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

arXiv:nlin/0101018

Decoherence in chaotic and integrable systems: A random matrix approach

T. Gorin, T. H. Seligman

Published Jan 9, 2001• 1 citation
arXivHTMLPDF

Abstract

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce a random matrix model that permits to vary the coupling strength between the subsystems. The case of strong coupling is analyzed in detail, and we find at intermediate times a weak effect of spectral correlations that is reminiscent of the correlation hole.

DOI
10.48550/arxiv.nlin/0101018

Related papers

A random matrix approach to decoherence

T. Gorin, T. H. Seligman

In order to analyse the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish the effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing two subsystems. We introduce a random matrix model that allows us to vary the coupling strength between the subsystems. The case of strong coupling is analysed in detail, and we find no significant differences except for very low-dimensional spaces.

arXiv:quant-ph/0112030•Journal of Optics B Quantum and Semiclassical Optics•Aug 1, 2002•36 citations

Out-of-Time-Order Correlators in Bipartite Nonintegrable Systems

Ravi Prakash, Arul Lakshminarayan

Out-of-time-order correlators being explored as a measure of quantum chaos, are studied here in a coupled bipartite system.Each of the subsystems can be chaotic or regular and lead to very different out-of-time-order correlators growths both before and after the scrambling or the Ehrenfest time.We present preliminary results then on weakly coupled subsystems which have very different Lyapunov exponents.We also review the case when both the subsystems are strongly chaotic when a random matrix model can be pressed into service to derive an exponential relaxation to saturation.

arXiv:1911.02829•Acta Physica Polonica A•Nov 1, 2019•9 citations

Chaos and Randomness in Strongly-Interacting Quantum Systems

Nicholas Hunter-Jones

Quantum chaos entails an entropic and computational obstruction to describing a system and thus is intrinsically difficult to characterize. An understanding of quantum chaos is fundamentally related to the mechanism of thermalization in many-body systems and the quantum nature of black holes. In this thesis we adopt the view that quantum information theory provides a powerful framework in which to elucidate chaos in strongly-interacting quantum systems. We first push towards a more precise understanding of chaotic dynamics by relating different diagnostics of chaos, studying the time-evolution of random matrix Hamiltonians, and quantifying random matrix behavior in physical systems. We derive relations between out-of-time ordered correlation functions, spectral quantities, and frame potentials to relate the scrambling of quantum information, decay of correlators, and Haar-randomness. We give analytic expressions for these quantities in random matrix theory to explore universal aspects of late-time dynamics. Motivated by our random matrix results, we define k-invariance in order to capture the onset of random matrix behavior in physical systems. We then refine our diagnostics in order to study chaotic systems with symmetry by considering Haar-randomness with respect to quotients of the unitary group, and in doing so we generalize our quantum information machinery. We further consider extended random matrix ensembles in the context of strongly-interacting quantum systems dual to black holes. Lastly, we study operator growth in classes of random quantum circuits.

•Jun 4, 2018•12 citations

Rapid decoherence in integrable systems: A border effect

R. M. Angelo, K. Furuya, Maria Carolina Nemes +1 more

We show that rapid decoherence, usually associated with chaotic dynamics, is not necessarily a hallmark of nonintegrability: border effects in integrable systems may produce similarly drastic decoherence rates. These can be found when the subsystem under observation possesses an energy limitation as, e.g., in the N-atom Jaynes-Cummings model. We show for this model that special initial coherent wave packets exhibit entropy production rates strikingly similar to the chaotic case. Also, a (de)localization phenomenon is found to be a function of the proximity to the phase-space border.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Nov 1, 1999•34 citations

Decoherence by a chaotic many-spin bath

José Lages, V. V. Dobrovitski, Mikhail I. Katsnelson +2 more

We numerically investigate decoherence of a two-spin system (central system) by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical regime of the bath has been varied from quantum chaos to regular, while all other dynamical characteristics have been kept practically intact. We explicitly demonstrate that for a many-body quantum bath, the onset of quantum chaos leads to significantly faster and stronger decoherence compared to an equivalent non-chaotic bath. Moreover, the non-diagonal elements of the system's density matrix, the linear entropy, and the fidelity of the central system decay differently for chaotic and non-chaotic baths. Therefore, knowledge of the basic parameters of the bath (strength of the system-bath interaction, and the bath's spectral density of states) is not always sufficient, and much finer details of the bath's dynamics can strongly affect the decoherence process.

