Critical temperature of Bose-Einstein condensation in an external potential

Abstract

Expressions for critical temperature of Bose-Einstein condensation (BEC) in an e xternal potential, which are different from published results in the literatur e, are presente d. The results reveal the relation between the critical temperature of BECgas and the external potential, and demonstrates proporti onality of critical temperature in external potential to the value T0c at which th e potential is absent. In addition, a criterion for the validity of potential is also prese nted, which is based on the comparison between the potential and the product  kT 0c. This comparison shows that only when the external potential is nearly eq ual to or larg er than kT0c, the increase of critical temperature is significant. A s the potential is much smaller than kT０c, the potential has no effects on the BEC gas.