Exact solution of a stochastic dimer problem with single-site energy modulation

In the framework of the generalized master equation we have investigated the absorption line shape and the dynamics of excitation in a simple two-site system with stochastic modulation of local energy at just one site. We have obtained new exact results for a general type of stochastic process, which is composed of M independent dichotomic Markoff processes. Particularly, our analysis yields an exact solution for the two frequently used process, that is, for the dichotomic Markoff process (M = 1) and for the Gaussian Markoff process (M→∞). Rigorous expressions are derived in the form of continued fractions and they are discussed under various physical conditions and compared with commonly used approximations (such as the noninteracting blip approximation or the white noise approximation).