Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers

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Quantum Mechanics

Quantum MechanicsQuantum mechanics is a fascinating and complex field of physics that has revolutionized our understanding of the universe at the smallest scales. At its core, quantum mechanics deals with the behavior of particles at the quantum level, where the classical laws of physics break down and give way to a whole new set of rules. This field has given rise to many groundbreaking theories and technologies, such as quantum computing and quantum cryptography, that have the potential to revolutionize the way we live and interact with the world around us. One of the key principles of quantum mechanics is the concept of superposition, which states that a particle can exist in multiple states simultaneously until it is observedor measured. This idea challenges our classical intuition, which tells us that an object can only be in one place or state at a time. The famous thought experiment known as Schr?dinger's cat illustrates this concept, where a cat in a box is both alive and dead until the box is opened and the cat is observed. This idea of superposition has profound implications for the nature of reality and has led to many thought-provoking philosophical debates about the nature of existence. Another important concept in quantum mechanics is entanglement, where twoparticles become interconnected in such a way that the state of one particle is directly linked to the state of the other, regardless of the distance between them. This phenomenon, famously referred to as "spooky action at a distance" by Albert Einstein, challenges our understanding of causality and suggests that particlescan communicate instantaneously with each other, defying the limitations of space and time. This idea has been experimentally verified through a series of groundbreaking experiments and has opened up new possibilities for quantum communication and teleportation. The implications of quantum mechanics extend far beyond the realm of theoretical physics and have the potential to revolutionize technology in ways we can only begin to imagine. Quantum computing, for example, harnesses the principles of superposition and entanglement to perform calculations at speeds that far surpass classical computers. This has the potential to revolutionize fields such as cryptography, drug discovery, and artificial intelligence, unlocking new possibilities for innovation and discovery. Similarly, quantum cryptography uses the principles of quantum mechanics to create securecommunication channels that are theoretically impossible to hack, offering a new level of security and privacy in an increasingly digital world. Despite the incredible potential of quantum mechanics, there are still many challenges and mysteries that remain to be solved. The field is notoriously complex and counterintuitive, with many of its fundamental principles defying our classical understanding of the world. This has led to many debates and disagreements among physicists about the true nature of quantum mechanics and how best to interpretits implications. The famous Copenhagen interpretation, for example, posits that particles exist in a state of superposition until they are observed, while the many-worlds interpretation suggests that every possible outcome of a quantum event actually occurs in a separate parallel universe. These differing interpretations highlight the deep philosophical questions that quantum mechanics raises about the nature of reality and our place in the universe. In conclusion, quantum mechanics is a field that continues to push the boundaries of our understanding of the universe and challenge our most deeply held beliefs about the nature of reality. Its principles of superposition, entanglement, and uncertainty have revolutionized our understanding of the quantum world and opened up new possibilities for technology and innovation. While there are still many mysteries and debates surrounding quantum mechanics, its potential to revolutionize fields such as computing, communication, and cryptography is undeniable. As we continue to explore the implications of quantum mechanics, we are sure to uncover even more profound insights into the nature of the universe and our place within it.。

海底两万里中物理学的句子

海底两万里中物理学的句子英文回答：Physics plays a significant role in Jules Verne's novel "Twenty Thousand Leagues Under the Sea." As the story follows the adventures of Professor Aronnax, Ned Land, and Conseil aboard the Nautilus, many instances highlight the application of physics principles.One example is the concept of buoyancy. The Nautilus, being a submarine, must maintain neutral buoyancy to navigate underwater. This is achieved by adjusting the amount of water in the ballast tanks. By controlling the density of the Nautilus, Captain Nemo ensures that the upward force exerted by the water equals the downward force of the submarine, allowing it to float at a desired depth. This demonstrates Archimedes' principle, which states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.Another physics concept explored in the novel is pressure. As the Nautilus dives deeper into the ocean, the pressure increases significantly. The characters experience this firsthand when they descend to great depths and feel the pressure on their bodies. This aligns with Pascal's principle, which states that pressure is transmitted uniformly in all directions in a fluid. The immense pressure at great depths is a result of the weight of the water above pressing down on the submarine.Furthermore, the novel touches upon the principles of electricity and magnetism. The Nautilus is powered by electricity, and Verne describes the use of electric motors to propel the submarine through the water. The concept of electromagnetism is also evident in the use of magnetic fields to navigate and detect underwater objects. These applications of physics showcase the integration of scientific knowledge into the fictional world of the Nautilus.中文回答：物理学在朱尔·凡尔纳的小说《海底两万里》中起着重要的作用。

Using a quantum computer to investigate quantum chaos

1 (p + 1) , if 2q − 1, 2
< q ≤ 1.
(1)
This corresponds to compressing the unit square in the p direction and stretching it in the q direction, while preserving the area, then cutting it vertically, and ﬁnally stacking the right part on top of the left part—in analogy to the way a baker kneads dough. To deﬁne the quantum baker’s map [10], we quantize the unit square following [11,24]. To represent the unit square in D -dimensional Hilbert space, we start with unitary “displaceˆ and V ˆ , which produce displacements in the “momentum” and “position” ment” operators U directions, respectively, and which obey the commutation relation [24] ˆV ˆ =V ˆU ˆǫ , U (2)
′ (FL )kj = pk |qj =
√
1 h 2π h ¯ e−ipk qj /¯ = √ e−2πikj/D . D
(4)
There is no unique way to quantize a classical map. Here we adopt the quantized baker’s map introduced by Balazs and Voros [10] and deﬁned by the matrix

用初中英语简要介绍双缝实验

用初中英语简要介绍双缝实验The Double-Slit ExperimentThe double-slit experiment is a fundamental experiment in quantum mechanics that demonstrates the wave-particle duality of light and other quantum particles. It was first performed by the English physicist Thomas Young in 1801, and it has since become one of the most famous experiments in the history of science.The basic setup of the double-slit experiment is as follows. A source of light, such as a laser or a monochromatic light source, is directed towards a barrier that has two narrow slits cut in it. The light passing through the slits is then projected onto a screen or a detector. When the light passes through the two slits, it creates an interference pattern on the screen, with alternating bright and dark regions.This interference pattern is a clear demonstration of the wave-like nature of light. If light were simply a stream of particles, one would expect to see two separate bright spots on the screen, corresponding to the two slits. However, the interference pattern shows that the light is behaving like a wave, with the waves from the two slits interfering with each other.The double-slit experiment can also be performed with other quantum particles, such as electrons or atoms. When these particles are directed towards the double slit, they also exhibit an interference pattern, indicating that they too have a wave-like nature.The wave-particle duality of quantum particles is a fundamental concept in quantum mechanics. It means that particles can exhibit both wave-like and particle-like properties, depending on the experiment being performed. This is a departure from the classical view of the world, where objects were either waves or particles, but not both.The double-slit experiment has been used to demonstrate the wave-particle duality of various quantum particles, including electrons, neutrons, atoms, and even large molecules. In each case, the interference pattern observed on the screen is a clear indication of the wave-like nature of the particles.One of the most interesting aspects of the double-slit experiment is the role of the observer. When the experiment is set up to detect which slit the particle goes through, the interference pattern disappears, and the particles behave like classical particles. This suggests that the act of measurement or observation can affect the behavior of quantum particles.This is a concept known as the "observer effect" in quantum mechanics, and it has profound implications for our understanding of the nature of reality. It suggests that the very act of observing or measuring a quantum system can alter its behavior, and that the observer is not a passive participant in the experiment.The double-slit experiment has also been used to explore the concept of quantum entanglement, which is another fundamental concept in quantum mechanics. Quantum entanglement occurs when two or more quantum particles become "entangled" with each other, such that the state of one particle is dependent on the state of the other.In the double-slit experiment, the interference pattern can be used to demonstrate the phenomenon of quantum entanglement. For example, if two particles are entangled and then directed towards the double slit, the interference pattern observed on the screen will depend on the state of the entangled particles.Overall, the double-slit experiment is a powerful and versatile tool for exploring the fundamental nature of reality at the quantum level. It has been used to demonstrate the wave-particle duality of light and other quantum particles, the observer effect, and the phenomenon of quantum entanglement. As such, it remains one ofthe most important and influential experiments in the history of science.。

有关量子力学的英语作文

有关量子力学的英语作文Quantum mechanics, a fundamental theory in physics, has been a subject of fascination and debate since its inception in the early 20th century. It describes the behavior of matter and energy at the smallest scales, where the classical laws of physics no longer apply. This essay aims to explore the key principles of quantum mechanics, its implications for our understanding of the universe, and the ongoing challenges it presents to scientists and philosophers alike.Firstly, the concept of wave-particle duality is central to quantum mechanics. This principle posits that all particles, such as electrons, can exhibit both wave-like and particle-like properties. This duality is demonstrated in the famous double-slit experiment, where particles create aninterference pattern when not observed, but act as discrete entities when measured. The act of observation, therefore, plays a critical role in determining the state of a quantum system.Secondly, the superposition principle is another cornerstone of quantum mechanics. It states that a quantum system can exist in multiple states simultaneously until it is measured. This is exemplified by the thought experiment known asSchrödinger's cat, where a cat in a sealed box is considered to be both alive and dead until the box is opened and thecat's state is observed.Entanglement, a phenomenon where particles become interconnected and the state of one instantaneously influences the state of another, regardless of the distance between them, is another intriguing aspect of quantum mechanics. This has led to the development of quantum computing, which promises to revolutionize information processing by performing calculations at speeds unattainable by classical computers.However, quantum mechanics also presents significant challenges. The interpretation of quantum theory is a subject of ongoing debate. The Copenhagen interpretation suggeststhat the act of measurement collapses the wave function, determining the outcome, while the many-worlds interpretation proposes that all possible outcomes of a quantum event exist in separate, non-interacting parallel universes.Moreover, the reconciliation of quantum mechanics with general relativity, the theory of gravity, remains an unsolved problem in physics. The two theories operate under fundamentally different principles, and finding a unified theory that encompasses both has been a holy grail for physicists.In conclusion, quantum mechanics has reshaped our understanding of the microscopic world and has profound implications for technology, philosophy, and the very fabric of reality. As research continues, it is likely that the mysteries of quantum mechanics will continue to inspire awe and provoke thought about the nature of existence itself.。

