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 Letters

Vectorial Interactions and Quantum Chaos

H. M. Fried, Y. Gabellini, Bruce H. J. McKellar

Published May 29, 1995• 7 citations
Publisher

Abstract

Vectorial interactions (e.g., QED) introduce the possibility of chaos into new, nonperturbative Green's function representations of potential theory. The full, radiative corrections of quantum field theory, however, remove such chaos in an explicit example of ``environment-induced decoherence.''
DOI
10.1103/physrevlett.74.4373

Related papers

Quantum chaos and vectorial interactions

H. M. Fried

The possibility of quantum chaos for vectorial interactions is here described in some detail, along with its apparent suppression when the radiative corrections of quantum field theory (quantum fluctuations of the classical, “external” electromagnetic field) are introduced. Based on these quantum-mechanical ideas, an application is made to classical-chaotic systems, of perhaps the simplest form – a forced Duffing model, without damping – where it is found that the chaos is first suppressed and then (apparently) removed by introducing couplings to random and/or chaotic sources. This may be characterized as “quantum mechanics with ħ ∼ 1”, and suggests a brute-force method by which the chaos of a classical system may be at least diminished. A similar effect is noted for a different classical system that displays chaos – a pair of coupled oscillators – independently of any external forcing. First-quantization chaos The reader is now asked to return to the G c [ A ] representations for vectorial interactions of the previous chapter; for simplicity, the arguments of this chapter are presented only for QED in a relativistic context, but have obvious generalizations to non-relativistic QED, and to relativistic QCD. The map (5.31) defines the quantity Ω μ ( s′ ), which is needed for the explicit solution of (5.33). It is the existence of such a map which carries with it the inescapable possibility of chaotic behavior, at least in the present context of vectorial interactions in potential theory. The analysis used here is given directly in terms of proper time τ, of which x μ (τ) is a function.

Cambridge University Press eBooks•Oct 10, 2002•0 citations

Open Quantum Systems, Entropy and Chaos

Hans-Thomas Elze

Entropy generation in quantum sytems is tied to the existence of a nonclassical environment (heat bath or other) with which the system interacts. The continuous `measuring' of the open system by its environment induces decoherence of its wave function and entropy increase. Examples of nonrelativistic quantum Brownian motion and of interacting scalar fields illustrate these general concepts. It is shown that the Hartree-Fock approximation around the bare classical limit can lead to spurious semiquantum chaos, which may affect the determination of entropy production and thermalization also in other cases.

•Oct 30, 1997•0 citations

Open Quantum Systems, Entropy and Chaos

Hans-Thomas Elze

Entropy generation in quantum sytems is tied to the existence of a nonclassical environment (heat bath or other) with which the system interacts. The continuous `measuring' of the open system by its environment induces decoherence of its wave function and entropy increase. Examples of nonrelativistic quantum Brownian motion and of interacting scalar fields illustrate these general concepts. It is shown that the Hartree-Fock approximation around the bare classical limit can lead to spurious semiquantum chaos, which may affect the determination of entropy production and thermalization also in other cases.

arXiv:quant-ph/9710063•Oct 30, 1997•4 citations

Entanglement-induced decoherence and energy eigenstates

Wen-ge Wang, Jiangbin Gong, Giulio Casati +1 more

Using recent results in the field of quantum chaos we derive explicit expressions for the time scale of decoherence induced by the system-environment entanglement. For a generic system-environment interaction and for a generic quantum chaotic system as environment, conditions are derived for energy eigenstates to be preferred states in the weak coupling regime. A simple model is introduced to numerically confirm our predictions. The results presented here may also help with understanding the dynamics of quantum entanglement generation in chaotic quantum systems.

arXiv:0712.0059•Physical Review A•Jan 22, 2008•35 citations

Quantum chaos in open systems: a quantum state diffusion analysis

Todd A Brun, Ian Colin Percival, Rüdiger Schack

Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wavepackets in the neighbourhood of phase space points. This is due to decoherence from the interaction with the environment, and makes the quasiclassical limit of such systems both more realistic and simpler in many respects than the more familiar quasiclassical limit for closed systems. A linearized version of this theory leads to the correct classical dynamics in the macroscopic limit, even for nonlinear and chaotic systems. We apply the theory to the forced, damped Duffing oscillator, comparing the numerical results of the full and linearized equations, and argue that this can be used to make explicit calculations in the decoherent histories formalism of quantum mechanics.

