Kinetic Properties of a Bose-Einstein Gas at Finite Temperature

TL;DR

This paper investigates the kinetic behavior of a Bose-Einstein gas at finite temperatures using the Boltzmann-Nordheim equation, revealing critical slowing down near the transition temperature and discussing experimental implications.

Contribution

It introduces a new numerical algorithm for solving the Boltzmann-Nordheim equation and analyzes the relaxation dynamics of a boson gas near the Bose-Einstein transition.

Findings

Relaxation time scales as (T - T_c)^(-1/2) near T_c.

Quantum effects increase collision rates dramatically near T_c.

Transition from collisionless to hydrodynamic behavior is discussed.

Abstract

We study, in the framework of the Boltzmann-Nordheim equation (BNE), the kinetic properties of a boson gas above the Bose-Einstein transition temperature $T_c$. The BNE is solved numerically within a new algorithm, that has been tested with exact analytical results for the collision rate of an homogeneous system in thermal equilibrium. In the classical regime ($T > 6~ T_c$), the relaxation time of a quadrupolar deformation in momentum space is proportional to the mean free collision time $\tau_{relax} \sim T^{-1/2}$. Approaching the critical temperature ($T_c < T < 2.7~ T_c$), quantum statistic effects in BNE become dominant, and the collision rate increases dramatically. Nevertheless, this does not affect the relaxation properties of the gas that depend only on the spontaneous collision term in BNE. The relaxation time $\tau_{relax}$ is proportional to $(T - T_c)^{-1/2}$, exhibiting a critical slowing down. These phenomena can be experimentally confirmed looking at the damping properties of collective motions induced on trapped atoms. The possibility to observe a transition from collisionless (zero-sound) to hydrodynamic (first-sound) is finally discussed.