Rate theory for solids. V. Quantum Brownian-motion model

Publisher Website
Google Scholar
Abstract
A model for interstitial diffusion is studied in which the impurity atom is regarded as a Brownian particle constrained to move in a single direction and subject to a periodic potential. A quantum mechanical theory is developed for the rate at which atoms leave a given potential well. The theory makes use of an ensemble of minimum-uncertainty wave packets to describe thermal equilibrium in the well and computes the tunneling probability through the potential barrier on the basis of the Schrödinger-Langevin equation in order to incorporate the effect of an interacting heat bath. The result of the interactions is to reduce the departure rate at a given temperature level, but the qualitative nature of the rate expression remains unchanged and predicts Arrhenius plots with straight-line behavior at high-temperature levels and curvature due to tunneling at low-temperature levels. The dynamics of the wave packet after it leaves a well is studied by computer solution of the Schrödinger-Langevin equation and it is found that the persistence of motion decreases with increasing strength of interaction with the heat bath.