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arXiv · 1508.05799

The thermodynamics of Fermi gases in three dimensional fuzzy space

F. G. Scholtz·J. N. Kriel·H. W. Groenewald
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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.

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F. G. Scholtz, J. N. Kriel, H. W. Groenewald. 2015-08-24. The thermodynamics of Fermi gases in three dimensional fuzzy space. https://doi.org/10.1103/physrevd.92.125013

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