Analytic methods for the dynamics of multilevel systems
Savva V.A., Mazurenko A.S., Dolya Z.E., Zelenkov V.I., Kharitonchik A.V.
A method to obtain exact analytic solutions of the multilevel systems dynamics equations has been generalized to take into account non-equidistant and degenerate energy levels, non-resonant excitation, a laser pulse form. The method uses bath orthogonal polynomials and orthogonal functions. A lot of examples of exact solutions for various multilevel systems have been considered. Peculiarities of the dynamics of these systems have been studied. A correspondence between any orthogonal polynomial sequence and some definite multilevel system, excited in concrete conditions has been determined. Under the fixed kind of the integral transform the correspondence can be basis for natural classification of multilevel systems.