The QCD vacuum

a r X i v :h e p -l a t /9709066v 1 18 S e p 19971INLO-PUB-7/97The QCD vacuum ∗Pierre van BaalaaInstituut-Lorentz for Theoretical Physics,University of Leiden,PO Box 9506,NL-2300RA Leiden,The NetherlandsWe review issues involved in understanding the vacuum,long-distance and low-energy structure of non-Abelian gauge theories and QCD.The emphasis will be on the role played by instantons.1.INTRODUCTIONThe term “QCD vacuum”is frequently abused.Only in the case of the Hamiltonian formulation is it clear what we mean by the vacuum:it is the wave functional associated with the lowest energy state.Observables create excitations on top of this vacuum.Knowing the vacuum is knowing all:We should know better.Strictly speaking the vacuum is empty.Nev-ertheless its wave functional can be highly non-trivial,deviating considerably from that of a non-interacting Fock space,based on a quadratic the-ory.Even in the later case the result of probing the vacuum by boundaries is non-trivial as we know from Casimir.The probe is essential:one needs to disturb the vacuum to study its prop-erties.Somewhat perversely the vacuum may be seen as a relativistic aether.It promises to mag-ically resolve our problems,from conﬁnement to the cosmological constant.For the latter super-symmetry is often called for to remove the other-wise required ﬁne-tuning.It merely hides the rel-ativistic aether,even giving it further structure.Remarkably it seems to have enough structure to give a non-trivial example of the dual supercon-ductor at work [1].Most will indeed put their bet on the dual su-perconductor picture for the QCD vacuum [2],and this has motivated the hunt for magnetic monopoles using lattice techniques,long before supersymmetric duality stole the show [1].The deﬁnitions rely on choosing an abelian projec-tion [3]and the evidence is based on the no-tion of abelian dominance [4],establishing the dual Meissner eﬀect [5],or the construction of22.V ACUUM DEMOCRACYThe model we wish to describe here starts from the physics in a small volume,where asymptotic freedom guarantees that perturbative results are valid.The assumption is made,that at least for low-energy observables,integrating out the high-energy degrees of freedom is well-deﬁned pertur-batively and all the non-perturbative dynamics is due to a few low-lying modes.This is most easily deﬁned in a Hamiltonian setting,since we are in-terested in situations where the non-perturbative eﬀects are no longer described by semiclassical methods.plete gaugeﬁxingDue to the action of the gauge group on the vectorﬁelds,aﬁnite dimensional slice through the physical conﬁguration space(gauge inequivalent ﬁelds)is bounded.One way to demonstrate this is by using the complete Coulomb gaugeﬁxing, achieved by minimising the L2norm of the gauge ﬁeld along the gauge orbit.At small energies,ﬁelds are suﬃciently smooth for this to be well deﬁned and it can be shown that the space under consideration has a boundary,deﬁned by points where the norm is degenerate.These are by deﬁ-nition gauge equivalent such that the wave func-tionals are equal,possibly up to a phase factor in case the gauge transformation is homotopically non-trivial.The space thus obtained is called a fundamental domain.For a review see ref.[10].2.2.Non-perturbative dynamicsGiven a particular compact three dimensional manifold M on which the gauge theory is deﬁned, scaling with a factor L allows one to go to larger volumes.It is most convenient to formulate the Hamiltonian in scale invariantﬁeldsˆA=LA.Di-viding energies by L recovers the L dependence in the classical case,but the need of an ultraviolet cutoﬀand the resulting scale anomaly introduces a running coupling constant g(L),which in the low-energy eﬀective theory is the only remnant of the breaking of scale invariance.When the volume is very small,the eﬀective coupling is very small and the wave functional is highly localised,staying away from the bound-aries of the fundamental domain.We may com-pare with quantum mechanics on the circle,seen as an interval with identiﬁcations at its bound-ary.At which points we choose these boundaries is just a matter of(technical)convenience.The fact that the circle has non-trivial homotopy,al-lows one to introduce aθparameter(playing the role of a Bloch momentum).Expressed inˆA,the shape of the fundamental domain and the nature of the boundary condi-tions,is independent of L.Due to the rise of the running coupling constant with increasing L the wave functional spreads out over the fundamental domain and will start to feel the boundary iden-tiﬁcations.This is the origin of non-perturbative dynamics in the low-energy sector of the theory. Quite remarkably,in all known examples(for the torus and sphere geometries),the sphalerons lie exactly at the boundary of the fundamental domain,with the sphaleron mapped into the anti-sphaleron by a homotopically non-trivial gauge transformation.The sphaleron is the saddle point at the top of the barrier reached along the tun-nelling path associated with the largest instanton, its size limited by theﬁnite volume.For increasing volumes the wave functionalﬁrst starts to feel the boundary identiﬁcations at these sphalerons,“biting its own tail”.When the en-ergy of the state under consideration becomes of the order of the energy of this sphaleron,one can no longer use the semiclassical approximation to describe the transition over the barrier and it is only at this moment that the shift in energy be-comes appreciable and causes sizeable deviations from the perturbative result.This is in particular true for the groundstate energy.Excited states feel these boundary identiﬁcations at somewhat smaller volumes,but nodes in their wave func-tional near the sphaleron can reduce or postpone the inﬂuence of boundary identiﬁcations.This has been observed clearly for SU(2)on a sphere[11].The scalar and tensor glueball mass is reduced considerably due to the boundary identi-ﬁcations,whereas the oddball remains unaﬀected (seeﬁg.1).These non-perturbative eﬀects re-move an unphysical near-degeneracy in perturba-tion theory(with the pseudoscalar even slightly lower than the scalar glueball mass).The dom-inating conﬁgurations involved are associated to3instantonﬁelds,in a situation where semiclassical techniques are inappropriate for computing the magnitude of the eﬀect.When boundary identi-ﬁcations matter,the path integral receives large contributions from conﬁgurations that have non-zero topological charge,and in whose background the fermions have a chiral zero mode,its conse-quences to be discussed later.fFigure1.The low-lying glueball spectrum on a sphere of radius R as a function of f=g2(R)/2π2 atθ=0.Approximately,f=0.28corresponds to a circumference of1.3fm.From ref.[11].At some point technical control is lost,since so far only the appropriate boundary conditions near the sphalerons can be implemented.As soon as the wave functional starts to become apprecia-ble near the rest of the boundary too,this is no longer suﬃcient.This method has in particular been very suc-cessful to determine the low-lying spectrum on the torus in intermediate volumes,where for SU(2)agreement with the lattice Monte Carlo re-sults has been achieved within the2%statistical errors[10,12].In this case the non-perturbative sector of the theory was dominated by the en-ergy of electricﬂux(torelon mass),which van-ishes to all orders in perturbation theory.The leading semiclassical result is exp(−S0/g(L)),due to tunnelling through a quantum induced barrier of height E s=3.21/L and action S0=12.5.Al-ready beyond0.1fm this approximation breaks down.Oneﬁnds,accidentally in these small vol-umes,the energy to be nearly linear in L.The eﬀective Hamiltonian in the zero-momen-tum gaugeﬁelds,derived by L¨u scher[13],and later augmented by boundary identiﬁcations to include the non-perturbative eﬀects[12],breaks down at the point where boundary identiﬁca-tions in the non-zero momentum directions as-sociated with instantons become relevant.The sphaleron has an energy72.605/(Lg2(L))and was constructed numerically[14].Its eﬀect be-comes noticeable beyond volumes of approxi-mately(0.75fm)3.For SU(3)this was veriﬁed directly in a lattice Monte Carlo calculation of theﬁnite volume topological susceptibility[15]. The results for the sphere have shown that also these eﬀects can in principle be included reliably, but the lack of an analytic instanton solution on T3×I R has prevented us from doing so in practise.2.3.Domain formationThe shape of the fundamental domain depends on the geometry.Assuming that g(L)keeps on growing with increasing L,causing the wave func-tional to feel more and more of the boundary,one would naturally predict that the inﬁnite volume limit depends on the geometry.This is clearly unacceptable,but can be avoided if the ground state obtained by adiabatically increasing L is not stable.Thus we conjecture that the vacuum is unstable against domain formation.This is the minimal scenario to make sure that at large vol-umes,the spectrum is independent of its geome-try.Domains would naturally explain why a non-perturbative physical length scale is generated in QCD,beyond which the coupling constant will stop running.However,we have no guess for the order parameter,let alone an eﬀective theory de-scribing excitations at distances beyond these do-mains.Postulating their existence,nevertheless a number of interesting conclusions can be drawn. The best geometry to study domain formation is that of a box since it is space-ﬁlling.We can exactlyﬁll a larger box by smaller ones.This is not true for most other geometries.In small to intermediate volumes the vacuum energy density is a decreasing function[12]of L,but in analogy to the double well problem one may expect that at stronger coupling the vacuum energy density rises again with a minimum at some value L0, assumed to be0.75fm.For L suﬃciently larger than L0it thus becomes energetically favourable to split the volume in domains of size L30.Since the ratio of the string tension to the4scalar glueball mass squared shows no structure around(0.75fm)3,we may assume that both have reached their large volume value within a domain. The nature of theirﬁnite size corrections is suﬃ-ciently diﬀerent to expect these not to cancel ac-cidentally.The colour electric string arises from the fact thatﬂux that enters the box has to leave it in the opposite direction.Flux conservation with these building blocks automatically leads to a string picture,with a string tension as com-puted within a single domain and a transverse size of the string equal to the average size of a domain,0.75fm.The tensor glueball in an in-termediate volume is heavily split between the doublet(E+)and triplet(T+2)representations of the cubic group,with resp.0.9and1.7times the scalar glueball mass.This implies that the tensor glueball is at least as large as the average size of a domain.Rotational invariance in a domain-like vacuum comes about by averaging over all orien-tations of the domains.This is expected to lead to a mass which is the multiplicity weighted average of the doublet and triplet,yielding a mass of1.4 times the scalar glueball mass.Domain formation in this picture is driven by the largeﬁeld dynam-ics associated with sphalerons.Which state gets aﬀected most depends in an intricate way on the behaviour of the wave functionals(cmp.ﬁg.1). In the four dimensional euclidean context,O(4) invariance makes us assume that domain forma-tion extends in all four directions.As is implied by averaging over orientations,domains will not neatly stack.There will be dislocations which most naturally are gauge dislocations.A point-like gauge dislocation in four dimensions is an in-stanton,lines give rise to monopoles and surfaces to vortices.In the latter two cases most natu-rally of the Z N type.We estimate the density of these objects to be one per average domain size. We thus predict an instanton density of3.2fm−4, with an average size of1/3fm.For monopoles we predict a density of2.4fm−3.If an eﬀective colour scalarﬁeld will play the role of a Higgsﬁeld,abelian projected monopoles will appear.It can be shown[16]that a monopole (or rather dyon)loop,with its U(1)phase rotat-ing Q times along the loop(generating an elec-tricﬁeld),gives rise to a topological charge Q.In abelian projection it has been found that an instanton always contains a dyon loop[17].We thus argue this result to be more general,leading to further ties between monopoles and instantons.2.4.Regularisation andθIt is useful to point out that the non-trivial ho-motopy of the physical conﬁguration space,like non-contractable loops associated to the instan-tons(π1(A/G)=π3(G)=Z Z),is typically de-stroyed by the regularisation of the theory.This is best illustrated by the example of quantum me-chanics on the circle.Suppose we replace it by an annulus.As long as the annulus does notﬁll the hole,or we force the wave function to vanish in the middle,theta is a well-deﬁned parameter associated to a multivalued wave function.We may imagine the behaviour for small instantons in gauge theories to be similar to that at the cen-ter in the above model.Indeed,the gauge in-variant geodesic length of the tunnelling path for instantons on M×I R,given byℓ= ∞−∞dt4) 2)), with the instanton size deﬁned byρ≡(1+b2)−15ter by mixing the electricﬁeld withθtimes themagneticﬁeld,E→E−θB/(2π)2.In these ap-proaches theta is simply a parameter added to the theory.Whether or not one will retrieve the ex-pected periodic behaviour in the continuum limit becomes a dynamical question.It should be pointed out that in particular forSU(N)gauge theories in a box(in sectors with non-trivial magneticﬂux)there is room to arguefor a2πN,as opposed to a2π,periodicity fortheθdependence.However,the spectrum is pe-riodic with a period2π,and the apparent dis-crepancy is resolved by observing that there is a non-trivial spectralﬂow[19].This may lead tophase transitions at some value(s)ofθ,relatedto the oblique conﬁnement mechanism[3].Sim-ilarly for supersymmetric gauge theories this in-terpretation,supported by the recent discoveryof domain walls between diﬀerent vacua[20],re-moves the need for semiclassical objects with acharge1/N.Such solutions do exist for the torus, but the fractional charge is related to magneticﬂux and the interpretation is necessarily as statedabove!The“wrong”periodicity in theta has long been used to argue against the relevance of in-stantons,but in the more recent literature this isnow phrased more cautiously[21,22].3.INSTANTONSInstantons are euclidean solutions responsiblefor the axial anomaly,breaking the U A(1)sub-group of the U(N f)×U(N f)chiral symmetry for N fﬂavours of massless fermions[23],as dictatedby the anomaly, f∂µ¯Ψfγµγ5Ψf(x)=2N f q(x). The breaking of U A(1)manifests itself in thesemiclassical computations through the presenceof fermion zero modes,with their number and chiralityﬁxed by the topological charge,through the Atiyah-Singer index theorem[24].Integra-tion over the fermion zero modes leads to the so-called’t Hooft vertex or eﬀective interaction[23]. The integration over the scale parameter of the instanton ensemble is infrared dominated and a non-perturbative computation is desirable.In addition it is believed that the instantons are responsible for chiral symmetry breaking,where a chiral condensate is formed,which breaks the axial gauge group U A(N f)completely.This spon-taneous breaking is dynamical and it is less well established that instantons are fully responsible.It is the basis of the instanton liquid model as developed by Shuryak over the years.For a com-prehensive recent review see ref.[9].The details of the instanton ensemble play an important role. Only a liquid-like phase,as opposed to the di-lute or crystalline phases,will give rise to a chiral condensate.The model also makes a prediction for the average size and the topological suscep-tibility.In particular the latter quantity should be well-deﬁned beyond a semiclassical approxima-tion.For large sizes the instanton distribution is exponentially cut-oﬀand instantons do not give rise to an area law for the Wilson loop.Whenlarge instantons are more weakly suppressed the situation may diﬀer[25],but a semiclassical anal-ysis in this case should not be trusted. Remarkably the topological susceptibility in pure gauge theories can be related to theη′mass through the so-called Witten-Veneziano relation,f2π(m2η+m2η′−2m2K)/2N f= d4x<T(q(x)q(0))>R ≡χt,leading to the predictionχt∼(180MeV)4. This is based on the fact that the U A(1)symme-try is restored in the planar limit[26,27],withχt of order1/N2.From the requirement that in the presence of massless quarksχt(and the thetadependence)disappears,the pure gauge suscep-tibility can be related to the quark-loop contri-butions in the pseudoscalar channel.Pole dom-inance requires the lightest pseudoscalar meson to have a mass squared of order1/N.Relating the residue to the pion decay constant gives the desired result[27].The index R indicates the ne-cessity of equal-time regularisation[26].A deriva-tion on the lattice using Wilson and staggered fermions was obtained in ref.[28],making use of Ward-Takahashi identities.Finally,also the coarse grained partition function of the instan-ton liquid model[9]allows one to directly deter-mine the’t Hooft eﬀective Lagrangian[23],from which the Witten-Veneziano formula can be read oﬀ[29].This formula is almost treated as the holy grail of instanton physics.It is important to realise that some approximations are involved, although it is gratifying there are three indepen-dent ways to obtain it[26,27,28,29].63.1.Field theoretic methodA direct computation ofχt= d4x<q(x)q(0)> on the lattice requires a choice of discretisation for the charge density.A particularly simple one is[30]q L(x)=− T r(Uµν(x)˜Uµν(x))/16π2, where Uµν(x)=17 cutoﬀbreaks the scale and rotational invariance,we would expect that the action is no longer con-stant on the continuum moduli space.Indeed,fora smooth instanton the Wilson action behaves asS W(ˆρ≡ρ/a)=8π2(1−ˆρ−2/5+O(ˆρ−4))and causesthe instanton to shrink,until it becomes of thesize of the cutoﬀand falls through the lattice.Cooling willﬁrst remove high-frequency modesand one is left with a slow motion along the mod-uli space,giving rise to a plateau in the coolinghistory,used to identify the topological charge.One will miss instantons smaller than someﬁxedvalueˆρc.Assuming asymptotic freedom,one eas-ily shows that the error vanishes in the contin-uum limit.Note that by construction,the coolingmethod never will associate charge to a disloca-tion with an action smaller than96π2/11N,theentropic bound,which would spoil scaling[36].For extracting the size distribution,cooling andunder-relaxed(or slow)cooling[37]is problematicas the size clearly will depend on where alongthe plateau one analyses the data[38].The sizedistribution can be made to scale properly onlyat the expense of carefully adjusts the number ofcooling steps[39]when going to diﬀerentβ.One can avoid loosing instantons under coolingby modifying the action such that the scaling vio-lations change sign[35],for example by adding a2×2plaquette to the Wilson action.This so-calledover-improved action has the property that in-stantons grow under cooling,until stopped by theﬁnite volume.Consequently it would still muti-late the size distribution.This can be avoided byimproving the action so as to minimise the scalingviolations[40].A particularly eﬃcient choice isthe so-calledﬁve-loop improved(5Li)lattice ac-tion:S5Li= m,n c m,n x,µνTr(1−P mµ,nν(x)),where P mµ,nν(x)is the m×n plaquette andc1,1=65720,c1,2=−890andc3,3=18bining results forβ=2.4(averaged over the diﬀer-ent lattice types and boundary conditions after20 cooling sweeps)and forβ=2.6(after50cooling sweeps).The solid curve is aﬁt to the formula P(ρ)∝ρ7/3exp(−(ρ/w)p),with w=0.47(9)fm and p=3(1),which atsmall sizes coincides withthe semiclassical result[23].The peak of this dis-tribution occurs atρ=0.43(5)fm.Under pro-longed cooling,up to300sweeps,I-A instantonannihilations and in particularﬁnite size eﬀectsin the charge one sector do aﬀect the distribu-tion somewhat,but not the average size,whichtherefore seems to be quite a robust result.Figure3.SU(2)instanton size distribution forβ=2.4(squares)and2.6(crosses)in a volume1.44fm across at lattice spacings a=0.12and0.06fm.The dotted and dashed lines representthe cutoﬀat aˆρc for both lattices.From ref.[40].It would be advantageous if one could come upwith a deﬁnition for the size that is related to aphysical quantity,since now the notion is basedon the semiclassical picture.This is neverthe-less appropriate for the comparison with the in-stanton liquid.The relatively large value of theaverage size as compared to that of1/3fm pre-dicted by the instanton liquid[9]is a point ofworry,typically leading to stronger interactionsthat may lead to a crystal(without chiral sym-metry breaking),rather than a liquid.Neverthe-less,in ref.[40]it has been tested that the pseu-doparticles are homogeneously distributed with adensity of2−3fm−4and occupying nearly halfthe volume.This is the case when only close I-Apairs have annihilated and therefore depends onthe amount of improved cooling.It does,how-ever,show that the pseudoparticles are relativelydense(more so than assumed in the instanton liq-uid[9]).The value of3.2fm−4for the density,de-rived earlier in the context of the domain pictureis quite realistic in the light of these results.3.3.SmoothingAnother method to study instantons on thelattice is based on the classicalﬁxed point ac-tions[41],deﬁned through the saddle point equa-tion S F P(V)=min{U}(S F P(U)+κT(U,V)).It isobtained as the weak coupling limit of the block-ing transformation with a positive deﬁnite ker-nelκT(U,V),which maps a lattice{U}to{V},coarser by a factor two.Reconstructing theﬁnefrom the coarse lattice is called inverse blocking.It can be shown to map a solution of the latticeequations of motion to a solution on theﬁner lat-tice with the same action.Iterating the inverseblocking,the lattice can be made arbitrarilyﬁne,thereby proving the absence of scaling violationsto any power in the lattice spacing[41].Thisclassically perfect action still looses instantons be-low a critical size,which is typically smaller thana lattice spacing.For solutions this most likelyhappens at the point where the continuum inter-polation of the latticeﬁeld is ambiguous,causingthe integer geometric charge[42]to jump.Forrough conﬁgurations that are not solutions,in-verse blocking typically reduces the action by afactor32and makes it more smooth.Theﬁxedpoint topological charge is deﬁned as the limit-ing charge after repeated inverse blockings.Thisguarantees no charge will be associated to disloca-tions(of any action below the instanton action).The classicalﬁxed point action,although op-timised to be short range,still has an inﬁnitenumber of terms andﬁnding a suitable trunca-tion is a practical problem.From examples ofparametrisations,the success of reducing scalingviolations in quantities like the heavy quark po-tential(tested by restoring rotational invariance)is evident,for recent reviews see ref.[45].In prac-tise only a limited number of inverse blockings isfeasible and theﬁxed point topological charge hasto rely on a rapid convergence.The closer one isable to construct theﬁxed point action the bet-9ter this convergence is expected to be.For two di-mensional non-linear sigma models suﬃcient con-trol was achieved to demonstrate that more than one inverse blockingdid not appreciably change the topological charge [43].In four dimensional gauge theories,both ﬁnd-ing a manageable parametrisation and doing re-peated inverse blockings is a major eﬀort.It goes without saying that if no good approximation to the ﬁxed point action is used,one cannot rely on its powerful theoretical properties.Studies of in-stantons for SU (2)gauge theories were performed in ref.[44].A 48term approximation to the ﬁxed point action was used to verify the theoretical properties.The geometric charge was measured after one inverse blocking and it was shown that for Q =1the instanton action was to within a few percent from the continuum action (slightly above it due to ﬁnite size eﬀects),whereas for Q =0the action was always lower.Subsequently a simpliﬁed eight parameter form was used on which the instanton action was somewhat poorly reproduced,but such that the Q =1boundary stayed above the entropic bound for the action.A value of χt =(235(10)MeV)4was quoted on a 84lattice with physical volumes of up to 1.6fm,taking full advantage of the fact that ﬁxed point actions can be simulated at rather large lat-tice spacings.However,<Q 2>measured on the coarse lattice was up to a factor 4larger than on the ﬁne lattice (for the two dimensional study much closer agreement was seen [43]).Further inverse blocking to check stability of the charge measurement was not performed.The same eight parameter action was used in ref.[46],but they did their simulations on the ﬁne lattice and performed an operation called smoothing:ﬁrst blocking and then inverse block-ing.They changed the proportionality factor κin the blocking kernel,requiring that the saddle point condition is satisﬁed for the blocked lat-tice.Due to the change of κthe properties of the ﬁxed point action that inspired these authors can unfortunately no longer be called upon as a justiﬁcation.This smoothing satisﬁes the prop-erties of cooling (the action always decreases and stays ﬁxed for a solution)and should probably by judged as such.(See for further comments be-low.)They consider their study exploratory and concentrate on ﬁnite temperature near and be-yond the deconﬁnement transition.In ref.[47]the number of terms to parametrise the ﬁxed point action was extended to four powers of resp.the plaquette,a six-link and an eight-link Wilson loop.The latter was required to improve on the properties for the classical solutions.They achieved ˆρc =0.94,still considerably smaller than for S 5Li ,and reproduced the continuum instan-ton action to a few percent for ρ>ρc .To increase the quality of the ﬁt a constant was added,which should vanish in the continuum limit (as it drops out of the saddle point equation).Possible rami-ﬁcations of this at ﬁnite coupling are not yet suf-ﬁciently understood.After one inverse blocking insuﬃcient smooth-ing is achieved to extract the pseudoparticle po-sitions and sizes and further inverse blocking was considered computationally too expensive.Like in ref.[46],they also introduced a smoothing cy-cle,but now by blocking the ﬁne lattice back to the coarse one.Such a cycle would not change the action when the blocking is indeed to the same coarse lattice.However,there are 24diﬀerent coarse sublattices associated to a ﬁne one and in ref.[47]the smoothing cycle involved blocking to the coarse lattice shifted along the diagonal over one lattice spacing on the ﬁne lattice.Unlike in ref.[46],the smoothing cycle will be repeated.Figure 4.Example of the smoothing after 1and 9cycles,shown on the ﬁne lattice.From ref.[47].Although the ﬁxed point nature of the action guarantees it is close to a perfect classical action it needs to be demonstrated that it preserves the topological charge at suﬃciently large scales.For cooling this is argued from the local nature of the updates,not aﬀecting the long distance be-haviour.Improved cooling is in this sense less。

