Statistical fluctuations of ground-state energies and binding energies in nuclei

The statistical fluctuations of the ground-state energy and of the binding energy of nuclei are investigated using both perturbation theory and supersymmetry. The fluctuations are induced by the experimentally observed stochastic behavior of levels in the vicinity of neutron threshold. The results are compared with a recent analysis of binding-energy fluctuations by Bohigas and Leboeuf, and with theoretical work by Feshbach et al.Comment: 8 pages, 2 figure

Missing levels in correlated spectra

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.Comment: 14 pages and two figure

Quantum thermodynamic fluctuations of a chaotic Fermi-gas model

We investigate the thermodynamics of a Fermi gas whose single-particle energy levels are given by the complex zeros of the Riemann zeta function. This is a model for a gas, and in particular for an atomic nucleus, with an underlying fully chaotic classical dynamics. The probability distributions of the quantum fluctuations of the grand potential and entropy of the gas are computed as a function of temperature and compared, with good agreement, with general predictions obtained from random matrix theory and periodic orbit theory (based on prime numbers). In each case the universal and non--universal regimes are identified.Comment: 23 pages, 4 figures, 1 tabl

Regular Tunnelling Sequences in Mixed Systems

We show that the pattern of tunnelling rates can display a vivid and regular pattern when the classical dynamics is of mixed chaotic/regular type. We consider the situation in which the dominant tunnelling route connects to a stable periodic orbit and this orbit is surrounded by a regular island which supports a number of quantum states. We derive an explicit semiclassical expression for the positions and tunnelling rates of these states by use of a complexified trace formula.Comment: submitted to Physica E as a contribution to the workshop proceedings of "Dynamics of Complex Systems" held at the Max Planck Institute for the Physics of Complex Systems in Dresden from March 30 to June 15, 199

Distance matrices and isometric embeddings

We review the relations between distance matrices and isometric embeddings and give simple proofs that distance matrices defined on euclidean and spherical spaces have all eigenvalues except one non-negative. Several generalizations are discussed.Comment: 17 page

Quantum chaos and regularity in Φ4\Phi^4 theory

We check the eigenvalue spectrum of the $\Phi^{4}_{1+1}$ Hamiltonian against Poisson or Wigner behavior predicted from random matrix theory. We discuss random matrix theory as a tool to discriminate the validity of a model Hamiltonian compared to an analytically solvable Hamiltonian or experimental data.Comment: 3 pages, 6 figures,(eps), Lattice2003(Theory

On the distribution of the total energy of a system on non-interacting fermions: random matrix and semiclassical estimates

We consider a single particle spectrum as given by the eigenvalues of the Wigner-Dyson ensembles of random matrices, and fill consecutive single particle levels with n fermions. Assuming that the fermions are non-interacting, we show that the distribution of the total energy is Gaussian and its variance grows as n^2 log n in the large-n limit. Next to leading order corrections are computed. Some related quantities are discussed, in particular the nearest neighbor spacing autocorrelation function. Canonical and gran canonical approaches are considered and compared in detail. A semiclassical formula describing, as a function of n, a non-universal behavior of the variance of the total energy starting at a critical number of particles is also obtained. It is illustrated with the particular case of single particle energies given by the imaginary part of the zeros of the Riemann zeta function on the critical line.Comment: 28 pages in Latex format, 5 figures, submitted for publication to Physica