The effect of interactions on Bose-Einstein condensation in a two-dimensional harmonic trap

TL;DR

This paper investigates how interactions affect Bose-Einstein condensation in a two-dimensional harmonic trap, revealing that interactions do not induce condensation and that the system's properties align with fractional exclusion statistics.

Contribution

It demonstrates that a dilute interacting Bose gas in 2D remains uncondensed and exhibits properties equivalent to an ideal gas obeying fractional exclusion statistics.

Findings

Density profile matches that of an ideal fractional exclusion statistics gas

Energy of the system is identical to that of an ideal fractional exclusion statistics gas

Interactions do not lead to Bose-Einstein condensation in the 2D trap

Abstract

A dilute bose gas in a quasi two-dimensional harmonic trap and interacting with a repulsive two-body zero-range potential of fixed coupling constant is considered. Using the Thomas-Fermi method, it is shown to remain in the same uncondensed phase as the temperature is lowered. Its density profile and energy are identical to that of an ideal gas obeying the fractional exclusion statistics of Haldane. PACS: ~03.75.Fi, 05.30.Jp, 67.40.Db, 05.30.-d