Anomalous Diffusion Induced by External Force in the Standard Map. II : Condensed Matter and Statistical Physics

概要

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We study the nonlinear response of diffusion processes in Hamiltonian systems that are represented by the standard map with an external force. If an external force is applied to the standard map, in which there exist normal islands of tori and accelerator-mode islands of tori, then chaotic orbits exhibit Levy flight due to intermittent sticking to the normal and accelerator-mode islands. The probability distribution function P(v;n) of the coarse-grained velocity v_n over chaotic orbits of length n turns out to obey the anomalous scaling law n^<-β+1>(v^^- - v)^<-β-1> with a sticking exponent β (> 1) of the normal islands for 0 < v < v^^-, v^^- being the mean velocity, and n^<-β'+1>(v - v^^-)^<-β'-1> with a sticking exponent β'(> 1) of the accelerator-mode islands for v^^- < v < 1.
理論物理学刊行会の論文
1998-12-25