Classical and quantum chaos in the generalized parabolic lemon-shaped billiard

Two-dimensional billiards of a generalized parabolic Iemonlike shape are in vestigated classically and quantum mechanically depending on the shape para meter delta. Quantal spectra are analyzed by means of the nearest-neighbor spacing distribution method. Calculated results are well accounted for by t he proposed new two-parameter distribution function P(s), which is a genera lization of Brody and Berry-Robnik distributions. Classically, Poincare dia grams are shown and interpreted in terms of the lowest periodic orbits. For delta=2, the billiard has some unique characteristics resulting from the f ocusing property of the parabolic mirror. Comparison of the classical and q uantal results shows an accordance with the Bohigas, Giannoni, and Schmit c onjecture and confirms the relevance of the new distribution for the analys is of realistic spectral data. [S1063-651X(99)00401-8].