Effect of magnetic field on the charge and thermal transport properties of hot and dense QCD matter

Abstract

We have studied the effect of strong magnetic field on the charge and thermal transport properties of hot QCD matter at finite chemical potential. For this purpose, we have calculated the electrical ($σ_{\rm el}$) and thermal ($κ$) conductivities using kinetic theory in the relaxation time approximation, where the interactions are subsumed through the distribution functions within the quasiparticle model at finite temperature, strong magnetic field and finite chemical potential. This study helps to understand the impacts of strong magnetic field and chemical potential on the local equilibrium by the Knudsen number ($Ω$) through $κ$ and on the relative behavior between thermal conductivity and electrical conductivity through the Lorenz number ($L$) in the Wiedemann-Franz law. We have observed that, both $σ_{\rm el}$ and $κ$ get increased in the presence of strong magnetic field, and the additional presence of chemical potential further increases their magnitudes, where $σ_{\rm el}$ shows decreasing trend with the temperature, opposite to its increasing behavior in the isotropic medium, whereas $κ$ increases slowly with the temperature, contrary to its fast increase in the isotropic medium. The variation in $κ$ explains the decrease of the Knudsen number with the increase of the temperature. However, in the presence of strong magnetic field and finite chemical potential, $Ω$ gets enhanced and approaches unity, thus, the system may move slightly away from the equilibrium state. The Lorenz number ($κ/(σ_{\rm el} T))$ in the abovementioned regime of strong magnetic field and finite chemical potential shows linear enhancement with the temperature and has smaller magnitude than the isotropic one, thus, it describes the violation of the Wiedemann-Franz law for the hot and dense QCD matter in the presence of a strong magnetic field.