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

TL;DR

This paper proves that in a weakly interacting Bose gas, the probability of finding a certain number of particles outside the condensate decreases exponentially, providing insight into the system's quantum state structure.

Contribution

It establishes an exponential decay bound for the number of excitations in the ground state of a mean-field Bose gas, a novel quantitative result.

Findings

Exponential decay of excitation probabilities in the Bose gas

Ground state exhibits Bose--Einstein condensation with controlled excitations

Provides rigorous bounds on particle number fluctuations outside the condensate

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 $.