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 - Umanskii 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. This paper corrects our previous one [Phys. Rev. A, 63 052101 (2001)] and its results are in a full agreement with the ones of Joye, Mileti and Pfister [Phys. Rev. A, 44 4280 (1991)].