Finite temperature theory of the trapped two dimensional Bose gas

TL;DR

This paper develops a Hartree-Fock-Bogoliubov theoretical framework for the two-dimensional trapped Bose gas at finite temperature, clarifying previous semiclassical approaches and demonstrating trap stabilization of the condensate.

Contribution

It introduces a fully quantum mechanical HFB theory within the Popov approximation for the 2D trapped Bose gas, highlighting the role of the trap in stabilizing the condensate.

Findings

Trap stabilizes the condensate against long wavelength fluctuations

Identification of phase fluctuations leading to quasicondensate formation

Clarification of semiclassical approximation limitations

Abstract

We present a Hartree-Fock-Bogoliubov (HFB) theoretical treatment of the two-dimensional trapped Bose gas and indicate how semiclassical approximations to this and other formalisms have lead to confusion. We numerically obtain results for the fully quantum mechanical HFB theory within the Popov approximation and show that the presence of the trap stabilizes the condensate against long wavelength fluctuations. These results are used to show where phase fluctuations lead to the formation of a quasicondensate.