5.Density of states per unit cell as a function of energy ͑in units of t ͒computed from the energy dispersion ͑5͒,t Ј=0.2t ͑top ͒and t Ј=0͑bottom ͒.Also shown is a zoom-in of the density of states close to the neutrality point of one electron per site.For the case t Ј=0,the electron-hole nature of the spectrum is apparent and the density of states close to the neutrality point can be approximated by ␳͑⑀͒ϰ͉⑀͉.114Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009where the index i =1͑i =2͒refers to the K ͑K Ј͒point.These new ﬁelds,a i ,n and b i ,n ,are assumed to vary slowly over the unit cell.The procedure for deriving a theory that is valid close to the Dirac point con-sists in using this representation in the tight-binding Hamiltonian and expanding the opera-tors up to a linear order in ␦.In the derivation,one uses the fact that ͚␦e ±i K ·␦=͚␦e ±i K Ј·␦=0.After some straightforward algebra,we arrive at ͑Semenoff,1984͒H Ӎ−t͵dxdy ⌿ˆ1†͑r ͒ͫͩ3a ͑1−i ͱ3͒/4−3a ͑1+i ͱ3͒/4ͪץx +ͩ3a ͑−i −ͱ3͒/4−3a ͑i −ͱ3͒/4ͪץy ͬ⌿ˆ1͑r ͒+⌿ˆ2†͑r ͒ͫͩ3a ͑1+i ͱ3͒/4−3a ͑1−i ͱ3͒/4ͪץx +ͩ3a ͑i −ͱ3͒/4−3a ͑−i −ͱ3͒/4ͪץy ͬ⌿ˆ2͑r ͒=−i v F͵dxdy ͓⌿ˆ1†͑r ͒␴·ٌ⌿ˆ1͑r ͒+⌿ˆ2†͑r ͒␴*·ٌ⌿ˆ2͑r ͔͒,͑18͒with Pauli matrices ␴=͑␴x ,␴y ͒,␴*=͑␴x ,−␴y ͒,and ⌿ˆi†=͑a i †,b i †͒͑i =1,2͒.It is clear that the effective Hamil-tonian ͑18͒is made of two copies of the massless Dirac-like Hamiltonian,one holding for p around K and the other for p around K Ј.Note that,in ﬁrst quantized lan-guage,the two-component electron wave function ␺͑r ͒,close to the K point,obeys the 2D Dirac equation,−i v F ␴·ٌ␺͑r ͒=E ␺͑r ͒.͑19͒The wave function,in momentum space,for the mo-mentum around K has the form␺±,K ͑k ͒=1ͱ2ͩe −i ␪k /2±e i ␪k /2ͪ͑20͒for H K =v F ␴·k ,where the Ϯsigns correspond to the eigenenergies E =±v F k ,that is,for the ␲*and ␲bands,respectively,and ␪k is given by Eq.͑9͒.The wave func-tion for the momentum around K Јhas the form␺±,K Ј͑k ͒=1ͱ2ͩe i ␪k /2±e −i ␪k /2ͪ͑21͒for H K Ј=v F ␴*·k .Note that the wave functions at K and K Јare related by time-reversal symmetry:if we set the origin of coordinates in momentum space in the M point of the BZ ͑see Fig.2͒,time reversal becomes equivalent to a reﬂection along the k x axis,that is,͑k x ,k y ͒→͑k x ,−k y ͒.Also note that if the phase ␪is rotated by 2␲,the wave function changes sign indicating a phase of ␲͑in the literature this is commonly called a Berry’s phase ͒.This change of phase by ␲under rotation is char-acteristic of spinors.In fact,the wave function is a two-component spinor.A relevant quantity used to characterize the eigen-functions is their helicity deﬁned as the projection of the momentum operator along the ͑pseudo ͒spin direction.The quantum-mechanical operator for the helicity has the formhˆ=12␴·p ͉p ͉.͑22͒It is clear from the deﬁnition of h ˆthat the states ␺K͑r ͒and ␺K Ј͑r ͒are also eigenstates of h ˆ,h ˆ␺K ͑r ͒=±12␺K͑r ͒,͑23͒and an equivalent equation for ␺K Ј͑r ͒with inverted sign.Therefore,electrons ͑holes ͒have a positive ͑negative ͒helicity.Equation ͑23͒implies that ␴has its two eigen-values either in the direction of ͑⇑͒or against ͑⇓͒the momentum p .This property says that the states of the system close to the Dirac point have well deﬁned chiral-ity or helicity.Note that chirality is not deﬁned in regard to the real spin of the electron ͑that has not yet ap-peared in the problem ͒but to a pseudospin variable as-sociated with the two components of the wave function.The helicity values are good quantum numbers as long as the Hamiltonian ͑18͒is valid.Therefore,the existence of helicity quantum numbers holds only as an asymptotic property,which is well deﬁned close to the Dirac points K and K Ј.Either at larger energies or due to the presence of a ﬁnite t Ј,the helicity stops being a good quantum number.1.Chiral tunneling and Klein paradoxIn this section,we address the scattering of chiral elec-trons in two dimensions by a square barrier ͑Katsnelson et al.,2006;Katsnelson,2007b ͒.The one-dimensional scattering of chiral electrons was discussed earlier in the context on nanotubes ͑Ando et al.,1998;McEuen et al.,1999͒.We start by noting that by a gauge transformation the wave function ͑20͒can be written as115Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009。

用Mathematica计算氢原子二级斯塔克效应

关键词氢原子；斯塔克效应；微扰论；二级修正；Mathematica
I
2002 级物理学专业毕业论文
英文摘要
Abstract
In Quantum Mechanics, the energy-levels of Hydrogen atom are usually degeneration. The degeneration energy-levels of Hydrogen atom which is put into lower uniform electric field are split. Such these systems were dealt with the degeneration perturbation theory. Because of degeneration energy-levels of Hydrogen atom wasn’t completely removed in the first order Stark-effect. In the paper, we have calculated the second order Stark-effect with Mathematica.It was found that the degeneration energy-levels were fully removed, but not completely.
通过实验观察发现，处于均匀弱电场中的第一激发态氢原子所产生的谱线发生了分裂现象，由于这种现象最初是由德国物理学家斯塔克（Johnnes Stark,1874-1957）观测到，所以被人们称为氢原子的斯塔克效应[2]。利用简并微扰论计算氢原子的一级斯塔克效应[3~4]发现，原来简并的能级在外电场作用下分裂为三个能级，一个在原来的上面，另一个在原来的下面，而且能量差是相等的。这样，没有外电场时的一条谱线，在外电场中就分裂成三条；它们的频率一条比原来稍小，一条比原来稍大，另一条与原来相等，且上下两条谱线关于中间那条谱线对称。由于第一激发态氢原子的简并度为 4，根据目前的理论推断，能级最终应该分裂成四条，所以能级简并没有完全消除。

那神奇的纳米时代英语作文

那神奇的纳米时代英语作文The Miraculous Nanotech Era.As technology relentlessly advances, we stand on the cusp of a remarkable era: the Nanotech Era. This transformative field involves manipulating matter at the atomic and molecular scale, unlocking unprecedented possibilities for innovation and progress.The Essence of Nanotechnology.Nanotechnology operates on an incredibly small scale. A nanometer is one billionth of a meter, roughly the size of a few atoms. At this scale, matter exhibits unique properties and behaviors that differ significantly from its macroscopic counterparts. These unique characteristics stem from quantum effects, the laws that govern the subatomic world.Revolutionary Applications.Nanotechnology has far-reaching applications across diverse industries, paving the way for groundbreaking advancements in healthcare, energy, electronics, manufacturing, and more.In Medicine:Targeted Drug Delivery: Nanoparticles can be designed to deliver drugs directly to diseased cells, enhancing efficacy and minimizing side effects.Tissue Engineering: Nanomaterials can be used to grow and repair damaged tissues, offering hope for treating degenerative diseases.Diagnostics: Nanosensors can detect minute amounts of biomarkers, enabling early diagnosis and personalized treatment.In Energy:Solar Energy Harvesting: Nanoengineered materials can improve the efficiency of solar cells, capturing more sunlight and generating more electricity.Fuel Cells: Nanocatalysts can enhance the performance and durability of fuel cells, providing a cleaner and more efficient energy source.Batteries: Nanomaterials can lead to the development of higher-capacity, longer-lasting batteries for portable devices and electric vehicles.In Electronics:Miniaturization: Nanotechnology allows for the creation of smaller, more powerful electronic devices with enhanced capabilities.Advanced Computing: Nanomaterials can enable faster processing speeds and increased memory capacity in computers.Nanophotonics: Nanostructures can manipulate light in novel ways, opening up possibilities for optical computing and ultra-high-speed data transmission.In Manufacturing:Lightweight Materials: Nanomaterials can be engineered to create lightweight, ultra-strong materials for aerospace and automotive applications.Self-Cleaning Surfaces: Nanoparticles can impart self-cleaning properties to surfaces, reducing the need for harsh chemicals and detergents.Antimicrobial Textiles: Nanomaterials can be incorporated into textiles to provide antimicrobial protection, preventing the growth of bacteria and viruses.Challenges and Ethical Considerations.While nanotechnology holds immense promise, it also presents challenges and ethical considerations that need tobe carefully addressed.Environmental Impact: The potential environmental impact of nanomaterials requires thorough assessment and responsible disposal practices.Health and Safety: The health and safety implications of nanomaterials must be fully understood and managed to ensure their safe use.Ethical Responsibility: The rapid advancement of nanotechnology raises ethical concerns about its potential use for malicious purposes or exacerbation of existing inequalities.Conclusion.The Nanotech Era presents both unparalleled opportunities and challenges. By embracing the responsible development and application of nanotechnology, we have the potential to unlock transformative solutions to some of the world's most pressing problems. From revolutionizinghealthcare to addressing the energy crisis, nanotechnology holds the key to shaping a brighter and more sustainable future.。

量子点具有量子力学的

量子点具有量子力学的英文回答：Quantum dots exhibit quantum mechanical effects due to their nanoscale dimensions. These effects include:Quantization of energy levels: The energy levels of electrons in quantum dots are discrete, meaning they can only occupy certain specific energies. This is in contrast to the continuous energy levels of electrons in bulk materials.Tunable bandgap: The bandgap of a quantum dot is the energy difference between the valence band and the conduction band. The bandgap of a quantum dot can be tuned by changing the size of the dot. This allows quantum dots to be used in a variety of optoelectronic applications.Enhanced optical properties: Quantum dots have enhanced optical properties, such as high photoluminescenceefficiency and narrow emission spectra. These properties make quantum dots ideal for use in applications such as light-emitting diodes (LEDs), lasers, and solar cells.中文回答：量子点由于其纳米尺度的尺寸而表现出量子力学效应。

