Abstract
Nowadays, much attention is paid to the properties of the so-called ”quantum chaos” (see, e.g. [1–3]). The latter term is commonly used for dynamical quantum systems which are chaotic in the classical limit. Since properties of quantum systems turned out to be different from classical ones even in a deep semiclassical region (see [4–5]), one of the important problems of quantum chaos is to find proper quantities to describe the degree of chaos in quantum systems. The most known approach in this direction is related to the study of fluctuations in energy spectra in dependence of properties of correspondent classical systems. It is now well established that for systems which are integrable in the classical limit the spectrum statistics is close to uncorrected one. Unlike, for classically completely chaotic systems the fluctuations in energy spectra are of the specific form and may be compared to that ones of eigenvalues of random matrices.
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