Electric conductivity of hot and dense quark matter in a magnetic field with Landau level resummation via kinetic equations

TL;DR

This paper calculates the electric conductivity of hot, dense quark matter in a magnetic field, including Landau level effects, revealing how conductivity varies with magnetic field and chemical potential, relevant for understanding the chiral magnetic effect.

Contribution

It extends previous models by incorporating Landau level resummation via kinetic equations to compute conductivity beyond the lowest Landau level approximation.

Findings

Longitudinal conductivity shows mild dependence on chemical potential and quark mass.

Conductivity first decreases then increases with magnetic field, matching experimental signatures.

Results are consistent with lattice-QCD estimates at zero magnetic field.

Abstract

We compute the electric conductivity of quark matter at finite temperature $T$ and quark chemical potential $\mu$ under a magnetic field $B$ beyond the Lowest Landau level approximation. The electric conductivity transverse to $B$ is dominated by the Hall conductivity $\sigma_H$. For the longitudinal conductivity $\sigma_\parallel$, we need to solve kinetic equations. Then, we numerically find that $\sigma_\parallel$ has only mild dependence on $\mu$ and the quark mass $m_q$. Moreover, $\sigma_\parallel$ first decreases and then linearly increases as a function of $B$, leading to an intermediate $B$ region which looks consistent with the experimental signature for the chiral magnetic effect. We also point out that $\sigma_\parallel$ at nonzero $B$ remains within the range of the lattice-QCD estimate at $B=0$.