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$p$-adic description of characteristic relaxation in complex systems. (English) Zbl 1049.82051
Summary: This work is a further development of an approach to the description of relaxation processes in complex systems on the basis of the $p$-adic analysis. We show that three types of relaxation fitted into the Kohlrausch-Williams-Watts law, the power decay law and the logarithmic decay law, are similar random processes. Inherently, these processes are ultrametric and are described by the $p$-adic master equation. The physical meaning of this equation is explained in terms of a random walk constrained by a hierarchical energy landscape. We also discuss relations between the relaxation kinetics and the energy landscapes.

##### MSC:
 82C31 Stochastic methods in time-dependent statistical mechanics 11Z05 Miscellaneous applications of number theory