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We modify the anomalous hydrodynamic equations of motion to account fordissipative effects due to QCD sphaleron transitions. By investigating thelinearized hydrodynamic equations, we show that sphaleron transitions lead tonontrivial effects on vector and axial charge transport phenomena in thepresence of a magnetic field. Due to the dissipative effects of sphalerontransitions, a wavenumber threshold $k_{\rm CMW}$ emerges characterizing theonset of chiral magnetic waves. Sphaleron damping also significantly impactsthe time evolution of both axial and vector charge perturbations in a QCDplasma in the presence of a magnetic field. Based on our analysis of thelinearized hydrodynamic equations, we also investigate the dependence of thevector charge separation on the sphaleron transition rate, which may haveimplications for the experimental search for the Chiral Magnetic Effect inHeavy Ion Collisions.

Sphaleron damping and effects on vector and axial charge transport in high-temperature QCD plasmas