Proof of Bose-Einstein Condensation for Interacting Gases with a One-Particle Spectral Gap

TL;DR

This paper proves the occurrence of Bose-Einstein condensation in interacting gases with a spectral gap, using a mean-field reference system to establish a positive lower bound on condensate density.

Contribution

It introduces a novel method to demonstrate standard homogeneous Bose-Einstein condensation in systems with superstable interactions and a spectral gap.

Findings

Positive lower bound on condensate density established

First proof of BEC in such interacting systems

Applicable to continuous Bose gases with spectral gaps

Abstract

Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose-Einstein condensation for such interacting systems.