Stochastic Theory for Nonadiabatic Level Crossing with Fluctuating Off-Diagonal Coupling

Abstract

A simple stochastic model is presented describing the nonadiabatic transitions in the level crossing with fluctuating off-diagonal coupling, in which the fluctuation is assumed to obey the Markoffian Gaussian process. The probability P that the transition occurs from one diabatic state to another is calculated exactly in the two limiting situations: In the slow fluctuation limit, P is given by \(P{=}1-\{1+(4{\pi}J^{2}/\hbar|v|)\}^{-1/2}\), where J is the averaged amplitude of the off-diagonal term and v is the velocity of the change of the energy difference between the crossing levels. In the rapid fluctuation limit, P is given by \(P{=}\{1-{\exp}(-4{\pi}J^{2}/\hbar|v|)\}/2\). The intermediate case is studied numerically by the Wiener-Hermite expansion method. Generally, P approaches not 1 but 1/2 in the limit of slow passage, namely, v →0.