共查询到20条相似文献,搜索用时 69 毫秒
1.
Vladimir V. Kisil 《International Journal of Theoretical Physics》2012,51(3):964-984
In the spirit of geometric quantisation we consider representations of the Heisenberg(–Weyl) group induced by hypercomplex
characters of its centre. This allows to gather under the same framework, called p-mechanics, the three principal cases: quantum
mechanics (elliptic character), hyperbolic mechanics and classical mechanics (parabolic character). In each case we recover
the corresponding dynamic equation as well as rules for addition of probabilities. Notably, we are able to obtain whole classical
mechanics without any kind of semiclassical limit ħ→0. 相似文献
2.
3.
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open.
In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the
classical motion of macroscopic bodies. In this paper, we shall formulate the classical limit as a scaling limit in terms
of an adimensional parameter ε. We shall take the first steps toward a comprehensive understanding of the classical limit, analyzing special cases of classical
behavior in the framework of a precise formulation of quantum mechanics called Bohmian mechanics which contains in its own
structure the possibility of describing real objects in an observer-independent way. 相似文献
4.
The classical and quantum physics seem to divide nature into two domains macroscopic and microscopic. It is also certain that
they accurately predict experimental results in their respective regions. However, the reduction theory, namely, the general
derivation of classical results from the quantum mechanics is still a far cry. The outcome of some recent investigations suggests
that there possibly does not exist any universal method for obtaining classical results from quantum mechanics. In the present
work we intend to investigate the problem phenomenonwise and address specifically the phenomenon of scattering. We suggest
a general approach to obtain the classical limit formula from the phase shiftδ
l, in the limiting value of a suitable parameter on whichδ
l depends. The classical result has been derived for three different potential fields in which the phase shifts are exactly
known. Unlike the current wisdom that the classical limit can be reached only in the high energy regime it is found that the
classical limit parameter in addition to other factors depends on the details of the potential fields. In the last section
we have discussed the implications of the results obtained. 相似文献
5.
J.N. Fuchs M. Holzmann F. Laloë 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(4):463-478
The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with
exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification
of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between
the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the
linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the
subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles)
and show that each Ursell operator Un with n≥ 3 contains a “tree-reducible part”, which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles
in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles
interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles,
and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered
at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach,
in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum
statistics and dynamics.
Received 18 October 2001 相似文献
6.
In the classical theory of electromagnetism, the permittivity ε
0 and the permeability μ
0 of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space
of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could
arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined
by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally,
our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values
of ε
0 and μ
0 and for the volume of a virtual pair. Such an interpretation would provide an intriguing connection between the celebrated
theory of classical electromagnetism and the quantum theory in the weak-field limit. 相似文献
7.
N.M. Chepilko A.V. Romanenko 《The European Physical Journal C - Particles and Fields》2001,21(4):757-767
Using the extended Schwinger quantization approach, quantum mechanics on a Riemannian manifold M with the given action of an intransitive group of isometries is developed. It was shown that quantum mechanics can be determined
unequivocally only on submanifolds of M where G acts simply transitively (orbits of G action). The remaining part of the degrees of freedom can be described unequivocally after introducing some additional assumptions.
Being logically unmotivated, these assumptions are similar to the canonical quantization postulates. Besides this ambiguity
which is of a geometrical nature there is an undetermined gauge field of the order of (or higher), vanishing in the classical limit .
Received: 19 February 2001 / Revised version: 10 May 2001 / Published online: 6 July 2001 相似文献
8.
We propose new criteria to evaluate the average time spent by particles in a tunneling barrier. First we construct asojourn time, on the basis of statistical information provided by quantum mechanics, which seems to be an appropriate measure of the time
spent byall particles within the barrier. A simple, stochastic treatment is then used to deal with the particles that actually traverse
the barrier, in order to study their interaction time. The results obtained show that opaque barriers have important effects
on the particlesbefore they enter the potential region, confirming previously published numerical findings. No arbitrarily high effective velocities
appear anywhere in the present treatment. 相似文献
9.
