Application of Tsallis Nonextensive Statistics to the Anomalous Diffusion of the Standard Map

The anomalous diffusion due to accelerator-mode islands in the Standard Map is analyzed with the aid of Tsallis nonextensive statistics. In this treatment, we introduce a new variable x, which represents the displacement per jump while the chaotic orbit is trapped by the accelerator-mode islands. We...

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Bibliographic Details
Published in:Progress of theoretical and experimental physics 2005-11, Vol.114 (5), p.943-952
Main Authors: Ishizaki, Ryuji, Inoue, Masayoshi
Format: Article
Language:English
Subjects:
Exact sciences and technology
Physics
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Summary:The anomalous diffusion due to accelerator-mode islands in the Standard Map is analyzed with the aid of Tsallis nonextensive statistics. In this treatment, we introduce a new variable x, which represents the displacement per jump while the chaotic orbit is trapped by the accelerator-mode islands. We have shown numerically that the one-jump distribution function p(x) is qualitatively similar to the function pq (x) derived using the maximum Tsallis entropy principle with appropriate conditions. [C. Tsallis, J. Stat. Phys. 52 (1988), 479; Phys. Lett. A 195 (1994), 329.] We find that the n-jump distribution function p(x, n) converges to the n-jump distribution function obtained from the Lévy-Gnedenko central-limit theorem in the n → ∞ limit.
ISSN:0033-068X
2050-3911
1347-4081
DOI:10.1143/PTP.114.943