Variational approach for the two-dimensional trapped Bose Einstein condensate

TL;DR

This paper develops a Gaussian variational method for analyzing the properties of a two-dimensional trapped Bose-Einstein condensate, accounting for interactions and non-condensate effects beyond simple mean-field models.

Contribution

It introduces a novel variational approach that incorporates non-condensate back action and extends perturbative results to higher densities in 2D Bose gases.

Findings

Derived the equation of state for the system.

Analyzed stability of vortex configurations.

Validated the approach against known limits.

Abstract

We construct a many-body Gaussian variational approach for the two-dimensional trapped Bose gas in the condensate phase. Interaction between particles is modelized by a generalized pseudo-potential of zero range that allows recovering perturbative results in the ultra-dilute limit, while back action of non-condensate particles on the condensate part is taken into account for higher density. As an application, we derive the equation of state and solve stability problems encountered in similar mean-field formalisms for a single vortex configuration.