  We report on the stationary dynamics in classical Sinai billiard (SB)
corresponding to the unit cell of the periodic Lorentz gas (LG) formed by
square lattice of length $L$ and dispersing circles of radius $R$ placed in the
center of unit cell. Dynamic correlation effects for classical particles,
initially distributed by random way, are considered within the scope of
deterministic and stochastic descriptions. A temporal analysis of elastic
reflections from the SB square walls and circle obstacles is given for distinct
geometries in terms of the wall-collision and the circle-collision
distributions. Late-time steady dynamic regimes are explicit in the diffusion
exponent $z(R)$, which plays a role of the order-disorder crossover dynamical
parameter. The ballistic ($z_{0}=1$) ordered motion in the square lattice (R=0)
switches to the superdiffusion regime with $z_{1}=1.5$, which is
geometry-independent when $R<L\sqrt{2}/4$. This observed universal dynamics is
shown to arise from long-distance particle jumps along the diagonal and
nondiagonal Bleher corridors in the LG with the infinite horizon geometry. In
the corresponding SB, this universal regime is caused by the long-time
wall-collision memory effects attributed to the bouncing-ball orbits. The
crossover nonuniversal behavior with $1.5<z<2$ is due to geometry with
$L\sqrt{2}/4\leq R<L/2$, when only the nondiagonal corridors remain open. All
the free-motion corridors are closed in LG with finite horizon ($R\geq L/2$)
and the interplay between square and circle geometries results in the chaotic
dynamics ensured by the normal Brownian diffusion ($z_{2}=2$) and by the normal
Gaussian distribution of collisions.
