The Magnetized Electron Gas in terms of Hurwitz Zeta Functions
Mathematical Physics
2009-10-31 v2 Astrophysics
Condensed Matter
math.MP
Abstract
We obtain explicit expressions for thermodynamic quantities of a relativistic degenerate free electron gas in a magnetic field in terms of Hurwitz Zeta functions. The formulation allows for systematic expansion in all regimes. Three energy scales appear naturally in the degenerate relativistic gas: the Fermi energy Ef, the temperature T and an energy related to the magnetic field or Landau level spacing, eB/Ef. We study the cold and warm scenarios, T << eB/Ef and eB/Ef << T, respectively. We reproduce the oscillations of the magnetization as a function of the field in the cold regime and the dilution of them in the warm regime.
Keywords
Cite
@article{arxiv.math-ph/0012010,
title = {The Magnetized Electron Gas in terms of Hurwitz Zeta Functions},
author = {Claudio O. Dib and Olivier R. Espinosa},
journal= {arXiv preprint arXiv:math-ph/0012010},
year = {2009}
}
Comments
33 pages, 6 figures, LaTeX 2e, uses epsf. v2: References added, minor additions to contents