Damped bounces of an isolated perfect quantum gas

TL;DR

This paper investigates the non-thermal relaxation behavior of an isolated perfect quantum gas under gravity, showing that its density profile evolves towards a non-equilibrium steady state distinct from thermal equilibrium.

Contribution

It demonstrates that a pure state of a non-interacting quantum gas behaves like a microcanonical ensemble and relaxes to a non-thermal steady state, providing insights into quantum thermalization.

Findings

Density relaxes to a non-thermal asymptotic profile

Pure states are equivalent to microcanonical mixed states at the same energy

The density evolution depends on a few thermodynamic parameters

Abstract

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 which depends on the initial gas state only via a few thermodynamic parameters. Though we consider non-interacting particles, the density relaxes into an asymptotic profile, but which is not the thermal equilibrium one determined by the gas energy and particle number.