A well-known conjecture in mathematical physics asserts that the interacting Bose gas exhibits Bose-Einstein condensation (BEC) thermodynamic limit. We consider on certain hyperbolic spaces. In this setting, one obtains a short proof of BEC infinite-volume limit from existence volume-independent spectral gap Laplacian.

Due to the observation of Bose-Einstein condensation in dilute atomic 87Rb and 23Na vapors last year, there is currently a great interest in the properties of a degenerate Bose gas. One aspect that is not yet understood is the effect of the interatomic interactions on the critical temperature of the phase transition. We present here a renormalization group study of the weakly-interacting Bose g...

Abstract: We present an analysis of Bose-Einstein condensation for a system of noninteracting spin-0 particles in a harmonic oscillator confining potential trap. We discuss why a confined system of particles differs both qualitatively and quantitatively from an identical system which is not confined. One crucial difference is that a confined system is not characterized by a critical temperature...