  We study the dynamics of a Brownian quantum particle hopping on an infinite
lattice with a spin degree of freedom. This particle is coupled to free boson
gases via a translation-invariant Hamiltonian which is linear in the creation
and annihilation operators of the bosons. We derive the time evolution of the
reduced density matrix of the particle in the van Hove limit in which we also
rescale the hopping rate. This corresponds to a situation in which both the
system-bath interactions and the hopping between neighboring sites are small
and they are effective on the same time scale. The reduced evolution is given
by a translation-invariant Lindblad master equation which is derived
explicitly.
