Electrical conductivity and Hall conductivity of a hot and dense hadron gas in a magnetic field: a relaxation time approach

Abstract

We estimate the electrical conductivity and the Hall conductivity of a hot and dense hadron gas using the relaxation time approximation for the solution of the Boltzmann transport equation in the presence of an electromagnetic field. We investigate the temperature and the baryon chemical potential dependence of these transport coefficients in the presence of a magnetic field. The explicit calculation is performed within the ambit of the hadron resonance gas model. In general, it is observed that the electrical conductivity decreases in the presence of a magnetic field. While at vanishing magnetic field the electrical conductivity decreases monotonically with temperature, in the presence of a magnetic field the same shows a nonmonotonic behavior with a peak. The Hall conductivity, on the other hand, shows a nonmonotonic behavior with respect to the dependence on a magnetic field as well as with temperature. We argue that for a pair plasma (particle-antiparticle plasma) where 𝜇𝐵 =0 , Hall conductivity vanishes. Only for a nonvanishing baryon chemical potential, Hall conductivity has a nonzero value. We also estimate the electrical conductivity and the Hall conductivity as a function of the center of mass energy along the freeze-out curve as may be relevant for relativistic heavy-ion collision experiments.