量子力学英文读物

量子力学英文读物以下是一些关于量子力学的英文读物推荐：1. "Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality" by Manjit Kumar2. "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory" by Brian Greene3. "The Quantum World: Quantum Physics for Everyone" by Kenneth W. Ford4. "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili5. "Quantum Physics: A Beginner's Guide" by Alastair Rae6. "Quantum Computing for Computer Scientists" by Noson S. Yanofsky and Mirco A. Mannucci7. "Quantum Physics for Babies" by Chris Ferrie (a simplified introduction for children and adults)8. "The Strange World of Quantum Mechanics" by Daniel F. Styer这些书籍从不同的角度介绍了量子力学的基本原理、应用、历史以及相关的思想争论。

根据你的兴趣和程度，选择适合你的读物开始探索量子世界吧！。

关于量子物理的科普书

关于量子物理的科普书English Answer：Quantum physics is a branch of physics that studies the behavior of matter at the atomic and subatomic level. It is one of the most important and successful scientific theories ever developed, and it has had a profound impact on our understanding of the universe.One of the most important concepts in quantum physics is the wave-particle duality of matter. This means that matter can behave like both a wave and a particle, depending on the experiment being performed. For example, light can act like a wave when it is diffracted through a narrow slit, but it can also act like a particle when it interacts with matter.Another important concept in quantum physics is the uncertainty principle. This principle states that it is impossible to know both the position and momentum of aparticle with perfect accuracy. The more precisely you know one variable, the less precisely you can know the other.Quantum physics has many applications in the real world. For example, it is used in the development of lasers, transistors, and other electronic devices. It is also usedin the study of nuclear physics and particle physics.There are many popular science books that can help youto learn more about quantum physics. Some of the best books include:"Quantum Mechanics: A Graduate Text" by DavidGriffiths."Quantum Mechanics for Mathematicians" by James Glimm and Arthur Jaffe."The Quantum Universe" by Brian Greene."Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality" by Manjit Kumar."The Fabric of Reality" by David Deutsch.中文回答：量子物理学是研究原子和亚原子层面物质行为的物理学分支。

