Relaxation in Self-Similar Hierarchical Spaces

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Abstract
A new model of a hierarchical space with arbitrary transfer rates is introduced. The topology is determined by a self-similar coupling scheme. It is closely related to the topology of a corresponding ultrametric space. The model allows exact solutions to the random-walk problem, the intermediate scattering function, and the autocorrelation function. The solutions are identical in structure to the exact solution of the problem of energy transfer in disordered media which corresponds to parallel rather than to sequential coupling schemes.

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