Thermalization of boosted charged AdS black holes by an ionic Lattice

We investigate thermalization process of boosted charged AdS black holes in the Einstein-Maxwell system in the presence of an ionic lattice formed by spatially varying chemical potential. We calculate perturbations of the black holes by the lattice and investigate how the momentum relaxation occurs through umklapp scattering. In the WKB approximation, both of the momentum relaxation rate and entropy production rate are analytically obtained and the first law of black holes is derived in the irreversible process. Interestingly, both the analytical and numerical calculations show that the momentum relaxation rate or the entropy production rate does not approach zero in the zero temperature limit unless the velocity of the black hole is zero. In the dual field theory side, this indicates that persistent current does not exist even in the zero temperature limit, implying that the "ionic lattice" does not behave as a perfect lattice in a strongly coupled dual field theory.