湍流燃烧模型

Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 2. Balance equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
194
D. Veynante, L. Vervisch / Progress in Energy and Combustion Science 28 (2002) 193±266
6. Tools for turbulent combustion modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.2. Scalar dissipation rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 6.3. Geometrical description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 6.3.1. G-®eld equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 6.3.2. Flame surface density description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.3.3. Flame wrinkling description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.4. Statistical approaches: probability density function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.4.2. Presumed probability density functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 6.4.3. Pdf balance equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 6.4.4. Joint velocity/concentrations pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 6.4.5. Conditional moment closure (CMC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 6.5. Similarities and links between the tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

科学的而非想象的论述英语作文

科学的而非想象的论述英语作文Scientific Argumentation, Not Speculation: A Critique of Pseudoscience.In the realm of human knowledge, the pursuit of truth and understanding has long been a fundamental endeavor. Science, as a systematic and rigorous methodology, has emerged as the most reliable and effective approach to unraveling the complexities of the natural world. However, alongside the advancements of scientific inquiry, a persistent shadow lingers—pseudoscience, a deceptive and often harmful imitation of scientific practice.Pseudoscience manifests in various forms, but its defining characteristic lies in its reliance on unsubstantiated claims, anecdotal evidence, and a disregard for the fundamental principles of scientific investigation. Unlike science, which is characterized by empirical observation, hypothesis testing, and rigorous peer review, pseudoscience often resorts to sensationalism, confirmationbias, and appeals to emotion or authority.One of the most insidious aspects of pseudoscience isits ability to mimic the trappings of legitimate scientific inquiry. Practitioners may employ scientific jargon, invoke technical-sounding terminology, and even conductsuperficial experiments that appear to support their claims. However, closer scrutiny invariably reveals fundamental flaws—a lack of methodological rigor, a selective interpretation of data, or a reliance on unverified sources.The allure of pseudoscience stems from its appeal toour inherent desire for certainty and simplicity. In an uncertain world, pseudoscientific claims offer easy answers, promising to unlock secrets and solve complex problems. Yet, these claims are often nothing more than empty promises, leading to wasted resources, misguided beliefs, and potentially dangerous consequences.Anti-vaccine sentiments, for example, represent a prime example of the harmful effects of pseudoscience. Fueled by unfounded fears and misinformation, the anti-vaccinemovement has spread distrust in legitimate scientific research, leading to outbreaks of preventable diseases and putting vulnerable populations at risk.Another instance of pseudoscience is the promotion of alternative medicine practices that lack a sound scientific basis. While some alternative therapies may have beneficial effects, the efficacy and safety of many are unproven or even contradicted by scientific evidence. Uncritical acceptance of these practices can delay or interfere with conventional medical treatment, potentially compromising patients' health and well-being.The proliferation of pseudoscience is not merely an academic concern. It has significant implications for public policy, education, and the overall health of our society. When pseudoscientific claims gain traction in the public discourse, they can undermine trust in science and erode the very foundations of evidence-based decision-making.Combating pseudoscience requires a multi-prongedapproach. Firstly, it is essential to promote scientific literacy and critical thinking skills throughout the educational system. Students must be equipped with thetools to discern between credible scientific information and pseudoscientific claims.Secondly, scientists and educators have aresponsibility to actively engage with the public, debunking pseudoscientific myths and promoting a nuanced understanding of scientific principles. Scientific outreach programs, public lectures, and media campaigns can help bridge the gap between the scientific community and society at large.Furthermore, it is crucial to strengthen scientific integrity and uphold the highest ethical standards within the research community. Misconduct, conflicts of interest, and the publication of questionable findings can erode public trust in science and create fertile ground for pseudoscience to flourish.In conclusion, pseudoscience poses a serious threat tothe pursuit of knowledge and the well-being of our society. It is not merely a harmless indulgence but a deceptive and potentially harmful practice that undermines the very principles of scientific inquiry. By promoting scientific literacy, supporting evidence-based decision-making, and strengthening scientific integrity, we can foster a society where reason and evidence, not speculation and wishful thinking, guide our understanding of the world.。

新发展大学英语阅读与写作3课文翻译What Is a Scientific Theory 什么是科学理论

What Is a Scientific Theory?In order to talk the mature of the universe and to discuss questions such as whether it has a beginning or an end, you have to be clear about what a scientific theory is. I shall take the simple-minded view that a a theory is just a model of the universe, of a restricted part of it, and a set of rules that relate quantities in the model to observations that we make, It exists only in our minds an does not have any other reality (whatever that night mean). A theory is a good theory if it satisfies two requirements: It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations. For exampl e, Aristotle’s theory that everything was made out of four elements, earth, air, fire, and water, was simple enough to qualify, but it did not make any definite predictions. On the other hand, Newton’s theory was proportional to a quantity called their mass and inversely proportional to the square of the distance between them. Yet it predicts the motions of the sun, the moon, and the planets to a high degree of accuracy.Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments, agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory. As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation. Each time new experiments are observed to agree with the predictions the theory survives, and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory. At least that is what is supposed to happen, but you can always question the competence of the person who carried out the observation.In practice, what often happens is that a new theory is devised that is really an extension of the previous theory. For example, very accurate observations of the planet Mercury revealed a small difference between its motion and the predictions of Newton’s theory of gravity. Einstein’s general theory of relativity predicted a slightly different motion from Newton’s theory. The fact that Einstein’s predictions matched what was seen, while Newton’s did not, was one of the crucial confirmations of the new theory. However, we still use Newton’s theory for all practical purposes because the difference between its predictions and those of general relativity is very small in the situations that we normally deal with. (Newton’s theory also has the great advantage that it is much simpler to work with than Einstein’s!)The eventual goal of science is to provide a single theory that describes the whole universe. However, the approach most scientists actually follow is to separate the problem into two parts. First, there are the laws that tell us how the universe changes with time. (If we know what the universe is like at any one time, these physical laws tell us how it will look at any later time.) Second, there is the question of the initial state of the universe. Some people feel that science should be concerned with only the first part; they regard the question of the initial situation as a matter for meta-physics of religion. They would say that God, being omnipotent, could have made it develop in a company way he wanted. That may be so, but in that case he also could have made it develop in a completely arbitrary way. Yet it appears that he chose to make it evolve in a very regular way according to certain laws. It therefore seems equally reasonable to suppose that there are also laws governing the initial state.It turns out to be very difficult to device a theory to describe the universe all in one go. Instead, we break the problem up into bits and invent a number of partial theories. Each of these partial theories describes and predicts a certain limited class of observations, neglecting the effects of other quantities, or representing them by simple sets of numbers. It may be that this approach is completely wrong. If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution by investigating parts of the past. The classic example again is the Newtonian theory of gravity, which tells us that the gravitational force between two bodies depends only on one number associated with each body, its mass, but is otherwise independent of what the bodies are made of. Thus one does not need to have a theory of the structure and constitution of the sun and the planets in order to calculate their orbits.Today scientists describe the universe in terms of two basic partial theories –the general theory of relativity and quantum mechanics. They are the great intellectual achievements of the first half of this century. The general theory of relativity describes the force of gravity and the large-scale structure of the universe, that is , the structure on scales from only a few miles to as large as a million million million (1 with zeros after it) miles, the size of the observable universe. Quantum mechanics, on the other hand, deals with phenomena ion extremely small scales, such as a millionth of a millionth of an inch. Unfortunately, however, these two theories are known to be inconsistent with each other – they cannot both be correct. One of the major endeavors in physics today, is the search for a new theory, and we may still be a long way from having one, but we do already know many of the properties that it must have.o什么是科学理论?为了谈宇宙的成熟和讨论这样的问题是否有一个开始或结束,你必须清楚科学理论是什么。

SCI 投稿经历

今天收到邮件，我的一篇Journal of Applied Physics 论文已被接收，心情当时还是有点激动。

虽然这个杂志的影响因子不是很高，大概2.2左右吧，这也不是我的第一篇SCI论文，但回想这一年发文章的坎坎坷坷，以及亲身经历的四川大地震，心里还是有很多的感触。

这篇论文是我在2008年二月份完成的最初稿，于二月九号投到Physics Letters A上，在经历了Technical check，with editor，under review后，于三月二十号收到编辑的决定信，当时就傻了－拒稿！受打击了。

下面是编辑的信以及审稿意见，我想把它贴出来与虫友们分享，一方面我认为，通过看审稿人的意见，可以帮助大家更好地写作，提高自己的科研水平和能力，另一方面也是答谢小木虫上很多无私的虫友们，是他们将自己的投稿经历贴在网上，与大家分享，我想我没有理由不拿出来哈！同时，也希望小木虫的虫子们能继续发扬这种精神，大家同舟共济，共同提高！好了，废话说了一大堆，不说了，下面是Physics Letters A 的审稿意见：Ms. Ref. No.: ××××××Title: ×××××Physics Letters ADear professor ××,Reviewers' comments on your work have now been received. You will see that they are advising against publication of your work. Therefore I must reject it.For your guidance, I append the reviewers' comments below.Thank you for giving us the opportunity to consider your work.Yours sincerely,×××（编辑名）EditorPhysics Letters AReviewers' comments:Reviewer #2: ManuscriptThe authors present results of the 3D electron potential ofa gated quantum point contact in a AlGaAs/GaAs heterostructure.In contrast to earlier studies, it is now possible to derive thepotential landshape without any adjustable parameter. The resultsstill agree with earlier investigations using simpler phenomenologicalmodels. Since the used nextnano3 program is available since acouple of years, I wonder why this has not been done earlier.The authors emphasize an application of their results. Havingthe complete potential landshape might help, in the future,to better understand the quantized acoustoelectric current inSETSAW devices and to improve their performance.However, the authors do not show or even discuss how this canbe achieved. Therefore I believe that in the present form the paperis not suitable for publication.The authors should consider the following suggestions, questions,and remarks.1) Page 1, first paragraph'... due to the negatively applied gate voltage ...'. It is the SAWthat drives the electrons through the contact, not the gate voltage.Maybe replace this sentence by '..., depending on the applied gatevoltage'.2) Page 3, paragraph starting with 'Generally, the quantized ...''... with fixed x = 1050 nm and ...'. Skip the '.0'. One could addthat this is exactly at the center of the device.3) At the end of the same paragraph is '... once the bias is below ...'Should this not be the gate instead of the bias voltage?4) Page 4, paragraph starting with 'As we know, in the ...''... To be different from previous calculations ...' replace by'... In contrast to previous calculations ...'.5) The strongly different behaviour above and below the pinch-offvoltage is not obvious for the non-experts. All curves look moreor less the same. One could, for example, add another figure, orinsert, to show the potential height versus gate voltage.6) How do these theoretical results of potential height versus gatevoltage compare with experiments? There exists at least onereport to determine the potential height of quantum-point contactsbelow pinch-off as function of gate voltage (Gloos et al., Phys.Rev. B 73, 125326 (2006)). Possibly, one could also compare thepresent data with 3D simulations of quantum dots (Vasileska et al., Semicond. Sci. Technol. 13, A37 (1998)).7) Figure 1，It would be better to mark the distance between the two metal gatesas the relevant parameter, and not the size of one gate.8) Figure 3The numbering of the two density axes looks rather odd. Could it notbe done with integers, like 3 instead of 3.2 or 3.0?9) Figure 5 (b)Should there not be an anomaly or kink in the potential near the Fermilevel?在仔细读了审稿人的意见后，我觉得审稿人提出的5）和6)意见非常好，后来自己想想，决定把文章来个彻底的修改。

量子物理的秘密英语作文

量子物理的秘密英语作文The Secrets of Quantum Physics。

Quantum physics is a branch of science that deals with the behavior of particles at the atomic and subatomic levels. It is a field that has fascinated scientists and researchers for decades, and continues to be the subject of much study and debate. The secrets of quantum physics are both mysterious and intriguing, and have the potential to revolutionize our understanding of the universe.One of the most fascinating aspects of quantum physics is the concept of duality, which refers to the idea that particles can exhibit both wave-like and particle-like behavior. This duality is best exemplified by the famous double-slit experiment, in which particles such as electrons are fired at a barrier with two slits. When the particles pass through the slits, they create an interference pattern on the other side, as if they were waves. However, when a detector is placed to observe whichslit the particles pass through, the interference pattern disappears and the particles behave as individual particles. This phenomenon has baffled scientists for years, and continues to be a subject of much debate and speculation.Another intriguing aspect of quantum physics is the concept of entanglement, which refers to the phenomenon in which two particles become connected in such a way that the state of one particle is instantly correlated with thestate of the other, regardless of the distance between them. This phenomenon was famously described by Albert Einsteinas "spooky action at a distance," and has been the subjectof much study and experimentation. The implications of entanglement are profound, and have the potential to revolutionize the field of communication and information technology.Furthermore, quantum physics has also led to the development of new and exciting technologies, such as quantum computing and quantum cryptography. Quantum computing utilizes the principles of quantum mechanics to perform complex calculations at speeds that are far beyondthe capabilities of traditional computers. This has the potential to revolutionize fields such as cryptography,drug discovery, and materials science. Quantum cryptography, on the other hand, utilizes the principles of quantum mechanics to create secure communication channels that are immune to eavesdropping and hacking. This has the potential to revolutionize the field of cybersecurity and information technology.In conclusion, the secrets of quantum physics are both mysterious and intriguing, and have the potential to revolutionize our understanding of the universe. The concepts of duality, entanglement, and quantum technologies have the potential to transform the way we think about the world around us, and have the potential to revolutionize fields such as communication, computing, and cybersecurity. As our understanding of quantum physics continues to evolve, it is likely that we will continue to unlock the secrets of the universe and develop new and exciting technologies that will shape the future of humanity.。

