  The elements of the quantum mechanical diffusion matrix, leading to a Gibbs
equilibrium state for a set of $N$ coupled quantum harmonic oscillators are
derived within Lindblad's axiomatic approach. Consequences of the fundamental
constraints on the quantum friction coefficients are discussed. We derive the
equations of motion for the expectation values and variances, and we solve them
analytically. We apply our results to the description of the charge and mass
asymmetry coordinates in heavy-ion collisions, and we investigate the effect of
dissipation on tunneling in sub-barrier processes.
