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Title: Random walk on p-adics and hierarchical systems

Abstract

We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical systems. For our purposes, we specify the Markov stochastic process considered by Albeverio and Karwowski. As a result we have obtained a random walk on the p-adic integer numbers, which provides the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.

Authors:
;  [1];  [2]
  1. Institute of Physics, University of Zielona Gora, ul. Z. Szafrana 4a, 65-516 Zielona Gora (Poland)
  2. (Poland)
Publication Date:
OSTI Identifier:
20787909
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevB.73.054419; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; DECAY; LATTICE FIELD THEORY; MARKOV PROCESS; RANDOMNESS; RELAXATION; TEMPERATURE DEPENDENCE

Citation Formats

Lukierska-Walasek, K., Topolski, K., and Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw. Random walk on p-adics and hierarchical systems. United States: N. p., 2006. Web. doi:10.1103/PHYSREVB.73.0.
Lukierska-Walasek, K., Topolski, K., & Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw. Random walk on p-adics and hierarchical systems. United States. doi:10.1103/PHYSREVB.73.0.
Lukierska-Walasek, K., Topolski, K., and Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw. Wed . "Random walk on p-adics and hierarchical systems". United States. doi:10.1103/PHYSREVB.73.0.
@article{osti_20787909,
title = {Random walk on p-adics and hierarchical systems},
author = {Lukierska-Walasek, K. and Topolski, K. and Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw},
abstractNote = {We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical systems. For our purposes, we specify the Markov stochastic process considered by Albeverio and Karwowski. As a result we have obtained a random walk on the p-adic integer numbers, which provides the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.},
doi = {10.1103/PHYSREVB.73.0},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 5,
volume = 73,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2006},
month = {Wed Feb 01 00:00:00 EST 2006}
}