Physical insight into superdiffusive dynamics of Sinai billiard through collision statistics

We report on distinct steady-motion dynamic regimes in chaotic Sinai billiard (SB). A numerical study on elastic reflections from the SB boundary (square wall of length L and circle obstacle of radius R) is carried out for different R/L. The research is based on the exploration of the generalized diffusion equation and on the analysis of wall-collision and the circle-collision distributions observed at late times. The asymptotes for the diffusion coefficientDR and the corresponding diffusion exponentzR are established for all geometries. The universal (R-independent) diffusion with D1∽t1/3 and z1=1.5 replaces the ballistic motion regime (z0=1) attributed to square billiard (R=0). Geometrically, this superdiffusive regime is bounded by small radii 0