Generalization of Kramers formula for open quantum systems

Solving the master equation for the reduced density matrix of open quantum systems, we study the influence of friction and diffusion coefficients on the probability rate for crossing potential barriers and apply the formalism to selected problems of nuclear physics. Taking into account the diffusion coefficient in coordinate, Kramers-type formulas for the decay rate are analytically derived and numerically checked for different barriers and temperatures. The effect of transient time is analysed.