Exponential decay of the number of excitations in the weakly interacting Bose gas

Abstract

We consider $N$ trapped bosons in the mean-field limit with coupling constant $\lambda_N=1 / (N-1)$. The ground state of such systems exhibits Bose--Einstein condensation. We prove that the probability of finding $\ell$ particles outside the condensate wave function decays exponentially in $\ell $.