Ultrametric Analysis and Interbasin Kinetics

We discuss ultrametric pseudodifferential operators and wavelets and applications to models of interbasin kinetics. We show, that, using the language of ultrametric pseudodifferential operators, it is possible to describe interbasin kinetics for general complex landscape.

[1]  S. V. Kozyrev,et al.  Replica Symmetry Breaking Related to a General Ultrametric Space Ii: Rsb Solutions and the N → 0 Limit , 2022 .

[2]  Ogielski,et al.  Dynamics on ultrametric spaces. , 1985, Physical review letters.

[3]  S. V. Kozyrev,et al.  Replica Symmetry Breaking Related to a General Ultrametric Space I: Replica Matrices and Functionals , 2022 .

[4]  J. Benedetto,et al.  A wavelet theory for local fields and related groups , 2003, math/0312036.

[5]  V. Avetisov,et al.  p-Adic description of characteristic relaxation in complex systems , 2002, cond-mat/0210447.

[6]  S. V. Kozyrev,et al.  Application of p-adic analysis to models of breaking of replica symmetry , 1999 .

[7]  V A Avetisov,et al.  p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes , 2002 .

[8]  A. Khrennikov,et al.  Wavelets on ultrametric spaces , 2005 .

[9]  P. Freund,et al.  p-adic numbers in physics , 1993 .

[10]  Stillinger.  Relaxation behavior in atomic and molecular glasses. , 1990, Physical review. B, Condensed matter.

[11]  Edward Witten,et al.  ADELIC STRING AMPLITUDES , 1987 .

[12]  Sibani,et al.  Diffusion in hierarchies. , 1988, Physical review. A, General physics.

[13]  A. Khrennikov,et al.  Pseudodifferential operators on ultrametric spaces and ultrametric wavelets , 2004 .

[14]  Sergei Kozyrev,et al.  Wavelet analysis as a p-adic spectral analysis , 2008 .

[15]  I. Volovich,et al.  On the adelic string amplitudes , 1988 .

[16]  Hierarchical diffusion, aging and multifractality , 1996, cond-mat/9604033.

[17]  F. Stillinger,et al.  Packing Structures and Transitions in Liquids and Solids , 1984, Science.

[18]  Thomas A. Weber,et al.  Hidden structure in liquids , 1982 .