相关论文: Symmetric Classical Mechanics

The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion…

We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing.…

In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…

Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…

We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…

If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…

We study classical and quantum dynamics of two spinless particles confined in a quantum wire with repulsive or attractive Coulomb interaction. The interaction induces irregular dynamics in classical mechanics, which reflects on the quantum…

We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…

Quantum dynamics of driven open systems should be compatible with both quantum mechanic and thermodynamic principles. By formulating the thermodynamic principles in terms of a set of postulates we obtain a thermodynamically consistent…

We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…

Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…

Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good…

In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires…

In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…

We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…

In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…

A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…

We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…

A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…

Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…