Abstract
We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution leads to an unconventional dynamical behavior of local number fluctuations. In particular, we show, both analytically and numerically, the emergence of an anomalous diffusive evolution in configuration space at short times and, at long times, an unconventional dynamics dominated by rare events. Such rare events, common in disordered and frustrated systems, are due here to strong interactions. This complex two-stage dynamics reveals information on the level structure of the strongly interacting gas.