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Motivated by recent optical lattice experiments [J.-y. Choi et al., Science352, 1547 (2016)], we study the dynamics of strongly interacting bosons in thepresence of disorder in two dimensions. We show that Gutzwiller mean-fieldtheory (GMFT) captures the main experimental observations, which are a resultof the competition between disorder and interactions. Our findings highlightthe difficulty in distinguishing glassy dynamics, which can be captured byGMFT, and many-body localization, which cannot be captured by GMFT, andindicate the need for further experimental studies of this system.

Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder