Planck Scale Physics and Bogoliubov Spaces in a Bose-Einstein Condensate

TL;DR

This paper investigates how quantum gravity-inspired modifications to dispersion relations affect the thermodynamic properties of a Bose-Einstein condensate, providing potential constraints on quantum gravity models through observable effects.

Contribution

It introduces a novel analysis of the impact of deformed dispersion relations on Bose-Einstein condensates, linking quantum gravity theories with measurable thermodynamic corrections.

Findings

Corrections to pressure, sound speed, and healing length due to dispersion relation deformation.

Thermodynamic property corrections depend on particle density and deformation parameters.

Potential to constrain quantum gravity models through condensate measurements.

Abstract

We analyze the consequences caused by a deformed dispersion relation, suggested in several quantum gravity models, upon a bosonic gas. Concerning the ground state of the Bogoliubov space of this system, we deduce the corrections in the pressure, the speed of sound, and the corresponding healing length. Indeed, we prove that the corrections in the relevant thermodynamic properties associated with the ground state, defines a non trivial function of the density of particles and the deformation parameters, allowing us to constrain, in principle, the form of the modified energy-momentum dispersion relation.