共查询到20条相似文献,搜索用时 265 毫秒
1.
John C. Baez 《Foundations of Physics》1989,19(1):91-95
E. P. Wigner's argument that the probability of the existence of self-reproducing units, e.g., organisms, is zero according to standard quantum theory is stated and analyzed. Theorems are presented which indicate that Wigner's mathematical result in fact should not be interpreted as asserting the improbability of self-reproducing units. 相似文献
2.
The Wigner's Theorem states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex
Hilbert space which preserves orthogonality is induced by either a unitary or an anti-unitary operator. There exist many Wigner-type
theorems, in particular in indefinite metric spaces, von Neumanns algebras and Banach spaces and we try to find a common origin
of all these results by using properties of the lattice subspaces of certain topological vector spaces. We prove a Wigner-type
theorem for a pair of dual spaces which allows us to obtain, as particular cases, the usual Wigner's Theorem and some of its
generalizations.
PACS: 02.40.Dr, 03.65.Fd,03.65.Ta
AMS Subject Classification (1991): 06C15, 46A20, 81P10. 相似文献
3.
MáTé Gy?ry 《Reports on Mathematical Physics》2004,54(2):159-167
In our paper we present a new, elementary proof for Wigner's famous unitary-antiunitary theorem. 相似文献
4.
Lajos Molnár 《Communications in Mathematical Physics》2000,210(3):785-791
We present a generalization of Wigner's unitary-antiunitary theorem for pairs of ray transformations. As a particular case, we get a new Wigner-type theorem for non-Hermitian indefinite inner product spaces. 相似文献
5.
We introduce a dynamical system, for which it is possible to get such a large number of eigenvalues that deviations from Wigner's surmise are visible. The obtained level-spacing distribution agrees much better with the distribution derived from random matrix theory. 相似文献
6.
Lajos Molnár 《Communications in Mathematical Physics》2001,217(2):409-421
Wigner's classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated,
for example, in the following way: Every bijective transformation on the set ℒ of all 1-dimensional subspaces of a Hilbert
space H which preserves the angle between the elements of ℒ is induced by either a unitary or an antiunitary operator on H. The aim of this paper is to extend Wigner's result from the 1-dimensional case to the case of n-dimensional subspaces of H with n∈ℕ fixed.
Received: 28 August 2000 / Accepted: 30 October 2000 相似文献
7.
We consider quasi-free quantum systems and we derive the Euler equation using the so-called hydrodynamic limit. We use Wigner's well-known distribution function and discuss an extension to band distribution functions for particles in a periodic potential. We investigate the bosonic system of hard rods and calculate fluctuations of the density. 相似文献
8.
The morphology-dependent resonances (MDRs) in a dielectric sphere that contains many tiny inclusions are studied by use of a recently developed degenerate perturbation method. Degenerate MDRs in the sphere split into multiplets because of the loss of spherical symmetry and manifest themselves as broadened spectral lines in the scattering cross section. Furthermore, the distribution of MDRs in a multiplet is found to obey Wigner's semicircular theorem. 相似文献
9.
Using the time-dependent wave function we have studied the properties of the atomic transverse motion in an interferometer, and the cause of the non-classical behavior of atoms reported by Kurtsiefer, Pfau, and Mlynek [Nature
386, 150 (1997)]. The transverse wave function is derived from the solution of the two-dimensional Schrödinger's equation, written in the form of the Fresnel–Kirchhoff diffraction integral. It is assumed that the longitudinal motion is classical. Comparing data of the space distribution and of the transverse momentum distribution in interferometers with one and two open slits, it follows that the atomic motion is influenced by the atomic matter wave and violates the laws of classical mechanics. However, the negative values of Wigner's function should not be taken as evidence that the atoms in an interferometer violate the classical statistical law of the addition of positive probabilities. This inference follows from the comparison of properties of Wigner's function and of the de Broglian probability density in phase space. 相似文献
10.
Quantum systems capable of chaotic motion in the classical limit can display linear, quadratic, or quartic level repulsion. For a given (time independent or time dependent) Hamiltonian the degree of level repulsion is determined by the full group of its unitary and antiunitary symmetries. We establish this connection for kicked systems, using Wigner's theory of corepresentations, and the appropriate generalization of Pechukas' phase space flow. We illustrate the theory in terms of two systems of kicked spins both of which are time reversal invariant, one showing linear and the other quadratic level repulsion. 相似文献
11.
Antoine Royer 《Foundations of Physics》1992,22(5):727-736
For a wave packet evolving quantum mechanically, the rates of change of the expectations and uncertainties of the position and momentum are exactly the same as if Wigner's function instantaneously obeyed a classical Liouville equation (whatever the Hamiltonian). This extension of Ehrenfest's theorem should be useful for dealing with the evolution and manipulation of quantum states. 相似文献
12.