光子阻塞效应

学号：201105774题目名称: 强耦合下的光子阻塞效应研究题目类型: 研究论文学生姓名: 董昌瑞院（系）: 物理与光电工程学院专业班级: 物理11102班指导教师: 邹金花辅导教师: 邹金花时间: 2015年1月至2015年6月目录毕业论文任务书` (I)指导教师评审意见 (VIII)评阅教师评语 (IX)答辩记录及成绩评定 (X)中文摘要 (XI)外文摘要 (XII)1引言 (1)2 基础理论知识 (1)2.1 光力振子系统 (1)2.2二能级原子与光场相互作用的全量子理论 (2)2.3光场关联函数 (5)2.4 光子计数统计 (8)3 模型方程与结果分析 (10)3.1模型方程 (10)3.2 方程分析 (12)4总结与展望 (14)参考文献 (14)致谢 (16)毕业论文任务书`院（系）物理与光电工程学院专业物理班级物理11102 学生姓名董昌瑞指导教师/职称邹金花/副教授1.毕业论文(设计)题目：强耦合下的光子阻塞效应研究2.毕业论文(设计)起止时间： 2015 年1月1 日～2015 年 6月10 日3．毕业论文(设计)所需资料及原始数据（指导教师选定部分）[1] A Ridolfo, M Leib, S Savasta, M J Hartmann. Photon Blockade in the Ultrastrong CouplingRegime [J]. Phys. Rev. Lett., 2012, 109: 193602-1~193602-5[2] Jieqiao Liao, C K Law. Cooling of a mirror in cavity optomechanics with a chirped pulse [J]. Phys. Rev. A, 2011, 84: 053838-1~053838-6[3] P Komar, S D Bennett, K Stannigel, S J M Habraken, P Rabl, P Zoller, M D Lukin. Single-photon nonlinearities in two-mode optomechanics [J]. Phys. Rev. A, 2013, 87: 013839-1~013839-10[4] T Ramos, V Sudhir, K Stannigel, P Zoller, T Kippenbrg. Nonlinear quantum optomechanics viaindividual intrinsic two-level defects [J]. Phys. Rev. Lett., 2013, 110: 193602-1~193602-5 [5] G Anetsberger, O Arcizet, Q P Unterreithmeier, R Riviere, A Schliesser, E M Weig, J P Kotthaus,T Kippenberg. Near-field cavity optomechanics with nanomechanical oscillators [J]. Nat. Phys., 2009, 5: 909~914[6] S J M Habraken, W Lechner, P Zoller. Resonances in dissipative optomechanics withnanoparticles: Sorting, speed rectification, and transverse coolings [J]. Phys. Rev. A, 2013, 87: 053808-1~053808-8[7] K Qu, G S Agarwal. Fano resonances and their control in optomechanics [J]. Phys. Rev. A, 2013,87: 063813-1~063813-7[8] A Nunnenkamp, K Borkje, S M Girvin. Cooling in the single-photon strong-coupling regime ofcavity optomechanics [J]. Phys. Rev. A, 2012, 85: 051803-1~051803-4[9] Y C Liu, Y F Xiao, X S Luan, C W Wong. Dynamic Dissipative Cooling of a MechanicalResonator in Strong Coupling Optomechanics [J]. Phys. Rev. A, 2013, 110: 153606-1~153606-5[10] A Nunnekamp, K Borkie, S M Girvin. Single-photon optomechanics [J]. Phys. Rev. Lett., 2011,107: 063602-1~063602-5[11] J M Dobrindt, I Wilson-Rae, T J Kippenbeg. Parametric Normal-Mode Splitting in CavityOptomechanics [J]. Phys. Rev. Lett., 2008, 101: 263602-1~263602-4[12]樊菲菲. 光力振子与原子间量子纠缠和振子压缩的研究[D]. 华中师范大学，2014[13] 张文慧. 光机械腔系统的动力学行为[D]. 华中师范大学，2014[14]詹孝贵. 腔光机械系统中电磁诱导透明及其相关现象的理论研究[D]. 华中科技大学，20134．毕业论文(设计)应完成的主要内容在阅读大量文献的基础上，完成开题报告，并通过开题答辩。

量子信息和量子纠缠理论

Multipartite Schmidt-correlated State
Fully separable
PPT
Fully separable (maximally entangled)
~ 1 (N)
M.J. Zhao, S.M. Fei and Z.X. Wang, Phys. Lett. A 372(2008)2552
S. Albeverio, S.M. Fei, Phys. Lett. A 276(2000)8 S. Albeverio, S.M. Fei and W.L. Yang, Comm. Theor. Phys. 38 (2002) 301
S. Albeverio, S.M. Fei and W.L. Yang, Phys. Rev. A 66 (2002) 012301 M. Horodecki, P. Horodecki and R. Horodecki, Phys. Rev. A 60, 1888 (1999)
Separable! Separable！
Separability of mixed states: no general criteria a) Peres (PPT) criterion:
Peres PRL 77, 1413 (1996)
2x2, 2x3:
PPT
Separable
Horodeckis, Phys. Lett. A 223,1 (1996)
Caltech (Kimble et al)
/~qoptics/teleport.html
Nature 390(1997) 575
Science 282(1998) 706
Wigner functions before &after

杨泰勒效应

HS: d7
Energy level splitting of d-orbitals in octahedron
Cu: 1s2 2s2 2p6 3s2 3p6 3d10 4s1 Cu2+: 1s2 2s2 2p6 3s2 3p6 3d9 dz2，dx -y dz2，dx -y
2 2 2
2
d9
z VS
d9
z
y x x z
y
y x
Energy level splitting of d-orbitals in octahedron
Octahedral with shorter z Octahedral with longer z
d z2 dx -y
2
dz2，dx -y
2
2
dx -y
2
2
1
2
d z2 dxy
2
dxz, dyz dxy
dxy, dxz, dyz
dxz, dyz
CFSE=0.5 1
Energy level splitting of d-orbitals in octahedron
Ni: 1s2 2s2 2p6 3s2 3p6 3d10 Ni2+: 1s2 2s2 2p6 3s2 3p6 3d8
Filling types with spherically symmetric electron cloud
d0
Empty
HS d5
Half filled
d10
Full filled
No Jahn-Teller effect
Filling types with octahedrally symmetric electron cloud

关于quantum的雅思阅读理解 (2)

关于quantum的雅思阅读理解引言概述：Quantum physics, also known as quantum mechanics, is a branch of physics that deals with the behavior of matter and energy at the smallest scales. Understanding quantum concepts is crucial for advancements in various fields, including technology, medicine, and communication. In this article, we will delve into the topic of quantum physics and its significance in IELTS reading comprehension.正文内容：1. Quantum Theory and Its Principles1.1 Wave-Particle Duality: Quantum theory proposes that particles, such as electrons and photons, exhibit both wave-like and particle-like behavior. This principle challenges classical physics, where particles were considered solely as particles or waves.1.2 Superposition: According to quantum theory, particles can exist in multiple states simultaneously. This concept is known as superposition, and it allows for the potential of quantum computing and cryptography.1.3 Quantum Entanglement: Quantum entanglement refers to the phenomenon where two or more particles become correlated in such a way that the state of one particle is instantly linked to the state of another, regardless of the distance between them. This principle has implications for secure communication and quantum teleportation.2. Applications of Quantum Physics2.1 Quantum Computing: Quantum computers utilize the principles of superposition and entanglement to perform complex calculations at an exponential speed compared to classical computers. This technology has the potential to revolutionize fields such as cryptography, optimization problems, and drug discovery.2.2 Quantum Communication: Quantum communication involves the transmission of information using quantum states. Quantum encryption ensures secure communication by exploiting the principles of entanglement and uncertainty. This technology has the potential to protect sensitive information from hacking.2.3 Quantum Sensing: Quantum sensors utilize the unique properties of quantum particles to measure physical quantities with unprecedented precision. This has applications in fields such as navigation, medical imaging, and environmental monitoring.3. Challenges in Quantum Physics3.1 Measurement Problem: The act of measuring a quantum system can disturb its state, leading to the collapse of the superposition. This measurement problem raises questions about the nature of reality and the role of the observer in quantum physics.3.2 Quantum Decoherence: Quantum systems are highly sensitive to their surroundings, which can cause decoherence. This phenomenon disrupts the delicate quantum states and poses challenges for maintaining coherence in quantum technologies.3.3 Quantum Interpretations: The interpretation of quantum mechanics is still a subject of debate among physicists. Different interpretations, such as the Copenhagen interpretation and the Many-Worlds interpretation, offer different explanations for the behavior of quantum systems.4. Quantum Physics in IELTS Reading Comprehension4.1 Vocabulary: Familiarity with quantum-related terms and concepts is essential for understanding reading passages that discuss quantum physics. Being well-versed in terms like superposition, entanglement, and decoherence will aid in comprehending the content.4.2 Inference: IELTS reading passages often require candidates to make inferences based on the information provided. Understanding the principles and applications of quantum physics will enable candidates to make accurate inferences when encountering quantum-related texts.4.3 Critical Analysis: IELTS reading tests candidates' ability to critically analyze information. Being knowledgeable about the challenges and interpretations in quantum physics will help candidates evaluate the validity and implications of the given information.总结：In conclusion, quantum physics plays a crucial role in various scientific and technological advancements. Understanding the principles of quantum theory, its applications, and the challenges it poses is essential for comprehending quantum-related passages in IELTS reading comprehension. By familiarizing oneself with quantum vocabulary, making accurate inferences, and critically analyzing information, candidates can enhance their performance in this aspect of the IELTS examination.。

Two-dimensional Quantum Field Theory, examples and applications

Abstract The main principles of two-dimensional quantum ﬁeld theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of four-dimensional quantum ﬁeld theory. The dynamics of conﬁnement and theta vacuum are explained by using the non-perturbative methods developed in two dimensions. We describe in detail how the eﬀective action of string theory in non-critical dimensions can be represented by Liouville gravity. By comparing the helicity amplitudes in four-dimensional QCD to those of integrable self-dual Yang-Mills theory, we extract a four dimensional version of two dimensional integrability.
2 48 49 52 54 56
5 Four-dimensional analogies and consequences 6 Conclusions and Final Remarks

