Prog. Theor. Phys. Vol. 97 No. 3 (1997) pp. 363-378

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Scaling Laws of Moments in Sinai's Billiard Systems. I

— The Case of Rectangular Lattice —

Shinji Koga

Department of Physics, Osaka Kyoiku University, Kashiwara 582

(Received October 16, 1996)

Abstract:

We investigate Sinai's billiard system in 2 dimensions with an emphasis on the scaling laws of the moments of the free path length in the case of the rectangular lattice. By adopting the mean free path as the scaling variable, the moments of the non-integer power expressed by the integral formula are governed by the scaling laws. The scaling exponents turn out to be almost independent of the manner in which we change the ellipse-shaped scatterer. We also discuss the singularity problem of the free path length associated with the problem of whether the moments exist or not.

URL : http://ptp.ipap.jp/link?PTP/97/363/
DOI : 10.1143/PTP.97.363

References:

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Citing Article(s) :

Journal of the Physical Society of Japan 69 (2000) pp. 2011-2033 :
Numerical Evidence of Universal Scaling Laws of Moments in 2D Sinai's Billiard Systems

Shinji Koga