Large Deviations for the Bose--Einstein Condensate of the Ideal Gas in the Canonical Ensemble

Abstract

We consider a non-interacting Bose gas governed by a general one-particle Hamiltonian in the canonical ensemble. Our main results are large-deviation estimates for the number of particles in the Bose--Einstein condensate. We show that the left- and right-tail probabilities decay at different exponential rates as the number of particles tends to infinity.

arXiv comment27 pages