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Physica E Low-dimensional Systems and Nanostructures

Chaos in dissipative quantum maps: a Wigner function description

Daniel Braun

Published Mar 1, 2001• 2 citations
Publisher
DOI
10.1016/s1386-9477(00)00252-6

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1 Dissipative Chaos in Quantum Distributions

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We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions.For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field.This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes.Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories.Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincaré section and quantum Poincaré section calculated on a single quantum trajectory.The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.

•Aug 14, 2016•2 citations
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory number statistics for the model of a nonlinear dissipative oscillator. It is shown that the probability distributions and variances of oscillatory number states are strongly transformed in the order-to-chaos transition. A nonclassical, sub-Poissonian statistics of oscillatory excitation numbers is established for chaotic dissipative dynamics in the framework of the Fano factor and Wigner functions. It is proposed to use these results in experimental studies of the quantum dissipative chaos.
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the framework of the statistical ensemble of quantum trajectories in a quantum state diffusion approach. The quantum dynamical manifestations of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement, are studied by numerical simulation of the ensemble averaged Wigner function and von Neumann entropy.
We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions.For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field.This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes.Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories.Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincaré section and quantum Poincaré section calculated on a single quantum trajectory.The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.