Relativistic Bose-Einstein condensation with disorder

TL;DR

This paper studies how weak disorder affects the thermodynamics and phase transition behavior of a relativistic charged scalar field, revealing increased critical temperatures and altered chemical potential dependencies, with implications for various physical systems.

Contribution

It introduces a detailed analysis of disorder effects on relativistic Bose-Einstein condensation, highlighting how weak disorder modifies critical temperatures and chemical potential behavior.

Findings

Disorder increases the mean-field critical temperature for BEC.

Significant deviations in chemical potential temperature dependence occur with increased noise.

No BEC occurs at fixed charge to entropy ratio in the presence of weak disorder.

Abstract

We investigate the thermodynamics of a self-interacting relativistic charged scalar field in the presence of weak disorder. We consider quenched disorder which couples linearly to the mass of the scalar field. After performing noise averages over the free energy of the system, we find that disorder increases the mean-field critical temperature for Bose-Einstein condensation at finite density. The effect of disorder on the temperature dependence of the chemical potential for a fixed charge density is investigated. Significant differences from the mean-field temperature dependence of the chemical potential are observed as the strength of the noise intensity increases. Finally, the temperature dependence of the chemical potential with fixed total charge and entropy is investigated. It is found that there is no Bose-Einstein condensation for a fixed charge to entropy ratio in the presence of weak disorder. The possible relevance of the findings in the present paper in different areas is discussed.