Condensation of interacting bosons

TL;DR

This paper proves that in three or more dimensions, interacting bosons at low temperatures or high densities form long permutation cycles, leading to Bose-Einstein condensation.

Contribution

It establishes the link between permutation cycle divergence and Bose-Einstein condensation for positive, positive-type pair potentials in higher dimensions.

Findings

Permutation cycles diverge proportionally with particle number

Bose-Einstein condensation occurs under specified conditions

Results extend previous theoretical frameworks

Abstract

In this third paper of a series that started with arXiv:2106.10032 [math-ph] and continued with arXiv:2108.02659 [math-ph] we show that in $d\geq 3$ dimensions at low temperatures or high densities bosons interacting via pair potentials that are both positive and positive type form permutation cycles whose length diverges proportionally with the number of particles. Based on the second-cited paper, this implies Bose-Einstein condensation.