Contour-time approach to the 2D disordered Bose-Hubbard model in the strong coupling regime.

We develop a strong-coupling approach for calculating spatio-temporal correlations in the disordered Bose-Hubbard model. We consider systems that are prepared in highly-excited out-of-equilibrium density patterns and derive equations of motion for the disorder-averaged single-particle Green's function, allowing us to study the relaxation dynamics. We discuss how our formalism can be applied to the study of Bose glass and possibly many-body localized states in the context of recent cold experiments.