Phase transition in an ideal bose gas in an external field

Abstract

Bose-Einstein condensation is analyzed in an ideal Bose gas in an external field at temperatures at which the energy spectrum can be assumed continuous. The nature of the phase transition depends on the behavior of the potential near its minima. Criteria are derived which show in which fields the condensation is a second-order phase transition, a third-order phase transition with an infinite discontinuity in ∂CV/∂T, or a third-order phase transition with a finite discontinuity in ∂CV/∂T.