Pathological anomalous diffusion generated by a generalized shift map

The dynamics of a decimal point of two-sided infinite sequences (... at(-2) at(-1). at(0) at(1) ...) is studied, where the motion of the point is governed by a generalized shift (GS) map. Diffusive motion and fluctuated drift motion are observed which depend on the rule of GS. We introduce a paramet...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2002-03, Vol.71 (3), p.739-743
Main Authors: ISHIZAKI, Ryuji, SHIRAISHI, Hiroyuki, KANIE, Masato, INOUE, Masayoshi
Format: Article
Language:English
Subjects:
Exact sciences and technology
Nonlinear dynamics and nonlinear dynamical systems
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:The dynamics of a decimal point of two-sided infinite sequences (... at(-2) at(-1). at(0) at(1) ...) is studied, where the motion of the point is governed by a generalized shift (GS) map. Diffusive motion and fluctuated drift motion are observed which depend on the rule of GS. We introduce a parameter P which is the probability of a(i+1)0 whose value is the same with a(i)0. We calculate the mean square displacement σ2(n) ∝ nζ for a fluctuated drift rule, and find that super-diffusive (ζ∼eq 1.96) and sub-diffusive (ζ∼eq 0.93) for P=0.5. Pathological anomalous diffusion (ζ > 2) is observed if P approaches to 1.
ISSN:0031-9015
1347-4073
DOI:10.1143/JPSJ.71.739