Adiabatic limit interference effects for two energy level transition amplitudes and Nikitin - Umanskii formula studied by fundamental solution method

A method of fundamental solutions has been used to study adiabatic transition amplitudes in two energy level systems for a class of Hamiltonians allowing some simplifications of Stokes graphs corresponding to such transitions. It has been shown that for simplest such cases the amplitudes take the Nikitin Umanski form but for more complicated ones they are formed by a sum of terms strictly related to a structure of Stokes graph corresponding to such cases. PACS number(s): 03.65.-W , 03.65.Sq , 02.30.Lt , 02.30.Mv