Olbert's kappa Fermi and Bose distributions

Abstract

The quantum version of Olbert's kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi energy and momentum. We provide the Olbert-generalized expressions of the Olbert-Fermi partition function and entropy which may serve determining all relevant statistical mechanical quantities. Possible applications are envisaged to condensed matter physics, possibly quantum plasmas, and dense astrophysical objects like the interior state of terrestrial planets, neutron stars, magnetars where quantum effects come into play, dominate the microscopic scale but may have macroscopic consequences.

Brief Communication, 13 pages, 1 figure

References in corpus (5)

• Gibbsian theory of power law distributions
• On the Relation between Kappa Distribution Functions and the Plasma Beta Parameter in the Earth Magnetosphere: THEMIS observations
• The $\kappa$-cookbook: a novel generalizing approach to unify $\kappa$-like distributions for plasma particle modeling
• On the Generation of Compressible Mirror-mode Fluctuations in the Inner Heliosheath
• Lorentzian Entropies and Olbert's $\kappa$-distribution