Instability of Bose-Einstein condensation on quantum graphs under repulsive perturbations

TL;DR

This paper demonstrates that even minimal repulsive interactions in quantum graph systems can eliminate Bose-Einstein condensation, extending prior findings to more complex interactions and the thermodynamic limit.

Contribution

It shows that repulsive two-particle interactions, including singular models like Lieb-Lininger, destroy Bose-Einstein condensation on quantum graphs.

Findings

Repulsive interactions destroy BEC in quantum graphs.

Results extend to singular interactions like Lieb-Lininger.

Condensate is eliminated even with arbitrarily small repulsive forces.

Abstract

In this Note we investigate Bose-Einstein condensation in interacting quantum many-particle systems on graphs. We extend previous results obtained for particles on an interval and show that even arbitrarily small repulsive two-particle interactions destroy a condensate in the non-interacting Bose gas. Our results also cover singular two-particle interactions, such as the well-known Lieb-Lininger model, in the thermodynamic limit.