遇事不决量子力学英语

遇事不决量子力学英语Quantum Mechanics in Decision-MakingIn the face of complex and uncertain situations, traditional decision-making approaches often fall short. However, the principles of quantum mechanics, a field of physics that explores the behavior of matter and energy at the subatomic level, can provide valuable insights and a new perspective on problem-solving. By understanding and applying the fundamental concepts of quantum mechanics, individuals and organizations can navigate challenging scenarios with greater clarity and effectiveness.One of the key principles of quantum mechanics is the idea of superposition, which suggests that particles can exist in multiple states simultaneously until they are observed or measured. This concept can be applied to decision-making, where the decision-maker may be faced with multiple possible courses of action, each with its own set of potential outcomes. Rather than prematurely collapsing these possibilities into a single decision, the decision-maker can embrace the superposition and consider the various alternatives in a more open and flexible manner.Another important aspect of quantum mechanics is the principle of uncertainty, which states that the more precisely one property of a particle is measured, the less precisely another property can be known. This principle can be applied to decision-making, where the decision-maker may be faced with incomplete or uncertain information. Instead of trying to eliminate all uncertainty, the decision-maker can acknowledge and work within the constraints of this uncertainty, focusing on making the best possible decision based on the available information.Furthermore, quantum mechanics introduces the concept of entanglement, where two or more particles can become inextricably linked, such that the state of one particle affects the state of the other, even if they are physically separated. This idea can be applied to decision-making in complex systems, where the actions of one individual or organization can have far-reaching and unpredictable consequences for others. By recognizing the interconnectedness of the various elements within a system, decision-makers can better anticipate and navigate the potential ripple effects of their choices.Another key aspect of quantum mechanics that can inform decision-making is the idea of probability. In quantum mechanics, the behavior of particles is described in terms of probability distributions, rather than deterministic outcomes. This probabilistic approach can be applied to decision-making, where the decision-maker canconsider the likelihood of different outcomes and adjust their strategies accordingly.Additionally, quantum mechanics emphasizes the importance of observation and measurement in shaping the behavior of particles. Similarly, in decision-making, the act of observing and gathering information can influence the outcomes of a situation. By being mindful of how their own observations and interventions can impact the decision-making process, decision-makers can strive to maintain a more objective and impartial perspective.Finally, the concept of quantum entanglement can also be applied to the decision-making process itself. Just as particles can become entangled, the various factors and considerations involved in a decision can become deeply interconnected. By recognizing and embracing this entanglement, decision-makers can adopt a more holistic and integrated approach, considering the complex web of relationships and dependencies that shape the outcome.In conclusion, the principles of quantum mechanics offer a unique and compelling framework for navigating complex decision-making scenarios. By embracing the concepts of superposition, uncertainty, entanglement, and probability, individuals and organizations can develop a more nuanced and adaptable approach to problem-solving. By applying these quantum-inspired strategies, decision-makers can navigate the challenges of the modern world with greater clarity, resilience, and effectiveness.。

恒星撞击实验作文英语

恒星撞击实验作文英语英文回答：In the depths of cosmic vastness, where celestial bodies dance in an eternal ballet, there exists a realm of extreme phenomena, where cosmic titans collide with unimaginable force. These stellar cataclysms, while rare occurrences in our observable universe, hold the potential to reshape the celestial tapestry and ignite the imaginations of stargazers and scientists alike.In a secluded corner of the cosmos, a cosmic drama of unparalleled proportions was about to unfold. Two celestial behemoths, each a star in its own right, were hurtling towards an inevitable collision. Their combined masses were staggering, their gravitational pull warping the fabric of space-time like a celestial lens. As the cosmic giants drew closer, their dance became both beautiful and terrifying.With each passing moment, the stars accelerated, theirsurfaces glowing with an incandescent brilliance. The celestial symphony reached its crescendo as the two cosmic leviathans finally collided in a blinding explosion of light and energy. The impact sent shockwaves rippling through the surrounding void, triggering a cosmic fireworks display that illuminated the celestial canvas.In the aftermath of the cataclysmic impact, a new celestial entity emerged from the cosmic debris. The fusion of the two stars had created a brilliant newborn star, its radiant glow illuminating the void where its predecessors once existed. The newly formed star, a testament to the chaotic beauty of the cosmos, embarked on its own journey through the galactic tapestry.The stellar collision experiment, as it came to be known, not only captivated the scientific community but also ignited the imaginations of poets and philosophers. It served as a cosmic parable about the transience of existence, the power of creation, and the indomitable spirit of the universe.As we gaze up at the night sky, shimmering with countless stars, let us remember the cosmic drama that played out in that distant corner of the cosmos. It is a reminder that even in the vast emptiness of space, life, death, and rebirth dance in an eternal cycle, shaping the grand narrative of the universe.中文回答：在宇宙浩瀚的深处，天体们在永恒的芭蕾中起舞，那里存在着极端的现象，宇宙巨兽以难以想象的力量相撞。

塔诺基量子力学第三卷

塔诺基量子力学第三卷英文回答：Quantum mechanics, as described in the third volume of the Tannocky series, is a fascinating and complex field of study. It deals with the behavior of particles at the quantum level, where classical physics no longer applies.In this realm, particles can exist in multiple states simultaneously and can exhibit wave-particle duality.One of the fundamental principles of quantum mechanicsis superposition. This concept states that a particle can exist in multiple states or positions at the same time. For example, imagine a particle that can be in either the "up"or "down" state. In classical physics, the particle wouldbe in one state or the other. However, in quantum mechanics, the particle can exist in a superposition of both states simultaneously. It is only when a measurement is made that the particle "chooses" one of the states.Another important principle in quantum mechanics is entanglement. This phenomenon occurs when two particles become linked in such a way that the state of one particle is dependent on the state of the other, regardless of the distance between them. This concept is often described using the famous thought experiment of two entangled particles, known as "spooky action at a distance." For example, if two entangled particles are in a superposition of "up" and "down" states, measuring one particle will instantaneously determine the state of the other particle, even if they are light-years apart.Quantum mechanics also introduces the concept of uncertainty, as described by Heisenberg's uncertainty principle. This principle states that certain pairs of physical properties, such as position and momentum, cannot both be precisely known at the same time. The more precisely one property is known, the less precisely the other can be known. This inherent uncertainty at the quantum level is a fundamental aspect of the nature of reality.Overall, quantum mechanics is a highly mathematical and abstract field, but its principles have been successfully applied in various technological advancements. For example, quantum computers utilize the principles of superposition and entanglement to perform calculations at a much faster rate than classical computers. Quantum cryptography also relies on the principles of quantum mechanics to ensure secure communication.中文回答：量子力学是塔诺基系列第三卷中描述的一个引人入胜且复杂的研究领域。

