Abstract
Abstract In relaxation models based on the independent relaxation events, the necessary and sufficient condition for the stretched exponential relaxation is the existence of (asymmetric) Levy stable distribution of relaxation rates. The connection of the rate distribution with the statistics of the complex potential energy hypersurface, the energy ‘landscape’, 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 exponential relaxation results, when distribution of the matrix elements 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.
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