Dissipative Quantum Tunneling : Quantum Langevin Equation Approach

The quantum Langevin equation is used as the basis for a discussion of dissipative quantum tunneling. A general analysis, including strong coupling and non-markovian (memory) effects, is given for the case oftunneling through a parabolic barrier at zero temperature in the presenceof linear passive dissipation. It is shown that dissipation always decreases the tunneling rate below the barrier and increases transmission above the barrier. As a particular application, the case of the resistively shunted Josephson junction is considered. Simple closed form expressions for the tunneling rate and for the noise power spectrum are obtained and compared with results in the literature.