A semiclassical theory of quantum noise in open chaotic systems

Details A semiclassical theory of quantum noise in open chaotic systems A semiclassical theory of quantum noise in open chaotic systems

1998-11-13

arxiv.org/abs/chao-dyn/9811016v1

Physica D, 125 (1999) 47

Physics

Condensed Matter

Statistical Mechanics

Plain Latex, 27 pages, 6 ps figure, To appear in Physica D

Scientific paper

We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on $\hbar$-scaling of an equation for time evolution of the Wigner's quasi-probability distribution function in presence of dissipation and thermal diffusion we derive a semiclassical equation for quantum fluctuations. This identifies an early regime of evolution dominated by fluctuations in the curvature of the potential due to classical chaos and dissipation. A stochastic treatment of this classical fluctuations leads us to a Fokker-Planck equation which is reminiscent of Kramers' equation for thermally activated processes. This reveals an interplay of three aspects of evolution of quantum noise in weakly dissipative open systems; the reversible Liouville flow, the irreversible chaotic diffusion which is characteristic of the system itself, and irreversible dissipation induced by the external reservoir. It has been demonstrated that in the dissipation-free case a competition between Liouville flow in the contracting direction of phase space and chaotic diffusion sets a critical width in the Wigner function for quantum fluctuations. We also show how the initial quantum noise gets amplified by classical chaos and ultimately equilibrated under the influence of dissipation. We establish that there exists a critical limit to the expansion of phase space. The limit is determined by chaotic diffusion and dissipation. Making use of appropriate quantum-classical correspondence we verify the semiclassical analysis by the fully quantum simulation in a chaotic quartic oscillator.

Affiliated with

Also associated with

No associations

Rating

A semiclassical theory of quantum noise in open chaotic systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A semiclassical theory of quantum noise in open chaotic systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A semiclassical theory of quantum noise in open chaotic systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-309344