英语作文我最喜欢的一本书汤姆索亚历险记

英语作文我最喜欢的一本书汤姆索亚历险记Humanity has always been driven by a thirst for knowledge and a desire to understand the world around us. From the earliest civilizations to the modern era, we have constantly sought to unravel the mysteries of the universe, to delve into the depths of the unknown, and to push the boundaries of what is possible. This relentless pursuit of understanding has led to countless discoveries, innovations, and advancements that have transformed our lives and the world we live in.One of the most significant areas of human exploration and discovery has been the realm of science. Scientists, through meticulous observation, experimentation, and analysis, have uncovered the fundamental laws and principles that govern the natural world. From the smallest subatomic particles to the grandest cosmic structures, the scientific method has allowed us to gain a deeper understanding of the physical universe and the processes that shape it.The field of physics, for instance, has revealed the intricate workings of matter and energy, from the behavior of light and the nature of gravity to the complex dance of quantum mechanics. Advances inchemistry have unlocked the secrets of the elements and the compounds that make up our world, enabling us to create new materials and develop life-saving pharmaceuticals. Breakthroughs in biology have shed light on the mysteries of life itself, from the inner workings of cells to the evolution of species.In the realm of technology, human ingenuity has translated scientific knowledge into practical applications that have transformed the way we live, work, and communicate. The invention of the wheel, the printing press, the steam engine, and the computer have all been pivotal moments in human history, ushering in new eras of progress and prosperity. The rapid pace of technological advancement in recent decades, driven by the exponential growth of computing power and the interconnectivity of the digital age, has been truly astounding.Today, we stand on the cusp of even greater discoveries and innovations. The exploration of space, the development of renewable energy sources, the quest to unlock the secrets of the human brain, and the ongoing efforts to combat global challenges like climate change and disease are just a few of the frontiers that humanity is currently pushing. And as we continue to push these boundaries, we are not only expanding our understanding of the world but also shaping the future of our species and our planet.Yet, with all of these remarkable achievements, it is important to remember that the pursuit of knowledge and the application of science and technology are not without their challenges and ethical considerations. The power that comes with scientific and technological progress must be wielded with great care and responsibility. We have a duty to ensure that the knowledge and tools we create are used in ways that benefit humanity and the environment, rather than causing harm or exacerbating existing inequalities.This is a delicate balance that requires constant vigilance, critical thinking, and a deep understanding of the complex social, environmental, and ethical implications of our actions. As we continue to push the boundaries of what is possible, we must also grapple with the moral and philosophical questions that arise, questions about the nature of consciousness, the limits of human enhancement, the impact of artificial intelligence, and the responsibility we have to future generations and the planet we call home.In the end, the journey of human discovery and innovation is not just about uncovering the secrets of the universe or creating ever-more sophisticated technologies. It is also about understanding our place in the grand scheme of things and using our knowledge and capabilities to create a better world for all. It is about harnessing thepower of science and technology in service of the greater good and ensuring that the progress we achieve is sustainable, equitable, and aligned with our deepest values and aspirations.As we continue to explore the unknown and push the boundaries of what is possible, let us do so with a sense of wonder, humility, and a deep commitment to the betterment of our species and our planet. For in the end, the true measure of our success will not be found in the number of discoveries we make or the technological marvels we create, but in the positive impact we have on the world around us and the legacy we leave for future generations.。

量子力学入门英语

Until now , we know that both quantum mechanics and relativity theory are absolutely right . But there are some paradoxes between them ，which may be the origin of revolution theory . 迄今为止，我们知道量子力学与相对论都是非常正确的理论。但是，它们之间还是存在一些不兼容的地方。这些地方有可能成为未来革命性理论的起点。
Hello , everyone! My name is Zheng Zerui , from School of Materials Science and Engineering. My teammates are Zhang Yuhan , Wang Yabo , Wu Qihang , Li Wei, Zhang Wei, Li Jiang , Chen Penghui. 大家好！我是材料学院的郑泽锐，我的队友有张宇寒、王亚博、吴起航、李伟、张维、李江、陈鹏辉。
schrödinger
For a general quantum system, Schrödinger equation is
ℏ2 ∂ iℏ Ψ (r , t ) = [− ∇ 2µ ∂t
2
+ V ( r )] Ψ ( r , t )
•
In conclusion , there are two points: A . Quantum mechanics is founded by the hypothesis that energy is discrete . B . The core work of quantum mechanics is calculating the Schrödinger equation. So quantum mechanics is very easy. 总而言之，这儿有两点比较重要： A . 量子力学是以能量是不连续为假设建立的。 B . 量子力学的核心工作就是计算薛定谔方程。所以说，量子力学是很简单的。

最具创意的英语作文

In the grand symphony of life, each individual is a unique instrument, harmoniously weaving their melodies into the vast tapestry of human experience. This composition is not merely a musical analogy but a profound exploration of the multifaceted dimensions that define our existence. It is a metaphorical journey that transcends disciplinary boundaries, encompassing philosophy, psychology, sociology, and even quantum physics, to provide a comprehensive understanding of life's intricate beauty and complexity.I. Prelude: The Philosophical ConductorThe philosophical conductor orchestrates this symphony, setting the tempo, tone, and thematic direction. He embodies the existential inquiries that have preoccupied thinkers since antiquity: What is the meaning of life? Is there a cosmic purpose, or do we create our own? The conductor's baton, symbolic of free will, guides each instrumentalist – each individual – in interpreting their part, granting them autonomy to infuse their performance with personal essence.In this metaphor, Aristotle's concept of eudaimonia, or flourishing, serves as the melodic motif. Each person strives to achieve harmony within themselves and with their surroundings, akin to an instrument tuning to the orchestra's central pitch. Plato's allegory of the cave further enriches the symphony, reminding us that our understanding of reality is often limited by our subjective perceptions, much like how an instrument's sound can be muffled or amplified by the acoustics of the concert hall.II. Movement I: The Psychological SoloistsThe psychological soloists in this symphony are the various aspects of our psyche, each contributing its distinct timbre. The rational mind, represented by a violin, elegantly articulates logical reasoning and decision-making, while the emotional heart, embodied by a cello, resonates with profound depth, expressing our joys, sorrows, fears, and desires. The unconscious, symbolized by a mysterious double bass, hums beneath the surface, influencing our actions and thoughts in ways we may not fully comprehend.Freud's psychoanalytic theory provides the structural framework for thismovement, highlighting the interplay between the id, ego, and superego – the violin, cello, and double bass respectively. Jung's concept of individuation, the process of integrating these diverse elements into a cohesive whole, mirrors the gradual unification of disparate melodies into a harmonious ensemble.III. Movement II: The Sociological EnsembleAs the symphony progresses, the psychological soloists merge into a sociological ensemble, reflecting our interconnectedness and the influence of societal norms and structures on individual lives. Here, each person is a member of a larger section – strings, woodwinds, brass, or percussion – symbolizing different social groups, roles, and identities.Durkheim's concept of collective consciousness serves as the guiding principle, synchronizing the rhythms and harmonies of the ensemble. Social institutions, such as education, religion, and politics, correspond to different sections, each contributing its unique color and texture to the overall composition. Conflict theories, represented by dissonant passages, remind us of the power dynamics and inequalities that can disrupt the harmony, while functionalist perspectives echo in the moments of consonance, emphasizing the stability and cohesion brought about by social systems.IV. Movement III: The Quantum InterludeIn a daring deviation from traditional symphonic structure, our metaphorical composition introduces a quantum interlude. This section explores the enigmatic realm where the boundaries of classical physics dissolve, analogous to the frontiers of human consciousness and the mysteries of existence.Quantum entanglement, where two particles become inextricably linked regardless of distance, symbolizes the profound interconnectedness of all life, transcending time and space. The observer effect, where the act of observation alters the observed reality, challenges our understanding of free will and determinism, much like how the conductor's gaze can subtly influence a musician's performance. Schrödinger's cat, suspended in a state of both life and death until observed, represents the coexistence of infinite possibilities in ourlives, awaiting the moment of manifestation through conscious choice.V. Finale: The Universal CrescendoThe symphony culminates in a universal crescendo, where the individual instruments, psychological elements, societal forces, and quantum mysteries converge into a resplendent anthem of unity in diversity. This climax embodies the idea that despite our differences and the complexities of existence, we are all integral parts of a grand cosmic symphony, playing out our unique melodies in concert with one another.This finale draws inspiration from Teilhard de Chardin's concept of the noosphere, a collective consciousness emerging from humanity's intellectual and spiritual evolution. It echoes the wisdom of ancient philosophies like Taoism, which espouse the harmonious balance of yin and yang, and the interconnectedness of all things in the universe. The symphony concludes with a profound sense of awe and wonder, inviting us to embrace the mystery and majesty of life, celebrating our individual roles while recognizing our shared destiny in the grand cosmic score.In conclusion, the metaphorical symphony of life transcends disciplinary boundaries, offering a multi-dimensional perspective on our existence. It underscores the importance of harmony within ourselves, with others, and with the cosmos, while acknowledging the complexities and contradictions that make life both challenging and beautiful. As we continue to play our parts in this eternal composition, may we do so with mindfulness, creativity, and a deep appreciation for the intricate symphony of which we are all a part.。

