Exact analytical solution of theN-level Landau - Zener-type bow-tie model

The non-stationary Schrödinger equation in a finite basis of states is considered for the Hamiltonian matrix linearly depending on time. Exact analytical solutions of asymptotic transition probabilities are obtained for a bow-tie model, in which an arbitrary number of linear time-dependent diabatic potential curves cross at one point and only a particular horizontal curve has interactions with the others. Based on the contour integral method used, some mathematical aspects such as a possible generalization of the Whittaker functions are also briefly discussed.