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Dynamics of a Many-Body-Localized System Coupled to a Bath

Coupling a many-body-localized system to a dissipative bath necessarily leads to delocalization. Here, we investigate the nature of the ensuing relaxation dynamics and the information it holds on the many-body-localized state. We formulate the relevant Lindblad equation in terms of the local integrals of motion of the underlying localized Hamiltonian. This allows to map the quantum evolution deep in the localized state to tractable classical rate equations. We consider two different types of dissipation relevant to systems of ultra-cold atoms: dephasing due to inelastic scattering on the lattice lasers and particle loss. Only the latter mechanism shows a pronounced effects of interactions on the relaxation of observables.