Simple criterion for the occurrence of Bose-Einstein condensation and the Meissner-Ochsenfeld effect

TL;DR

This paper establishes a simple criterion for Bose-Einstein condensation in both nonrelativistic and relativistic systems, linking it to the spectral dimension and connecting it with the Meissner-Ochsenfeld effect.

Contribution

It provides a universal condition based on spectral dimension for the occurrence of Bose-Einstein condensation and relates it to the Meissner-Ochsenfeld effect.

Findings

Condensation occurs only if spectral dimension q ≥ 3.

The criterion applies to both nonrelativistic and relativistic systems.

The Meissner-Ochsenfeld effect is closely linked to Bose-Einstein condensation.

Abstract

We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation is given. We show that condensation can occur only if $q\geq 3$, where $q$ is the dimension associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. Furthermore we show that the criterion for the appearance of the Meissner-Ochsenfeld effect is closely connected with that for the appearance of Bose-Einstein condensation.