Thermodynamical properties of a trapped interacting Bose gas

TL;DR

This paper investigates the thermodynamic behavior of interacting Bose gases in harmonic traps using mean-field theory, revealing how interactions influence critical temperature and condensate properties.

Contribution

It provides a mean-field analysis of interacting Bose gases, identifying the chemical potential with the Gross-Pitaevskii eigenvalue and deriving universal condensation relations.

Findings

Critical temperature decreases with increasing interactions.

Condensate fraction follows a universal power law below T_c.

Eigenvalue of Gross-Pitaevskii equation acts as the chemical potential.

Abstract

The thermodynamical properties of interacting Bose atoms in a harmonic potential are studied within the mean-field approximation. For weak interactions, the quantum statistics is equivalent to an ideal gas in an effective mean-field potential. The eigenvalue of the Gross-Pitaevskii equation is identified as the chemical potential of the ideal gas. The condensation temperature and density profile of atoms are calculated. It is found that the critical temperature $T_c$ decreases as the interactions increase. Below the critical point, the condensation fraction exhibits a universal relation of $N_0/N=1-(T/T_c)^{\gamma}$, with the index $\gamma\approx 2.3$ independent of the interaction strength, the chemical potential, as well as the frequency of the confining potential.