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}={π}{}/d², where d is the lattice constant, and also for very weak damping.
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Weiß et al. (1988) studied this question.
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