Translational symmetry and microscopic preparation in oscillator models of quantum dissipation

It is shown that models of quantum dissipation based on interactions which are linear both in the bath and in the particle position coordinate cannot be strictly invariant under translations, even if counterterms are included. This lack of symmetry manifests itself in an unphysical dependence of the long time dynamics on the choice of initial conditions for the particle-bath interaction. By properly expanding a Fröhlich type Hamiltonian, a simple model of homogeneous dissipation is developed that is insensitive to the chosen microscopic preparation.