Spectral properties of linear chain with one-point dynamical disorder

Abstract

We have investigated the one-dimensional model of an exciton moving along a (finite or semi-infinite) chain of sites with the local energy at one specific site being randomly modulated. The modulation is described by the Markoff stochastic process and we do not invoke the white-noise assumption. For this model, we give an approximation-free calculation of the density of states, the projected density of states and the optical absorption spectrum. The exact solution is found for a broad family of stochastic processes which bridges (and includes) the dichotomic process and the Gaussian one. The results are discussed in various physical limits such as whitenoise limit, weak-perturbation limit and weak-tunneling limit. Particularly, in the slow-modulation (or static) limit, our model represents a chain with a static distribution of energy at the distinguished impurity site and the spectral characteristics reveal a nontrivial dependence on the width of this energy distribution.