  We consider a single impurity atom confined to an optical lattice and
immersed in a homogeneous Bose-Einstein condensate (BEC). Interaction of the
impurity with the phonon modes of the BEC leads to the formation of a stable
quasiparticle, the polaron. We use a variational mean-field approach to study
dispersion renormalization and derive equations describing non-equilibrium
dynamics of polarons by projecting equations of motion into mean-field (MF)
type wavefunctions. As a concrete example, we apply our method to study
dynamics of impurity atoms in response to a suddenly applied force and explore
the interplay of coherent Bloch oscillations and incoherent drift. We obtain a
non-linear dependence of the drift velocity on the applied force, including a
sub-Ohmic dependence for small forces for dimensionality d>1 of the BEC. For
the case of heavy impurity atoms we derive a closed analytical expression for
the drift velocity. Our results show considerable differences with the commonly
used phenomenological Esaki-Tsu model.
