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

International Conference on Nuclear Reaction and Beyond

Time Evolution of Wave Packets in Quantum Chaotic Systems —A Manifestation of Quantum Chaos

Junqing Li, Fang Liu, Luo Yi-Xiao, Xu Gong-ou

Published Dec 1, 2000• 0 citations
Publisher
DOI
10.1142/9789812791832_0022

Related papers

Time evolution of chaotic quantum systems

Annals of Physics•Nov 1, 1992•0 citations

Chaos and the correspondence limit in the periodically kicked pendulum

Ronald F. Fox, Boon Leong Lan

The correspondence limit is illustrated for the periodically kicked pendulum. The classical dynamics of this system can be represented by a discrete map. A corresponding quantum map is derived and then rendered in the Ehrenfest formulation for expectation values. The Ehrenfest representation is studied for a minimum uncertainty Gaussian wave packet. It is shown that as \ensuremath{\Elzxh} gets very small, followed by a decrease in the variance of the wave packet, the quantum map shadows the classical map with an error approaching zero for a length of time approaching infinity. The Gaussian form of the wave packet is preserved by the time evolution provided ${\mathrm{\ensuremath{\omega}}}_{0}$T\ensuremath{\ll}1. This constraint implies that the classical map is predominantly not chaotic with very small regions of very weak chaos. As ${\mathrm{\ensuremath{\omega}}}_{0}$T approaches 1, where the classical map becomes strongly chaotic, the propagation in time of the Gaussian wave packet completely breaks down. The possible significance of this breakdown is discussed.

Physical Review A•Mar 1, 1990•21 citations

Manifestations of chaos in relativistic quantum systems - A study based on out-of-time-order correlator

Chen-Di Han, Hong-Ya Xu, Liang Huang +1 more

Previous work in the field of relativistic quantum chaos has revealed initial evidence that the manifestations of classical chaos in relativistic quantum systems tend to be weakened as compared with those in nonrelativistic quantum systems. To place this finding on a firmer ground, we investigate the relativistic quantum fingerprints of classical chaos using the out-of-time-order correlator (OTOC). OTOC has recently been applied to a number of fields in physics and it holds special promises for the field of quantum chaos, but existing work focused exclusively on nonrelativistic quantum systems. Calculating and analyzing OTOC for relativistic quantum billiard systems described by the massless Dirac equation, we find that the signatures of classical chaos are indeed characteristically less pronounced in relativistic than in nonrelativistic quantum systems. The finding is substantiated by studying four different aspects of OTOC. Firstly, in the energy eigenspace, in the short time regime there is a complete lack of any signature of chaos associated with the evolution of OTOC in the Dirac billiard due to the relativistic quantum phenomenon of Zitterbewegung, in contrast to nonrelativistic quantum billiard systems where chaos leaves behind a quite distinct signature. Secondly, weakening of the relativistic quantum manifestations of classical chaos occurs in the long time regime as well. Thirdly, evolution of the wave packet based OTOC also reveals that the fingerprints of chaos are much less pronounced in the Dirac billiard systems as compared with the Schrödinger billiards. Fourthly, the level spacing statistics of the OTOC operators in systems with classically integrable and chaotic dynamics, which are characteristically distinct in the Schrödinger billiards, bear a strong similarity in the Dirac billiards, indicating again the dwindling effects of chaos. The OTOC based results suggest that the impacts of classical chaos are generally weaker in relativistic than in nonrelativistic quantum systems, a fundamental issue that warrants further investigation.