arXiv:quant-ph/9509015•Journal of Physics A Mathematical and General•May 7, 1996•83 citations

On Quantum Field Brownian Motion, Decoherence and Semiquantum Chaos

Hans-Thomas Elze

Entropy production in quantum (field) systems requiring environment-induced decoherence is described in a Gaussian variational approximation. The new phenomenon of Semiquantum Chaos is reported. (Presented at the International Conference on Nonlinear Dynamics, Chaotic and Complex Systems, Zakopane (Poland), 7-12.11.95.)

arXiv:quant-ph/9511043•Nov 30, 1995•0 citations
The possibility of quantum chaos for vectorial interactions is here described in some detail, along with its apparent suppression when the radiative corrections of quantum field theory (quantum fluctuations of the classical, “external” electromagnetic field) are introduced. Based on these quantum-mechanical ideas, an application is made to classical-chaotic systems, of perhaps the simplest form – a forced Duffing model, without damping – where it is found that the chaos is first suppressed and then (apparently) removed by introducing couplings to random and/or chaotic sources. This may be characterized as “quantum mechanics with ħ ∼ 1”, and suggests a brute-force method by which the chaos of a classical system may be at least diminished. A similar effect is noted for a different classical system that displays chaos – a pair of coupled oscillators – independently of any external forcing. First-quantization chaos The reader is now asked to return to the G c [ A ] representations for vectorial interactions of the previous chapter; for simplicity, the arguments of this chapter are presented only for QED in a relativistic context, but have obvious generalizations to non-relativistic QED, and to relativistic QCD. The map (5.31) defines the quantity Ω μ ( s′ ), which is needed for the explicit solution of (5.33). It is the existence of such a map which carries with it the inescapable possibility of chaotic behavior, at least in the present context of vectorial interactions in potential theory. The analysis used here is given directly in terms of proper time τ, of which x μ (τ) is a function.
Entropy generation in quantum sytems is tied to the existence of a nonclassical environment (heat bath or other) with which the system interacts. The continuous `measuring' of the open system by its environment induces decoherence of its wave function and entropy increase. Examples of nonrelativistic quantum Brownian motion and of interacting scalar fields illustrate these general concepts. It is shown that the Hartree-Fock approximation around the bare classical limit can lead to spurious semiquantum chaos, which may affect the determination of entropy production and thermalization also in other cases.
Entropy generation in quantum sytems is tied to the existence of a nonclassical environment (heat bath or other) with which the system interacts. The continuous `measuring' of the open system by its environment induces decoherence of its wave function and entropy increase. Examples of nonrelativistic quantum Brownian motion and of interacting scalar fields illustrate these general concepts. It is shown that the Hartree-Fock approximation around the bare classical limit can lead to spurious semiquantum chaos, which may affect the determination of entropy production and thermalization also in other cases.
Using recent results in the field of quantum chaos we derive explicit expressions for the time scale of decoherence induced by the system-environment entanglement. For a generic system-environment interaction and for a generic quantum chaotic system as environment, conditions are derived for energy eigenstates to be preferred states in the weak coupling regime. A simple model is introduced to numerically confirm our predictions. The results presented here may also help with understanding the dynamics of quantum entanglement generation in chaotic quantum systems.
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wavepackets in the neighbourhood of phase space points. This is due to decoherence from the interaction with the environment, and makes the quasiclassical limit of such systems both more realistic and simpler in many respects than the more familiar quasiclassical limit for closed systems. A linearized version of this theory leads to the correct classical dynamics in the macroscopic limit, even for nonlinear and chaotic systems. We apply the theory to the forced, damped Duffing oscillator, comparing the numerical results of the full and linearized equations, and argue that this can be used to make explicit calculations in the decoherent histories formalism of quantum mechanics.