1,796 research outputs found

### 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 $\Phi^4$ 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

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