Damped bounces of an isolated perfect quantum gas.

The issue of the thermalization of an isolated quantum system is addressed by considering a perfect gas confined by gravity and initially trapped above a certain height. As we are interested in the behavior of truly isolated systems, we assume the gas is in a pure state of macroscopically well-defined energy. We show that, in general, for single-particle distributions, such a state is strictly equivalent to the microcanonical mixed state at the same energy. We derive an expression for the time-dependent gas density that depends on the initial gas state only via a few thermodynamic parameters. Though we consider noninteracting particles, the density relaxes into an asymptotic profile, but it is not the thermal equilibrium one determined by the gas energy and particle number.