1984 年 53 巻 1 号 p. 108-117
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∞=PLZ≡1−exp (−2πJ2⁄h|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∞=PSD≡{1−exp (−4πJ2⁄h|v|)}⁄2.
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