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

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Breaking time for the quantum chaotic attractor

Alexander Iomin, G. M. Zaslavsky

Published Feb 24, 2003• 19 citations
Publisher

Abstract

A model of a quantum dissipative system is considered in the regime when the classical limit corresponds to a chaotic attractor, and the breaking time tau(Planck) of the classical-quantum correspondence is obtained. The model describes a periodically kicked harmonic oscillator (or a particle in a constant magnetic field) with a dissipation. Another analog of this problem is the dissipative kicked Harper model. It is shown that in the limit of the so-called dying attractor, the breaking time tau(Planck) can be arbitrarily large.

DOI
10.1103/physreve.67.027203

Related papers

Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator

Andre R. R. Carvalho, R. L. de Matos Filho, L. Davidovich

We discuss the roles of the macroscopic limit and different system-environment interactions in a quantum-classical transition for a chaotic system. We consider the kicked harmonic oscillator subject to reservoirs that correspond in the classical case to purely dissipative or purely diffusive behavior, a situation that can be implemented in ion trap experiments. In the dissipative case, we derive an expression for the time at which quantum and classical predictions become different (breaking time) and show that complete quantum-classical correspondence is not possible in the chaotic regime. For the diffusive environment we estimate the minimum value of the diffusion coefficient necessary to retrieve the classical limit and also show numerical evidence that, for diffusion below this threshold, the breaking time behaves, essentially, like that in the case of a system without a reservoir.

arXiv:quant-ph/0405009•Physical Review E•Aug 24, 2004•34 citations

Decoherence and the quantum-classical limit in phase space (Invited Paper)

L. Davidovich, Fabricio Toscano, R. L. de Matos Filho

We discuss the emergence of the classical description from quantum mechanics for chaotic systems. We consider a specific model, which corresponds to an ion trapped in a harmonic potential and submitted to a sequence of laser pulses: the kicked harmonic oscillator, under conditions that lead to chaotic behavior for the classical system. We show that noise plays an essential role in the transition from quantum to classical behavior. This transition is described in terms of the separation between the classical phase space distribution and the Wigner function corresponding to the quantum system, obtained by integrating over the whole phase space the magnitude of the difference between the two distributions. It is shown that, in the semiclassical limit, this separation is governed by a single parameter, which depends on the diffusion coefficient, the Lamb-Dicke parameter, and the kick strength. The Lamb-Dicke parameter plays the role of a dimensioneless Planck constant. As this parameter goes to zero, we show that both distributions remain close together for all times.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 23, 2005•0 citations

Quantum Chaotic Attractor in a Dissipative System

W. Vincent Liu, William C. Schieve

A dissipative quantum system is treated here by coupling it with a heat bath of harmonic oscillators. Through quantum Langevin equations and Ehrenfest's theorem, we establish explicitly the quantum Duffing equations with a double-well potential chosen. A quantum noise term appears the only driving force in dynamics. Numerical studies show that the chaotic attractor exists in this system while chaos is certainly forbidden in the classical counterpart.

arXiv:chao-dyn/9703012•Physical Review Letters•Apr 28, 1997•15 citations

Quantum-to-classical transition in a system with mixed classical dynamics

Fabricio Toscano, Diego A. Wisniacki

We study how decoherence rules the quantum-classical transition of the kicked harmonic oscillator. The system presents classical dynamics that ranges from regular to strong chaotic behavior depending on the amplitude of the kicks. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and quantum phase space distributions is proportional to a single parameter chi identical to K Planck's (eff)(2)/4D(3/2) , which relates the effective Planck constant, Planck's (eff), to the kicking strength, K, and the diffusion constant, D. This relation between classical and quantum distributions is valid when chi<1 , a case that is always attainable in the semiclassical regime, independent of the value of the strength of noise given by D. Our results extend a recent study performed in the chaotic regime.

arXiv:quant-ph/0606024•Physical Review E•Nov 27, 2006•6 citations

Kicked fluxonium with quantum strange attractor

Alexei D. Chepelianskii, Dima L. Shepelyansky

The quantum dissipative time evolution of a fluxonium under a pulsed field (kicks) is studied numerically and analytically. In the classical limit the system dynamics is converged to a strange chaotic attractor. The quantum properties of this system are studied for the density matrix in the frame of Lindblad equation. In the case of dissipative quantum evolution the steady-state density matrix is converged to a quantum strange attractor being similar to the classical one. It is shown that depending on the dissipation strength there is a regime when the eigenstates of density matrix are localized at a strong or moderate dissipation. At a weak dissipation the eigenstates are argued to be delocalized being linked to the Ehrenfest explosion of quantum wave packet. This phenomenon is related with the Lyapunov exponent and Ehrenfest time for the quantum strange attractor. Possible experimental realisations of this quantum strange attractor with fluxonium are discussed.

