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The Magnetized Electron Gas in terms of Hurwitz Zeta Functions

Claudio O. Dib·Olivier R. Espinosa
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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.

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Claudio O. Dib, Olivier R. Espinosa. 2001-06-05. The Magnetized Electron Gas in terms of Hurwitz Zeta Functions. https://doi.org/10.1016/s0550-3213(01)00360-1

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