Stochastic liouville equations for interacting quasi-particles in the generalized Haken-Strobl model

Abstract

A generalization of the one-particle Haken-Strobl model for the exciton-phonon interaction to the case of interacting excitons is proposed. In the framework of this model the exact set of stochastic Liouville equations for the exciton subsystem density matrix is obtained. In the case of strong transverse relaxation and weak resonance transfer of molecular excitations it is reduced to a chain of coupled equations describing random walks of incoherent excitons with allowance for their dynamic interaction (the main result of the work). These equations with a Lorentz-type jump probability dependence on the exciton-phonon and exciton-exciton interaction parameters and, moreover, those ones generalized in a way discussed in the paper are relevant to a number of applications including the description of exciton annihilation, recombination of point defects in crystals and many others. The connection of the obtained random-walk equations with classical diffusion equations for a system of interacting brownian particles is also discussed.