# Characteristic relaxation rates of a Bose gas in the classical, quantum and condensed regimes

## Abstract

We obtain the characteristic relaxation rates and relaxation modes of a Bose gas in three regimes. The classical regime corresponds to a classical gas of hard spheres and the quantum regime corresponds to an interacting quantum Bose gas with no Bose-Einstein condensate present. In the condensed regime a Bose-Einstein condensate is present and modifies the behavior of the gas. In each regime there is a different kinetic equation that describes the evolution of the relevant distribution function. The classical kinetic equation is the Boltzmann equation and the quantum kinetic equation with no condensate present is the Uehling-Uhlenbeck equation. When a condensate is present, we derive a new kinetic equation that describes the evolution of the momentum distribution of Bogoliubov excitations or bogolons. For each of the three kinetic equations, we linearize the collision integral and use it to generate the elements of a collision matrix. The eigenvalues of this matrix give us the characteristic relaxation rates and the eigenvectors give us the relaxation modes. We report numerical results for the eigenvalues in each regime as the particle species, density and temperature of the gas are varied.