Dynamics of the one-dimensional Anderson insulator coupled to various bosonic baths

We study a particle which propagates in a one-dimensional strong random potential and is coupled to a bosonic bath. We independently test various properties of bosons (hopping term, hard-core effects, and generic boson-boson interaction) and show that bosonic itineracy is the essential ingredient governing the dynamics of the particle. Coupling of the particle to itinerant phonons or hard-core bosons alike leads to delocalization of the particle by virtue of a subdiffusive (or diffusive) spread from the initially localized state. Delocalization remains in effect even when the boson frequency and the bandwidth of itinerant bosons remain an order of magnitude smaller than the magnitude of the random potential. When the particle is coupled to localized bosons, its spread remains logarithmic or even sublogarithmic. The latter result together with the survival probability shows that the particle remains localized despite being coupled to bosons.