Equivalence of dynamics in ultrametric and hierarchical spaces

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Abstract
Ultrametric and self-similar hierarchical spaces are introduced. The underlying coupling schemes are different; nevertheless, they exhibit identical dynamical behavior. The autocorrelation function of the self-similar hierarchical space is identical in form to the time decay function of energy transfer from a donor to randomly distributed acceptors, though the character of the coupling schemes is sequential and parallel, respectively. Due to specific interference effects, the time decay of the intermediate scattering function depends strongly on the phase shift and differs considerably from the decay pattern of the corresponding autocorrelation function.