Finite temperature scaling theory for the collapse of Bose-Einstein condensate

TL;DR

This paper develops a finite temperature scaling theory for Bose-Einstein condensates in harmonic traps, predicting how the critical particle number varies with temperature using the Hartree-Fock approximation.

Contribution

It extends scaling theory to inhomogeneous, finite-temperature Bose condensates and quantifies the critical particle number dependence on temperature.

Findings

Critical particle number increases dramatically near condensation temperature.

Scaling theory effectively describes finite-temperature effects in trapped Bose gases.

Hartree-Fock approximation provides quantitative predictions for critical behavior.

Abstract

We show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperatures. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached.