Analytical calculation of nonadiabatic transition probabilities from the monodromy of differential equations

Abstract

The nonadiabatic transition probabilities in the two-level systems are calculated analytically by using the monodromy matrix determining the global feature of the underlying differential equation. We study the time-dependent 2 × 2 Hamiltonian with the tanh-type plus sech-type energy difference and with constant off-diagonal elements as an example to show the efficiency of the monodromy approach. We also discuss the application of this method to multi-level systems.