A new perspective on matter coupling in 2d quantum gravity

a rXiv:h ep-th/99412v12A pr1999NBI-HE-99-15AEI-1002Apr 1999A New Perspective on Matter Coupling in 2d Quantum Gravity J.Ambjørn,a,1K.N.Anagnostopoulos a,2and R.Loll b,3a The Niels Bohr Institute,Blegdamsvej 17,DK-2100Copenhagen Ø,Denmark b Max-Planck-Institut f¨u r Gravitationsphysik,Albert-Einstein-Institut,Am M¨u hlenberg 5,D-14476Golm,Germany AbstractWe provide compelling evidence that a previously introduced model of non-perturba-tive 2d Lorentzian quantum gravity exhibits (two-dimensional)ﬂat-space behaviour when coupled to Ising spins.The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter sys-tem.This weak-coupling behaviour lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions,with a diﬀerent,and much ‘smoother’critical behaviour.1IntroductionAt the end of the twentieth century,the non-perturbative quantization of gravity remains an elusive goal for theoretical researchers.There is not even a consensus on how the problem should best be tackled.For example,considering pure-gravity approaches,we have on the one hand Euclidean path-integral methods,which are close to usual formulations of(non-generally covariant)quantumﬁeld theories and well-suited for numerical simulations.On the other hand,in canonical quantization approaches it is–at least in principle–easier to address questions about the be-haviour of spatial three-geometries,but the complicated structure of the constraints tends to lead to computational diﬃculties.4Unfortunately,very little is known about the relation between the covariant and canonical approaches.In part this is due to the‘signature problem’of the path-integral formulations:the sum over all space-time geometries is usually taken over Riemannian,and not over the physical Lorentzian(pseudo-Riemannian)four-metrics modulo diﬀeomorphisms.The prob-lem of how to relate the two sectors by an appropriately generalized Wick rotation remains unresolved.Our aim is to investigate the possible consequences of taking the Lorentzian structure seriously within a path-integral approach.In order to gauge the diﬃculties this involves and to circumvent technical problems,weﬁrst addressed the issue in two space-time dimensions,where there already exists a well-understood theory of (Euclidean)quantum gravity,namely,Liouville gravity.In[1],we proposed a new, Lorentzian model of2d quantum gravity,obtained by taking the continuum limit of a state sum of dynamically triangulated two-geometries.The Lorentzian aspects of the model were two-fold:ﬁrstly,the sum was taken only over those two-geometries which are generated by evolving a one-dimensional spatial slice and which allow for the introduction of a causal structure.Secondly,the Lorentzian propagator was obtained by a suitable analytic continuation in the coupling constant.The ﬁrst aspect turned out to be the crucial one,leading to a continuum theory of2d quantum gravity inequivalent to the usual Liouville gravity.This was shown in [1],where both the loop-to-loop propagator and various geometric properties of the model were calculated explicitly.The Hausdorﬀdimension of the quantum geometry is d H=2,and points to a much smoother behaviour than that of the Euclidean case (where d H=4).However,we must emphasize that d H=2does not imply aﬂat geometry.The model of Lorentzian gravity deﬁned in[1]allows for arbitrarily largeﬂuctuations of the spatial volume from one time-slice to the next.This is illustrated by Fig. 1,which shows a typical surface generated by the Monte Carlo simulations,to be described in Sec.3.The length of the compact spatial sliceﬂuctuates strongly with time(pointing along the vertical axis).Using the results of[1],one easily derivesFigure1:A typical discrete history of pure Lorentzian gravity with volume N=1024. that in the thermodynamic limit and for large times the average spatial volume Landﬂuctuations around L behave likeL =1Λand ∆L = √unmodiﬁed model without branching baby universes,i.e.the model of2d quantum gravity that does not lie in the same universality class as Liouville gravity.We also would like to point out that from the point of view of a canonical quantization the Lorentzian model is much more natural.The inclusion of topology changes of space into a canonical scheme would require a so-called third quantization of geometry.In Liouville gravity,matter couples strongly to geometry,perhaps even too strongly in the sense that the combined system becomes inconsistent when the cen-tral charge of the(conformal)matter exceeds one.Arguments have been presented which link the strong deformation of geometry to the creation of baby universes [9].It is therefore conceivable that the Lorentzian model of gravity–where baby universes are absent–has a weaker and less pathological coupling to matter.In order to understand the behaviour of the combined gravity-matter system, we are considering here the coupling of the gravitational model of reference[1]to an Ising model of spin-1that in the presence of gravity,the matter behaviour is‘softened’to a third-orderphase transition,characterized by critical exponentsα=−1,β=0.5,andγ=2[7].On the other hand,the geometry is‘roughened’,as exempliﬁed by the increase from −1/2(pure2d Liouville gravity)to−1/3of the entropy exponentγstring for baby universes on manifolds of spherical topology.It is not entirely straightforward to apply the methods used to obtain these ex-act solutions to the Lorentzian gravity model.For example,one can write down an expression for the transfer matrix generalizing that of the Onsager solution by im-posing a length cutoﬀl0on the length of spatial slices.However,a major stumbling block to understanding the behaviour of its eigenvalues as l0→∞is the fact that as a consequence of the gravitational degrees of freedom,transitions between spa-tial slices of diﬀerent length are allowed.This makes the use of Fourier transforms problematic,which are an essential ingredient of this and other algebraic solution schemes.Moreover,the Hilbert space dimension for the discrete,ﬁnite model is given by l0l=12l,which grows rapidly with l0.In the absence of an analytic exact solution5,one way to try to extract infor-mation about the matter-coupled model is by performing a series expansion of the partition function Z at high or low temperature,or of suitable derivatives of Z.For ﬂat,regular lattice geometries,these have been studied extensively since the early days of the Ising model.It is well-known that the high-T expansion,in particular, that of the magnetic susceptibilityχat zeroﬁeld is well-suited for obtaining infor-mation about the critical behaviour of the theory.We will show that the same is true for the coupled gravity-Ising model,after taking into account some peculiarities to do with the fact that we have an ensemble ofﬂuctuating geometries instead of a ﬁxed lattice.In the limit of large lattice size N,there is a well-deﬁned expansion in terms of u:=tanhβ,where the couplingβis proportional to the inverse temper-ature,whose coeﬃcients can be determined by diagrammatic techniques.Given a plausible ansatz for the singularity structure of the thermodynamic functions,one can then extract estimates for the critical point and critical exponents from theﬁrst few terms of such an expansion.These results are corroborated by performing a Monte Carlo simulation of Lorentzian gravity coupled to the Ising model.Apart from being in good agreement with the high-T expansion,the simulations also allow us to measure the quantum geometrical properties of the model.2The high-T expansionRecall the usual high-T expansion of the Ising model on aﬁxed lattice of volume N,with partition functionZ(β,N)= {σi=±1}eβ<ij>σiσj+H iσi,β=JN ln Z(β,N)=sNln2+ n≥1ω(0)n u n,(6)whereω(0)n is obtained by taking the term linear in N inΩn and setting N=1. Note that both connected and disconnected graphs contribute toω(0)n.A simi-lar relation can be obtained for the magnetic susceptibility at zeroﬁeld,χ(N)= kT∂2The coeﬃcients ω(2)n are the exact analogues of ω(0)n in eq.(6),where the counting now refers to polygon graphs with two odd vertices (vertices with an odd number of incoming links),and all other vertices even (c.f.[8],but beware of the diﬀerence in notation for the number of vertices).Since we are primarily interested in the bulk behaviour of the gravity-matter system,we will in the following for simplicity choose the boundary conditions to be periodic.That is,we will identify the top and bottom spatial slices of the cylindrical histories introduced in [1].Clearly this is not going to aﬀect the local properties of the model.As above,we will denote the discrete volume,i.e.the number of triangles of a given two-dimensional geometry (with torus topology),by N .It follows immediately that such a geometry contains N time-like links,N/2space-like links,N/2vertices and 3N/2nearest-neighbour pairs.In quantum gravity the volume N becomes a dynamical variable.For ﬁxed topology,the only coupling constant appearing in the action of pure 2d quantum gravity is the cosmological constant,multiplying the volume term.The partition function of the Ising model coupled to 2d Lorentzian quantum gravity is given byG (λ,t,β)=T ∈T t e −λN T Z T (β)= T ∈T t e −λN T {σi (T )}e β ij ∈T σi σj ,(8)where the sum is taken over all triangulations T with the topology of a torus and t time-slices,N T is the number of triangles in T ,and Z T (β)the Ising partition function (2)deﬁned on T .Fortunately,the summation over volumes in eq.(8)does not lead to additional complications in the analysis of the thermodynamic properties of the spin system,since the state sums for ﬁxed and ﬂuctuating volume are simply related by a Laplace transformation.Rewrite relation (8)asG (λ,t,β)= N e −λN ˜Z (β,N,t ):= N e −λN T ∈T N,t Z T (β),(9)where T N,t denotes the toroidal triangulations of volume N and length t in the time direction.Analogous to eq.(6),we expect the matter part f (β)of the free energy density in the gravitational ensemble to behave in the thermodynamic limit (N →∞and t ∝√6Note that with the conventions used in deﬁnition (2),the ground state energy is −3βN/2and the free energy density f (β)is negative.122N2ln coshβ+1T∈T N,t1=e N˜f(u).(15) The coeﬃcients˜Ωof the power series now depend on the triangulation T.When counting diagrams of a given type and order n,we must keep in mind that the vertex neighbourhoods do not look all the same,as they do in the case of a regular lattice,but that the distribution of coordination numbers(numbers of links meeting at a vertex)is subject to a probability distribution.The coeﬃcients in the high-T expansion therefore count the average occurrence of a certain diagram type in the ensemble of triangulations of aﬁxed volume N,for large N.Starting to evaluate the series in(13)order by order,one immediately notices a qualitative diﬀerence from the regular case.If we had considered a regular triangular lattice(coordination number6),theﬁrst non-trivial contribution to the counting of even diagrams would have appeared at n=3,where one obtainsΩ3(N)=N, coming from closed triangle graphs.However,when looking at all two-dimensional random lattices contributing to the sum over geometries in the gravity case,there are geometries which have one or several‘pinches’.A pinch is a spatial slice of minimal length l=1,which consists of a single link and a single vertex(see Fig.2). Pinches occur even if the total volume of the two-geometry is keptﬁxed,since in the presence of gravity the length of spatial slices is aﬂuctuating dynamical variable.Figure2:A two-dimensional geometry with a‘pinch’of length1.For the gravitationally coupled Ising model,the lowest-order contribution to the power series in u in(13)occurs therefore already at order n=1.Clearly, such pinching contributions will be present at all orders,in both connected and disconnected diagrams,on top of the ordinary‘bulk’contributions,coming from diagrams which do not wind around the spatial direction of the torus in a non-trivial way.The former have no analogue on regular lattices.Fortunately,it turns out that the pinch contributions are irrelevant,in the sense that they contribute at a lower order of N,whereas the bulk contributions in˜Ωn go like N k,k≥1.This can be seen most easily by considering the Laplace-transformed partition function.Let us begin by evaluating the zeroth-order term of eq.(13), G(˜λ,t)= N e−˜λN T∈T N,t1:= N e−λN(coshβ)3N2 T∈T N,t1,(16) where for notational brevity we have deﬁned an‘eﬀective cosmological constant’˜λ=λ−32ln2,in accordance with eq.(14).The left-hand side of(16)can be computed asG(˜λ,t)= dx x;e−˜λ;t),(17) given the explicit form of the propagator derived in ref.[1],to which we also refer for details of notation.The term proportional to u1in the Laplace transform of(13) is∼u1: N e−˜λN T∈T l=1N,t1=G(˜λ,t)˜Ωnorm1(˜λ),(18)where the second summation is over triangulations with a single‘pinch’of spatiallength l=1.To arrive at the last expression on the right-hand side,the factorG(˜λ,t)has been pulled out.In terms of quantities derived in[1],the normalized coeﬃcient˜Ωnorm1is most easily computed as˜Ωnorm 1(˜λ)=t−1˜t=1G˜λ(x,l=1;˜t)G˜λ(l=1,y;t−˜t)(l1−k−1)!(l2−k−1)!k!.(20)By contrast,let us now calculate theﬁrst bulk contribution,which occurs at order u3.The contribution to˜Ω3is simply N,from counting the number of triangle graphs in the2d geometry.Taking the Laplace transform,we obtainN e−˜λN N≡−∂∂˜λG(˜λ,t)(22)a→0−→−4(1−e−2T √Λ(1−e−2T√a2Λ(1−e−2T√a2√7Let us take the opportunity to correct some misprints in equation(29)of[1],which has been used in deriving formula(20).The correct equation readsGλ(l1,l2;t)=F2t(1−F2)2B l1+l2t(l1−k−1)!(l2−k−1)!k!−A t C tFigure3:The triangles contributing to the weight at the vertex i.We conclude that in the thermodynamic limit,pinching terms will be suppressed since their number is proportional to N0,whereas the(connected)bulk diagrams behave like∼N1.For large N,the pinch contributions must therefore factorize according to(1+ n≥1˜Ωn(T)u n)=(1+N0 m≥1p m(T)u m)(1+N n≥1˜ωn(T)u n+O(N2)).