Incoherent tunneling in a double well

Abstract

We give a detailed presentation of a method for calculating the rate of incoherent tunneling between the minima of damped systems, described by a double-well potential. The method does not require that the dynamics of the system be truncated onto a two-state model. This has the advantage that all the quantities that enter into our final expression for the tunneling rate, especially the prefactor, are defined in terms of the parameters describing the potential well and the dissipation strength. We present a model potential for which all the necessary steps can be performed exactly, within the semiclassical limit. We obtain an exact expression for the decay rate that can be compared with estimates used in the context of the truncation schemes. The exponential part of the tunneling rate agrees quite well with the truncation-scheme approximations. However, there have been no corresponding estimates of the behavior of the prefactor. We find an exact expression for this prefactor, which shows only a very weak dependence on the strength of the dissipation mechanism. This is in strong contrast to the dependence of the prefactor for the tunneling decay of a metastable state into a continuum. © 1987 The American Physical Society.