Nonadiabatic Transitions in Level Crossing with Energy Fluctuation. I. Analytical Investigations

Abstract

A simple stochastic model is proposed describing the nonadiabatic transitions in level crossing with energy fluctuation. The model is an extension of Zener's model having a diagonal energy term fluctuating as a Markoffian Gaussian process. The transition rate P ∞ defined in terms of the diabatic basis is calculated exactly by the formal perturbation expansion with respect to the off-diagonal coupling in the two limiting cases: In the slow fluctuation limit, P ∞ coincides with the Landau-Zener formula, \(P_{\infty}=P_{\text{LZ}} \equiv 1 - \exp (-2 \pi J^{2}/\hbar |v|)\), where J is the off-diagonal coupling constant and v is the velocity of the change of the mean energy difference. In the strong damping limit, which is a limiting case of large fluctuation amplitude in the rapid fluctuation limit, P ∞ is given by the formula, \(P_{\infty}=P_{\text{SD}} \equiv \{1 - \exp (-4 \pi J^{2}/\hbar |v|)\}/2\).