Dynamics on rugged landscapes of energy and ultrametric diffusion

We discuss the interbasin kinetics approximation for random walk on a complex (rugged) landscape of energy. In this approximation the random walk is described by the system of kinetic equations corresponding to transitions between the local minima of energy. If we approximate the transition rates between the local minima by the Arrhenius formula then the system of kinetic equations will be hierarchical. We discuss for a generic landscape of energy the anzats of interbasin kinetics which is equivalent to the ultrametric diffusion generated by an ultrametric pseudodifferential operator.

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