CHARACTERIZATION OF QUANTUM CHAOS BY THE AUTOCORRELATION FUNCTION OF SPECTRAL DETERMINANTS

The autocorrelation function of spectral determinants is proposed asa convenient tool for the characterization of spectral statistics in gen eral, and for the study of the intimate link between quantum chaos and the random matrix theory, in particular. For this purpose, the correl ation functions of spectral determinants are evaluated for various ran dom matrix ensembles, and are compared with the corresponding semiclas sical expressions. The method is demonstrated by applying it to the sp ectra of the quantized Sinai billiards in two and three dimensions.