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:cond-mat/9604084 · Journal of Physics A Mathematical and General

Spectral properties of quantumN-body systems versus chaotic properties of their mean-field approximations

Patrizia Castiglione, Giovanni Jona-Lasinio, Carlo Presilla A

Published Oct 7, 1996• 15 citations
arXivHTMLPDF

Abstract

We present numerical evidence that in a system of interacting bosons there exists a correspondence between the spectral properties of the exact quantum Hamiltonian and the dynamical chaos of the associated mean-field evolution. This correspondence, analogous to the usual quantum-classical correspondence, is related to the formal parallel between the second quantization of the mean field, which generates the exact dynamics of the quantum N-body system, and the first quantization of classical canonical coordinates. The limit of infinite density and the thermodynamic limit are then briefly discussed.

DOI
10.1088/0305-4470/29/19/005

Related papers

Chaotic Properties of Quantum Many-Body Systems in the Thermodynamic Limit

Giovanni Jona-Lasinio, Carlo Presilla A

By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction strength drives the system away from integrability. A correspondence with the dynamical chaoticity of an associated $c$-number system is then used to infer properties of the quantum system in the thermodynamic limit.

arXiv:cond-mat/9601056•Physical Review Letters•Nov 18, 1996•39 citations

Quantum chaos without classical counterpart

Giovanni Jona-Lasinio, Carlo Presilla A, Federico Capasso

We describe a quantum many-body system undergoing multiple resonant tunneling which exhibits chaotic behavior in numerical simulations of a mean field approximation. This phenomenon, which has no counterpart in the classical limit, is due to effective nonlinearities in the tunneling process and can be observed in principle within a heterostructure. 03.65.-w, 05.45.+b, 73.40.Gk Typeset using REVT E X In current studies the problem of quantum chaos is usually posed in the following terms. We are given a system which exhibits chaotic behavior classically: does this property survive quantization? Typically one studies the spectrum of the quantum mechanical Hamiltonian operator. However spectral differences at the quantum level between classically integrable and chaotic systems do not seem to imply dramatic differences in the time evolution of the quantum mechanical observables. Relics of classical chaos exist in low dimensional systems in short wavelength or large quantum numbers limits ...

Unknown eBooks•Oct 1, 1991•0 citations

Chaos in time-dependent variational approximations to quantum dynamics

Fred Cooper, John F. Dawson, Salman Habib +1 more

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first note that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict our attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large-$N$ (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schr\"odinger equation.

arXiv:quant-ph/9610013•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 1, 1998•46 citations

Quantum-classical correspondence in a triple-well bosonic model: From integrability to chaos

Erick R. Castro, Karin Wittmann Wilsmann, Jorge Chávez-Carlos +3 more

In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to chaos in classical dynamics is visualized through Poincar\'e sections. Classical trajectories in phase space closely resemble the projections of the Husimi functions of eigenstates with similar energy, even in chaotic cases. It is demonstrated that this correlation is more evident when projecting the eigenstates onto the Fock states. The analysis is carried out at a critical energy where the eigenstates are maximally delocalized in the Fock basis. Despite the imperfect delocalization, its influence is present in the classical and quantum properties under investigation. The study systematically establishes quantum-classical correspondence for a bosonic many-body system with more than two wells, even within the chaotic region.

arXiv:2311.13189•Physical Review A•Mar 27, 2024•12 citations

Quantum-classical correspondence via Liouville dynamics. II. Correspondence for chaotic Hamiltonian systems

Joshua Wilkie, Paul W. Brumer

We prove quantum-classical correspondence for bound conservative classically chaotic Hamiltonian systems. In particular, quantum Liouville spectral projection operators and spectral densities, and hence classical dynamics, are shown to approach their classical analogs in the h\ensuremath{\rightarrow}0 limit. Correspondence is shown to occur via the elimination of essential singularities. In addition, applications to matrix elements of observables in chaotic systems are discussed.

arXiv:chao-dyn/9608014•Physical Review A•Jan 1, 1997•54 citations

Emergence of nonlinear behavior in the dynamics of ultracold bosons

Benoît Vermersch, Jean Claude Garreau

We study the evolution of a system of interacting ultracold bosons which presents nonlinear, chaotic behaviors in the limit of a very large number of particles. Using the spectral entropy as an indicator of chaos and three different numerical approaches---exact diagonalization, the truncated Husimi method, and the mean-field (Gross-Pitaevskii) approximation---we put into evidence the destructive impact of quantum noise on the emergence of nonlinear dynamics.

arXiv:1501.07042•Physical Review A•Apr 6, 2015•7 citations
We present numerical evidence that in a system of interacting bosons there exists a correspondence between the spectral properties of the exact quantum Hamiltonian and the dynamical chaos of the associated mean-field evolution. This correspondence, analogous to the usual quantum-classical correspondence, is related to the formal parallel between the second quantization of the mean field, which generates the exact dynamics of the quantum N-body system, and the first quantization of classical canonical coordinates. The limit of infinite density and the thermodynamic limit are then briefly discussed.
By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction strength drives the system away from integrability. A correspondence with the dynamical chaoticity of an associated ccc-number system is then used to infer properties of the quantum system in the thermodynamic limit.
We describe a quantum many-body system undergoing multiple resonant tunneling which exhibits chaotic behavior in numerical simulations of a mean field approximation. This phenomenon, which has no counterpart in the classical limit, is due to effective nonlinearities in the tunneling process and can be observed in principle within a heterostructure. 03.65.-w, 05.45.+b, 73.40.Gk Typeset using REVT E X In current studies the problem of quantum chaos is usually posed in the following terms. We are given a system which exhibits chaotic behavior classically: does this property survive quantization? Typically one studies the spectrum of the quantum mechanical Hamiltonian operator. However spectral differences at the quantum level between classically integrable and chaotic systems do not seem to imply dramatic differences in the time evolution of the quantum mechanical observables. Relics of classical chaos exist in low dimensional systems in short wavelength or large quantum numbers limits ...
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first note that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict our attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large-NNN (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schr\"odinger equation.
In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to chaos in classical dynamics is visualized through Poincar\'e sections. Classical trajectories in phase space closely resemble the projections of the Husimi functions of eigenstates with similar energy, even in chaotic cases. It is demonstrated that this correlation is more evident when projecting the eigenstates onto the Fock states. The analysis is carried out at a critical energy where the eigenstates are maximally delocalized in the Fock basis. Despite the imperfect delocalization, its influence is present in the classical and quantum properties under investigation. The study systematically establishes quantum-classical correspondence for a bosonic many-body system with more than two wells, even within the chaotic region.