No abstract available

[en] Complete spectroscopy (measurements of a complete sequence of consecutive levels) is often considered as a prerequisite to extract fluctuation properties of spectra. It is shown how this goal can be achieved even if only a fraction of levels are observed. The case of levels behaving as eigenvalues of random matrices, of current interest in nuclear physics, is worked out in detail

[en] Some general properties of strength distributions and their moments (sum-rules) are discussed. Special emphasis is made on selfconsistent-RPA-sum-rules. The experimental information on electric monopole, dipole and quadrupole strength is reviewed and discussed

No abstract available

[en] Effects of short range correlations on the form factor and the momentum distribution of nuclear systems are investigated. The present analysis, performed in the framework of the Jastrow approach, indicates that an independent-particle wave function (Slater determinant) cannot reproduce simultaneously the form factor and the momentum distribution is strongly affected by correlations beyond 2 fm^-1

No abstract available

[en] We investigate the fluctuation properties of the eigenvalues of the Laplacian in two dimensions with Dirichlet boundary conditions on a stadium. They are found to be consistent with the fluctuations of eigenvalues of random matrices (GOE). It is conjectured that this is true for any boundary such that the motion of a free particle elastically reflected by the boundary is a strongly chaotic motion

[en] Invariant random matrix ensembles with weak confinement potentials of the eigenvalues, corresponding to indeterminate moment problems, are investigated. These ensembles are characterized by the fact that the mean density of eigenvalues tends to a continuous function with increasing matrix dimension contrary to the usual cases where it grows indefinitely. It is demonstrated that the standard asymptotic formulae are not applicable in these cases and that the asymptotic distribution of eigenvalues can deviate from the classical ones. (author)

[en] The distribution of roots of polynomials of high degree with random coefficients is investigated which, among others, appear naturally in the context of 'quantum chaotic dynamics'. It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, the particular case of self-inverse random polynomials is studied, and it is shown that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wavefunctions is also considered. Special attention is devoted to the role of symmetries in the distribution of roots of random polynomials. (author)

[en] It is well known that atomic nuclei show collective properties. One important aspect of collective motion is the concentration in energy of excitation strength. This is best illustrated by the nuclear photo effect which has the following two main characteristics: (1) the photoabsorption cross-section shows, all over the periodic table, a broad peak that takes a large part of the integrated photo cross-section; (2) the variation of the peak energy is a smooth function of the mass number A. Two main routes can be followed in order to describe such a behavior: (1) the more detailed, in which the strength function S(E) is calculated at all energies E, and (2) a more global in which only some energy moments of the strength function S(E) are computed. The purpose of this talk is to describe some methods and applications corresponding mainly to the second route. A description of the strength distribution by its energy moments or sum-rules will be especially suited when the excitation strength is highly collective, in which case one can hope that the knowledge of a very limited number of moments will give the salient features of S(E). Would S(E) have a complicated structure as a function of E then many moments would be required in order to reproduce its properties