Quantum localization and the rate of exploration of phase space

Abstract

Nonstationary phase-space distributions \ensuremath{\rho}(t) are shown to sweep out phase space at a rate scrR which can be determined from the autocorrelation function, P(t)=${h}^{N}$Tr[\ensuremath{\rho}\ensuremath{\rho}(t)]. It is demonstrated that, after the initial decay of P(t), subsequent recurrences (increases) of P(t) cause permanent slowdowns in the rate scrR. Such slowdowns may cause localization of quantum eigenstates, whereas no such implications apply to the classical stationary distributions. The localization is discussed in terms of the fraction of the available phase space which the dynamics accesses, and the phase-space distribution of individual eigenfunctions.