Diffusion and friction coefficients in equation for Wigner distribution function

In the framework of the axiomatic approach for open quantum systems various sets of the friction and diffusion coefficients are considered. The sets of diffusion coefficients are found when the quantum approach is close the classical one. Due to the presence of the friction in coordinate in the quantum diffusion equation the dissipation supports tunneling through the barrier but reduces the crossing of the barrier for energies above the barrier.