Physics Open•Sep 4, 2019•4 citations

Time evolution of chaotic quantum systems

Hanns Ludwig Harney, Frank-Michael Dittes, Axel Müller–Groeling

Annals of Physics•Dec 1, 1992•50 citations

The dynamical aspects of quantum chaos

Sankhasubhra Nag

•Jan 1, 2007•0 citations

Chaos and low-order corrections to classical mechanics or geometrical optics

Bala Sundaram, Peter W. Milonni

Based on simple first-order quantum corrections to classical equations of motion, which we show to be closely related to Gaussian wave-packet dynamics (GWD) and a time-dependent variational principle (TDVP), we deduce that quantum corrections to classical dynamics should typically become most pronounced when the classical system becomes chaotic. The time duration over which classical dynamics, GWD, or TDVP may provide good approximations is much shorter when the classical dynamics are chaotic. However, for certain situations involving very short laser pulses, these approximations can be very accurate. The same concepts are applicable to paraxial wave optics, which may offer simpler experimental studies of ``quantum chaos'': the distinction between classical and ``quantum'' chaos is in large part the distinction between ray versus wave behavior.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 1, 1995•47 citations
The correspondence limit is illustrated for the periodically kicked pendulum. The classical dynamics of this system can be represented by a discrete map. A corresponding quantum map is derived and then rendered in the Ehrenfest formulation for expectation values. The Ehrenfest representation is studied for a minimum uncertainty Gaussian wave packet. It is shown that as \ensuremath{\Elzxh} gets very small, followed by a decrease in the variance of the wave packet, the quantum map shadows the classical map with an error approaching zero for a length of time approaching infinity. The Gaussian form of the wave packet is preserved by the time evolution provided ${\mathrm{\ensuremath{\omega}}}_{0}$T\ensuremath{\ll}1. This constraint implies that the classical map is predominantly not chaotic with very small regions of very weak chaos. As ${\mathrm{\ensuremath{\omega}}}_{0}$T approaches 1, where the classical map becomes strongly chaotic, the propagation in time of the Gaussian wave packet completely breaks down. The possible significance of this breakdown is discussed.
Previous work in the field of relativistic quantum chaos has revealed initial evidence that the manifestations of classical chaos in relativistic quantum systems tend to be weakened as compared with those in nonrelativistic quantum systems. To place this finding on a firmer ground, we investigate the relativistic quantum fingerprints of classical chaos using the out-of-time-order correlator (OTOC). OTOC has recently been applied to a number of fields in physics and it holds special promises for the field of quantum chaos, but existing work focused exclusively on nonrelativistic quantum systems. Calculating and analyzing OTOC for relativistic quantum billiard systems described by the massless Dirac equation, we find that the signatures of classical chaos are indeed characteristically less pronounced in relativistic than in nonrelativistic quantum systems. The finding is substantiated by studying four different aspects of OTOC. Firstly, in the energy eigenspace, in the short time regime there is a complete lack of any signature of chaos associated with the evolution of OTOC in the Dirac billiard due to the relativistic quantum phenomenon of Zitterbewegung, in contrast to nonrelativistic quantum billiard systems where chaos leaves behind a quite distinct signature. Secondly, weakening of the relativistic quantum manifestations of classical chaos occurs in the long time regime as well. Thirdly, evolution of the wave packet based OTOC also reveals that the fingerprints of chaos are much less pronounced in the Dirac billiard systems as compared with the Schrödinger billiards. Fourthly, the level spacing statistics of the OTOC operators in systems with classically integrable and chaotic dynamics, which are characteristically distinct in the Schrödinger billiards, bear a strong similarity in the Dirac billiards, indicating again the dwindling effects of chaos. The OTOC based results suggest that the impacts of classical chaos are generally weaker in relativistic than in nonrelativistic quantum systems, a fundamental issue that warrants further investigation.
Based on simple first-order quantum corrections to classical equations of motion, which we show to be closely related to Gaussian wave-packet dynamics (GWD) and a time-dependent variational principle (TDVP), we deduce that quantum corrections to classical dynamics should typically become most pronounced when the classical system becomes chaotic. The time duration over which classical dynamics, GWD, or TDVP may provide good approximations is much shorter when the classical dynamics are chaotic. However, for certain situations involving very short laser pulses, these approximations can be very accurate. The same concepts are applicable to paraxial wave optics, which may offer simpler experimental studies of ``quantum chaos'': the distinction between classical and ``quantum'' chaos is in large part the distinction between ray versus wave behavior.