  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 timescales 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
timescales. 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.
