The Magnetized Electron Gas in terms of Hurwitz Zeta Functions

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.

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

References in corpus (5)

• Analytic results for the effective action
• QED effective action at finite temperature and density
• Real-Time Thermal Propagators and the QED Effective Action for an External Magnetic Field
• Temperature Expansions for Magnetic Systems
• A Note on QED with Magnetic Field and Chemical Potentia

Cited by in corpus (16)

• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Black hole determinants and quasinormal modes
• Neutral meson properties in hot and magnetized quark matter: a new magnetic field independent regularization scheme applied to NJL-type model
• Fluctuating temperature and baryon chemical potential in heavy-ion collisions and the position of the critical end point in the effective QCD phase diagram
• On the critical end point in a two-flavor linear sigma model coupled to quarks
• Field-Induced Degeneracy Regimes in Quantum Plasmas
• Partition Functions in Even Dimensional AdS via Quasinormal Mode Methods
• Kicks of magnetized strange quark stars induced by anisotropic emission of neutrinos
• Magnetization Cooling of an Electron Gas
• Neutrino emission rates in highly magnetized neutron stars revisited
• Gravitational collapse of a magnetized fermion gas with finite temperature
• Onset of Electron Captures and Shallow Heating in Magnetars
• Exact Nonlinear Excitations in Double-Degenerate Plasmas
• Locating the critical end point using the linear sigma model coupled to quarks
• Orbital Ferromagnetism and the Chandrasekhar Mass-Limit
• Using the Linear Sigma Model with quarks to describe the QCD phase diagram and to locate the critical end point