Quantum chaos in triangular billiards

We present an extensive numerical study of spectral statistics and eigenfunctions quantized triangular billiards. compute two million consecutive eigenvalues for six representative cases billiards, three with generic angles irrational ratios $\ensuremath{\pi}$, whose classical dynamics is presumably mixing, exactly one angle rational which are only weakly mixing or even nonergodic in case right triangles. find excellent agreement short- long-range the Gaussian orthogonal ensemble random matrix theory most triangle, while other show small but significant deviations attributed either to a scarring superscarring mechanism. This result, extends quantum chaos conjecture systems dynamical absence hard (Lyapunov) chaos, has been corroborated by analyzing distributions phase-space localization measures eigenstates inspecting structure characteristic typical atypical eigenfunctions.