RANDOM TRANSITION RATE MODEL OF STRETCHED EXPONENTIAL RELAXATION .2. SELF-SIMILAR RATES FROM A COMPLEX ENERGY LANDSCAPE

In relaxation models based on the independent relaxation events, the n ecessary and sufficient condition for the stretched exponential relaxa tion is the existence of (asymmetric) Levy stable distribution of rela xation rates. The connection of the rate distribution with the statist ics of the complex potential energy hypersurface, the energy 'landscap e', of the underlying many-body system is studied. The dynamics in the complex energy landscape are described by a Hamiltonian, whose matrix elements have self-similar distribution. It is shown that stretched e xponential relaxation results, when distribution of the matrix element s of the Hamiltonian form a Levy matrix. When Gaussian statistics are recovered, the system can be described by a single rate and relaxation becomes exponential.