Modified Bosonic Gas Trapped in a Generic 3-dim Power Law Potential

TL;DR

This paper investigates how a proposed quantum-gravity-inspired deformation of particle dispersion relations affects the thermodynamics of Bose-Einstein condensates in a 3D power-law trap, suggesting potential bounds on deformation parameters.

Contribution

It demonstrates that such deformations cause measurable shifts in the condensation temperature, providing a new way to test quantum-gravity effects in cold atom systems.

Findings

Condensation temperature is shifted by dispersion relation deformation.

The temperature shift depends on particle number and trap parameters.

The shift can serve as a criterion for quantum-gravity effects in finite systems.

Abstract

We analyze the consequences caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose-Einstein condensate trapped in a generic 3-dimensional power-law potential. We prove that the condensation temperature is shifted as a consequence of such deformation and show that this fact could be used to provide bounds on the deformation parameters. Additionally, we show that the shift in the condensation temperature, described as a non-trivial function of the number of particles and the trap parameters, could be used as a criterion to analyze the effects caused by a deformed dispersion relation in weakly interacting systems and also in finite size systems.