Ideal-Modified Bosonic Gas Trapped in an Arbitrary Three Dimensional Power-Law Potential

TL;DR

This paper investigates how a proposed quantum-gravity-inspired modification to particle dispersion relations affects the thermodynamics of a trapped Bose-Einstein condensate, potentially constraining new physics parameters.

Contribution

It derives the temperature shift due to deformed dispersion relations in a generic power-law trap and analyzes stability criteria related to particle number fluctuations.

Findings

Temperature shift depends on particle number and trap shape.

Deformed dispersion relations can be constrained by condensate thermodynamics.

Instability from fluctuations can be mitigated by considering the system's lowest energy state.

Abstract

We analyze the effects 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 shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. Additionally, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.