(24) Taking the logarithm,we see that the sum(1+ p m(T)u m)∼N0will only con-tribute a constant term to the free energy,which does not aﬀect the universal be-haviour of the model.We will make no attempt to calculate it explicitly.Similar considerations apply to the high-T expansion of the magnetic susceptibility in the presence of gravity.The pinch contributions factorize,and we will only need to com-pute the multiplicity˜ω(2)n of bulk polygon graphs with two odd vertices per triangle inχ∼(1+ n≥1˜ω(2)n u n).(25)Our next step will be to derive the probability distribution of the coordination numbers in the Lorentzian gravity model,in the thermodynamic limit as the cos-mological constantλ→λc=ln2.Recall that when generating an interpolating space-time between an initial and aﬁnal spatial geometry,the geometry of each space-time‘sandwich’with∆t=1is independent of the previous one in the sense that there are no local constraints on how the numbers k i≥1of time-like future-pointing links can be chosen at each vertex i[1].Having reached a spatial slice at time t,we can generate the space-time between t and t+1proceeding from‘left to right’.To each vertex i at time t we associate k i time-like links(ending at vertices of the subsequent spatial slice at t+1)and the space-like link to the right of the vertex. There are therefore exactly k i triangles associated with the vertex i,contributing with a weight factor e−kλto the action,as illustrated in Fig.3.Since the assignmentof the order k i of outgoing time-like links to the vertex is completely independent of the k-assignments of other vertices,the probability distribution for k outgoing future-directed links is given bypλ(k)=e−kλ(eλ−1).(26) Strictly speaking,the argument leading to eq.(26)is only correct in the continuum limit in which‘extreme pinching’to vanishing spatial length l=0does not occur (for oﬀ-criticalλ,relation(26)must be modiﬁed to account for the fact that moves changing the torus topology are forbidden).Fortunately this is the only case we are interested in,and theﬁnal probability distribution is therefore obtained by setting e−λ=1/2in(26),yieldingp(k)≡pλc (k)=12j−2,j≥4.(28) With the distribution(27)in hand,we can now embark on the actual counting of diagrams contributing to the susceptibility coeﬃcients˜ω(2)n in(25).We will only quote the results up to order n=5.Further details of the counting procedure will appear elsewhere.The average numbers of diagrams per triangle(i.e.per unit volume)are listed in the table below.n open disconnected2022022026−176618182Open graphs are connected graphs without any self-intersections.Closed graphs are connected graphs which are not open.The disconnected graphs consist of two or more components and contribute with a minus sign.In order to double-check our results at order4and5,where the counting becomes slightly involved,we have performed a numerical check on the coeﬃcients˜ω(2)n listedabove.This was done by computer-generating histories of length∆t∼100,with an initial spatial slice of length∆l=200,and counting diagrams of a given type. The results are given in the table below and in very good agreement with the exact calculation.They are based on a total of∼3×105vertices at order4and∼9×105vertices at order5.We have not listed the counting of disconnected graphs separately,since it follows closely the counting of closed connected graphs.n open13.996±0.007134.197±0.0982.1Evaluation of resultsIn order to evaluate the results from the high-T expansion,we assume a simple behaviour of the susceptibility of the formχ(u)∼A 1−u˜ω(2)n−1=1n .(30)Plotting the ratios r n linearly against1/n for n∈1...n max,we have extracted the following estimates for the critical point u c and the critical susceptibility exponent γ:n max critical pointγ=1.820γ=1.789γ=1.783The estimates for the critical exponent should be compared to the exact values forγfor the Ising model on aﬁxed,regular lattice and on dynamically triangulated lattices(Ising spins coupled to Euclidean quantum gravity),which areγreg=1.75and γdt =2respectively.The data from the high-T expansion clearly favour γ=1.75in our model.Indeed,the estimates for γare remarkably close to this value,given that we are working only up to order 5in the expansion parameter u =tanh β.The conclusion that the critical exponents of the Ising model coupled to Lorentzian quantum gravity coincide with those found on regular lattices is also supported by the Monte Carlo simulations we have performed.However,before turning to a detailed description of the simulations we would like to illustrate how well the high-T expansion works even at this rather low order.We will compare the β–dependent cosmological constant λc (β)deﬁned in eq.(14),which can be measured directly in the Monte Carlo simulation,with the same quantity obtained from the high-T expansion.Recall that in the thermodynamic limit λc (β)is essentially given by the spin free energy,eq.(11),whichcan be computed in thesmall-βexpansion.We have determined the density ˜f (u ),deﬁned in eq.(15),bycounting closed polygon graphs in the high-T expansion up to order 6.Inserting this into formula (14)leads toλhigh −T c (β)=λc +12ln cosh β+u 3+59u 5+2632ln 2for β→0and λc =ln 2for β→∞,both of which are well satisﬁed.In order to quantify the eﬀect of the u -expansion,we have plotted both the zeroth-order expression F 1(β)=λc +12ln cosh β−32β.The latter agrees well with the measured Monte Carlo values right up to the neighbourhood of the critical Ising coupling βc .At the critical point βc the measured function λc (β)exhibits a cusp.This reﬂects the singular part contained in λc (β)which of course cannot be captured by simply plotting the analytic function (14).3The Monte Carlo simulationMonte Carlo simulations have been used successfully in the study of Euclidean 2d quantum gravity.The formalism known as ‘dynamical triangulations’provides a regularization of the functional integral well-suited for such simulations,allowing in addition for a straightforward matter coupling of Gaussian ﬁelds as well as of spin degrees of freedom.Extensive computer simulations of the combined gravity-matter systems have been performed,leading to results in perfect agreement with exact results derived from Liouville theory and matrix model calculations.0.40.50.60.70.80.911.11.21.31.400.20.40.60.81λββc F 1[β]F 2[β]3/2 ln(2)ln(2)0.680.70.720.740.760.780.80.20.220.240.260.280.3λββcF 1[β]F 2[β]ln(2)Figure 4:The critical cosmological constant as a function of the Ising coupling β,as measured by Monte Carlo simulations (t =32,N =2048),and compared to the corresponding high-T expansions F 1(β)and F 2(β)at order 0and order 6.Figure5:The move used in the Monte Carlo updating of the geometry.The Lorentzian model resembles the dynamically triangulated model in that its dynamics is associated with theﬂuctuating connectivity of the triangulations con-tributing to the path integral.This allows us to take over many of the techniques from the computer simulations of the dynamically triangulated models.We must specify the update of both the geometry and the matterﬁelds,the latter being stan-dard:for a given triangulation we update the spin conﬁgurations by the same spin cluster algorithms used for dynamical triangulations.This presents no problems since our conﬁgurations form a subset of the full set of dynamical triangulations used in Euclidean quantum gravity(on the torus).During the update of geometry, we want to keep the number of time-slicesﬁxed while allowing any space-likeﬂuc-tuations compatible with the model.A local change of geometry or‘move’which is clearly ergodic(i.e.can generate any of the allowed conﬁgurations when applied successively)is shown in Fig.5.It consists in deleting the two triangles adjacent to a given space-like link(if the resulting conﬁguration is allowed).Its inverse is a‘split’of a given vertex and two neighbouring time-like links into two,thereby creating a new space-like link,as well as two new triangles.This is a special case of the so-called‘grand canonical move’sometimes used in dynamical triangulation simulations[12,13,2],and does not preserve the total volume of space-time.Detailed balance equations for the move can be derived from standard consid-erations[2].Let N V denote the number of vertices(N V=N/2,where N is the number of triangles),and v a speciﬁc vertex.For pure Lorentzian gravity without matter,the equation for detailed balance readsP(N V)P(N V→N V+1)N V!is the probability distribution for labelled triangulations,and k in and k out count the incoming and outgoing time-like links at v(see Fig.5).We are still free to choose P(N V→N V+1)and P(N V+1→N V)such that condition(32)is satisﬁed.Once a transition probability P(N V+1→N V),say,has been chosen,it will be tested during the simulation against the uniform probability distribution between0and1as follows.Choose a random number r∈]0,1].Then, if the move is allowed(i.e.if the resulting triangulation belongs to the allowed class of conﬁgurations)it is accepted if P(N V+1→N V)>r.If it is not allowed,one proceeds to the next move.It is straightforward to generalize the updating of geometry to include Ising spins. The spin Hamiltonian is included in P(N V),which now becomes a function of both N V and the spin conﬁgurations.When inserting a vertex v,one has to specify at the same time a spin associated with v.The choice of spin up or down is made with probability1/2,and theﬁnal result tested as in the case of the pure geometry update.We have performed the computer simulation for surfaces with toroidal topology and for system sizes of N=2048,4050,8192,16200and32768triangles,and with a number t=32,45,64,90and128of time-slices respectively.Since the moves are not volume-preserving,ﬁxing the system size to N is implemented as follows:we allow the volume toﬂuctuate within a certain,not too wide range,and collect for every sweep theﬁrst conﬁguration with volume N.The volumeﬂuctuations are controlled by adding a termδλ(∆N)2to the action,where∆N is the deviation of the volume from its desired value N.This term does not aﬀect the ensemble of conﬁgurations collected,since for all of them∆N=0.Weﬁnd that ∆N −1∼√∼N1/νd H(D ln|m|≡d ln|m||m|∼N1/νd H(D ln m2≡d ln m2m2time.For aﬂat space-time(where of course d H=d=2),we haveνd=2,whereas for the Ising model coupled to Euclidean quantum gravityνd H=3(and d H≈4).The internal energy density e and the magnetization m of the spin system are deﬁned bye=−1dβ,m=1dH H=0.(36) In order toﬁnd the critical pointβc,we can use the fact that the pseudo-critical couplingβc(N)at volume N is expected to behave likecβc(N)∼βc+=1u c=tanhβcνd HD ln|m|0.2522(2)D ln m20.2520(1)Observable111—D ln|m|0.47(2)0.521(3)0.531(1)value atβcχ0.883(1)gravity this notion of distance becomes proportional to the true geodesic distance between the vertices in the inﬁnite-volume limit.We will assume this is also true for the present model.All diﬀeomorphism-invariant correlation functions of matter ﬁelds must be functions of this geodesic distance.Both the geodesic distance and the fractal dimension appear in the expression for the volumeN(r)∼r d H for r≪N1/d H,(38)which denotes the number of vertices(or triangles)inside a ball(a disc in dimension 2)of link-radius r.If n v(r)denotes the number of vertices at distance r from aﬁxed vertex v,relation(38)implies thatn v(r)∼r d H−1for r≪N1/d H.(39) Finite-size scaling for an observable A then leads to a scaling of the correlation function integrated over all points at distance r from a vertex according toA(r)A(0) N∼N1−1/d H−∆A F A(x),x=r/N1/d H.(40) The factor N1−1/d H comes from the integration over points at distance r from vertex v,using(39),while∆A is the genuine dynamical exponent of the correlator.By measuring correlation functions for various volumes N,one can determine d H and the critical exponents.We will concentrate here on the Hausdorﬀdimensiond H.Oneﬁrst rescales the height of the measured distributions A(r)A(0)N to acommon value.However,the distributions measured for diﬀerent N will still have diﬀerent width as functions of r.By appropriately rescaling r,they can then be made to overlap in a single,universal function F A(x).From a technical point of view it is important to work with the shifted variablex=r+a A00.20.40.60.811.200.511.522.5S V (l )l/N 1/d h 20484050819216200Figure 6:The distribution of spatial volumes SV (l )at β=βc ,rescaled according to eq.(42).We have set d H =2.0.our statistics was not good enough to determine it with more accuracy.However,the fact that it is non-vanishing justiﬁes its introduction in the ﬁrst place.After a suitable normalization,we expect the volume distribution to behave likeSV (l )∼f (l/N 1/d H ).(42)Fig.6demonstrates clearly that for the Ising model at β=βc ,SV (l )scales as anticipated when we set d H =2.0.Scaling the Ising distributions at β=βc (N ),the pseudo-critical point of the magnetic susceptibility,or considering pure gravity leads to similar results.We conclude from Table 1that the Hausdorﬀdimension of 2d Lorentzian quan-tum gravity is close to the ﬂat-space value d H =2.This is clearly diﬀerent from the Euclidean situation which is characterized by d H =4for pure gravity and d H ≥4in the presence of Ising spins.The results for the Lorentzian gravity-matter system are particularly convincing for the purely geometric observables n v (r )and SV (l ),which basically coincide with the corresponding measurements obtained in Lorentzian pure gravity.4ConclusionsWe have presented compelling evidence,coming from a high-T expansion as well as Monte Carlo simulations,that the critical exponents of the Ising model cou-pled to Lorentzian gravity are identical to the exponents in ﬂat space.This is in。

