Higher-order finite-element distributions in statistical theory of nuclear spectra.

Abstract

There are several standard methods that allow for the identification of a description of quantum chaotic systems. In this paper we discuss characteristics of quantum chaos, namely, the distributions of the following finite elements: asymmetrical three point first finite element of the three adjacent energy levels, the symmetrical three point first finite element of the three adjacent energy levels, and the second difference. The probability density functions of these three cases were calculated for the three-dimensional Gaussian orthogonal ensemble, Gaussian unitary ensemble, Gaussian symplectic ensemble, and for the quantum integrable three level system. We compare these distributions with the experimental data aiming at better classification of quantum systems (determining whether they are chaotic or integrable). A hypothesis is formulated: for both integrable and chaotic systems the energy levels have a tendency towards homogeneity. Finally we discuss the role of the discrete analogy to the curvature of levels. \textcopyright{} 1996 The American Physical Society.