Upper bounds for the Poincaré recurrence time in quantum mixed states

Abstract

In this paper we use geometric techniques to provide upper bounds for the Poincaré recurrence time of a quantum mixed state with a discrete spectrum of energies. We obtain two types of upper bounds. One of them depends on the uncertainty in the energy or on the average of the gap of energies and extends previous results obtained for pure states. The other upper bound depends only on the number of relevant states. The first upper bound tends to zero at the classical limit, while the other bound is related with the number of relevant states and survives at the classical limit.