关于科技发展的忧患英语作文素材摘抄

全文分为作者个人简介和正文两个部分：作者个人简介：Hello everyone, I am an author dedicated to creating and sharing high-quality document templates. In this era of information overload, accurate and efficient communication has become especially important. I firmly believe that good communication can build bridges between people, playing an indispensable role in academia, career, and daily life. Therefore, I decided to invest my knowledge and skills into creating valuable documents to help people find inspiration and direction when needed.正文：关于科技发展的忧患英语作文素材摘抄全文共3篇示例，供读者参考篇1The Paradox of Technological ProgressWe live in an era of unprecedented technological advancement. Every day, new innovations emerge that have the potential to revolutionize our lives, from artificial intelligenceand quantum computing to gene editing and renewable energy sources. These breakthroughs promise to solve some of humanity's most pressing challenges, such as disease, climate change, and resource scarcity. However, as a student witnessing the rapid pace of these developments, I can't help but feel a sense of unease – a growing concern that our relentless pursuit of technological progress may come at a cost we are not fully prepared to pay.One of the primary issues that worry me is the potential impact of technology on employment and the future of work. As machines become more sophisticated and capable of performing tasks that were once exclusively human domains, the risk of widespread job displacement looms large. Automation has already disrupted several industries, and experts warn that millions of jobs could be made redundant in the coming decades. While technology has always disrupted labor markets throughout history, the current pace and scale of change are unprecedented, and the consequences could be severe if we fail to adapt and retrain our workforce adequately.Moreover, the concentration of wealth and power in the hands of a few tech giants raises concerns about monopolistic practices, data privacy, and the erosion of individual freedoms.These companies wield immense influence over our digital lives, collecting and monetizing vast troves of personal data with little oversight or accountability. As we become increasingly dependent on their products and services, we risk surrendering our autonomy and privacy to entities driven primarily by profit motives.Another area of concern is the potential for technology to exacerbate existing social inequalities and create new divides. Access to cutting-edge technologies and the skills required to harness them are often concentrated among the privileged few, widening the gap between the haves and have-nots. This digital divide threatens to perpetuate cycles of poverty and marginalization, leaving entire communities behind in the race for technological progress.Furthermore, the rapid pace of technological change raises ethical and philosophical questions that we have yet to fully grapple with. As we develop technologies with the potential to enhance human capabilities, alter our genetic code, or create artificial superintelligence, we must confront complex issues surrounding the boundaries of what is acceptable, the potential consequences of our actions, and the responsibilities that come with wielding such immense power.Perhaps one of the most pressing concerns is the impact of technology on our environment and the sustainability of our planet. While technological solutions hold promise for mitigating climate change and reducing our ecological footprint, the manufacturing, energy consumption, and waste associated with many technologies contribute significantly to environmental degradation. We must strike a delicate balance between pursuing innovation and preserving the fragile ecosystems upon which all life depends.As I contemplate these issues, I am reminded of the words of Albert Einstein, who famously said, "It has become appallingly obvious that our technology has exceeded our humanity." This sentiment resonates deeply with me, as I witness the incredible advancements in science and technology, yet worry that our ethical and moral frameworks have not kept pace.However, it would be shortsighted to dismiss technology outright or to embrace a luddite mentality. The benefits and potential of technological progress are undeniable, fromlife-saving medical treatments and energy-efficient solutions to educational tools and platforms for global communication and collaboration. The challenge lies in striking the right balance –harnessing the power of technology while mitigating its negativeconsequences and ensuring that its development aligns with our shared values and priorities.As students and the inheritors of this rapidly evolving world, we have a vital role to play in shaping the future of technology. We must cultivate a critical and ethical mindset, questioning the assumptions and motivations behind technological developments and advocating for responsible innovation that prioritizes the well-being of humanity and our planet.We must also strive to acquire the necessary skills and knowledge to navigate the technological landscape, embracing lifelong learning and adapting to the ever-changing demands of the job market. Education systems must evolve to equip us with the multidisciplinary expertise and problem-solving abilities required to tackle the complex challenges that lie ahead.Furthermore, we must actively participate in public discourse and policymaking, engaging with experts, policymakers, and stakeholders to ensure that technological progress is guided by democratic principles and serves the greater good. We cannot afford to be passive bystanders in this era of rapid transformation.Ultimately, technology is a double-edged sword – a powerful tool that can either uplift or oppress, depending onhow we wield it. As we stand at this crossroads, we must exercise wisdom, foresight, and ethical responsibility in our pursuit of progress. We must embrace the benefits of technology while remaining vigilant against its potential pitfalls, always mindful of our shared humanity and the delicate balance of our world.It is a great responsibility that falls upon our shoulders, but one that we must embrace with courage, creativity, and a deep commitment to shaping a future where technology serves as a force for good, empowering and uplifting all of humanity, rather than dividing and diminishing us.篇2The Paradox of Technological ProgressWe live in an age of unprecedented technological advancement. Every year, it seems there are new breakthroughs and innovations that reshape how we interact with the world around us. From artificial intelligence and robotics to genetic engineering and renewable energy sources, the human capacity for scientific discovery appears to know no bounds. And yet, amid all this rapid progress, I can't help but feel a sense of trepidation about where these technologies may be leading us.At the core of my concerns is the question of whether we as a society are capable of developing these powerful new tools as rapidly as we are without proper consideration for their potential consequences. Will the machines we create to make our lives easier one day become so intelligent that they render humanity obsolete? Could the same gene editing techniques that could cure devastating diseases also be weaponized into a terrifying new form of biological warfare? As we unlock the ability to reshape the world on a molecular level, how do we ensure that capability is not abused by those with nefarious intentions?I think back to the origins of nuclear energy and how quickly the pursuit of that scientific knowledge led to the creation of one of the most destructive forces ever known. The nuclear arms race showed in stark terms how technological advancement, when not accompanied by wisdom and ethics, can quickly spiral out of control with catastrophic results. While regulated nuclear powers have thankfully helped prevent another world war over the past several decades, the threat of nuclear proliferation still looms. Are today's powerful new technologies like AI, bioengineering, and molecular manufacturing laying the groundwork for a similar escalating arms race, but this time driven by radical advances that are even harder to control?Beyond the existential risks of these technologies, I also worry about the impact they are having on our personal lives and humanity's relationship with the natural world. As we become more machinelike in our efficiency and reliance on tools and automation, are we losing some of our core traits that make us human – our creativity, our appreciation for the natural world, our ability to find meaning in struggle and suffering? By achieving such a high level of mastery over our environment through technology, are we also distancing ourselves from the world that gave rise to our existence in the first place?It's easy to dismiss these kinds of concerns as the woolly philosophizing of a Luddite who fails to see the immense potential that technologies like AI, genetic engineering, and nanotechnology possess. After all, aren't they the keys that could help us eventually cure diseases, end poverty, reverse aging, clean up environmental disasters, and unlock other amazing benefits that could dramatically improve the human condition? I absolutely agree that these revolutionary technologies, if developed responsibly and with proper safeguards, could indeed be a great force for reducing suffering in the world.And yet, I can't shake the feeling that in our relentless pursuit of progress and our desire to exercise increasing masteryand control over our environment, we are perched precariously at the edge of a precipice. Like playing with profoundly powerful forces we don't yet fully understand, these technologies could easily become a modern-day version of Pandora's box if we aren't extremely careful in how we wield them. One mishap, one bug in a software update, one rogue scientist, could potentially have catastrophic, irreversible consequences that ripple across the world.This is the great paradox I struggle with regarding technology – that the very tools that could help uplift and empower humanity may also contain the seeds of our own potential undoing if we don't approach them with a sense of profound humility and respect. We would do well to reflect on past technological revolutions as an omen: While the industrial age brought immense material progress, it also triggered problematic consequences like environmental degradation and the jarring social dislocations of industrialized urban life that still ripple today. While the digital revolution brought convenience and efficiency to our lives through computers and the internet, it also unleashed issues like social media addiction, surveillance capitalism, and cyber threats that challenge core values like privacy and truth.So as we stand at the dawn of an era where technologies like artificial general intelligence, genetic engineering, nanotechnology, and others have the potential to reshape the human condition and alter life itself, I believe we would be wise to hit the pause button on unrestrained technological development. We desperately need a broader public debate, guided by moral philosophy and ethics, to carefully consider the ramifications and establish robust governing frameworks for how these world-altering tools get developed and employed.Some may argue that this is simply fanciful thinking – that the profit motives of industry and the competitive vigor of nations jockeying for technological supremacy make it impossible to pumthe brakes on scientific progress. That may unfortunately be true to a certain degree. But even so, I still hold out hope that we can instill some level of caution and oversight into how transformative new technologies get introduced through clearsighted policymaking and enforceable global agreements.篇3The Perils of Unchecked Technological AdvancementAs I scroll endlessly through social media feeds and observe my peers constantly glued to their screens, I can't help but feel a sense of unease about the role technology now plays in our lives. Don't get me wrong, I'm not a complete Luddite – I appreciate the conveniences modern tech affords us. However, the breakneck pace of technological progress has me questioning whether we are losing our humanity in the process.It seems like every day, a new technological "disruption" emerges that fundamentally alters how we live, work, and interact. While these innovations are often celebrated for their economy-boosting potential or ability to solve complex challenges, I fear we aren't critically examining their societal impacts down the line. We've become so enamored with the promise of emerging technologies that we've developed a dangerous case of ritual conformity.Take artificial intelligence as an example. While still in its infancy, AI has already begun to reshape entire industries through automation. From driving trucks to analyzing medical scans, AI can tackle cognitive tasks more efficiently than humans. Most concerning to me, however, is the AI artisan economy rapidly gaining steam. Advanced language models can now generate extremely convincing written and visual content withjust a simple prompt. As AI art floods the market, displacing human artists and thinkers, where does that leave individuality and creativity? A core part of being human is our capacity for original thought and self-expression. If we allow AI to automate that away, are we sacrificing a piece of our souls?Then there's the data mining and surveillance capitalism that has become symptomatic of the tech industry. Our every move online is tracked, quantified, and fed into inscrutable algorithms. All to more efficiently advertise to us and engineer addictive digital experiences that keep eyeballs glued to screens. I understand the commercial incentives driving this, but it feels like a fundamental violation of privacy and personal autonomy. How can we maintain free will when our behaviors and desires are constantly being nudged by faceless algorithms optimizing us into predictable consumption machines?My anxiety about the tech world doesn't stop there. I have serious concerns about the perpetuation of online misinformation and hate speech emboldened by the anonymity of the internet. The rise of state cyber warfare capabilities and weaponized misinformation is chilling. There are the potential climate implications of energy-intensive technologies like blockchain and cryptomining. The list goes on.Please don't mistake this critique as blind technophobia. I'm not advocating for descending back into the Stone Age. The benefits technological advancement has brought to medicine, transportation, energy production, and scientific exploration are indisputable. I'm simply arguing that we need to be more judicious about how we develop and implement new technologies moving forward. We can't let the intoxicating allure of novelty cloud our judgment about the ramifications.We need a new paradigm of ethical technology policy and development that places human and environmental welfare over the single-minded pursuit of innovation. We have to think critically about which technologies we allow to reshape our society and which we proactively stunt or abandon for the greater good. There needs to be a public body providing oversight, ensuring new technologies don't undermine core values like privacy, self-determination, and human agency before they're unleashed into the world.Perhaps most importantly, we need to techlash against technologies designed to erode our free will and independent cognition. We should be highly skeptical of models like thead-driven attention economy that trivialize us into mindless consumption automatons. We must reject AI systems thatcentralize the power of creative expression and unique thought. We can't let our humanity be incrementally diminished and reformatted into a digital capitalist hell przn run by extractive algorithms and unchecked corporate greed.I realize I'm asking for a drastic philosophical shift in how we develop and implement new technologies. But I truly believe tapping the brakes on unchecked technological zeal is crucial for our collective wellbeing and flourishing. My generation has inherited a perfect storm of compounding technological threats to our autonomy, provacy, and creative freedom. It's up to us to be stewards and protect the human soul from being optimized out of existence by the merciless efficiency god that is modern capitalism.Resist solutionism. Reject the quantification of human experience into data points. Be wary of any technology that turns you and your attention into an extractable product. Instead, we must cultivate an ethos of empowering technologies that enhance and celebrate our humanity rather than subjugating it. By all means, let's harness the staggering potential of exponential technological progress. But we need a new ethical framework to ensure we aren't casually trading away the essenceof our humanity in the blinding pursuit of innovation and economic growth.。

