  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 sub-logarithmic. The latter
result together with the survival probability shows that the particle remains
localized despite being coupled to bosons.
