  We investigate the effects of a nearly uniform Bose-Einstein condensate (BEC)
on the properties of immersed trapped impurity atoms. Using a weak-coupling
expansion in the BEC-impurity interaction strength, we derive a model
describing polarons, i.e., impurities dressed by a coherent state of Bogoliubov
phonons, and apply it to ultracold bosonic atoms in an optical lattice. We show
that, with increasing BEC temperature, the transport properties of the
impurities change from coherent to diffusive. Furthermore, stable polaron
clusters are formed via a phonon-mediated off-site attraction.
