The thermodynamics of Fermi gases in three dimensional fuzzy space

TL;DR

This paper investigates the thermodynamics of Fermi gases in three-dimensional fuzzy space, revealing non-commutative effects, a minimal volume for incompressibility, and dualities in the system's spectrum, with implications for gravity confinement.

Contribution

It introduces a detailed analysis of Fermi gases in fuzzy space, highlighting non-commutative corrections, dualities, and novel gravitational confinement features not previously explored.

Findings

Identification of non-commutative corrections at low densities and temperatures

Existence of a minimal volume where the gas becomes incompressible

Discovery of a mass-radius relation and entropy behavior in gravity-confined gases

Abstract

We use the recently derived density of states for a particle confined to a spherical well in three dimensional fuzzy space to compute the thermodynamics of a gas of non-interacting fermions confined to such a well. Special emphasis is placed on non-commutative effects and in particular non-commutative corrections to the thermodynamics at low densities and temperatures are computed where the non-relativistic approximation used here is valid. Non-commutative effects at high densities are also identified, the most prominent being the existence of a minimal volume at which the gas becomes incompressible. The latter is closely related to a low/high density duality exhibited by these systems, which in turn is a manifestation of an infra-red/ultra violet duality in the single particle spectrum. Both non-rotating and slowly rotating gasses are studied. Approximations are benchmarked against exact numerical computations for the non-rotating case and several other properties of the gas are demonstrated with numerical computations. Finally, a non-commutative gas confined by gravity is studied and several novel features regarding the mass-radius relation, density and entropy are highlighted.