Critical Temperature of a Trapped Interacting Bose Gas in the Local Density Approximation

TL;DR

This paper derives an analytical expression for how the critical temperature of Bose-Einstein condensation in a trapped interacting Bose gas depends on interactions within a power-law potential using the local density approximation.

Contribution

It provides a new analytical formula linking interaction strength and critical temperature in trapped Bose gases with power-law potentials.

Findings

Analytical dependence of critical temperature on interactions

Application of local density approximation to trapped gases

Generalization to power-law external potentials

Abstract

The Bose gas in an external potential is studied by means of the local density approximation. An analytical result is derived for the dependence of the critical temperature of Bose-Einstein condensation on the mutual interaction in a generic power-law potential.