Nonadiabatic Transitions in Level Crossing with Energy Fluctuation. II. Numerical Investigations

The transition rate P ∞ in the level crossing with energy fluctuation is investigated numerically by the Wiener-Hermite expansion technique for the stochastic variable. It is shown that the fluctuation tends to modify the transition rate as if the nonadiabaticity is effectively increased and that the values of the Landau-Zener formula \(PLZ ≡ 1 - exp (-2 π J²/ |v|)\) and the strong damping formula \(PSD ≡ \{1 - exp (-4 π J²/ |v|)\}/2\) give the upper and the lower bounds of P ∞ , respectively, for given values of J 2 /| v |, where J is the off-diagonal coupling constant and v is the velocity of the change of the mean energy difference.