Characterization of Quantum Chaos by the Autocorrelation Function of Spectral Determinants

Details Characterization of Quantum Chaos by the Autocorrelation Function of Spectral Determinants Characterization of Quantum Chaos by the Autocorrelation Function of Spectral Determinants

1996-11-04

arxiv.org/abs/chao-dyn/9611001v1

Nonlinear Sciences

Chaotic Dynamics

LaTeX, 32 pages, 6 figures

Scientific paper

10.1088/0305-4470/30/10/035

The autocorrelation function of spectral determinants is proposed as a convenient tool for the characterization of spectral statistics in general, and for the study of the intimate link between quantum chaos and random matrix theory, in particular. For this purpose, the correlation functions of spectral determinants are evaluated for various random matrix ensembles, and are compared with the corresponding semiclassical expressions. The method is demonstrated by applying it to the spectra of the quantized Sinai billiards in two and three dimensions.

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