<i>p</i>-adic models of ultrametric diffusion constrained by hierarchical energy landscapes

Abstract

We demonstrate that p-adic analysis is a natural basis for the construction\nof a wide variety of the ultrametric diffusion models constrained by\nhierarchical energy landscapes. A general analytical description in terms of\np-adic analysis is given for a class of models. Two exactly solvable examples,\ni.e. the ultrametric diffusion constraned by the linear energy landscape and\nthe ultrametric diffusion with reaction sink, are considered. We show that such\nmodels can be applied to both the relaxation in complex systems and the rate\nprocesses coupled to rearrangenment of the complex surrounding.\n