Thermodynamics of a Bose-Einstein Condensate with Weak Disorder

TL;DR

This paper investigates how weak disorder affects the thermodynamics of a dilute Bose gas, deriving shifts in critical temperatures and constructing a phase diagram using an extended finite-temperature approach.

Contribution

It extends the zero-temperature Bogoliubov approach to finite temperatures by combining Popov and many-body T-matrix approximations, including quasi-particle interactions.

Findings

Disorder causes shifts in Bose-Einstein critical temperature.

Disorder affects the superfluid transition temperature.

The phase diagram aligns with previous replica-based theories.

Abstract

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random delta-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasi-particle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.