Quantization rule for transition suppression in dynamic two-level system

The transmission probability in a generic two-quasi-state system is addressed. An approximate expression for the transmission probability between the two quasi-states is derived for the case where the energy gap between the two states varies. Unlike the Landau-Zener formula, the temporal change can have a generic form and can vanish several times. In particular, when the energy gap vanishes twice, an analytical quantization rule for the suppression of transmission between two quasi-states is derived.