The Semiclassical Approach for Chaotic Systems

Sebastian Müller

Klaus Richter

Bidhan Chandra Bag, Shanta Chaudhuri, Jyotipratim Ray Chaudhuri +1 more

Kazuo Hida

The effect of dissipation on the recovery of the classical chaotic dynamics is discussed in the semiclassical regime of the quantum nonintegrable systems. In the classically chaotic Hamiltonian systems, the semiclassical approach breaks down within rather short time scale due to the interference of the wave function. It is shown that the dissipation suppresses the interference and confines the quantum fluctuation around the semiclassical trajectory which is described by the semiclassical Langevin equation. We also show that the semiclassical condition obtained by Schmid is equivalent to the condition for the suppression of interference. The discussion is valid regardless whether the classical motion is chaotic or not and therefore dissipation helps the recovery of the classical dynamics in the chaotic systems.

Benjamin D. Greenbaum, Salman Habib, Kosuke Shizume +1 more

An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one-dimensional chaotic dynamical systems. Environmental fluctuations-characteristic of all realistic dynamical systems-suppress the development of a fine structure in classical phase space and damp nonlocal contributions to the semiclassical Wigner function, which would otherwise invalidate the approximation. This dual regularization of the singular nature of the semiclassical limit is demonstrated by a numerical investigation of the chaotic Duffing oscillator.

Patrick W. O’Connor, Steven Tomsovic, Eric J. Heller