We investigate quantum mechanical implications of canonically inequivalent Hamilton formulations of the Newtonian dynamics. Generated alternative quantizations, being noncanonical, are consistent with the same equations of motion, i.e., they satisfy E.Wigner's principle of quantization. As illustration we consider a noncanonical one-dimensional harmonic oscillator. 相似文献
13.
V.Debierre 《理论物理通讯》2019,71(4):403-409
We propose a direct derivation of the Lorentz generators for the four-potential of electrodynamics on the basis of Wigner's theorem. The derivation relies on a study of the behaviour of polarisation vectors under k-space differentiation. The Coulomb and Lorenz gauges are discussed in that respect, and gauge invariance under Poincare′transformations is examined. The Poincar′e generators given by Bia lynicki-Birula and Bia lynicka-Birula are found to correspond to the Coulomb gauge case. 相似文献
14.
Quantal penetration through a (stationary) one-dimensional potential barrier is considered as a time evolution of an initially
prepared wave packet. The large-time asymptotics of the process is concerned. Locality of the potential imposes certain analytical
properties of the interaction amplitudes in the energy representation. The results are presented in terms of development of
the phase-space (Wigner's) quasi-distribution. The phase-space evolution kernel is constructed, and it is shown that in the
presence of a positive potential no part of the distribution is transported faster than the free particle. For the case of
a small initial momentum uncertainty, the deformation of the coordinate density is considered, including a possible advance
of its maximum, which would not mean any noncausal signal transport.
Supported by G. I. F. 相似文献
15.
It is shown experimentally that the nonspecular reflection of light on an interface induces a time delay, as predicted by Wigner's scattering theory. A differential femtosecond technique is used to directly isolate this delay, associated with the Goos-Hanchen spatial shift produced by a grating near a resonant Wood anomaly. A delay of 4.4 fs is observed between TE and TM pulses, in agreement with the expected Wigner delay obtained from phase shift dispersion measurements. 相似文献
16.
Prange RE 《Physical review letters》2003,90(7):070401
In quasiclassical spectral theory, "resurgence" means that long periodic orbits can be expressed by short ones in such a way that the spectral determinant is real. The question has thus long been posed whether long scattering orbits can be expressed by short orbits in such a way as to make the quasiclassical scattering matrix unitary. We here find a resurgent and manifestly Hermitean expression for Wigner's R matrix, implying a unitary scattering matrix. The result is particularly important if the average resonance width is comparable with the average resonance spacing. 相似文献
17.
The behavior of near-threshold cross sections for dissociation of a target into a pair of particles, as described by Wigner's threshold law, can depend sensitively on the angular momentum of the particles. In this Letter, we investigate the near-threshold nonresonant two-photon detachment process in the negative ion of gold. The expected s-wave threshold behavior is observed with linearly polarized light. Closure of the s-wave channel is realized by using circular polarization, allowing the first observation of a d-wave threshold. Practical applications are discussed, including extensions which could prove valuable for investigations of negative ions with near-threshold structure. 相似文献
18.
Nazakat Ullah 《Journal of statistical physics》1981,24(3):413-418
The probability density function of the single eigenvalue is expanded in terms of the reciprocal of the dimension of the matrix using Bessel functons. It is shown that for the new matrix ensembles this expansion gives Wigner's semicircle centered at the mean value of the matrix elements plus terms of the order ofN
–1, whereN is the dimension of the matrix. 相似文献
19.
After briefly putting algebraic quantum theory into the context of a probabilistic interpretation with emphasis on local measurements, certain general features of the theory are examined. Sectors are defined and shown to be the components of the pure state space in the norm topology. Transition probabilities are defined by a simple algebraic formula and it is shown how superpositions of pure states may be defined. With the aid of these results, symmetries are characterized and the connexion with Wigner's Theorem is established. 相似文献
20.
N. L. Harshman 《International Journal of Theoretical Physics》2003,42(10):2357-2370
This paper provides the mathematical tools for addressing issues of two kinds of causality in relativistic scattering theory: general causality, i.e., an effect can only be measured after its cause, and Einstein causality, i.e., no propagation of probability outside of the forward light cone. Starting from Wigner's unitary irreducible representations of the Poincaré group for noninteracting, one particle states, we describe the mathematical tools necessary to describe scattering states, the Lippmann-Schwinger Dirace kets, and to describe resonances and decaying states, the relativistic Gamow ket. An important step for their derivations is the Hardy space hypothesis. Investigating the transformation properties of scattering and resonance states under the dynamical Poincaré semigroup reveals that both kinds of causality result from this hypothesis about nature of the spaces of states and observables. 相似文献