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The Chiral Magnetic Effect (CME) -- the separation of positive and negativeelectric charges along the direction of the external magnetic field inquark-gluon plasma and other topologically non-trivial media -- is aconsequence of the coupling of electrodynamics to the topological gluon fieldfluctuations that form metastable $CP$-odd domains. In phenomenological modelsit is usually assumed that the domains are uniform and the influence of thedomain walls on the electric current flow is not essential. This paperchallenges the latter assumption. A simple model consisting of a uniformspherical domain in a uniform time-dependent magnetic field is introduced andanalytically solved. It is shown that (i) no electric current flows into or outof the domain, (ii) the charge separation current, viz. the total electriccurrent flowing inside the domain in the external field direction, is adissipative Ohm current, (iii) the CME effect can be produced either by theanomalous current or by the boundary conditions on the domain wall and (iv) thecharge separation current oscillates in plasma long after the external fielddecays. These properties are qualitatively different from the CME in aninfinite medium.

The impact of domain walls on the chiral magnetic effect in hot QCD matter