p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes

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.