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.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, 20162 citations

The interplay of chaos and dissipation in driven quantum systems

Doktors der Naturwissenschaften

Jan 1, 19992 citations

Quantum Dissipation due to the Interaction with Chaotic Degrees of Freedom and the Correspondence Principle

Doron Cohen

Both in atomic and in mesoscopic physics it is interesting to consider the energy time dependence of a parametrically driven chaotic system. We assume an Hamiltonian $H(Q,P;x(t))$ where $x(t)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}Vt$ . The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy spreading is studied. Dissipation is the associated irreversible growth of the average energy. It is found that a dimensionless velocity ${v}_{\mathrm{PR}}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence. A perturbative regime and a nonperturbative semiclassical regime are distinguished.Both in atomic and in mesoscopic physics it is interesting to consider the energy time dependence of a parametrically driven chaotic system. We assume an Hamiltonian $H(Q,P;x(t))$ where $x(t)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy spreading is studied. Dissipation is the associated irreversible growth of the average energy. It is found that a dimensionless velocity ${v}_{\mathrm{PR}}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence. A perturbative regime and a nonperturbative semiclassical regime are distinguished.

arXiv:cond-mat/9810395Physical Review LettersJun 21, 199970 citations

Dissipative Dynamics in the Quantum and the Classical Limits

Dong‐In Lee, Jun-Ho LEE*, Woon Hak Baek +1 more

New Physics Sae MulliOct 30, 20170 citations

DISSIPATIVE CHAOS IN QUANTUM DISTRIBUTIONS

T. V. GEVORGYAN, S. B. MANVELYAN, A. R. SHAHINYAN +1 more

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 Poincare section and quantum Poincare 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.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 Poincare section and quantum Poincare 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.

arXiv:1101.5750Jun 1, 20104 citations

Quantum Mechanics of Non-Hamiltonian and Dissipative Systems

Monograph series on nonlinear science and complexityJan 1, 200883 citations

Both in atomic and in mesoscopic physics it is interesting to consider the energy time dependence of a parametrically driven chaotic system. We assume an Hamiltonian

H(Q,P;x(t))

where

x(t)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}Vt

. The velocity

V

is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy spreading is studied. Dissipation is the associated irreversible growth of the average energy. It is found that a dimensionless velocity

{v}_{\mathrm{PR}}

determines the nature of the dynamics, and controls the route towards quantal-classical correspondence. A perturbative regime and a nonperturbative semiclassical regime are distinguished.