The spectral statistics of triangular quantum billiards

We study the spectral statistics of three triangular quantum billiards. We show that for an ergodic billiard the nearest neighbor spacings distribution in the low energy regime is strongly influenced by a neighboring integrable domain (equilateral triangle). With increasing energy we observe a transition towards a more chaotic-like pattern. We also show that for all three triangles the properties of the spectral distributions depend heavily on the energy range considered. This is specially true for the spectral rigidity, because of its essentially local character. The features of the distributions do not depend strongly on the genus of classical billiards.