Effect of a thermal bath on electronic resonance decay: A numerical path-integral study

Abstract

The effect of electron-vibrational coupling on the decay of a metastable electronic state is treated by a real-time path-integral method. The electronic resonance is described within the framework of the projection operator formalism of scattering theory. The effect of the bath is taken into account by the Feynman-Vernon influence functional technique. In this formulation, neither Born-type nor Markov-type approximations are invoked. The numerical evaluation of the time-discretized path integral is made possible by a recursive partial summation technique. This approach, which has previously been formulated for scattering amplitudes, is generalized to population probabilities that are given by a forward-backward double path integral. The performance of the method is demonstrated for model systems describing a $d$-wave shape resonance, which is linearly coupled to a bath with Ohmic spectral function. The effect of the bath is investigated as a function of coupling strength and temperature.