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

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 Λand \barΛ 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.

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• Hyperon polarization and its relation with directed flow in high-energy nuclear collisions
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• External magnetic field induced paramagnetic squeezing effect in heavy-ion collisions at the LHC
• Anisotropic linear waves and breakdown of the momentum expansion in spin magnetohydrodynamics
• First-order spin magnetohydrodynamics
• Dynamical Electromagnetic fields and Dynamical Electromagnetic Anomaly in heavy ion collisions at intermediate energies
• Guiding center hydrodynamics with spin