Decay of a metastable state: A variational approach

We evaluate the exponential suppression of the quantum tunneling rate due to the coupling with a thermal reservoir. The exponential dependence is calculated by a variational method, in which an approximate saddle point of the effective action is found. The effect of finite temperatures is accounted for. We calculate the exponential part of the rate for several potentials, some of which have not been considered previously. The method gives excellent agreement with numerically calculated values, where they exist. We also consider the effect of Ohmic damping mechanisms of Drude form (memory damping). This latter case may be of importance for experiments on rf superconducting quantum interference devices and Josephson junctions where frequency-dependent damping mechanisms have been observed. The trends exhibited by the variational approximation can be understood qualitatively on the basis of physical arguments.