The magnetized electron gas in terms of Hurwitz zeta functions |
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| Institution: | 1. Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan;2. WPI-AIMR, Tohoku University, Sendai 980-0845, Japan;3. Department of Mechanical Engineering, Tohoku University, Sendai 980-0845, Japan;1. Department of Physics, Faculty of Sciences, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran;2. Nanoscience and Nanotechnology Research Group, University of Mohaghegh Ardabili, Ardabil, Iran;3. Department of Engineering Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Namin, Iran |
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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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