Large deviations for the ground state of weakly interacting Bose gases

TL;DR

This paper establishes large deviation principles for the ground state of a weakly interacting Bose gas, revealing quantum fluctuation effects and providing bounds on the rate function in the mean-field limit.

Contribution

It introduces the first large deviation estimates for the ground state of Bose gases, characterizing quantum fluctuations around the condensate.

Findings

Large deviation estimates for the ground state law.

Matching upper and lower bounds on the rate function.

Quantum fluctuations characterized in the rate function.

Abstract

We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose-Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas' ground state correspond to dependent random variables due to the bosons' correlation. We prove that in the limit $N \rightarrow \infty$ bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.