2024英语年份的表达

2024英语年份的表达The year 2024 will undoubtedly be remembered as a pivotal moment in history, marking the conclusion of a decade that saw significant changes and advancements in various fields. From scientific breakthroughs to cultural shifts, the world is poised to embrace a new era of possibilities and challenges.In the realm of technology, 2024 will be remembered as a year of remarkable advancements. The pace of innovation in areas like artificial intelligence, robotics, and quantum computing will continue to accelerate, leading to groundbreaking discoveries that reshape our understanding of technology and its impact on society.One of the most significant technological advancements expected in 2024 is the widespread adoption of 5G technology. This next-generation wireless network promises faster speeds, lower latency, and increased reliability, revolutionizing the way we connect and communicate. 5G willpave the way for a range of new applications, includingself-driving cars, remote healthcare, and smart cities, among others.Moreover, 2024 could witness the emergence of new technologies that blur the lines between the physical and digital worlds. Augmented reality (AR) and virtual reality (VR) are expected to become more immersive and accessible, enabling users to engage with digital content in a more natural and intuitive manner. This will have profound implications for industries like entertainment, education, and healthcare, among others.On the environmental front, 2024 will be remembered as a year of critical turning points. The urgent need to address climate change and environmental degradation will drive global efforts to transition to renewable energy sources and implement sustainable practices. Governments and businesses alike will be pressured to take bold action, and innovative solutions will be needed to balance economic growth with environmental protection.One of the most promising areas of research in this regard is the development of carbon capture and storage technologies. These technologies aim to capture carbon dioxide emissions from industrial processes and store them safely, preventing them from entering the atmosphere and contributing to climate change. While these technologiesare still in their early stages, they hold the potential to transform the way we approach emissions reduction and mitigate the impacts of climate change.Beyond technology and the environment, 2024 will alsobe remembered for its impact on global politics and society. The rise of populism and nationalism in some parts of the world will continue to shape political landscapes and international relations. This trend will challenge the establishment and traditional political institutions, leading to不确定性和 instability in some regions.However, 2024 could also see the emergence of new coalitions and partnerships that aim to promote global cooperation and address shared challenges. The need for collective action on issues like climate change, pandemicresponse, and economic recovery will encourage nations to work together in pursuit of common goals.In the realm of culture and entertainment, 2024 will be marked by a diverse array of trends and movements. The influence of digital media and social networking will continue to reshape popular culture, leading to the emergence of new art forms, music genres, and media platforms. The rise of streaming services and on-demand content will further democratize access to culture and entertainment, enabling people from all backgrounds to engage with a diverse range of content.Moreover, 2024 could see the continuation of movements that advocate for social justice and equality. The global pandemic of 2020-2021 brought to light the deep-seated inequalities that exist within societies, sparking a renewed focus on issues like racial discrimination, gender inequality, and economic disparity. This focus will continue to drive social and political change in the coming years, leading to increased awareness and action on these important issues.In conclusion, 2024 will be remembered as a year of significant advancements and challenges that shape the future of our world. From technological breakthroughs to environmental crises and political upheaval, the year will present us with both opportunities and obstacles. It is up to us to seize the opportunities, rise to the challenges, and create a better future for ourselves and the next generation.。

