Exciton transfer in dimers under dichotomic colored noise: Memory functions of the generalized master equation

The excitation energy transfer between molecules in a dimer is investigated using a model, in which the influence of the static and dynamic (phonons) disorder is described by a dichotomic stochastic process with colored noise giving rise to modulations of the molecular excitation energies. The analytical solution of the time development of the site occupation probabilities (diagonal elements of the density matrix of the system), obtained by computer algebra, is used to determine algebraically the memory functions entering the generalized master equation (GME). The behavior of the roots and their weights in the memory function is discussed. The dependence of the coherence time on the stochastic parameters is derived analytically. In addition to the general case various limiting cases are investigated.