On the critical point of an interacting two-dimensional trapped Bose gas

Abstract

We consider a quantized vortex excitation in a two-dimensional, harmonically trapped Bose gas and derive an equation for the Berezinskii-Kosterlitz-Thouless transition temperature based on a simple free-energy argument. We relate the critical phase-space density at the transition to the ratio between the entropy gain and the corresponding cost in energy of creating a free vortex excitation in the system.