Numerical Evidence of Universal Scaling Laws of Moments in 2D Sinai's Billiard Systems

概要

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By numerical means we investigate moments for a free path length in 2D Sinai's billiard systems ranging from ergodic systems to non-ergodic ones individually. The starting point is a formula of a mean free path length<l>expressed as a phase space average over an entire Birkhoff space. On the basis of the formula, we investigate the moments<l^n>for 0 < n < 2 numerically, and search the relation between<l^n>and<l>. Investigating rectangular, triangular and honeycomb lattices in which either an ellipse-shaped scatterer or a segment-shaped scatterer is located, for 0 < n < 1.2, we find almost universal two scaling indices representing the behavior of the moments irrespective of the details of the systems, when we adopt the mean free path length as a scaling variable. These results imply that the mean free path length can be interpreted as a relevant scaling variable in all cases. We also discuss some theoretical reasoning about the universality.
社団法人日本物理学会の論文
2000-07-15