arXiv:quant-ph/0406001•Physical Review E•Aug 31, 2005•60 citations

Universal spectral correlations in interacting chaotic few-body quantum systems

Felix Fritzsch, Maximilian F. I. Kieler

The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in interacting chaotic few- and many-body systems, modeled by suitable random-matrix ensembles, and obtain exact results for large Hilbert space dimensions. The transition of the spectral form factor from the non-interacting to the strongly interacting case can be described as a simple combination of these two limiting cases, which we confirm by extensive numerical studies in few-body systems. This transition is universally governed by a single scaling parameter. Moreover, our approach accurately captures spectral correlations in actual physical system, which we demonstrate for coupled kicked rotors.

arXiv:2302.08983•Feb 17, 2023•0 citations
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce a random matrix model that permits to vary the coupling strength between the subsystems. The case of strong coupling is analyzed in detail, and we find at intermediate times a weak effect of spectral correlations that is reminiscent of the correlation hole.
Out-of-time-order correlators being explored as a measure of quantum chaos, are studied here in a coupled bipartite system.Each of the subsystems can be chaotic or regular and lead to very different out-of-time-order correlators growths both before and after the scrambling or the Ehrenfest time.We present preliminary results then on weakly coupled subsystems which have very different Lyapunov exponents.We also review the case when both the subsystems are strongly chaotic when a random matrix model can be pressed into service to derive an exponential relaxation to saturation.
Quantum chaos entails an entropic and computational obstruction to describing a system and thus is intrinsically difficult to characterize. An understanding of quantum chaos is fundamentally related to the mechanism of thermalization in many-body systems and the quantum nature of black holes. In this thesis we adopt the view that quantum information theory provides a powerful framework in which to elucidate chaos in strongly-interacting quantum systems. We first push towards a more precise understanding of chaotic dynamics by relating different diagnostics of chaos, studying the time-evolution of random matrix Hamiltonians, and quantifying random matrix behavior in physical systems. We derive relations between out-of-time ordered correlation functions, spectral quantities, and frame potentials to relate the scrambling of quantum information, decay of correlators, and Haar-randomness. We give analytic expressions for these quantities in random matrix theory to explore universal aspects of late-time dynamics. Motivated by our random matrix results, we define k-invariance in order to capture the onset of random matrix behavior in physical systems. We then refine our diagnostics in order to study chaotic systems with symmetry by considering Haar-randomness with respect to quotients of the unitary group, and in doing so we generalize our quantum information machinery. We further consider extended random matrix ensembles in the context of strongly-interacting quantum systems dual to black holes. Lastly, we study operator growth in classes of random quantum circuits.
We show that rapid decoherence, usually associated with chaotic dynamics, is not necessarily a hallmark of nonintegrability: border effects in integrable systems may produce similarly drastic decoherence rates. These can be found when the subsystem under observation possesses an energy limitation as, e.g., in the N-atom Jaynes-Cummings model. We show for this model that special initial coherent wave packets exhibit entropy production rates strikingly similar to the chaotic case. Also, a (de)localization phenomenon is found to be a function of the proximity to the phase-space border.
We numerically investigate decoherence of a two-spin system (central system) by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical regime of the bath has been varied from quantum chaos to regular, while all other dynamical characteristics have been kept practically intact. We explicitly demonstrate that for a many-body quantum bath, the onset of quantum chaos leads to significantly faster and stronger decoherence compared to an equivalent non-chaotic bath. Moreover, the non-diagonal elements of the system's density matrix, the linear entropy, and the fidelity of the central system decay differently for chaotic and non-chaotic baths. Therefore, knowledge of the basic parameters of the bath (strength of the system-bath interaction, and the bath's spectral density of states) is not always sufficient, and much finer details of the bath's dynamics can strongly affect the decoherence process.
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in interacting chaotic few- and many-body systems, modeled by suitable random-matrix ensembles, and obtain exact results for large Hilbert space dimensions. The transition of the spectral form factor from the non-interacting to the strongly interacting case can be described as a simple combination of these two limiting cases, which we confirm by extensive numerical studies in few-body systems. This transition is universally governed by a single scaling parameter. Moreover, our approach accurately captures spectral correlations in actual physical system, which we demonstrate for coupled kicked rotors.