Relativistic Landau problem at finite temperature
C.G. Beneventano, E.M. Santangelo
TL;DR
This paper investigates the Casimir energy, fermion number, and Hall conductivity for Dirac fields in 2+1 dimensions under magnetic fields, extending to finite temperature and chemical potential, revealing key quantum effects.
Contribution
It introduces a finite-temperature analysis of the Landau problem with chemical potential and derives Hall conductivity via Lorentz boost techniques.
Findings
Finite-temperature Casimir energy and fermion number calculated.
Hall conductivity derived for crossed electric and magnetic fields.
Results enhance understanding of quantum Hall effects in relativistic systems.
Abstract
We study the zero temperature Casimir energy and fermion number for Dirac fields in a 2+1-dimensional Minkowski space-time, in the presence of a uniform magnetic field perpendicular to the spatial manifold. Then, we go to the finite-temperature problem with a chemical potential, introduced as a uniform zero component of the gauge potential. By performing a Lorentz boost, we obtain Hall's conductivity in the case of crossed electric and magnetic fields.
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