A semiclassical theory of dissipative Henon-Heiles system

Abstract

A semiclassical theory of dissipative Henon-Heiles system is proposed. Based on $\hslash$-scaling of an equation for evolution of Wigner quasiprobability distribution function in presence of dissipation and thermal diffusion, we derive a semiclassical equation for quantum fluctuations, governed by the dissipation and the curvature of the classical potential. We show how the initial quantum noise gets amplified by classical chaotic diffusion which is expressible in terms of correlation of stochastic fluctuations of the curvature of the potential due to classical chaos and ultimately settles down to equilibrium under the influence of dissipation. We also establish that there exists a critical limit to the expansion of phase space. The limit is set by chaotic diffusion and dissipation. Our semiclassical analysis is corroborated by numerical simulation of quantum operator master equation.

Revtex, 34 pages, 7 figures (ps file), to appear in Journal of Statistical Physics

References in corpus (1)

• Orbital instability and the loss of quantum coherence

Cited by in corpus (10)

• The noise properties of stochastic processes and entropy production
• Approach to Quantum Kramers' Equation and Barrier Crossing Dynamics
• Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions
• Upper bound for the time derivative of entropy for nonequilibrium stochastic processes
• A simple semiclassical approach to Kramers' problem
• Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production
• Dissipative quantum chaos: transition from wave packet collapse to explosion
• Chaos and information entropy production
• Fluctuation-dissipation relationship in chaotic dynamics
• Environment-induced dynamical chaos