Peter Mittelstaedt 《International Journal of Theoretical Physics》2008,47(1):104-113
The goal of quantum logic is the “bottom-top” reconstruction of quantum mechanics. Starting from a weak quantum ontology,
a long sequence of arguments leads to quantum logic, to an orthomodular lattice, and to the classical Hilbert spaces. However,
this abstract theory does not yet contain Planck’s constant ℏ. We argue, that ℏ can be obtained, if the empty theory is applied to real entities and extended by concepts that are usually considered as
classical notions. Introducing the concepts of localizability and homogeneity we define objects by symmetry groups and systems
of imprimitivity. For elementary systems, the irreducible representations of the Galileo group are projective and determined
only up to a parameter z, which is given by z=m/ℏ, where m is the mass of the particle and ℏ Planck’s constant. We show that ℏ has a meaning within quantum mechanics, irrespective of use the of classical concepts in our derivation. 相似文献
10.
We construct a stochastic mechanics by replacing Bohm‧s first-order ordinary differential equation of motion with a stochastic
differential equation where the stochastic process is defined by the set of Bohmian momentum time histories from an ensemble
of particles. We show that, if the stochastic process is a purely random process with n-th order joint probability density in the form of products of delta functions, then the stochastic mechanics is equivalent
to quantum mechanics in the sense that the former yields the same position probability density as the latter. However, for
a particular non-purely random process, we show that the stochastic mechanics is not equivalent to quantum mechanics. Whether
the equivalence between the stochastic mechanics and quantum mechanics holds for all purely random processes but breaks down for all non-purely random processes remains an open question. 相似文献
11.
Bart D’Hooghe 《International Journal of Theoretical Physics》2010,49(12):3069-3084
We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure
of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction
with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate
situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show
that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law
and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation
on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability
of a state transition in general not only depends on the two states involved, but also on the measurement context which induces
the state transition. 相似文献
12.
J. Kumičák 《Czechoslovak Journal of Physics》1977,27(9):967-979
We prove, using the methods of probability theory, that the density of particles in closed classical systems consisting of a finite numberN of non-interacting point particles constrained to move in a rectangular box of the volumeV will approach a uniform density as t , if the initial states of the systems were created by random attribution of positions and velocities to particles. The time evolution of the systems is assumed to be entirely determined by the initial state: the particle dynamics contains no element of randomness. It is shown that if the number of particlesN (V remaining constant), the systems behave thermodynamically, i.e. they do not show any fluctuations of relative density of particles. The proved behaviour serves as the first step in a new approach to mathematically rigorous derivation of the second law of thermodynamics from the classical mechanics which makes no use of thermodynamic limit. 相似文献
13.
14.
Gabriel Catren 《Foundations of Physics》2008,38(5):470-487
We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do
so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical
states is not incomplete, but rather that the classical notion is overdetermined. 相似文献
15.
By employing the technique of integral within an ordered product (IWOP) of operators we recast classical wavelet transform
to a matrix element of the squeezing-displacing operator U(μ,s) between the mother wavelet vector 〈ψ| and the state vector |f〉 to be transformed, i.e., we propose that 〈ψ|U(μ,s)|f〉 can be considered as a new kind of spectrum for analyzing the quantum state |f〉. In this way we do numerical calculation of wavelet-transform spectrum for the even- and odd-coherent states and then plot
their figures, respectively. Thus this kind of spectrum can be used to recognize a variety of quantum optical states. 相似文献
16.
We consider the time evolution of a system of N identical bosons whose interaction potential is rescaled by N
−1. We choose the initial wave function to describe a condensate in which all particles are in the same one-particle state.
It is well known that in the mean-field limit N → ∞ the quantum N-body dynamics is governed by the nonlinear Hartree equation. Using a nonperturbative method, we extend previous results on
the mean-field limit in two directions. First, we allow a large class of singular interaction potentials as well as strong,
possibly time-dependent external potentials. Second, we derive bounds on the rate of convergence of the quantum N-body dynamics to the Hartree dynamics. 相似文献
17.
C. Baladrón 《Foundations of Physics》2011,41(3):389-395
A sketchy subquantum theory deeply influenced by Wheeler’s ideas (Am. J. Phys. 51:398–404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare
matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three
Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics from
these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered. 相似文献
18.
No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical
field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical
variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures
ρ on Ω having zero mean value and dispersion σ2(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based
on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ2(ρ) = hn (for n = 2 we obtain the conventional quantum formalism). 相似文献
19.
20.
Miklós Banai 《International Journal of Theoretical Physics》1984,23(11):1043-1063
A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis' quantum relativity. The recently proposed classical relativistic quantum theory of Prugoveki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (elementary particles). The main new aspect of this quantum mechanics is that provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that quarks should be considered as quantum relativistic particles.Supported by the Hungarian Academy of Sciences. 相似文献