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

Abstract

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 P_LZ≡1−exp (−2πJ²⁄h|v|) and the strong damping formula P_SD≡{1−exp (−4πJ²⁄h|v|)}⁄2 give the upper and the lower bounds of P_∞, respectively, for given values of J²⁄|v|, where J is the off-diagonal coupling constant and v is the velocity of the change of the mean energy difference.