Prog. Theor. Phys. Supplement No.161 (2006) pp. 270-273
Crossover between Ballistic and Normal Diffusion
Department of Applied Analysis and Complex Dynamical Systems,
Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
(Received June 23, 2005)
Crossover between ballistic motion and normal diffusion
is studied based on the continuous-time random walk (CTRW) approach
in order to analyze universal properties of
strongly correlated motion and the decay process of correlation
in deterministic diffusion.
There exists a characteristic time scale τ.
For the time region t ≪τ, ballistic motion is observed,
which is followed by normal diffusion for t ≫τ.
Higher-order moments are analytically obtained,
and it is found that they obey scaling relations
that are reminiscent of the generalized extended self-similarity (GESS)
found in turbulent systems.
As a simple dynamical system for numerical simulations,
the climbing sine map in the vicinity of band crisis is considered.
Good agreement between the theory and the numerical simulations is observed.
DOI : 10.1143/PTPS.161.270
- P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).
- A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975).
R. Benzi, L. Biferale, S. Ciliberto, M. V. Struglia and R. Tripiccione, Physica D 96 (1996), 162[CrossRef].
- S. Miyazaki, T. Harada and A. Budiyono, Prog. Theor. Phys. 106 (2001), 1051[PTP].
- S. Miyazaki and K. Ito, Prog. Theor. Phys. 108 (2002), 999[PTP].
N. Tsukamoto, S. Miyazaki and H. Fujisaka, Phys. Rev. E 67 (2003), 016212[APS].
- S. Miyazaki, T. Harada, K. Ito and A. Budiyono, Recent Research Developments in Physics 4 (Transworld Research Network, Kerala, India, 2003), p. 155.
- K. Ito and S. Miyazaki, Prog. Theor. Phys. 110 (2003), 875[PTP].
G. Zumofen and J. Klafter, Phys. Rev. E 47 (1993), 851[APS].
M. Schell, S. Fraser and R. Kapral, Phys. Rev. A 26 (1982), 504[APS].
N. Korabel and R. Klages, Phys. Rev. Lett. 89 (2002), 214102[APS].
- S. Miyazaki, N. Mori, T. Yoshida, H. Mori, H. Hata and T. Horita, Prog. Theor. Phys. 82 (1989), 863[PTP].
- T. Yoshida, S. Miyazaki, H. Mori, T. Kobayashi, T. Horita and H. Hata, Prog. Theor. Phys. 82 (1989), 879[PTP].
- T. Yoshida and S. Miyazaki, Prog. Theor. Phys. Suppl. No. 99 (1989), 64[PTP].
Citing Article(s) :
Journal of the Physical Society of Japan 80 (2011) 044001
(6 pages) :
Chaos-Induced Diffusion in a Nonlinear Dissipative Mathieu Equation for a Charged Fine Particle in an AC Trap
Ryuji Ishizaki, Hiroki Hata, and Tatsuo Shoji