Abstract
We study relativistic magnetohydrodynamics with longitudinal boost invariance in the presence of chiral magnetic effects and finite electric conductivity. With initial magnetic fields parallel or anti-parallel to electric fields, we derive the analytic solutions of electromagnetic fields and the chiral number and energy density in an expansion of several parameters determined by initial conditions. The numerical solutions show that such analytic solutions work well in weak fields or large chiral fluctuations. We also discuss the properties of electromagnetic fields in the laboratory frame.
Highlights
Some novel transport phenomena of chiral fermions in strong electromagnetic (EM) fields have been extensively studied in relativistic heavy ion collisions and condensed matter physics
The strong magnetic field can lead to the chiral separation effect for the chiral charge current
The chiral separation can be induced by an electric field, which is called the chiral electric separation effect (CESE) [20,21,22,23]
Summary
Some novel transport phenomena of chiral (massless) fermions in strong electromagnetic (EM) fields have been extensively studied in relativistic heavy ion collisions and condensed matter physics. The strong magnetic field can lead to the chiral separation effect for the chiral charge current. At the very early stage of the quarkgluon plasma (QGP), the topological fluctuations in nonAbelian gauge fields give rise to the imbalance of chirality from event to event (event by event) Such an imbalance of chirality may lead to the charge separation with respect to the reaction plane in heavy ion collisions. We choose the Levi-Civita tensor satisfying ε0123 1⁄4 −ε0123 1⁄4 þ1 and εμναβεμνρσ 1⁄4 −2!ðgαρgβσ − gασgβρÞ
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