Stretched exponential relaxation in disordered system

A simplified Fano-type physical model is proposed, which may capture the essential feature of various complex disordered systems exhibiting anomalous relaxation. The temporal behavior of the model system appears to be formulated into a unique integrodifferential equation being common for both classical and quantum-mechanical cases. The equation is asymptotically solved to yield an exponential form representation of relaxation patterns. By applying the analytical approach to photocarrier, dielectric and structural relaxation phenomena, we show that a stretched exponential relaxation emerges if very narrow but physically valid conditions are imposed.