Pseudochaos in Statistical Physics

A new generic dynamical phenomenon of pseudochaos and its relevance to the statistical physics both modern as well as traditional one are considered and explained in some detail. The pseudochaos is defined as a statistical behavior of the dynamical system with discrete energy and/or frequency spectrum. In turn, the statistical behavior is understood as time–reversible but nonrecurrent relaxation to some steady state, at average, superimposed with irregular fluctuations. The main attention is payed to the most important and universal example of pseudochaos, the so–called quantum chaos that is dynamical chaos in bounded mesoscopic quantum systems. The quantum chaos as a mechanism for implementation of the fundamental correspondence principle is also discussed. The quantum relaxation localization, a peculiar characteristic implication of pseudochaos, is reviewed in both time–dependent and conservative systems with special emphasis on the dynamical decoherence of quantum chaotic states. Recent results on the peculiar global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. Examples of pseudochaos in classical systems are given including linear oscillator and waves, digital computer and completely integrable systems. A far–reaching similarity between the dynamics of a few–freedom quantum system at high energy levels (n → ∞) and that of many–freedom one (N → ∞) is also discussed. A talk given at the Intern. Conference ”Nonlinear Dynamics, Chaotic and Complex Systems”, Zakopane, 1995