新的时代已经到来英语作文

新的时代已经到来英语作文Title: The Arrival of a New Era。

In the dawn of a new era, the world stands on the precipice of transformation. The rapid advancement of technology, the shifting geopolitical landscape, and the evolving social fabric herald the arrival of a paradigmshift unlike any before. As we navigate this uncharted territory, it becomes imperative to reflect on the implications, opportunities, and challenges that accompany such monumental change.One of the defining features of this new era is the unparalleled progression of technology. With breakthroughsin artificial intelligence, quantum computing, and biotechnology, the boundaries of human capability are constantly being pushed. Automation is reshaping industries, revolutionizing the way we work, and posing questions about the future of employment. The integration of technologyinto every aspect of our lives brings unprecedentedconvenience but also raises concerns about privacy, ethics, and the digital divide. As we embrace the promise of innovation, it is essential to ensure that technological advancement is accompanied by responsible stewardship and equitable access for all.Moreover, the geopolitical landscape is undergoing a profound transformation. The traditional power structures are being challenged by emerging global players, shifting alliances, and the rise of non-state actors. Issues such as climate change, pandemics, and economic inequality necessitate international cooperation and collective action. Yet, amidst this interconnectedness, nationalist sentiments and protectionist policies threaten to undermine global solidarity. Navigating this complex geopolitical terrain requires diplomacy, foresight, and a commitment to multilateralism in order to address shared challenges and foster sustainable development.In addition to technological and geopolitical shifts, the social fabric of society is also evolving. Demographic changes, cultural diversity, and evolving norms arereshaping the way we perceive identity, community, and belonging. Movements for social justice and equality are gaining momentum, demanding recognition, representation,and systemic change. However, entrenched prejudice, discrimination, and social inequalities continue to persist, highlighting the ongoing struggle for justice and inclusion. Embracing diversity, fostering empathy, and championing human rights are imperative as we strive to build a more inclusive and equitable society.Furthermore, the onset of this new era brings with it unprecedented opportunities for progress and prosperity. Advances in science and technology hold the potential to address pressing global challenges, from healthcare and education to environmental sustainability and renewable energy. The interconnectedness of the digital age allowsfor collaboration, innovation, and knowledge-sharing on a scale never before imagined. With the right policies, investments, and collective effort, we have the opportunity to create a future that is more just, sustainable, and prosperous for all.However, amidst these opportunities, we also face significant challenges and uncertainties. The rapid pace of change exacerbates existing inequalities, leaving behind those who are unable to adapt or access the benefits of progress. Disruptions caused by technological innovationand economic restructuring can lead to social upheaval and political instability if not managed effectively. Moreover, the existential threats posed by climate change, pandemics, and nuclear proliferation require urgent action and international cooperation to mitigate.In conclusion, the arrival of a new era heralds a timeof immense possibility and profound transformation. As we navigate the complexities of this changing world, it is essential to embrace innovation, foster cooperation, and uphold our shared humanity. By working together with vision, courage, and compassion, we can shape a future that is more inclusive, sustainable, and prosperous for generations to come.。

2023届上海市高三英语语法填空复习难题

2023届上海高三语法填空复习难题复附&华二联考（2022年11月）-语法填空Nobel Prize in Physics Is Awarded to 3 Scientists for Work in Quantum TechnologyThe Nobel Prize in Physics was awarded to Alain Aspect, John F. Clauser and Anton Zeilinger on T uesday for work that has “laid the foundation for a new era of technology,” the Nobel Committee for Physics said.The scientists have each conducted “experiments using quantum states, (21)____________ two behave like a single unit (22)___________ _________they are separated,” the committee said in a briefing. Their results, it said, for “new technology based upon quantum information.”The ’ research builds on the work of John Stewart Bell, a physicist who to the question of whether particles, (23)_____________ (flow) too far apart for there to be normal communication between them, (24)_____________still function .Eva Olsson, (25)___________ member of the Nobel Committee for Physics, noted that quantum information science had broad in areas like secure information transfer and quantum computing.Quantum information science is a “vibrant and rapidly developing field,”she said.”Its predictions have opened doors to another world,and it has also shaken the very foundation of (26)___________we interpret measurements.”The Nobel committee said the three scientists were being honored for their experiments with entangled photons(光子）, establishing the violation of Bell inequalities and pioneering quantum information science.“Being able to and manage quantum states and all their layers of properties (27)__________ (give) us access to tools with unexpected potential,” the committee said in a statement on Twitter.Dr. Zeilinger described the award as “ an encouragement to young people.”“The prize would not be possible (28)_____________more than 100 young people who worked with me over the years,”and made all this possible,” he said of the work that the award recognized. “My advice would be: Do what you find interesting, and don’t care too much about possible applications.”It was the second of several such prizes (29)_____________(award)over the coming week. The Nobels, among the highest honors in science, recognize groundbreaking contributions in a variety of fields.“I’m still kind of shocked, but it’s a very positive shock,” Dr. Zeilinger said of receiving the phone call (30)_____________(inform) him of the news.答案：21. where 22. even though/even if 23.having flown 24.can 25.a26.how 27.gives 28.without 29. to be awarded rming二、华师大二附中2022-2023学年高三英语测试-语法填空Sunscreen RecallThe burning heat of summer has us all reaching for sunscreens.But before you apply thatproduct to your skin,first to see if it is part of a voluntary recall by sunscreen brands Neutrogena and Aveeno.The companies recently pulled several sunscreens from market shelves after independenttesting had found they were contaminated (污染)with a cancer-chemical called benzene(苯).Benzene is a natural component of crude oil, gasoline and cigarette smoke. At room temperature, it is a colorless or light yellow liquid with a sweet odor.And while it evaporatesquickly, it is air and can sink into low-lying areas.“Exposureincreases the risk of developing leukemia and other blood disorders,” according to the National Cancer Institute.was not an ingredient in any of the sunscreens so experts suspect that contamination occurred during the manufacturing process.“It could be that some of those ingredient chemicals break down into benzene”said Scott Faber, the senior vice president of government affairs for the Environmental Working Group(EWG),But it’s very alarming,especially since the FDA does not require companies to testingredients for it require testing for such chemicals at a finished product stage.Consumers should stop using these specific products and appropriatelythrow them away. There is not a safe level of benzene that in sunscreen products.The vast majority of tested sunscreens, however,were free of benzene and experts stress theimportance of sunscreen use skin from the aging and cancerous effects of the sun.“It is not a reason to stop using sun protection, known to prevent skin cancer. To do so would be like hearing a particular car model was recalled and thento drive again,” dermatologist(皮肤病专家) Dr. Ranella Hirsch posted on Instagram.答案：21.check 22. causing 23. heavier 24. to 25.how26.nor 27. can 28. to protect 29.which 30.deciding三、向明中学高三月考Switzerland,15 September 2022 To my tennis family and beyond,Of all the gifts that tennis has given me over the years, the greatest, without a doubt, has been the people I’ve met along the way: my friends, my competitors, and most of all the fans who give the sport its life. Today, I want to share some news with all of you.As many of you know, the past three years present) me with challenges in the form of injuries and surgeries. I’ve worked hard to return to full competitive form. But I also know my body’s capacities and limits, and its message to me lately has been clear. I am 41 years old. I have played more than 1500 matches over 24 years. Tennis has treated me generously) than I ever would have dreamt, and now I must recognize when it is time to end my competitive career.The Laver Cup next week in London will be my final ATP event. I will play more tennis in the future, of course, but just not in Grand Slams or on the tour.This is a bittersweet decision, because I will miss everything the tour has given me. But at the same time, there is so much to celebrate. I consider myself one of the most fortunate people on Earth. I was given a special talent to play tennis, and I did it at a level that I never imagined, for much longer than I ever thought possible.I would like to especially thank my amazing wife Mirka, who has lived through every minute with me. She has warmed me up before finals, watch) countless matches even while over 8-months pregnant, and has endured my goofy side on the road with my team for over 20 years. I also want to thank my four wonderful children for supporting me, always eager to explorenew places and creating wonderful memories along the way. my family cheering me on from the stands is a feeling I will cherish forever.I would also like to thank and recognize my loving parents and my dear sister,withoutalways guided me in the right direction…you have been wonderful! And to Swiss Tennis, who believed in me as a young player and gave me an ideal start.I really want to thank and acknowledge my amazing team, Ivan, Dani, Roland, and particularly Seve and Pierre, who have given me the best advice and have always been there for me. Also Tony, for creatively managing my business for over 17 years. You are all incredible and I have loved every minute with you.I want to thank my loyal sponsors, who are really partners to me; and the hard-working teams and tournaments on the ATP Tour, who consistently welcomed all of us with kindness and hospitality.I would also like to thank my competitors on the court. I was lucky enough to play so many epic matches that I will never forget. We battled fairly, with passion and intensity, and I always tried my best to respect the history of the game. I feel extremely grateful. We pushed each other, and together we took tennis to new levels.Above all I offer a special thank you to my unbelievable fans. You will neverknow strength and belief you have given me. The inspiring feeling of walking into full stadiums and arenas has been one of the huge thrills in my life. Without you,those successes would have felt lonely, rather than filled with joy and energy.The last 24 years on tour have been an incredible adventure. While it sometimes feels like it went by in 24 hours, it has also been so deep and magical that it seems as if I’ve already lived a full lifetime. I have had the immense fortune to play in front of you in over 40 different countries.I have laughed and cried, felt joy and pain, and most of all I have felt incredibly alive. Through my travels, I have met many wonderful people who will remain friends for life, who consistently took time out of their busy schedules to come watch me play and cheer me on around the globe. Thank you.watch the players with a sense of wonder. They were like giants to me and I began to dream. My dreams led me to work harder and I started to believe in myself. Some success brought me confidence and I was on my way to the most amazing journey that has led to this day.So, I want to thank you all from the bottom of my heart, to everyone around the world whohas helped make the dreams of a young Swiss ball kidFinally, to the game of tennis: I love you and will never leave you.Roger Federer答案：21.have presented 22.more generously 23.watched 24.Seeing 25.without whom26.like 27.must 28.how much 29. When e。

能量子假设英文

能量子假设英文全文共四篇示例，供读者参考第一篇示例：Energy is the driving force behind all activities and processes in the universe. Modern physics has uncovered the intricate and complex nature of energy, revealing its various forms and interactions. One fascinating aspect of energy is the concept of quantum energy, which is based on the principles of quantum mechanics.第二篇示例：In the classical view of physics, energy was thought to be continuous and could take on any value. However, Planck's discovery that energy is quantized set the stage for the development of quantum theory and the subsequent advancement of modern physics.In conclusion, the energy quantization hypothesis has had a transformative impact on our understanding of the physical world and has paved the way for numerous advancements in physics and technology. By recognizing the discrete nature of energy and the fundamental role it plays in the behavior ofmatter and light, scientists have been able to unravel the mysteries of the quantum realm and push the boundaries of scientific knowledge. As we continue to explore the implications of energy quantization, we can expect to uncover even more profound insights into the nature of the universe and our place within it.第三篇示例：The idea of energy quanta, also known as energy packets or energy particles, is a fundamental concept in quantum physics. It is based on the concept that energy, like matter, can exist in discrete, indivisible units. In other words, energy is not continuous, but rather comes in specific amounts that cannot be divided any further. This idea was first proposed by a German physicist named Max Planck in the early 20th century.第四篇示例：The concept of energy quanta, also known as quantum of energy, is a fundamental principle in the field of physics that has revolutionized our understanding of the nature of energy and matter. In traditional physics, energy was thought to be continuous and infinitely divisible. However, the discovery of quantum mechanics in the early 20th century challenged thisbelief and introduced the idea that energy comes in discrete packets called quanta.。