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

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

Luca Bonci, Roberto Roncaglia, Bruce J. West, Paolo Grigolini A

Published Aug 1, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.56.2325

Related papers

Reply to “Comment on ‘Quantum suppression of chaos in the spin-boson model’ ”

G. A. Finney, Julio R. Gea-Banacloche

We dispute the claim by Bonci et al. [Phys. Rev. E 56, 2325 (1997)] that we have misidentified a chaotic trajectory, and point out that their new results actually support the main conclusions of our original article.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1997•0 citations

Quantum suppression of chaos in the spin-boson model

G. A. Finney, Julio R. Gea-Banacloche

We identify a transition to chaos in the semiclassical spin-boson model that occurs for relatively large boson fields, as one of two periodic orbits becomes unstable. We have studied the quantum dynamics in the vicinity of this transition, as characterized by (i) phase-space trajectories followed by quantum expectation values, (ii) spectra of such trajectories, (iii) subsystem entropies for the spin and boson systems, and (iv) growth of operator variances for the boson system. We find that the transition to chaos in the classical system has no apparent effect on any of these variables, in the spin-1/2 case. This is in disagreement with some claims made in earlier studies of this system. \textcopyright{} 1996 The American Physical Society.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1996•17 citations

Studies of Classically Chaotic Quantum Systems within the Pseudo-Probablilty Formalism

Roberto Roncaglia

The evolution of classically chaotic quantum systems is analyzed within the formalism of Quantum Pseudo-Probability Distributions. Due to the deep connections that a quantum system shows with its classical correspondent in this representation, the Pseudo-Probability formalism appears to be a useful method of investigation in the field of "Quantum Chaos." In the first part of the thesis we generalize this formalism to quantum systems containing spin operators. It is shown that a classical-like equation of motion for the pseudo-probability distribution ρw can be constructed, dρw/dt = (L_CL + L_QGD)ρw, which is rigorously equivalent to the quantum von Neumann-Liouville equation. The operator L_CL is undistinguishable from the classical operator that generates the semiclassical equations of motion. In the case of the spin-boson system this operator produces semiclassical chaos and is responsible for quantum irreversibility and the fast growth of quantum uncertainty. Carrying out explicit calculations for a spin-boson Hamiltonian the joint action of L_CL and L_QGD is illustrated. It is shown that the latter operator, L_QGD makes the spin system 'remember' its quantum nature, and competes with the irreversibility induced by the former operator. In the second part we test the idea of the enhancement of the quantum uncertainty triggered by the classical chaos by investigating the analogous effect of diffusive excitation in periodically kicked quantum systems. The classical correspondents of these quantum systems exhibit, in the chaotic region, diffusive behavior of the unperturbed energy. For the Quantum Kicked Harmonic Oscillator, in the case of quantum resonances, we provide an exact solution of the quantum evolution. This proves the existence of a deterministic drift in the energy increase over time of the system considered. More generally, this "superdiffusive" excitation of the energy is due to coherent quantum mechanical tunnelling between degenerate tori of the classical phase space. In conclusion we find that some of the quantum effects resulting from this fast increase do not have any classical counterpart, they are mainly tunnelling processes. This seems to be the first observation of an effect of this kind.

•Aug 1, 1992•0 citations

Quantum Irreversibility and Chaos

Bruce J. West, Paolo Grigolini A, Luca Bonci +1 more

Abstract Herein we establish a relation between quantum irreversibility and the chaotic semi-classical solutions for a spin-boson Hamiltonian system. We obtain quantum averages by numerically integrating the appropriate Liouville-Von Neumann equations of motion and find these averages to be less erratic than the corresponding chaotic semi-classical trajectories. However, the quantum averages are shown to be dissipative as measured by the entropy of the spin subsystem and to suppress the phenomenon of "revivals".

