Anomalous magnetohydrodynamics with temperature-dependent electric conductivity and application to the global polarization
Hao-Hao Peng, Sihao Wu, Ren-jie Wang, Duan She, Shi Pu
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 $\ensuremath{\hbar}$ 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 play 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 $\mathrm{\ensuremath{\Lambda}}$ and $\overline{\mathrm{\ensuremath{\Lambda}}}$ 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 electromagnetic fields may be insufficient to explain the global polarization of $\mathrm{\ensuremath{\Lambda}}$ and $\overline{\mathrm{\ensuremath{\Lambda}}}$ hyperons in the low energy collisions.