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p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes. (English) Zbl 1038.82077
Summary: We demonstrate that the p-adic analysis is a natural basis for the construction of a wide variety of models of ultrametric diffusion constrained by hierarchical energy landscapes. A general analytical description in terms of the p-adic analysis is given for a class of models. Two exactly solvable examples, i.e. the ultrametric diffusion constrained by the linear energy landscape and the ultrametric diffusion with a reaction sink, are considered. We show that such models can be applied to both the relaxation in complex systems and the rate processes coupled to rearrangement of the complex surrounding.
MSC:
82C44Dynamics of disordered systems (random Ising systems, etc.)
11Z05Miscellaneous applications of number theory
82D30Random media, disordered materials (statistical mechanics)