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Physical review. E

Effects of chaotic dynamics on quantum friction

Gabriel G. Carlo, Leonardo Ermann, Alejandro M. F. Rivas

Published Apr 22, 2019• 4 citations
Publisher

Abstract

By means of studying the evolution equation for the Wigner distributions of quantum dissipative systems we derive the quantum corrections to the classical Liouville dynamics, taking into account the standard quantum friction model. The resulting evolution turns out to be the classical one plus fluctuations that depend not only on the ℏ size but also on the momentum and the dissipation parameter (i.e., the coupling with the environment). On the other hand, we extend our studies of a paradigmatic system based on the kicked rotator, and we confirm that by adding fluctuations only depending on the size of the Planck constant we essentially recover the quantum behavior. This is systematically measured in the parameter space with the overlaps and differences in the dispersion of the marginal distributions corresponding to the Wigner functions. Taking into account these results and analyzing the Wigner evolution equation we conjecture that the chaotic nature of our system is responsible for the independence on the momentum, while the dependence on the dissipation is provided implicitly by the dynamics.

DOI
10.1103/physreve.99.042214

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By means of studying the evolution equation for the Wigner distributions of quantum dissipative systems we derive the quantum corrections to the classical Liouville dynamics, taking into account the standard quantum friction model. The resulting evolution turns out to be the classical one plus fluctuations that depend not only on the ℏ size but also on the momentum and the dissipation parameter (i.e., the coupling with the environment). On the other hand, we extend our studies of a paradigmatic system based on the kicked rotator, and we confirm that by adding fluctuations only depending on the size of the Planck constant we essentially recover the quantum behavior. This is systematically measured in the parameter space with the overlaps and differences in the dispersion of the marginal distributions corresponding to the Wigner functions. Taking into account these results and analyzing the Wigner evolution equation we conjecture that the chaotic nature of our system is responsible for the independence on the momentum, while the dependence on the dissipation is provided implicitly by the dynamics.
By means of studying the evolution equation for the Wigner distributions of quantum dissipative systems we derive the quantum corrections to the classical Liouville dynamics, taking into account the standard quantum friction model. The resulting evolution turns out to be the classical one plus fluctuations that depend not only on the ℏ\hbarℏ size but also on the momentum and the dissipation parameter (i.e. the coupling with the environment). On the other hand, we extend our studies of a paradigmatic system based on the kicked rotator, and we confirm that by adding fluctuations only depending on the size of the Planck constant we essentially recover the quantum behaviour. This is systematically measured in the parameter space with the overlaps and differences in the dispersion of the marginal distributions corresponding to the Wigner functions. Taking into account these results and analyzing the Wigner evolution equation we propose that the chaotic nature of our system is responsible for the independence on the momentum, while the dependence on the dissipation is provided implicitly by the dynamics.
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.
The paper deals with dynamics of a quantum chaotic system under influence of an environment. The effect of an environment is known to destroy the quantum coherence and can convert the quantum dynamics of a system to classical. We use a semiclassical technique for studying the process of decoherence. The condition for transition from quantum to classical dynamics is obtained in general form and checked numerically for a particular chaotic system, known as quantum the standard map on a torus. The relevance of the obtained results to the problem of correspondence between quantum and classical mechanics is briefly discussed. (c) 1996 American Institute of Physics.
Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.
Localization in the quantum kicked rotator (QKR) problem leads to nontrivial dynamical correlations that are absent in the classical limit. These correlations are related to the spectral properties of the model. The effect of noise on coherence is studied. Also, its effect on the dynamical correlations is investigated, and thus one is able to determine analytically the diffusion that is induced. If the noise is white, then coherence time is the same as that for the undriven system. For colored noise it is essential to take into account the nature of the dynamical correlations. It follows that a Markovian treatment of the dynamics for a system that is coupled to a low-temperature heat bath is not valid even if the system is classically chaotic. The formalism applies also to the problem of QKR with kicks that are not strictly periodic in time, and also to the quantum kicked particle problem, where a nonperturbative mechanism for destruction of coherence has been found.