Quantum dynamics of a damped particle in a tight-binding lattice.

Abstract

The motion of a quantum particle in a tight-binding lattice coupled to an Ohmic thermal reservoir is analyzed in the path-integral formalism. We derive exact formal expressions for moments of the probability distribution both for noncorrelated and correlated thermal initial states of the particle-plus-reservoir complex. Based on these expressions we discuss the role of initial conditions on the subsequent motion and calculate the differences in the transient behavior. For a particular value of the damping strength we find the exact solution of the dynamics in analytic form at any time, temperature, and bias for the two kinds of initial states.