Tomaschitz, R. (2010). Nearly degenerate electron distributions and superluminal radiation densities, Physica B 405, 1022-1032, DOI: 10.1016/j.physb.2009.10.048


Abstract (ScienceDirectSAO/NASA ADS)

Polylogarithmic fugacity expansions of the partition function, the caloric and thermal equations of state, and the specific heat of fermionic power-law distributions are derived in the nearly degenerate low-temperature/high-density quantum regime. The spectral functions of an ultra-relativistic electron plasma are obtained by averaging the tachyonic radiation densities of inertial electrons with Fermi power-laws, whose entropy is shown to be extensive and stable. The averaged radiation densities are put to test by performing tachyonic cascade fits to the γ-ray spectrum of the TeV blazar Markarian 421 in a low and high emission state. Estimates of the thermal electron plasma in this active galactic nucleus are extracted from the spectral fits, such as temperature, number count, and internal energy. The tachyonic cascades reproduce the quiescent as well as a burst spectrum of the blazar obtained with imaging atmospheric Cherenkov detectors. Double-logarithmic plots of the differential tachyon flux exhibit intrinsic spectral curvature, caused by the Boltzmann factor of the electron gas.


Keywords: Fermi power-law ensembles; Nearly degenerate electron plasma; Superluminal radiation; Tachyonic cascade spectra; Spectral curvature; γ-Ray blazars; Negative mass-square; Transversal and longitudinal radiation modes; Polylogarithms


PACS classification codes: 52.25.Kn; 52.27.Ny; 71.10.Ca; 95.30.Tg


Article Outline

1. Introduction

2. Ultra-relativistic Fermi power laws

3. Thermodynamic variables of nearly degenerate power-law distributions

4. Tachyonic cascade spectra

5. Conclusion


Appendix A. Incomplete integrals of fermionic power-law densities

A.1. Fugacity expansion at low temperature and high density

A.2. Zero-temperature degeneracy

A.3. Number count, internal energy, and partition function in the nearly degenerate regime

Appendix B. Polylogarithms, Stirling numbers, and Gegenbauer polynomials






Nearly degenerate electron distributions and superluminal radiation densities



Tomaschitz, Roman



AA(Department of Physics, Hiroshima University, 1-3-1 Kagami-yama, Higashi-Hiroshima 739-8526, Japan)



Physica B: Physics of Condensed Matter, Volume 405, Issue 3, p. 1022-1032.

Publication Date:






PACS Keywords:


Thermodynamics of plasmas, Relativistic plasmas, Electron gas, Fermi gas, Thermodynamic processes, conduction, convection, equations of state




Bibliographic Code:





description: Roman Tomaschitz (2010) Nearly degenerate electron distributions and superluminal radiation densities, Physica B 405, 1022.


Keywords: fermionic power-law ensembles, nearly degenerate electron gas, ultra-relativistic Fermi power laws, quantum statistics of nonthermal fermion systems, extensive entropy and thermodynamic stability, internal energy, specific heat, equations of state, fugacity expansion, polylogarithms, ultra-relativistic electron plasma of TeV γ-ray blazars, Markarian 421, superluminal spectral densities of ultra-relativistic electrons, tachyonic cascade spectra, transversal and longitudinal γ-ray cascades, intrinsic spectral curvature, tachyonic gamma-rays


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