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The nonadiabatic transition probabilities in the two-level systems arecalculated analytically by using the monodromy matrix determining the globalfeature of the underlying differential equation. We study the time-dependent2x2 Hamiltonian with the tanh-type plus sech-type energy difference and withconstant off-diagonal elements as an example to show the efficiency of themonodromy approach. The application of this method to multi-level systems isalso discussed.Comment: 13 pages, 2 figure

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