专八英语阅读

英语专业八级考试TEM-8阅读理解练习册（1）(英语专业2012级)UNIT 1Text AEvery minute of every day, what ecologist生态学家James Carlton calls a global ―conveyor belt‖, redistributes ocean organisms生物.It’s planetwide biological disruption生物的破坏that scientists have barely begun to understand.Dr. Carlton —an oceanographer at Williams College in Williamstown,Mass.—explains that, at any given moment, ―There are several thousand marine species traveling… in the ballast water of ships.‖ These creatures move from coastal waters where they fit into the local web of life to places where some of them could tear that web apart. This is the larger dimension of the infamous无耻的，邪恶的invasion of fish-destroying, pipe-clogging zebra mussels有斑马纹的贻贝.Such voracious贪婪的invaders at least make their presence known. What concerns Carlton and his fellow marine ecologists is the lack of knowledge about the hundreds of alien invaders that quietly enter coastal waters around the world every day. Many of them probably just die out. Some benignly亲切地，仁慈地—or even beneficially — join the local scene. But some will make trouble.In one sense, this is an old story. Organisms have ridden ships for centuries. They have clung to hulls and come along with cargo. What’s new is the scale and speed of the migrations made possible by the massive volume of ship-ballast water压载水— taken in to provide ship stability—continuously moving around the world…Ships load up with ballast water and its inhabitants in coastal waters of one port and dump the ballast in another port that may be thousands of kilometers away. A single load can run to hundreds of gallons. Some larger ships take on as much as 40 million gallons. The creatures that come along tend to be in their larva free-floating stage. When discharged排出in alien waters they can mature into crabs, jellyfish水母, slugs鼻涕虫，蛞蝓, and many other forms.Since the problem involves coastal species, simply banning ballast dumps in coastal waters would, in theory, solve it. Coastal organisms in ballast water that is flushed into midocean would not survive. Such a ban has worked for North American Inland Waterway. But it would be hard to enforce it worldwide. Heating ballast water or straining it should also halt the species spread. But before any such worldwide regulations were imposed, scientists would need a clearer view of what is going on.The continuous shuffling洗牌of marine organisms has changed the biology of the sea on a global scale. It can have devastating effects as in the case of the American comb jellyfish that recently invaded the Black Sea. It has destroyed that sea’s anchovy鳀鱼fishery by eating anchovy eggs. It may soon spread to western and northern European waters.The maritime nations that created the biological ―conveyor belt‖ should support a coordinated international effort to find out what is going on and what should be done about it. (456 words)1.According to Dr. Carlton, ocean organism‟s are_______.A.being moved to new environmentsB.destroying the planetC.succumbing to the zebra musselD.developing alien characteristics2.Oceanographers海洋学家are concerned because_________.A.their knowledge of this phenomenon is limitedB.they believe the oceans are dyingC.they fear an invasion from outer-spaceD.they have identified thousands of alien webs3.According to marine ecologists, transplanted marinespecies____________.A.may upset the ecosystems of coastal watersB.are all compatible with one anotherC.can only survive in their home watersD.sometimes disrupt shipping lanes4.The identified cause of the problem is_______.A.the rapidity with which larvae matureB. a common practice of the shipping industryC. a centuries old speciesD.the world wide movement of ocean currents5.The article suggests that a solution to the problem__________.A.is unlikely to be identifiedB.must precede further researchC.is hypothetically假设地，假想地easyD.will limit global shippingText BNew …Endangered‟ List Targets Many US RiversIt is hard to think of a major natural resource or pollution issue in North America today that does not affect rivers.Farm chemical runoff残渣, industrial waste, urban storm sewers, sewage treatment, mining, logging, grazing放牧,military bases, residential and business development, hydropower水力发电,loss of wetlands. The list goes on.Legislation like the Clean Water Act and Wild and Scenic Rivers Act have provided some protection, but threats continue.The Environmental Protection Agency (EPA) reported yesterday that an assessment of 642,000 miles of rivers and streams showed 34 percent in less than good condition. In a major study of the Clean Water Act, the Natural Resources Defense Council last fall reported that poison runoff impairs损害more than 125,000 miles of rivers.More recently, the NRDC and Izaak Walton League warned that pollution and loss of wetlands—made worse by last year’s flooding—is degrading恶化the Mississippi River ecosystem.On Tuesday, the conservation group保护组织American Rivers issued its annual list of 10 ―endangered‖ and 20 ―threatened‖ rivers in 32 states, the District of Colombia, and Canada.At the top of the list is the Clarks Fork of the Yellowstone River, whereCanadian mining firms plan to build a 74-acre英亩reservoir水库，蓄水池as part of a gold mine less than three miles from Yellowstone National Park. The reservoir would hold the runoff from the sulfuric acid 硫酸used to extract gold from crushed rock.―In the event this tailings pond failed, the impact to th e greater Yellowstone ecosystem would be cataclysmic大变动的，灾难性的and the damage irreversible不可逆转的.‖ Sen. Max Baucus of Montana, chairman of the Environment and Public Works Committee, wrote to Noranda Minerals Inc., an owner of the ― New World Mine‖.Last fall, an EPA official expressed concern about the mine and its potential impact, especially the plastic-lined storage reservoir. ― I am unaware of any studies evaluating how a tailings pond尾矿池，残渣池could be maintained to ensure its structural integrity forev er,‖ said Stephen Hoffman, chief of the EPA’s Mining Waste Section. ―It is my opinion that underwater disposal of tailings at New World may present a potentially significant threat to human health and the environment.‖The results of an environmental-impact statement, now being drafted by the Forest Service and Montana Department of State Lands, could determine the mine’s future…In its recent proposal to reauthorize the Clean Water Act, the Clinton administration noted ―dramatically improved water quality since 1972,‖ when the act was passed. But it also reported that 30 percent of riverscontinue to be degraded, mainly by silt泥沙and nutrients from farm and urban runoff, combined sewer overflows, and municipal sewage城市污水. Bottom sediments沉积物are contaminated污染in more than 1,000 waterways, the administration reported in releasing its proposal in January. Between 60 and 80 percent of riparian corridors (riverbank lands) have been degraded.As with endangered species and their habitats in forests and deserts, the complexity of ecosystems is seen in rivers and the effects of development----beyond the obvious threats of industrial pollution, municipal waste, and in-stream diversions改道to slake消除the thirst of new communities in dry regions like the Southwes t…While there are many political hurdles障碍ahead, reauthorization of the Clean Water Act this year holds promise for US rivers. Rep. Norm Mineta of California, who chairs the House Committee overseeing the bill, calls it ―probably the most important env ironmental legislation this Congress will enact.‖ (553 words)6.According to the passage, the Clean Water Act______.A.has been ineffectiveB.will definitely be renewedC.has never been evaluatedD.was enacted some 30 years ago7.“Endangered” rivers are _________.A.catalogued annuallyB.less polluted than ―threatened rivers‖C.caused by floodingD.adjacent to large cities8.The “cataclysmic” event referred to in paragraph eight would be__________.A. fortuitous偶然的，意外的B. adventitious外加的，偶然的C. catastrophicD. precarious不稳定的，危险的9. The owners of the New World Mine appear to be______.A. ecologically aware of the impact of miningB. determined to construct a safe tailings pondC. indifferent to the concerns voiced by the EPAD. willing to relocate operations10. The passage conveys the impression that_______.A. Canadians are disinterested in natural resourcesB. private and public environmental groups aboundC. river banks are erodingD. the majority of US rivers are in poor conditionText CA classic series of experiments to determine the effects ofoverpopulation on communities of rats was reported in February of 1962 in an article in Scientific American. The experiments were conducted by a psychologist, John B. Calhoun and his associates. In each of these experiments, an equal number of male and female adult rats were placed in an enclosure and given an adequate supply of food, water, and other necessities. The rat populations were allowed to increase. Calhoun knew from experience approximately how many rats could live in the enclosures without experiencing stress due to overcrowding. He allowed the population to increase to approximately twice this number. Then he stabilized the population by removing offspring that were not dependent on their mothers. He and his associates then carefully observed and recorded behavior in these overpopulated communities. At the end of their experiments, Calhoun and his associates were able to conclude that overcrowding causes a breakdown in the normal social relationships among rats, a kind of social disease. The rats in the experiments did not follow the same patterns of behavior as rats would in a community without overcrowding.The females in the rat population were the most seriously affected by the high population density: They showed deviant异常的maternal behavior; they did not behave as mother rats normally do. In fact, many of the pups幼兽，幼崽, as rat babies are called, died as a result of poor maternal care. For example, mothers sometimes abandoned their pups,and, without their mothers' care, the pups died. Under normal conditions, a mother rat would not leave her pups alone to die. However, the experiments verified that in overpopulated communities, mother rats do not behave normally. Their behavior may be considered pathologically 病理上，病理学地diseased.The dominant males in the rat population were the least affected by overpopulation. Each of these strong males claimed an area of the enclosure as his own. Therefore, these individuals did not experience the overcrowding in the same way as the other rats did. The fact that the dominant males had adequate space in which to live may explain why they were not as seriously affected by overpopulation as the other rats. However, dominant males did behave pathologically at times. Their antisocial behavior consisted of attacks on weaker male,female, and immature rats. This deviant behavior showed that even though the dominant males had enough living space, they too were affected by the general overcrowding in the enclosure.Non-dominant males in the experimental rat communities also exhibited deviant social behavior. Some withdrew completely; they moved very little and ate and drank at times when the other rats were sleeping in order to avoid contact with them. Other non-dominant males were hyperactive; they were much more active than is normal, chasing other rats and fighting each other. This segment of the rat population, likeall the other parts, was affected by the overpopulation.The behavior of the non-dominant males and of the other components of the rat population has parallels in human behavior. People in densely populated areas exhibit deviant behavior similar to that of the rats in Calhoun's experiments. In large urban areas such as New York City, London, Mexican City, and Cairo, there are abandoned children. There are cruel, powerful individuals, both men and women. There are also people who withdraw and people who become hyperactive. The quantity of other forms of social pathology such as murder, rape, and robbery also frequently occur in densely populated human communities. Is the principal cause of these disorders overpopulation? Calhoun’s experiments suggest that it might be. In any case, social scientists and city planners have been influenced by the results of this series of experiments.11. Paragraph l is organized according to__________.A. reasonsB. descriptionC. examplesD. definition12．Calhoun stabilized the rat population_________.A. when it was double the number that could live in the enclosure without stressB. by removing young ratsC. at a constant number of adult rats in the enclosureD. all of the above are correct13.W hich of the following inferences CANNOT be made from theinformation inPara. 1?A. Calhoun's experiment is still considered important today.B. Overpopulation causes pathological behavior in rat populations.C. Stress does not occur in rat communities unless there is overcrowding.D. Calhoun had experimented with rats before.14. Which of the following behavior didn‟t happen in this experiment?A. All the male rats exhibited pathological behavior.B. Mother rats abandoned their pups.C. Female rats showed deviant maternal behavior.D. Mother rats left their rat babies alone.15. The main idea of the paragraph three is that __________.A. dominant males had adequate living spaceB. dominant males were not as seriously affected by overcrowding as the otherratsC. dominant males attacked weaker ratsD. the strongest males are always able to adapt to bad conditionsText DThe first mention of slavery in the statutes法令，法规of the English colonies of North America does not occur until after 1660—some forty years after the importation of the first Black people. Lest we think that existed in fact before it did in law, Oscar and Mary Handlin assure us, that the status of B lack people down to the 1660’s was that of servants. A critique批判of the Handlins’ interpretation of why legal slavery did not appear until the 1660’s suggests that assumptions about the relation between slavery and racial prejudice should be reexamined, and that explanation for the different treatment of Black slaves in North and South America should be expanded.The Handlins explain the appearance of legal slavery by arguing that, during the 1660’s, the position of white servants was improving relative to that of black servants. Thus, the Handlins contend, Black and White servants, heretofore treated alike, each attained a different status. There are, however, important objections to this argument. First, the Handlins cannot adequately demonstrate that t he White servant’s position was improving, during and after the 1660’s; several acts of the Maryland and Virginia legislatures indicate otherwise. Another flaw in the Handlins’ interpretation is their assumption that prior to the establishment of legal slavery there was no discrimination against Black people. It is true that before the 1660’s Black people were rarely called slaves. But this shouldnot overshadow evidence from the 1630’s on that points to racial discrimination without using the term slavery. Such discrimination sometimes stopped short of lifetime servitude or inherited status—the two attributes of true slavery—yet in other cases it included both. The Handlins’ argument excludes the real possibility that Black people in the English colonies were never treated as the equals of White people.The possibility has important ramifications后果，影响.If from the outset Black people were discriminated against, then legal slavery should be viewed as a reflection and an extension of racial prejudice rather than, as many historians including the Handlins have argued, the cause of prejudice. In addition, the existence of discrimination before the advent of legal slavery offers a further explanation for the harsher treatment of Black slaves in North than in South America. Freyre and Tannenbaum have rightly argued that the lack of certain traditions in North America—such as a Roman conception of slavery and a Roman Catholic emphasis on equality— explains why the treatment of Black slaves was more severe there than in the Spanish and Portuguese colonies of South America. But this cannot be the whole explanation since it is merely negative, based only on a lack of something. A more compelling令人信服的explanation is that the early and sometimes extreme racial discrimination in the English colonies helped determine the particular nature of the slavery that followed. (462 words)16. Which of the following is the most logical inference to be drawn from the passage about the effects of “several acts of the Maryland and Virginia legislatures” (Para.2) passed during and after the 1660‟s?A. The acts negatively affected the pre-1660’s position of Black as wellas of White servants.B. The acts had the effect of impairing rather than improving theposition of White servants relative to what it had been before the 1660’s.C. The acts had a different effect on the position of white servants thandid many of the acts passed during this time by the legislatures of other colonies.D. The acts, at the very least, caused the position of White servants toremain no better than it had been before the 1660’s.17. With which of the following statements regarding the status ofBlack people in the English colonies of North America before the 1660‟s would the author be LEAST likely to agree?A. Although black people were not legally considered to be slaves,they were often called slaves.B. Although subject to some discrimination, black people had a higherlegal status than they did after the 1660’s.C. Although sometimes subject to lifetime servitude, black peoplewere not legally considered to be slaves.D. Although often not treated the same as White people, black people,like many white people, possessed the legal status of servants.18. According to the passage, the Handlins have argued which of thefollowing about the relationship between racial prejudice and the institution of legal slavery in the English colonies of North America?A. Racial prejudice and the institution of slavery arose simultaneously.B. Racial prejudice most often the form of the imposition of inheritedstatus, one of the attributes of slavery.C. The source of racial prejudice was the institution of slavery.D. Because of the influence of the Roman Catholic Church, racialprejudice sometimes did not result in slavery.19. The passage suggests that the existence of a Roman conception ofslavery in Spanish and Portuguese colonies had the effect of _________.A. extending rather than causing racial prejudice in these coloniesB. hastening the legalization of slavery in these colonies.C. mitigating some of the conditions of slavery for black people in these coloniesD. delaying the introduction of slavery into the English colonies20. The author considers the explanation put forward by Freyre andTannenbaum for the treatment accorded B lack slaves in the English colonies of North America to be _____________.A. ambitious but misguidedB. valid有根据的but limitedC. popular but suspectD. anachronistic过时的，时代错误的and controversialUNIT 2Text AThe sea lay like an unbroken mirror all around the pine-girt, lonely shores of Orr’s Island. Tall, kingly spruce s wore their regal王室的crowns of cones high in air, sparkling with diamonds of clear exuded gum流出的树胶; vast old hemlocks铁杉of primeval原始的growth stood darkling in their forest shadows, their branches hung with long hoary moss久远的青苔;while feathery larches羽毛般的落叶松,turned to brilliant gold by autumn frosts, lighted up the darker shadows of the evergreens. It was one of those hazy朦胧的, calm, dissolving days of Indian summer, when everything is so quiet that the fainest kiss of the wave on the beach can be heard, and white clouds seem to faint into the blue of the sky, and soft swathing一长条bands of violet vapor make all earth look dreamy, and give to the sharp, clear-cut outlines of the northern landscape all those mysteries of light and shade which impart such tenderness to Italian scenery.The funeral was over,--- the tread鞋底的花纹/ 踏of many feet, bearing the heavy burden of two broken lives, had been to the lonely graveyard, and had come back again,--- each footstep lighter and more unconstrained不受拘束的as each one went his way from the great old tragedy of Death to the common cheerful of Life.The solemn black clock stood swaying with its eternal ―tick-tock, tick-tock,‖ in the kitchen of the brown house on Orr’s Island. There was there that sense of a stillness that can be felt,---such as settles down on a dwelling住处when any of its inmates have passed through its doors for the last time, to go whence they shall not return. The best room was shut up and darkened, with only so much light as could fall through a little heart-shaped hole in the window-shutter,---for except on solemn visits, or prayer-meetings or weddings, or funerals, that room formed no part of the daily family scenery.The kitchen was clean and ample, hearth灶台, and oven on one side, and rows of old-fashioned splint-bottomed chairs against the wall. A table scoured to snowy whiteness, and a little work-stand whereon lay the Bible, the Missionary Herald, and the Weekly Christian Mirror, before named, formed the principal furniture. One feature, however, must not be forgotten, ---a great sea-chest水手用的储物箱,which had been the companion of Zephaniah through all the countries of the earth. Old, and battered破旧的，磨损的, and unsightly难看的it looked, yet report said that there was good store within which men for the most part respect more than anything else; and, indeed it proved often when a deed of grace was to be done--- when a woman was suddenly made a widow in a coast gale大风，狂风, or a fishing-smack小渔船was run down in the fogs off the banks, leaving in some neighboring cottage a family of orphans,---in all such cases, the opening of this sea-chest was an event of good omen 预兆to the bereaved丧亲者;for Zephaniah had a large heart and a large hand, and was apt有…的倾向to take it out full of silver dollars when once it went in. So the ark of the covenant约柜could not have been looked on with more reverence崇敬than the neighbours usually showed to Captain Pennel’s sea-chest.1. The author describes Orr‟s Island in a(n)______way.A.emotionally appealing, imaginativeB.rational, logically preciseC.factually detailed, objectiveD.vague, uncertain2.According to the passage, the “best room”_____.A.has its many windows boarded upB.has had the furniture removedC.is used only on formal and ceremonious occasionsD.is the busiest room in the house3.From the description of the kitchen we can infer that thehouse belongs to people who_____.A.never have guestsB.like modern appliancesC.are probably religiousD.dislike housework4.The passage implies that_______.A.few people attended the funeralB.fishing is a secure vocationC.the island is densely populatedD.the house belonged to the deceased5.From the description of Zephaniah we can see thathe_________.A.was physically a very big manB.preferred the lonely life of a sailorC.always stayed at homeD.was frugal and saved a lotText BBasic to any understanding of Canada in the 20 years after the Second World War is the country' s impressive population growth. For every three Canadians in 1945, there were over five in 1966. In September 1966 Canada's population passed the 20 million mark. Most of this surging growth came from natural increase. The depression of the 1930s and the war had held back marriages, and the catching-up process began after 1945. The baby boom continued through the decade of the 1950s, producing a population increase of nearly fifteen percent in the five years from 1951 to 1956. This rate of increase had been exceeded only once before in Canada's history, in the decade before 1911 when the prairies were being settled. Undoubtedly, the good economic conditions of the 1950s supported a growth in the population, but the expansion also derived from a trend toward earlier marriages and an increase in the average size of families; In 1957 the Canadian birth rate stood at 28 per thousand, one of the highest in the world. After the peak year of 1957, thebirth rate in Canada began to decline. It continued falling until in 1966 it stood at the lowest level in 25 years. Partly this decline reflected the low level of births during the depression and the war, but it was also caused by changes in Canadian society. Young people were staying at school longer, more women were working; young married couples were buying automobiles or houses before starting families; rising living standards were cutting down the size of families. It appeared that Canada was once more falling in step with the trend toward smaller families that had occurred all through theWestern world since the time of the Industrial Revolution. Although the growth in Canada’s population had slowed down by 1966 (the cent), another increase in the first half of the 1960s was only nine percent), another large population wave was coming over the horizon. It would be composed of the children of the children who were born during the period of the high birth rate prior to 1957.6. What does the passage mainly discuss?A. Educational changes in Canadian society.B. Canada during the Second World War.C. Population trends in postwar Canada.D. Standards of living in Canada.7. According to the passage, when did Canada's baby boom begin?A. In the decade after 1911.B. After 1945.C. During the depression of the 1930s.D. In 1966.8. The author suggests that in Canada during the 1950s____________.A. the urban population decreased rapidlyB. fewer people marriedC. economic conditions were poorD. the birth rate was very high9. When was the birth rate in Canada at its lowest postwar level?A. 1966.B. 1957.C. 1956.D. 1951.10. The author mentions all of the following as causes of declines inpopulation growth after 1957 EXCEPT_________________.A. people being better educatedB. people getting married earlierC. better standards of livingD. couples buying houses11.I t can be inferred from the passage that before the IndustrialRevolution_______________.A. families were largerB. population statistics were unreliableC. the population grew steadilyD. economic conditions were badText CI was just a boy when my father brought me to Harlem for the first time, almost 50 years ago. We stayed at the hotel Theresa, a grand brick structure at 125th Street and Seventh avenue. Once, in the hotel restaurant, my father pointed out Joe Louis. He even got Mr. Brown, the hotel manager, to introduce me to him, a bit punchy强力的but still champ焦急as fast as I was concerned.Much has changed since then. Business and real estate are booming. Some say a new renaissance is under way. Others decry责难what they see as outside forces running roughshod肆意践踏over the old Harlem. New York meant Harlem to me, and as a young man I visited it whenever I could. But many of my old haunts are gone. The Theresa shut down in 1966. National chains that once ignored Harlem now anticipate yuppie money and want pieces of this prime Manhattan real estate. So here I am on a hot August afternoon, sitting in a Starbucks that two years ago opened a block away from the Theresa, snatching抓取，攫取at memories between sips of high-priced coffee. I am about to open up a piece of the old Harlem---the New York Amsterdam News---when a tourist。

