Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Europhysics Letters (EPL)

Comment on “A Remark on the Problem of Quantum-Classical Correspondence in the Case of Chaotic Dynamics”

Juan Cesar Flores

Published Mar 10, 1995• 6 citations
Publisher

Abstract

In the paper by Kolovsky ( Europhys. Lett. , 27 (1994) 79) an equation for a mesoscopic particle, with internal structure, was proposed. Nevertheless, that equation is in confrontation with the stability of such a mesoscopic particle. This instability is independent of the chaotic character of the corresponding classical system.
DOI
10.1209/0295-5075/29/8/011

Related papers

Comment on “A Remark on the Problem of Quantum-Classical Correspondence in the Case of Chaotic Dynamics”

A. Pérez Ponce

In a very interesting article written by A. R. Kolovsky, a first-order multipole evolution equation for a mesoscopic particle with internal structure was proposed. In some physical cases the first-order approximation breaks down and it is the second order which must be considered. In this way, we reconsider the case of a mesoscopic particle constituted by identical particles.

Europhysics Letters (EPL)•Oct 1, 1995•3 citations

A Remark on the Problem of Quantum-Classical Correspondence in the Case of Chaotic Dynamics

Andrey R. Kolovsky

The paper discusses the problem of correspondence between the classical and quantum approaches to the description of chaotic dynamics of a mesoscopic particle. The condition for the equivalence of both approaches is given.

Europhysics Letters (EPL)•Jul 10, 1994•26 citations

Chaos in atomic physics

T. S. Monteiro

The influence of quantum chaos on small atomic systems is reviewed. It now seems clear that chaos in the usually understood sense (e.g. exponential sensitivity to perturbations) is not found in isolated quantum systems. However, there are phenomena which appear only when the corresponding classical system is chaotic. The stability of the classical dynamics, in other words whether it is regular or chaotic, has a profound effect on the character of the corresponding quantum spectrum and wavefunctions.

Contemporary Physics•Sep 1, 1994•6 citations

ON STRUCTURAL INSTABILITY OF STATES OF CHAOTIC QUANTUM-SYSTEMS

GO XU, QL JIE, XU, GO (reprint author), NANJING UNIV,DEPT PHYS,NANJING 210008,PEOPLES R CHINA.

Based on quantum canonical representations corresponding to the same subgroup chain of the dynamical group and the quantum canonical transformation between them, the structural instability of states of chaotic quantum systems due to a sensitive dependence on the initial condition is discussed. Numerical illustrations are provided with a model system which has been shown to be classically chaotic.

•Jan 16, 1995•0 citations

Quantum Chaos and Quantum-Classical Correspondence

Joseph Emerson

The quantum dynamics of a classically chaotic model are studied in the approach to the macroscopic limit. The quantum predictions are compared and contrasted with the classical predictions of both Newtonian and Liouville mechanics. The time-domain scaling of the optimal quantum-classical correspondence is analyzed in detail in the case of both classical theories. In both cases the correspondence for observable quantities is shown to break down on a time-scale that increases very slowly (logarithmically) with increasing system size. In the case of quantum-Liouville correspondence such a short time-scale does not imply a breakdown of correspondence since the largest quantum-Liouville differences reached on this time-scale decrease rapidly (as an inverse power) with increasing system size. Therefore the statistical properties of chaotic dynamics are, as expected, well described by quantum theory in the macroscopic limit. In contrast, the largest quantum-Newtonian differences reached on the log time-scale actually increase in proportion to the system size. Since the invariance properties of the Hamiltonian impose functional constraints on the time-varying chaotic coordinates, it is possible to show, moreover, that if the quantum predictions are believed to describe the coordinates of individual chaotic systems, then they also predict macroscopic violations of any kinematic or dynamic constants of the motion. These results for chaotic systems indicate that a valid description of the time-varying properties of individual macroscopic bodies is not available within the standard interpretive framework of quantum theory.

arXiv:quant-ph/0211035•Nov 7, 2002•10 citations

Comment on “Quantum suppression of chaos in the spin-boson model”

Luca Bonci, Roberto Roncaglia, Bruce J. West +1 more

We independently examine the case of a spin-$j$ particle interacting with a boson field studied by Finney and Gea-Banacloche. We concentrate on their conclusion that in the case $j=1/2$ the correspondence between the quantum and the semiclassical case is damaged to the point that the increase of entropy and quantum uncertainty for regular motion exceeds that for the chaotic case. We demonstrate by direct calculation that this conclusion is the result of mistakenly identifying a regular evolution of the spin-boson system as being chaotic.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1997•0 citations
The influence of quantum chaos on small atomic systems is reviewed. It now seems clear that chaos in the usually understood sense (e.g. exponential sensitivity to perturbations) is not found in isolated quantum systems. However, there are phenomena which appear only when the corresponding classical system is chaotic. The stability of the classical dynamics, in other words whether it is regular or chaotic, has a profound effect on the character of the corresponding quantum spectrum and wavefunctions.
The quantum dynamics of a classically chaotic model are studied in the approach to the macroscopic limit. The quantum predictions are compared and contrasted with the classical predictions of both Newtonian and Liouville mechanics. The time-domain scaling of the optimal quantum-classical correspondence is analyzed in detail in the case of both classical theories. In both cases the correspondence for observable quantities is shown to break down on a time-scale that increases very slowly (logarithmically) with increasing system size. In the case of quantum-Liouville correspondence such a short time-scale does not imply a breakdown of correspondence since the largest quantum-Liouville differences reached on this time-scale decrease rapidly (as an inverse power) with increasing system size. Therefore the statistical properties of chaotic dynamics are, as expected, well described by quantum theory in the macroscopic limit. In contrast, the largest quantum-Newtonian differences reached on the log time-scale actually increase in proportion to the system size. Since the invariance properties of the Hamiltonian impose functional constraints on the time-varying chaotic coordinates, it is possible to show, moreover, that if the quantum predictions are believed to describe the coordinates of individual chaotic systems, then they also predict macroscopic violations of any kinematic or dynamic constants of the motion. These results for chaotic systems indicate that a valid description of the time-varying properties of individual macroscopic bodies is not available within the standard interpretive framework of quantum theory.
We independently examine the case of a spin-jjj particle interacting with a boson field studied by Finney and Gea-Banacloche. We concentrate on their conclusion that in the case j=1/2j=1/2j=1/2 the correspondence between the quantum and the semiclassical case is damaged to the point that the increase of entropy and quantum uncertainty for regular motion exceeds that for the chaotic case. We demonstrate by direct calculation that this conclusion is the result of mistakenly identifying a regular evolution of the spin-boson system as being chaotic.