Zeitschrift für Naturforschung A•Feb 1, 1997•0 citations

Quantum-classical correspondence of strongly chaotic many-body spin models

Luis Benet, F. Borgonovi, Felix M. Izrailev +1 more

We study the quantum-classical correspondence for systems with interacting spin particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of individual spins. Our analysis of the Lyapunov spectra reveals that the largest Lyapunov exponent agrees with the Lyapunov exponent that determines the local instability of each individual spin moving under the influence of all other spins. Within this picture, we introduce a rigorous and simple test of ergodicity for the spin motion, and use it to identify when classical chaos is both strong and global in phase space. In the quantum domain, our analysis of the Hamiltonian matrix in a proper representation allows us to obtain the conditions for the onset of quantum chaos as a function of the model parameters. From the comparison between the quantum and classical domains, we demonstrate that quantum quantities, such as the local density of states (LDoS) and the shape of the chaotic eigenfunctions written in the noninteracting many-body basis, have well-defined classical counterparts. We also find a relationship between the Kolmogorov-Sinai entropy and the width of the LDoS, which is useful for studies of many-body dynamics.

arXiv:2211.10451•Physical review. B./Physical review. B•Apr 26, 2023•10 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
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.
We identify a transition to chaos in the semiclassical spin-boson model that occurs for relatively large boson fields, as one of two periodic orbits becomes unstable. We have studied the quantum dynamics in the vicinity of this transition, as characterized by (i) phase-space trajectories followed by quantum expectation values, (ii) spectra of such trajectories, (iii) subsystem entropies for the spin and boson systems, and (iv) growth of operator variances for the boson system. We find that the transition to chaos in the classical system has no apparent effect on any of these variables, in the spin-1/2 case. This is in disagreement with some claims made in earlier studies of this system. \textcopyright{} 1996 The American Physical Society.
The evolution of classically chaotic quantum systems is analyzed within the formalism of Quantum Pseudo-Probability Distributions. Due to the deep connections that a quantum system shows with its classical correspondent in this representation, the Pseudo-Probability formalism appears to be a useful method of investigation in the field of "Quantum Chaos." In the first part of the thesis we generalize this formalism to quantum systems containing spin operators. It is shown that a classical-like equation of motion for the pseudo-probability distribution ρw can be constructed, dρw/dt = (L_CL + L_QGD)ρw, which is rigorously equivalent to the quantum von Neumann-Liouville equation. The operator L_CL is undistinguishable from the classical operator that generates the semiclassical equations of motion. In the case of the spin-boson system this operator produces semiclassical chaos and is responsible for quantum irreversibility and the fast growth of quantum uncertainty. Carrying out explicit calculations for a spin-boson Hamiltonian the joint action of L_CL and L_QGD is illustrated. It is shown that the latter operator, L_QGD makes the spin system 'remember' its quantum nature, and competes with the irreversibility induced by the former operator. In the second part we test the idea of the enhancement of the quantum uncertainty triggered by the classical chaos by investigating the analogous effect of diffusive excitation in periodically kicked quantum systems. The classical correspondents of these quantum systems exhibit, in the chaotic region, diffusive behavior of the unperturbed energy. For the Quantum Kicked Harmonic Oscillator, in the case of quantum resonances, we provide an exact solution of the quantum evolution. This proves the existence of a deterministic drift in the energy increase over time of the system considered. More generally, this "superdiffusive" excitation of the energy is due to coherent quantum mechanical tunnelling between degenerate tori of the classical phase space. In conclusion we find that some of the quantum effects resulting from this fast increase do not have any classical counterpart, they are mainly tunnelling processes. This seems to be the first observation of an effect of this kind.
Abstract Herein we establish a relation between quantum irreversibility and the chaotic semi-classical solutions for a spin-boson Hamiltonian system. We obtain quantum averages by numerically integrating the appropriate Liouville-Von Neumann equations of motion and find these averages to be less erratic than the corresponding chaotic semi-classical trajectories. However, the quantum averages are shown to be dissipative as measured by the entropy of the spin subsystem and to suppress the phenomenon of "revivals".
We study the quantum-classical correspondence for systems with interacting spin particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of individual spins. Our analysis of the Lyapunov spectra reveals that the largest Lyapunov exponent agrees with the Lyapunov exponent that determines the local instability of each individual spin moving under the influence of all other spins. Within this picture, we introduce a rigorous and simple test of ergodicity for the spin motion, and use it to identify when classical chaos is both strong and global in phase space. In the quantum domain, our analysis of the Hamiltonian matrix in a proper representation allows us to obtain the conditions for the onset of quantum chaos as a function of the model parameters. From the comparison between the quantum and classical domains, we demonstrate that quantum quantities, such as the local density of states (LDoS) and the shape of the chaotic eigenfunctions written in the noninteracting many-body basis, have well-defined classical counterparts. We also find a relationship between the Kolmogorov-Sinai entropy and the width of the LDoS, which is useful for studies of many-body dynamics.
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.