Destruction of localization by thermal inclusions: Anomalous transport and Griffiths effects in the Anderson and André-Aubry-Harper models

We discuss and compare two recently proposed toy models for anomalous transport Griffiths effects in random systems near the Many-Body Localization transitions: dephasing model, which adds thermal inclusions an Anderson Insulator as local Markovian channels that heat up system, Gaussian Orthogonal Ensemble (GOE) approach them terms of ensembles regular graphs. For these settings we dissipative properties their statistics. show both types dissipation lead to similar Griffiths-like phenomenology, with GOE bath being less effective thermalising system due its finite bandwidth. then extend case a quasi-periodic potential described by André-Aubry-Harper model coupled inclusions, display, large strength quasiperiodic potential, phenomenology one purely case. In particular, emergence subdiffusive broad statistics density states, suggestive like arising from interplay between localization coupling baths.