Bose-Einstein condensation of a Knudsen gas

TL;DR

This paper clarifies the transition temperature behavior of Bose-Einstein condensation in dilute gases, revealing a crossover between ideal and interacting regimes influenced by the mean-free-path and scattering length.

Contribution

It demonstrates the existence of a crossover between Knudsen and hydrodynamic regimes affecting the transition temperature in Bose gases.

Findings

Deviation of transition temperature scales with scattering length in different regimes

Crossover between ideal and interacting Bose gas regimes identified

Potential observability in trapped or lattice-confined Bose gases

Abstract

We reconcile a long-standing controversy regarding the transition temperature of the Bose-Einstein condensation in a dilute interacting Bose gas, by showing that there is a crossover between ideal gas and interacting gas. The former corresponds to a Knudsen (or collisionless) regime, in which the mean-free-path is much larger than the system dimension, while the latter corresponds to the opposite hydrodynamic regime. The deviation of the transition temperature from that of the non-interacting gas is proportional to the square root of a in the Knudsen regime, and to a in the hydrodynamic regime, where a is the scattering length. This crossover may be observable in a Bose gas trapped in a potential or on an optical lattice.