For a class T of triangular step billiards (TSBs) we prove analytically the absence of elliptic islands in phase space. There is numerical evidence that TSBs are ergodic, sensitive, and mixing. Thus TSBs are chaotic, although their Kolmogorov-Sinai entropy is zero. We study the quantum implications of ray splitting (RS) in TSBs. The signature of non-Newtonian periodic RS orbits is identified in the Fourier transform of the TSB level density. The RS correction of the Weyl formula is tested in the TSB context. In contrast to the rich structure of split circle wave functions, TSB wave functions, except for the emergence of short-range correlations in the form of scarlets, appear featureless and homogeneous.

• Received 12 March 1997

DOI:https://doi.org/10.1103/PhysRevE.56.2691