The motion of a quantum particle with Ohmic damping in a tight-binding lattice is discussed. An exact series representation in powers of the tunnelmatrix element Δ for moments of the probability distribution is given. The dynamics at zero and at finite temperatures in the presence of an external force is solved exactly to all orders of Δ for a particular value of the friction coefficient, η=πħ/$d^2$, where d is the lattice constant, and also for very weak damping.

• Received 21 August 1987

DOI:https://doi.org/10.1103/PhysRevB.37.2729