  For classical billiards we suggest that a matrix of action or length of
trajectories in conjunction with statistical measures, level spacing
distribution and spectral rigidity, can be used to distinguish chaotic from
integrable systems. As examples of 2D chaotic billiards we considered the
Bunimovich stadium billiard and the Sinai billiard. In the level spacing
distribution and spectral rigidity we found GOE behaviour consistent with
predictions from random matrix theory. We studied transport properties and
computed a diffusion coefficient. For the Sinai billiard, we found normal
diffusion, while the stadium billiard showed anomalous diffusion behaviour. As
example of a 2D integrable billiard we considered the rectangular billiard. We
found very rigid behaviour with strongly correlated spectra similar to a Dirac
comb. These findings present numerical evidence for universality in level
spacing fluctuations to hold in classically integrable systems and in
classically fully chaotic systems.