某些奇怪的事情英文作文

某些奇怪的事情英文作文Title: Unraveling the Curious: Exploring Strange Phenomena。

Have you ever found yourself pondering the mysteries of the universe? Perhaps you've encountered something so strange, so inexplicable, that it left you questioning the very fabric of reality. In this essay, we delve into the realm of the peculiar, exploring strange phenomena that challenge our understanding of the world.One of the most perplexing phenomena is the Bermuda Triangle. Situated between Miami, Bermuda, and Puerto Rico, this region has gained notoriety for the inexplicable disappearances of ships and aircraft. Despite extensive investigations, no conclusive explanation has been reached. Theories range from magnetic anomalies to extraterrestrial interference, fueling speculation and intrigue.Another enigma that captivates the imagination is themystery of the Nazca Lines in Peru. These ancient geoglyphs, etched into the desert plains, depict various animals, geometric shapes, and humanoid figures. The sheer scale and precision of these drawings have led to speculation about their purpose, with hypotheses ranging from religiousrituals to astronomical calendars. Yet, the true intentions of the Nazca people remain shrouded in mystery.Moving from the terrestrial to the celestial, we encounter the phenomenon of black holes. These cosmic entities, formed from the collapse of massive stars, possess such intense gravitational pull that not even light can escape their grasp. Despite their theoretical existence being supported by astrophysical models, the true nature of black holes remains elusive. The paradoxes they present, such as the information paradox and the firewall paradox, challenge our understanding of fundamental physics.Closer to home, we find anomalies within the human mind itself. Synesthesia, for example, is a condition where sensory perceptions become intertwined, leading individuals to experience colors when hearing music or tasting flavorswhen seeing words. This blurring of sensory boundaries offers insights into the complexities of perception and cognition, yet its underlying mechanisms remain a subject of debate among neuroscientists.In the realm of biology, the phenomenon of bioluminescence adds another layer of intrigue. From glowing mushrooms in dark forests to luminous creatures in the depths of the ocean, bioluminescence is a testament to the wonders of nature. Yet, the evolutionary purpose behind this phenomenon is not always clear, leaving scientists to unravel its mysteries.The world of quantum mechanics introduces us to yet another realm of strangeness. Quantum entanglement, for instance, describes a phenomenon where particles become interconnected in such a way that the state of one particle instantaneously influences the state of another, regardless of the distance between them. This baffling concept challenges our classical notions of cause and effect, opening new frontiers in our quest to understand the nature of reality.As we journey through these strange phenomena, one thing becomes clear: the universe is far more mysterious and wondrous than we can comprehend. Each anomaly invites us to question, to wonder, and to explore the limits of our understanding. While we may never fully unravel the mysteries that surround us, the pursuit of knowledge remains an endless and exhilarating endeavor.。

量子是一种玄学方法英语

量子是一种玄学方法英语Quantum physics is a branch of science that has captivated the minds of scientists and non-scientists alike. It is a field filled with strange and counterintuitive phenomena that challenge our understanding of how the world works. Quantum mechanics, in particular, is known for its mind-bending concepts such as superposition, entanglement, and wave-particle duality. This branch of science is often referred to as a "mysterious" and "magical" method due to its puzzling and unpredictable nature.Quantum mechanics is based on the principles that govern the behavior of particles at the atomic and subatomic levels. Unlike classical physics, which deals with the macroscopic world, quantum mechanics focuses on the quantum realm, where particles exhibit wave-like properties and can exist in multiple states simultaneously until measured.One of the key features of quantum mechanics is superposition. This concept states that particles can exist in multiple states or locations at the same time until obser ved. Schrödinger's famous thought experiment, in which a cat inside a box is simultaneously alive and dead until the box is opened, illustrates this phenomenon. This mind-boggling idea challenges our intuition and raises questions about the nature of reality. Another intriguing aspect of quantum mechanics is entanglement. When two particles become entangled, their properties becomeinterdependent, regardless of the distance between them. This means that measuring the state of one particle instantaneously determines the state of the other, no matter how far apart they are. Einstein famously called this phenomenon "spooky action at a distance." The concept of entanglement has led to the development of quantum teleportation and quantum cryptography, which have the potential to revolutionize communication and computing.Furthermore, quantum mechanics challenges the classical concept of particles having definite properties. According to wave-particle duality, particles can behave as both waves and particles depending on the experimental setup. This means that particles can exhibit characteristics of both particles and waves simultaneously, adding to the mystery of quantum mechanics.Despite its success in explaining the behavior of atoms and subatomic particles, quantum mechanics is still not fully understood. It has been described as a "magical" and "mysterious" method due to its ability to produce unexpected and counterintuitive results. The probabilistic nature of quantum mechanics, where predictions are made based on the likelihood of outcomes rather than definitive results, adds to its enigmatic nature.The potential applications of quantum mechanics are vast. Quantum computers, currently in their infancy, have the potential to performcomplex calculations exponentially faster than classical computers. Quantum cryptography promises unbreakable encryption, ensuring secure communication in a world where digital security is crucial. Furthermore, quantum sensors have the ability to detect incredibly small changes in physical quantities, making them invaluable in fields like medicine, defense, and environmental monitoring.In conclusion, quantum mechanics is a field that continues to perplex and fascinate scientists and laypeople alike. Its counterintuitive concepts, such as superposition, entanglement, and wave-particle duality, make it appear as a mysterious and magical method. Despite its challenges, quantum mechanics holds immense potential for technological advancements and deeper understanding of the fundamental workings of the universe. As we continue to explore and unravel the mysteries of quantum physics, we embark on a thrilling journey into the unknown.。

有关科幻故事的英语作文

有关科幻故事的英语作文Title: A Journey Beyond Time: A Sci-Fi Story。

In the vast expanse of the cosmos, where stars twinkle like distant promises and galaxies weave intricate tapestries of light, there exists a realm where the boundaries of time and space blur into a surreal mosaic of possibilities. It is within this realm that our story unfolds, a tale of adventure, discovery, and the relentless pursuit of knowledge.In the not-so-distant future, humanity has unlocked the secrets of interstellar travel, harnessing the power of quantum propulsion to traverse the cosmos with unprecedented ease. Among those daring explorers is Captain Alex Reynolds, a seasoned veteran of the Galactic Exploration Corps, and her intrepid crew aboard thestarship Odyssey.Their mission: to chart unexplored sectors of thegalaxy, seeking out new worlds and civilizations beyond the reaches of known space. Equipped with state-of-the-art technology and fueled by an insatiable curiosity, they embark on a journey that will test the limits of their courage and resolve.As the Odyssey hurtles through the void, Captain Reynolds and her crew encounter wonders beyond imagination: planets teeming with exotic life forms, nebulae ablaze with iridescent hues, and phenomena that defy conventional laws of physics. Yet amid the splendor of the cosmos, they also confront dangers lurking in the shadows of the unknown.One fateful day, while navigating a remote sector of the galaxy, the Odyssey is ensnared by a mysterious anomaly—a rift in the fabric of space-time itself. Stranded in a realm where past, present, and future converge in a kaleidoscope of temporal anomalies, the crew must unravel the secrets of this enigmatic realm if they ever hope to find their way home.Driven by a mixture of scientific curiosity and adesire to reunite with their loved ones, Captain Reynolds leads her crew on a perilous journey through the tangled corridors of time. Along the way, they encounter echoes of their own past, alternate realities shaped by the choices they never made, and glimpses of a future yet to unfold.Amidst the chaos of temporal turbulence, bonds are forged, and friendships are tested as the crew grapples with the existential questions that lie at the heart of their journey. What does it mean to exist across multiple timelines? Can the past be changed, or are we mere passengers on the river of time?As they navigate the labyrinth of temporal anomalies, Captain Reynolds and her crew uncover a startling truth: the anomaly that brought them here was not a mere accident but a gateway to a realm beyond comprehension—a realm where the very fabric of reality is but a tapestry woven by the hands of gods.In the final showdown against forces that defy mortal understanding, Captain Reynolds and her crew must make achoice that will shape the destiny of not only their own universe but countless others across the multiverse. In a climactic battle against entropy itself, they stand united, their resolve unshaken by the vastness of the cosmos.And as the dust settles and the stars realign, the Odyssey emerges from the crucible of time, forever changed yet unbowed. For in the endless expanse of the cosmos,where the boundaries of reality are but a fleeting illusion, there are no endings—only new beginnings, waiting to be written in the annals of eternity.。

