A Study of Bose-Einstein Condensation in a Two-Dimensional Trapped Gas

Abstract

We examine the possibility of Bose-Einstein condensation (BEC) in two-dimensional (2D) system of interacting particles in a trap. We use a self-consistent mean-field theory of Bose particles interacting by a contact interaction in the Popov and WKB approximations. The equations show that the normal state has a phase transition at some critical temperature (T_{c}) but below (T_{c}) the Bose-Einstein condensed state is not a consistent solution of the equations in the thermodynamic limit. This result agrees with a theorem recently discussed by the author that shows that a BEC state is impossible for an interacting gas in a 2D trap in the thermodynamic limit.