DISSIPATIVE QUANTUM DYNAMICS IN A MULTIWELL SYSTEM

We investigate the dynamics of a quantum particle moving in a tight-binding lattice and coupled to a heat bath environment. Using the Feynman-Vernon influence functional method, we obtain an exact series representation in powers of the tunneling matrix for the generating functional of moments of the probability distribution which is valid for arbitrary temperatures and linear dissipation. We prove that the Einstein relation between the linear mobility and the diffusion coefficient holds to any order of the expansion for Ohmic, and for a restricted region of super-Ohmic dissipation. We also compute in the Ohmic case the mobility in certain regions of the parameter space. In particular, we find that the low temperature correction to the zero temperature mobility behaves as T2, and we also determine the prefactor. Finally, the exact solution of the dynamics for any times, temperatures and bias is presented for a particular value of the damping strength in the case of strict Ohmic dissipation.