Intermediate-time dynamics of a particle on a disordered tight-binding lattice: quantum dissipation versus disorder

We investigate by a generalized Born appriximation the quantum dynamics of a dissipative particle on a tight-binding disordered one-dimensional lattice. When the friction is ohmic or underohmic (at zero temperature), the particle evolution is shown to be governed at intermediate times by a generalized master equation (i.e. retarded) for the site-diagonal elements of the density matrix. This model allows for a discussion of the interplay of the effects of quantum noise and disorder.