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 offdiagonal coupling in the two limiting cases: In the slow fluctuation limit, P_{∞} coincides with the LandauZener formula, P_{∞}{=}P_{LZ}{\equiv}1\exp (2π J^{2}/\hbarv), where J is the offdiagonal 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_{∞}{=}P_{SD}{\equiv}\{1\exp (4π J^{2}/\hbarv)\}/2.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 January 1984
 DOI:
 10.1143/JPSJ.53.108
 Bibcode:
 1984JPSJ...53..108K