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a rXiv:h ep-th/9512162v12D ec1995Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers Taksu Cheon Department of Physics,Hosei University,Fujimi,Chiyoda-ku,Tokyo 102,Japan Takaomi Shigehara Computer Centre,University of Tokyo,Yayoi,Bunkyo-ku,Tokyo 113,Japan (October 3,1995)Abstract We argue that the random-matrix like energy spectra found in pseudointe-grable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system.It is shown that the behavior of the running coupling constant explains the key characteristics of the level statistics of pseudointegrable billiards.5.45.+b,3.65.Db,11.10.GhTypeset using REVT E XThe concepts of scale anomaly and the asymptotic freedom are among the key features of the gaugeﬁeld theories which describe the interaction of the elementary particles.It is less widely recognized,however,that the scale anomaly can be found in a vastly simpler setting of one particle quantum mechanics.A particle scattered oﬀa pointlike scatterer in two spacial dimension is known to have energy dependent s-wave phase shift defying the scale invariance of its classical analogue[1].There exists a sister problem of particle mo-tion conﬁned in a hard-wall boundary with a pointlike scatterer inside.When the shape of the boundary is a rectangle,the problem belongs to a larger category of systems known as pseudointegrable billiards[2–5].This system is known for puzzling statistical properties of its energy eigenvalues[3,5].It is shown through numerical experiments that the level statistics of the pseudointegrable billiard resembles to that of random-matrix ensembles[6] which is generally associated with chaotic dynamics[7].This is in seeming contradiction with the absence of chaotic dynamics in classical analogue system.Further,when the levels are collected at higher energy region,the level statistics moves toward the Poisson distribu-tion which characterizes the integrable classical dynamics.Also,the system tends to show more of Wigner-like statistics when the genus of the billiard is increased,that is,in the present context,when the number of the singular scatterers is increased.These facts have never received suﬃcient explanations,in spite of several attempted studies based on the semiclassical periodic orbit quantization theory[8,9].In this paper,we argue that the behavior of spectra of the pseudointegrable billiard with pointlike scatterers is a direct result of the scale anomaly of the system.Speciﬁcally,the dependence of the level statistics on the energy and the number of the scatterers is shown to be well explained by the high energy behavior of the eﬀective coupling strength of the pointlike scatterer.We consider a quantum particle of unit mass moving freely inside a boundary B in two spacial dimension on which its wave functions are assumed to vanish.We denote the eigenvalue and eigenfunction of the system asεn andφn,namely−1.(2)ω−εnWhen the shape of the boundary B is such that the classical motion of the particle is regular (as in the case of B being rectangular),the nearest neighbor spacing s n=εn+1−εn is distributed according to the Poisson distribution P(s)=exp(−s).We now place a pointlike scatterer at x0.Naively,one deﬁnes the scatterer in terms of the Dirac’s delta function in two dimensionV( x)=vδ( x− x0).(3) Under the scale transformation x→a x,the potential is transformed as V( x)→V( x)/a2. Since this behavior is identical to that of the Laplacian operator in eq.(1a),the system is scale invariant.One expects,therefore,that the dynamical properties of the system should not depend on the energy.Formally,the transition matrix T(T-matrix)in the presence of the scatterer V is given byT=V+V G(0)T.(4) The poles of T give the eigenvalues of the system.Because of the separability of the delta potential, φn Vφm =vφn( x0)φm( x0),the T-matrix is also separable:φn Tφm =t(ω)φn( x0)φm( x0).(5) Apart from the trivial solutionω=εn for the case ofφn( x0)=0,the poles of T are formally given by the roots of the equation1v−G (0)(ω)=0(6)with G (0)(ω)≡G (0)( x 0, x 0;ω)=∞ n =1φn ( x 0)2ω−εn ≈ φ( x 0)2∞ n =11ω−ε→∞(8)where φ( x 0)2 is the average value of φn ( x 0)2among various n .The divergence is brought about because the density of states is constant (which we denote ρ0)with respect to the energy.To handle the divergence,a scheme for regularization and renormalization is called for.The most mathematically satisfying scheme is given by the self-adjoint extension theory of functional analysis[10,11].Here we just quote the result.After the self-adjoint extension,the transition matrix t (ω)is given by11−e i Θ d x G (0)( x , x 0;ω)G (0)( x , x 0;i Λ)+(ω+i Λ)¯v −G (ω)=∞ n =1φn ( x 0)2 1ε2n +Λ2 (11)is the regularized version of G (0)(ω),and¯v= ΛsinΘε2n+Λ2 −1(12) is the formal(or renormalized)coupling strength of the scatterer.We stress that in spite of purely mathematical construction of eqs.(10)-(12),it does correspond to the physical small-size limit of the problem of aﬁnite-size obstacle.Since the series of eq.(11)is convergent,the problem is now well deﬁned.We look at the behavior of eq.(10)at high energy regionω>>Λ.For a given value ofω,we can approximate eq.(11)by truncating the summation at n=n x(ω)ω−εn +εnG=∞n=n x(ω)+1φn( x0)2 1ε2n+Λ2≈ φ( x0)2 ρ0 ∞εx(ω)dε 1ε2+Λ2≈− φ( x0)2 ρ20ωG.Once the summation is truncated atﬁnite terms,we can rewrite eq.(10)as1ω−εn=0(16) with the eﬀective strength v e f f(ω,¯v)deﬁned through1¯v−n x(ω)n=1φn( x0)2εnit acquires energy dependence.This is possibly the simplest example of the scale anomaly [1].The eﬀective coupling v e f f is also referred to as running coupling because of its energy dependence.When v e f f is large for the energy region of the interest,it induces the mixing among the basis states,and results in the Wigner form of the nearest neighbor spacing distribution P(s)=14πs2).It is known that v e f f is large only in one energy region determined by the value of¯v andΛ[5].Replacing the summation in eq.(17)with the integral as in eq.(14),we havev e f f(ω,¯v)≈¯v1+(n x(ω)/ρ0Λ)2.(18)At the limitω→∞,we have logφ( x0)2 ρ0logω(ω→∞).(19) Remarkably,the formal strength disappears from the expression of the eﬀective strength v e f f in the high energy limit.It is now easy to see the reason for the level statistics of pseudointegrable billiards becoming more Poisson-like at higher energy region,irrespective to the choice of the formal coupling¯v.The fact that the strength v e f f disappears at the limit ω→∞goes along well with our intuition that,at the classical limit,a pointlike obstacle has no eﬀect on the motion of a particle.At this limit,all the wave functions are unperturbed and the scale invariance is restored in a trivial manner.We note that when we replace the sum with the integral in obtaining eq.(18),we implicitly assume that the size of the billiard is far larger than the scale in discussion.That is the reason why the size of the billiard boundary,which obviously breaks the scale invariance,does not appear in our arguments.We next consider the case of two pointlike scatterers.We place the scatterers at x0and x1with the formal strengths¯v0and¯v1,respectively.The eigenvalues of this system are determined by1G00(ω)−G01(ω)−G10(ω)1G11(ω)=0(20)whereG ij (ω)=∞ n =1φn ( x i )φn ( x j ) 1ε2n +Λ2 (21)andG ij (ω)=∞ n =1φn ( x i )φn ( x j )G 00(ω)and √ρ0v (2)e f f (ω,¯v 0,¯v 1)−n x (ω) n =1φn ( x 0)2φ(x 0)2 ρ0log ω(ω→∞).(26)Namely,two closely placed pointlike scatterers with the same formal strength act as a single scatterer of twice the eﬀective strength.If we remove our assumption of two pointlike scatterers located closely,we have to deal with eq.(20)directly.However,we do not expect an essential change of the character of level statistics,since the statistical measures are known to be rather insensitive to the precise location of the scatterers.This allows us to generalize ourﬁndings to the case of more than two scatterers.Let us consider a billiard with an arbitrary(ﬁnite)number of pointlike scatterers inside.We classify the scatterers according to the magnitude of the formal strength;we collect the scatterers with the same order of magnitude of the formal strength as a single group.We can expect that the scatterers belonging to one of such groups disturb the particle motion in a coherent manner in the energy region determined by their own formal strength,while their inﬂuence never appears at diﬀerent energies.In particular, in the case of scatterers with a common formal strength,their eﬀects are additive.This essentially explains the known behavior of pseudointegrable billiards that by increasing the number of singular points one obtains more Wigner-like level statistics.We now place ourﬁndings in a broader context.The standard approach in quantum chaology has been the semiclassical periodic orbit theory[12,13]which is a truncation of WKB approximation.It cannot be easily applied to the problem with singular scatterers, since the classical orbit hitting the pointlike scatterer occupies a set of measure zero in the phase space.Our approach,on the contrary,is fully quantum mechanical without any resort to semiclassical approximations.Although the present approach is applicable only to the system with pointlike scatterers,our results certainly give an insight to the problem of quantum level statistics of generic pseudointegrable system.Speciﬁcally,we believe that it establishes aﬁrm ground to the earlier intuitive notion of”wave chaos”[3,4],that is the chaotic motion generated by the uncertainty principle in the motion of wave-natured quantum particles.The system studied here clearly is a pedagogical example of the quantum violation of classical scale invariance.We believe that it enhances the intuitive understanding of thescale invariance and asymptotic freedom which have been viewed as phenomena found only in the esoteric theories of elementary particles.Finally,we stress that,even apart from the arguments on quantum chaos,we could have arrived at the level statistics in search of the measurable consequence of scale anomaly of the system,since it gives a handy way to see the eﬀective strength of the pointlike scatterer in the absence of clear-cut measures to gauge its eﬀect on the individual states.In summary,we have derived the energy and number-of-scatterer dependence of the eﬀective coupling strength of pointlike scatterers in billiard systems.We have shown that it explains the key characteristics of the level statistics of the quantum pseudointegrable billiards.We express our thank to Profs.Izumi Tsutsui and Hidezumi Terazawa for the helpful discussions and comments.TC gratefully acknowledge the hospitable research environment oﬀered to him by the members of the Theory Division at Institute for Nuclear Study,Uni-versity of Tokyo.TS acknowledge the support of the Grant-in-Aid for Encouragement of Young Scientists(No.07740316)by the Ministry of Education,Science,Sports and Culture of Japan.REFERENCES[1]R.Jackiw,“Diverse Topics in Theoretical and Mathematical Physics”,(World Scientiﬁc,Singapore,1995).[2]R.J.Richens and M.V.Berry,Physica D2,495(1981).[3]T.Cheon and T.D.Cohen,Phys.Rev.Lett.62,2769(1989).[4]P.ˇSeba,Phys.Rev.Lett.64,1855(1990).[5]T.Shigehara,Phys.Rev.E50,4357(1994).[6]M.L.Mehta,“Random Matrices,second edition”(Academic Press,New York,1990).[7]O.Bohigas,M.J.Giannoni and C.Schmit,Phys.Rev.Lett.52,1(1983).[8]D.Biswas and S.Sinha,Phys.Rev.Lett.70,916(1993).[9]A.Shudo and Y.Shimizu,Phys.Rev.E47,54(1993).[10]S.Albeverio,F.Gesztesy,R.Høegh-Krohn and H.Holden,“Solvable Models in Quan-tum Mechanics”(Springer-Verlag,New York,1988).[11]J.Zorbas,J.Math.Phys.21,840(1980).[12]M.C.Gutzwiller,J.Math.Phys.11,1791(1970);ibid.12,343(1971).[13]E.B.Bogomolny,Physica31D,169(1989).。