The Magnetized Electron Gas in terms of Hurwitz Zeta Functions

Details The Magnetized Electron Gas in terms of Hurwitz Zeta Functions The Magnetized Electron Gas in terms of Hurwitz Zeta Functions

2000-12-06

arxiv.org/abs/math-ph/0012010v2

Nucl.Phys.B612:492-518,2001

Physics

Mathematical Physics

33 pages, 6 figures, LaTeX 2e, uses epsf. v2: References added, minor additions to contents

Scientific paper

10.1016/S0550-3213(01)00360-1

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.

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