Thermodynamics of a dilute Bose gas with condensate

Abstract

The partition function of a dilute Bose gas with repulsive interaction, fixed number of particles and in the presence of a condensate is computed up to first order in the interactions. An equilibrium condition appears for the fraction of particles in the condensate and. the chemical potential of the particles. We show that for a dilute gas the Bose-Einstein transition is not of second order. Moreover, the thermodynamical quantities obtained may look different from those in the literature, because the chemical potential enters in a nontrivial way in the quasi particle spectrum.