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Phys. Rev. A 40, 6130–6133 (1989)

Diffusion in Hamiltonian dynamical systems with many degrees of freedom

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Kunihiko Kaneko
Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Institute of Physics, College of Arts and Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan

Tetsuro Konishi
Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Department of Physics, School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-01, Japan

Received 12 July 1989; published in the issue dated November 1989

Hamiltonian dynamical systems with many degrees of freedom are investigated using symplectic map lattices. It is shown that anomalous diffusion exists only up to some crossover time beyond which the diffusion is normal. A diffusion constant, which is inversely proportional to the crossover time, exhibits a faster than any power-law dependence on the nonintegrability parameter, strongly suggesting the relevance of a bound by Nekhoroshev for Arnold diffusion. The motion in the standard mapping is also reexamined to show that the flicker noise is seen only down to some crossover frequency.

© 1989 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.40.6130
DOI:
10.1103/PhysRevA.40.6130
PACS:
05.45.+b, 05.20.-y, 05.40.+j
 
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