I. Koponen et P. Lintunen, RANDOM TRANSITION RATE MODEL OF STRETCHED EXPONENTIAL RELAXATION .2. SELF-SIMILAR RATES FROM A COMPLEX ENERGY LANDSCAPE, Journal of non-crystalline solids, 197(2-3), 1996, pp. 247-249
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.