Tunneling with Dissipation in Open Quantum Systems

Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The tunneling in the open quantum systems strongly depends on the coupling with environment. We found the cases when the dissipation prohibits tunneling through the barrier but decreases the crossing of the barrier for the energies above the barrier. As a particular application, the case of decay from the metastable state is considered. PACS: 03.65.-w, 05.30.-d, 24.60.-k Typeset using REVTEX 1 There has been considerable interest to the quantum tunneling of a particle through an energy barrier when the dissipation is present1–15. Using various models for the description of the quantum open system, the opposite dependences of tunneling rate on the dissipation have been observed. It is generally thought that tunneling probability decreases in the presence of coupling to the environment. Disregarding the stage of averaging over the intrinsic degrees of freedom, one can consider the tunneling effect starting right away from the general Markovian master equation for the reduced density matrix of the collective degree of freedom16–25 dρ̂(t) dt = − i h̄ [Ĥ0, ρ̂] + 1 2h̄ ∑