抄録
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 < ln> for 0<n<2 numerically, and search the relation between < ln> 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.
