Anomalous magnetohydrodynamics with temperature-dependent electric conductivity and application to the global polarization

TL;DR

This paper derives solutions for relativistic anomalous magnetohydrodynamics with temperature-dependent conductivity, highlighting its impact on electromagnetic field decay and hyperon polarization, and compares results with experimental data.

Contribution

It introduces temperature-dependent electric conductivity into anomalous MHD equations and analyzes its effects on field decay and hyperon polarization splitting.

Findings

Conductivity influences electromagnetic field decay rates.

Results suggest chemical potential gradients may dominate polarization effects.

Discrepancies with low energy collision data imply additional factors are important.

Abstract

We have derived the solutions of the relativistic anomalous magnetohydrodynamics with longitudinal Bjorken boost invariance and transverse electromagnetic fields in the presence of temperature or energy density dependent electric conductivity. We consider the equations of states in a high temperature limit or in a high chiral chemical potential limit. We obtain both perturbative analytic solutions up to the order of \hbar and numerical solutions in our configurations of initial electromagnetic fields and Bjorken flow velocity. Our results show that the temperature or energy density dependent electric conductivity plays an important role to the decaying of the energy density and electromagnetic fields. We also implement our results to the splitting of global polarization for \Lambda and \bar{\Lambda} hyperons induced by the magnetic fields. Our results for the splitting of global polarization disagree with the experimental data in low energy collisions, which implies that the contribution from gradient of chemical potential may dominate in the low energy collisions.