  We study chaotic behavior and diffusion in the 2D periodic Lorentz gas in the
finite-horizon regime. The dynamical observable which we consider is the length
of single particle's trajectories, which moves in a triangular array of rigid
disks. To analyze the chaoticity of this system, we construct a matrix of the
length of trajectories and perform a level spacing analysis of the spectrum of
this matrix. We find that a universal behavior occurs both in level spacing
distribution and spectral rigidity. In order to examine diffusion in this
classical system, we investigate the variance of the length of trajectories
versus number of collisions to disks. In the case where there is a
finite-horizon, such a variance scales linearly with number of bounces. This
shows that a normal diffusion exists and a central limit theorem is maintained
in this regime.