quant-pharXiv:2512.18644•Physics•Dec 23, 2025•1 citation

Chaos and magic in the dissipative quantum kicked top

Gianluca Passarelli, Procolo Lucignano, Davide Rossini +1 more

We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. In the thermodynamic limit, it is described by classical mean-field equations that can show regular and chaotic regimes. At finite size, we describe the system dynamics using stochastic quantum trajectories. We find that the asymptotic nonstabilizerness (alias the m a g i c , a measure of quantum complexity), averaged over trajectories, mirrors to some extent the classical chaotic behavior, while the entanglement entropy has no relation with chaos in the thermodynamic limit.

arXiv:2406.16585•Quantum•Mar 5, 2025•19 citations
A model of a quantum dissipative system is considered in the regime when the classical limit corresponds to a chaotic attractor, and the breaking time tau(Planck) of the classical-quantum correspondence is obtained. The model describes a periodically kicked harmonic oscillator (or a particle in a constant magnetic field) with a dissipation. Another analog of this problem is the dissipative kicked Harper model. It is shown that in the limit of the so-called dying attractor, the breaking time tau(Planck) can be arbitrarily large.
We discuss the roles of the macroscopic limit and different system-environment interactions in a quantum-classical transition for a chaotic system. We consider the kicked harmonic oscillator subject to reservoirs that correspond in the classical case to purely dissipative or purely diffusive behavior, a situation that can be implemented in ion trap experiments. In the dissipative case, we derive an expression for the time at which quantum and classical predictions become different (breaking time) and show that complete quantum-classical correspondence is not possible in the chaotic regime. For the diffusive environment we estimate the minimum value of the diffusion coefficient necessary to retrieve the classical limit and also show numerical evidence that, for diffusion below this threshold, the breaking time behaves, essentially, like that in the case of a system without a reservoir.
We discuss the emergence of the classical description from quantum mechanics for chaotic systems. We consider a specific model, which corresponds to an ion trapped in a harmonic potential and submitted to a sequence of laser pulses: the kicked harmonic oscillator, under conditions that lead to chaotic behavior for the classical system. We show that noise plays an essential role in the transition from quantum to classical behavior. This transition is described in terms of the separation between the classical phase space distribution and the Wigner function corresponding to the quantum system, obtained by integrating over the whole phase space the magnitude of the difference between the two distributions. It is shown that, in the semiclassical limit, this separation is governed by a single parameter, which depends on the diffusion coefficient, the Lamb-Dicke parameter, and the kick strength. The Lamb-Dicke parameter plays the role of a dimensioneless Planck constant. As this parameter goes to zero, we show that both distributions remain close together for all times.
We study how decoherence rules the quantum-classical transition of the kicked harmonic oscillator. The system presents classical dynamics that ranges from regular to strong chaotic behavior depending on the amplitude of the kicks. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and quantum phase space distributions is proportional to a single parameter chi identical to K Planck's (eff)(2)/4D(3/2) , which relates the effective Planck constant, Planck's (eff), to the kicking strength, K, and the diffusion constant, D. This relation between classical and quantum distributions is valid when chi<1 , a case that is always attainable in the semiclassical regime, independent of the value of the strength of noise given by D. Our results extend a recent study performed in the chaotic regime.
The quantum dissipative time evolution of a fluxonium under a pulsed field (kicks) is studied numerically and analytically. In the classical limit the system dynamics is converged to a strange chaotic attractor. The quantum properties of this system are studied for the density matrix in the frame of Lindblad equation. In the case of dissipative quantum evolution the steady-state density matrix is converged to a quantum strange attractor being similar to the classical one. It is shown that depending on the dissipation strength there is a regime when the eigenstates of density matrix are localized at a strong or moderate dissipation. At a weak dissipation the eigenstates are argued to be delocalized being linked to the Ehrenfest explosion of quantum wave packet. This phenomenon is related with the Lyapunov exponent and Ehrenfest time for the quantum strange attractor. Possible experimental realisations of this quantum strange attractor with fluxonium are discussed.
We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. In the thermodynamic limit, it is described by classical mean-field equations that can show regular and chaotic regimes. At finite size, we describe the system dynamics using stochastic quantum trajectories. We find that the asymptotic nonstabilizerness (alias the m a g i c , a measure of quantum complexity), averaged over trajectories, mirrors to some extent the classical chaotic behavior, while the entanglement entropy has no relation with chaos in the thermodynamic limit.