STOCHASTIC-MODELS OF EXCITON TRANSPORT - THE HAKEN-STROBL MODEL

Exciton dephasing in crystals due to the phonon scattering is studied within the framework of the stochastic Haken-Strobl model. The model corresponds to the extremely fast-modulation limit and is applicable to triplet excitons in molecular crystals. The model describes the crossover from the coherent (band) short-time exciton dynamics to incoherent diffusive motion on the long time scale. An efficient method for the determination of the moments of the exciton displacement is developed. Analytic expressions for the mean-square displacement tensor and for the fourth-order moment of exciton displacement on a three-dimensional lattice with inversion symmetry are derived. Solution of the model for arbitrary initial conditions is obtained. The equilibrium state of the system corresponds to the uniform population of the states in the exciton band. The equilibration time scale coincides with the time scale on which the crossover between coherent and diffusive motion occurs. It is given approximately by the inverse amplitude of the second-order correlation function of the stochastic modulation. Physical assumptions underlying the model and the range of its applicability are discussed.