Electrical conductivity of quark matter at finite T under external magnetic field

TL;DR

This paper calculates the electrical conductivity of quark matter at finite temperature under strong magnetic fields using the instanton-liquid model, providing results consistent with lattice QCD and analyzing magnetic field effects.

Contribution

It introduces a temperature-dependent instanton-liquid model to evaluate quark matter conductivity under magnetic fields, including parameterizations and photon emission rates.

Findings

Electrical conductivity ranges from 0.02 to 0.15 /fm for T=0-400 MeV.

Conductivity scales with T and relaxation time, sigma/T ~ (0.46-1.39)C_EM.

Magnetic field has minor impact on conductivity at high T.

Abstract

We investigate the electrical conductivity (sigma) of quark matter via the Kubo formula at finite temperature and zero quark density (T>0, mu=0) in the presence of an external strong magnetic field. For this purpose, we employ the dilute instanton-liquid model, taking into account its temperature modification with the trivial-holonomy caloron distribution. By doing that, the momentum and temperature dependences for the effective quark mass and model renormalization scale are carefully evaluated. From the numerical results, it turns out that sigma\approx(0.02 ~ 0.15)/fm for T=(0 ~ 400) MeV with the relaxation time tau=(0.3 ~ 0.9) fm. In addition, we also parameterize the electrical conductivity as sigma/T ~ (0.46,0.77,1.08,1.39)C_EM for tau=(0.3,0.5,0.7,0.9) fm, respectively. These results are well compatible with other theoretical estimations, including those from the lattice QCD simulations. It also turns out that the external magnetic field plays only a minor role for sigma even for the very strong one B_0 ~ m^2_pi*10 and becomes relatively effective for T\lesssim200 MeV. Moreover, we compute the soft photon emission rate from the quark-gluon plasma, using the electrical conductivity calculated.