Thermal resonant tunneling rates by a generalized flux averaging method

The calculation of the thermal rate constant as a time integral over flux-flux correlation functions is a challenging task when the potential energy along the reaction coordinate cannot be associated with a distinctive single barrier. In the case of resonant tunneling through a double barrier potential, the calculations may become formidable due to the population of long-lived resonance states and the corresponding long time-decay of the flux-flux correlation functions. The flux averaging method was introduced recently in order to circumvent this problem in cases where the long time dynamics is due to a single resonance state with the longest lifetime in the system. In this work we generalize the method for calculations of thermal resonant-tunneling rates in systems of many resonances, where the long time-decay is accompanied by an internal dynamics within the quasi-bound system. This extra complication is handled by additional averaging of flux-flux correlation funcation over the time period of the internal dynamics. The result is an exact expression for the rate constant in terms of a linear combination of time integrals over flux-flux correlation functions, which reaches its asymptotic time limit in a short (direct scattering) time, regardless of the long time-decay of the flux-flux correlation functions. This is derived for an analytic model system, and demonstrated in a numerical simulation of resonant tunneling through a double barrier potential.