Incoherent tunneling at weak bias: Weak quantum damping

Abstract

The quantum decay rate Γ = A exp(− B) of a metastable oscillator is studied for a quartic potential energy barrier model by means of a generalized version of Langer's “imaginary part of the free energy” method in the weak ohmic quantum damping regime. It is found (i) that the fully “dynamical” analytical continuation of the weak bias anomalous fluctuation mode of the “breathing bounce” configuration in the partition function for weak damping requires a generalization of the strong damping procedure presented in an earlier paper; (ii) that at sufficiently low temperature the dependence of Γ on the bias energy shows a characteristic transition from being thermal to quantal; and (iii) that upon accounting for the “inflection scattering” in the free exit space of an isolated single well system — i.e. at zero friction and at zero temperature — the result for Γ agrees with the escape rate found in another earlier paper from the pertinent Schrödinger equation by means of an extended WKB “outgoing waves” analysis. Inter alia the restrictions 12B exp(− h ̵ ω 0/2k B T) → 0 and 2πk B T/ h ̵ ω 0 → 0 arising from the “two-state” and “sudden-flip” approximations are removed, leading to e.g. typical T 2 - contributions in B similar to those occuring in the strong bias and strong damping regimes.