Seebeck effect in a thermal QCD medium in the presence of strong magnetic field

Abstract

The strongly interacting partonic medium created post ultrarelativistic heavy ion collision experiments exhibits a significant temperature-gradient between the central and peripheral regions of the collisions, which in turn, is capable of inducing an electric field in the medium; a phenomenon known as Seebeck effect. The effect is quantified by the magnitude of the induced electric field per unit temperature-gradient - the Seebeck coefficient ($S$). We study the coefficient, $S$ in the relativistic Boltzmann transport equation in relaxation-time approximation, as a function of temperature ($T$) and chemical potential ($\mu$), wherein we find that with current quark masses, the magnitude of $S$ for individual flavours as well as that for the medium as a whole decreases with $T$ and increases with $\mu$, with the electric charge of the flavour deciding the sign of $S$. The emergence of a strong magnetic field ($B$) in the non-central collisions at heavy-ion collider experiments motivates us to study the effect of $B$ on Seebeck effect. The strong $B$ affects $S$ in multifold ways, via : a) modification of phase-space due to the dimensional reduction, b) dispersion relation in lowest Landau level (occupation probability), and c) relaxation-time. We find that a strong $B$ not only decreases the magnitudes of $S$'s of individual species, it also flips their signs. This leads to a faster reduction of the magnitude of $S$ of the medium than its counterpart at $B=0$. We then explore how the interactions among partons in perturbative thermal QCD in the quasiparticle framework affect Seebeck effect, where we find that even in strong B, there is no more a flip of the sign of $S$ for individual species and an enhancement of the magnitudes of $S$ of individual species as well as that of the medium, compared to current quark mass description at either $B=0$ or $B \neq 0$.