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We study the thermalization of excitations generated by spontaneous emission events for cold bosons in an optical lattice. Computing the dynamics described by the many-body master equation, we characterize equilibration time scales in different parameter regimes. For simple observables, we find regimes in which the system relaxes rapidly to values in agreement with a thermal distribution, and others where thermalization does not occur on typical experimental time scales. Because spontaneous emissions lead effectively to a local quantum quench, this behavior is strongly dependent on the low-energy spectrum of the Hamiltonian, and undergoes a qualitative change at the Mott insulator--superfluid transition point. These results have important implications for the understanding of thermalization after localized quenches in isolated quantum gases, as well as the characterization of heating in experiments.
Schachenmayer et al. (Fri,) studied this question.