Breakdown of quantum-to-classical correspondence for diffusion in high temperature thermal environment

We re-consider the old problem of Brownian motion in homogeneous high-temperature thermal environment. The classical theory implies that the diffusion coefficient does not depend on whether the thermal fluctuations are correlated in space or disordered. We show that the corresponding quantum analysis exhibits a remarkable breakdown of quantum-to-classical correspondence. Explicit results are found for a tight binding model, within the framework of an Ohmic master equation, where we distinguish between on-site and on-bond dissipators.