Fermi-Dirac Integrals in Degenerate Regimes: A Novel Asymptotic Expansion
arXiv:2405.05287 · doi:10.1007/s10773-024-05695-8
Abstract
We characterize in a novel manner the physical properties of the low temperature Fermi gas in the degenerate domain as a function of temperature and chemical potential. For the first time we obtain low temperature results in the domain where several fermions are found within a de Broglie spatial cell. In this regime, the usual high degeneracy Sommerfeld expansion fails. The other known semi-classical Boltzmann domain applies when fewer than one particle is found in the de Broglie cell. We also improve on the understanding of the Sommerfeld expansion in the regime where the chemical potential is close to the mass and also in the high temperature regime. In these calculcations we use a novel characterization of the Fermi distribution allowing the separation of the finite and zero temperature phenomena. The relative errors of the three approximate methods (Boltzmann limit, Sommerfeld expansion, and the new domain of several particles in the de Broglie cell) are quantified.
arXiv comment35 pages 1+7 double figures, v2 format accepted for publication in the International Journal of Theoretical Physics
References in corpus (15)
- Equations of state for supernovae and compact stars
- Magnetars
- Dense Nuclear Matter Equation of State from Heavy-Ion Collisions
- Thermodynamics conditions of matter in neutron star mergers
- Finite-temperature extension for cold neutron star equations of state
- Thermodynamics of Neutrons in a Magnetic Field and its Implications for Neutron Stars
- Exploring thermal effects of the hadron-quark matter transition in neutron star mergers
- Relic neutrinos: Physically consistent treatment of effective number of neutrinos and neutrino mass
- A short survey of matter-antimatter evolution in the primordial universe
- Massive Fermi Gas in the Expanding Universe
- Fugacity and Reheating of Primordial Neutrinos
- Matter-antimatter origin of cosmic magnetism
- Presence versus absence of Two-Dimensional Fermi Surface Anomalies
- The muon abundance in the primordial Universe
- Reactions Governing Strangeness Abundance in Primordial Universe