Exponential bounds of the condensation for dilute Bose gases

TL;DR

This paper proves that in the Gross-Pitaevski regime, dilute Bose gases on a torus exhibit strong Bose-Einstein condensation at low temperatures, with the probability of particles outside the condensate decaying exponentially.

Contribution

It establishes exponential bounds on the condensation for dilute Bose gases, providing a rigorous quantitative description of the condensation behavior.

Findings

Exponential decay of particles outside the condensate at low temperatures.

Strong Bose-Einstein condensation in the Gross-Pitaevski regime.

Rigorous bounds on the probability distribution of particles outside the condensate.

Abstract

We consider N bosons on the unit torus $\Lambda = [0,1]^3$ in the Gross-Pitaevski regime where the interaction potential scales as $N^2 V (N(x -y))$. We prove that the thermal equilibrium at low temperatures exhibits the Bose-Einstein condensation in a strong sense, namely the probability of having $n$ particles outside of the condensation decays exponentially in $n$.