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In this talk, I shall discuss non-equilibrium dynamics of bosons in an optical
lattice using a projection operator approach. Our analysis for periodic dynamics of this model
shall reveal the presence of special frequencies at which the system wavefunction almost
comes back to itself after a cycle of the drive and thus lead to "dynamics induced freezing".
Time permitting, I shall also discuss the dynamics of bosons in the Mott phase in a tilted 1D lattice
and show that these systems provide perfect test bed for finite size Kibble-Zureck phenomenon.
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