Bose--Einstein condensation for particles with repulsive short-range pair interactions in a Poisson random external potential in $\mathbb R^d$

TL;DR

This paper investigates the absence of Bose--Einstein condensation in a repulsive Bose gas with random obstacles, showing that strong interactions prevent condensation into localized states in a non-percolating regime.

Contribution

It demonstrates that in a disordered environment with strong interactions, Bose--Einstein condensation into localized states does not occur, extending understanding of quantum gases in random potentials.

Findings

No Bose--Einstein condensation into localized states under strong interactions.

Results apply to eigenstates of the one-particle Hamiltonian.

Condensation is suppressed in the non-percolation regime with obstacles.

Abstract

We study Bose gases in $d$ dimensions, $d \ge 2$, with short-range repulsive pair interactions, at positive temperature, in the canonical ensemble and in the thermodynamic limit. We assume the presence of hard Poissonian obstacles and focus on the non-percolation regime. For sufficiently strong interparticle interactions, we show that almost surely there cannot be Bose--Einstein condensation into a sufficiently localized, normalized one-particle state. The results apply to the eigenstates of the underlying one-particle Hamiltonian.