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Prog. Theor. Phys. Vol. 97 No. 2 (1997) pp. 201-211

Anomalous Diffusion Induced by External Force in the Standard Map

Ryuji Ishizaki and Hazime Mori^*

Faculty of Integrated Humane Studies and Social Sciences, Fukuoka Prefectural University, Tagawa 825
^*Faculty of Engineering, Kyushu Kyoritsu University, Kitakyushu 807

(Received November 22, 1996)

Abstract:

The diffusion of chaotic orbits in a widespread chaotic sea is normal with a variance proportional to the time t even when islands of tori exist as long as there are no accelerator-mode islands. If an external driving force is applied, however, the diffusion becomes anomalous with a variance t^ζ, ζ> 1. Indded, if one uses the coordinate system moving with the mean velocity of chaotic orbits due to the driving force, the chaotic orbits become identical to the Lévy flight due to the intermittent sticking to the islands of tori. This is shown numerically using the standard map with an external force, i.e., the Josephson map. The probability distribution function of the coarse-grained velocity is determined explicitly and turns out to obey an anomalous scaling law characterized by the exponent ζ.

URL : http://ptp.ipap.jp/link?PTP/97/201/
DOI : 10.1143/PTP.97.201

[ Full Text PDF : FREE ACCESS (472K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 100 No. 6 (1998) pp. 1131-1144 :

   Anomalous Diffusion Induced by External Force in the Standard Map. II

   Ryuji Ishizaki and Hazime Mori

2. Progress of Theoretical Physics Vol. 103 No. 2 (2000) pp. 245-259 :

   Effects of External Noise on Anomalous Diffusion in Hamiltonian Dynamical Systems

   Ryuji Ishizaki, Hiroshi Shibata and Hazime Mori

3. Progress of Theoretical Physics Vol. 109 No. 1 (2003) pp. 145-149 :

   Anomalous Diffusion in a Hamiltonian System

   Tomoshige Miyaguchi and Yoji Aizawa

4. Progress of Theoretical Physics Vol. 109 No. 2 (2003) pp. 169-186 :

   Time Correlations and Diffusion of a Conservative Forced Pendulum

   Ryuji Ishizaki, Shoichi Kuroki, Hirotaka Tominaga, Nobuyuki Mori and Hazime Mori

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