11 research outputs found
p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes
We demonstrate that p-adic analysis is a natural basis for the construction
of a wide variety of the ultrametric diffusion models constrained by
hierarchical energy landscapes. A general analytical description in terms of
p-adic analysis is given for a class of models. Two exactly solvable examples,
i.e. the ultrametric diffusion constraned by the linear energy landscape and
the ultrametric diffusion with 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 rearrangenment of the complex surrounding.Comment: 14 pages, 6 eps figures, LaTeX 2.0
Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
Methods of p-adic analysis are applied to the investigation of the
spontaneous symmetry breaking in the models of spin glasses. A p-adic
expression for the replica matrix is given and moreover the replica matrix in
the models of spontaneous breaking of the replica symmetry in the simplest case
is expressed in the form of the Vladimirov operator of p-adic fractional
differentiation. Also the model of hierarchical diffusion (that was proposed to
describe relaxation of spin glasses) investigated using p-adic analysis.Comment: Latex, 8 page
p-Adic description of characteristic relaxation in complex systems
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, or 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.Comment: AMS-LaTeX (+iopart style), 9 pages, submitted to J.Phys.
p-Adic Mathematical Physics
A brief review of some selected topics in p-adic mathematical physics is
presented.Comment: 36 page
Some aspects of the -adic analysis and its applications to -adic stochastic processes
In this paper we consider a generalization of analysis on -adic numbers
field to the case of -adic numbers ring. The basic statements, theorems
and formulas of -adic analysis can be used for the case of -adic analysis
without changing. We discuss basic properties of -adic numbers and consider
some properties of -adic integration and -adic Fourier analysis. The
class of infinitely divisible -adic distributions and the class of -adic
stochastic Levi processes were introduced. The special class of -adic CTRW
process and fractional-time -adic random walk as the diffusive limit of it
is considered. We found the asymptotic behavior of the probability measure of
initial distribution support for fractional-time -adic random walk.Comment: 18 page