The RARE model: a generalized approach to random relaxation processes in disordered systems

摘要

This paper introduces and analyses a general statistical model, termed theRARE model, of random relaxation processes in disordered systems. The modelconsiders excitations, that are randomly scattered around a reaction center ina general embedding space. The model's input quantities are the spatialscattering statistics of the excitations around the reaction center, and thechemical reaction rates between the excitations and the reaction center as afunction of their mutual distance. The framework of the RARE model is robust,and a detailed stochastic analysis of the random relaxation processes isestablished. Analytic results regarding the duration and the range of therandom relaxation processes, as well as the model's thermodynamic limit, areobtained in closed form. In particular, the case of power-law inputs, whichturn out to yield stretched exponential relaxation patterns and asymptoticallyParetian relaxation ranges, is addressed in detail.