  We model the dynamics of two species of bosonic atoms trapped in an optical
lattice within the Mott regime by mapping the system onto a spin model. A field
gradient breaks the cloud into two domains. We study how the domain wall
evolves under adiabatic and diabatic changes of this gradient. We determine the
timescales for adiabaticity, and study how temperature evolves for slow ramps.
We show that after large, sudden changes of the field gradient, the system does
not equilibrate on typical experimental timescales. We find interesting spin
dynamics even when the initial temperature is large compared to the
super-exchange energy. We discuss the implication of our results for
experiments wishing to use such a two-component system for thermometry, or as
part of a cooling scheme.
