2,159 research outputs found
Different Facets of Chaos in Quantum Mechanics
Nowadays there is no universally accepted definition of quantum chaos. In
this paper we review and critically discuss different approaches to the
subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze
the problem of dynamical chaos and the time scales associated with chaos
suppression in quantum mechanics. Summary: 1. Introduction 2. Quantum Chaology
and Spectral Statistics 3. From Poisson to GOE Transition: Comparison with
Experimental Data 3.1 Atomic Nuclei 3.2 The Hydrogen Atom in the Strong
Magnetic Field 4. Quantum Chaos and Field Theory 5. Alternative Approaches to
Quantum Chaos 6. Dynamical Quantum Chaos and Time Scales 6.1 Mean-Field
Approximation and Dynamical Chaos 7. ConclusionsComment: RevTex, 25 pages, 7 postscript figures, to be published in Int. J.
Mod. Phys.
Order and Chaos in Roto--Vibrational States of Atomic Nuclei
Using a classical analytical criterion (that of curvature) and numerical
results (Poincar\`e sections and spectral statistics), a transition
order--chaos--order in the roto--vibrational model of atomic nuclei has been
shown. Numerical calculations were performed for some deformed nuclei.Comment: LaTex, 6 figures (available on request), accepted for publication in
Int. J. Mod. Phys.
Quantum Corrections to the Semiclassical Quantization of the SU(3) Shell Model
We apply the canonical perturbation theory to the semi--quantal hamiltonian
of the SU(3) shell model. Then, we use the Einstein--Brillowin--Keller
quantization rule to obtain an analytical semi--quantal formula for the energy
levels, which is the usual semi--classical one plus quantum corrections.
Finally, a test on the numerical accuracy of the semiclassical approximation
and of its quantum corrections is performed.Comment: LaTex, 17 pages, 1 figure (available upon request to the authors), to
be published in Modern Physics Letters
Anomalous Spectral Statistics of the Asymmetric Rotor Model
We investigate the spectral statistics of the asymmetric rotor model
(triaxial rigid rotator). The asymmetric top is classically integrable and,
according to the Berry-Tabor theory, its spectral statistics should be
Poissonian. Surprisingly, our numerical results show that the nearest neighbor
spacing distribution and the spectral rigidity do not
follow Poisson statistics.Comment: 9 pages, 4 figures, presented to the 7th International Spring Seminar
on Nuclear Physics, Maiori, May 27-31 (2001), to be published in the
proceedings, Ed. A. Covello (World Scientific, 2002
Coexistence of Ordered and Chaotic States in Nuclear Structure
In atomic nuclei, as in other many-body systems, the classical phase space is
mixed, so ordered and chaotic states generally coexist. In this contribution we
discuss some models, showing the transition from order to chaos. In several
cases a clear correspondence between classical and quantum chaos has been
established. In particular the transition from ordered to chaotic states will
be discussed in the framework of the shell and roto-vibrational models.Comment: Latex, 3 pages. Talk of Luca Salasnich to the International
Conference on Nuclear Data for Science and Technology, May 19-24, ICTP,
Trieste, Italy. To be published in the Proceeding
New Results on Quantum Chaos in Atomic Nuclei
In atomic nuclei, ordered and chaotic states generally coexist. In this paper
the transition from ordered to chaotic states will be discussed in the
framework of roto-vibrational and shell models. In particular for ,
in the roto-vibrational model, the Poincar\`e sections clearly show the
transition from order to chaos for different values of rotational frequency.
Furthermore, the spectral statistics of low-lying states of several shell
nuclei are studied with realistic shell-model calculations.Comment: Latex, 10 pages, invited talk of Prof. V.R. Manfredi to the
International Symposium on Large-Scale Collective Motion of Atomic Nuclei,
October 1996, Brolo (Messina), to be published in the Proceedings (World
Scientific, Singapore
Spectral Statistics of the Triaxial Rigid Rotator: Semiclassical Origin of their Pathological Behavior
In this paper we investigate the local and global spectral properties of the
triaxial rigid rotator. We demonstrate that, for a fixed value of the total
angular momentum, the energy spectrum can be divided into two sets of energy
levels, whose classical analog are librational and rotational motions. By using
diagonalization, semiclassical and algebric methods, we show that the energy
levels follow the anomalous spectral statistics of the one-dimensional harmonic
oscillator.Comment: 14 pages with 5 figures, to be published in Int. J. Mod. Phys.
A Note on the Toda Criterion for Interacting Dipole-Quadrupole Vibrations
The Toda criterion of the Gaussian curvature is applied to calculate
analytically the transition energy from regular to chaotic motion in a
schematic model describing the interaction between collective dipole and
quadrupole modes in atomic nuclei.Comment: Latex, 9 pages, 2 figures (available upon request), to be published
in Modern Physics Letters
Energy Level Quasi-Crossings: Accidental Degeneracies or Signature of Quantum Chaos?
In the field of quantum chaos, the study of energy levels plays an important
role. The aim of this review paper is to critically discuss some of the main
contributions regarding the connection between classical dynamics,
semi-classical quantization and spectral statistics of energy levels. In
particular, we analyze in detail degeneracies and quasi-crossings in the
eigenvalues of quantum Hamiltonians which are classically non-integrable.
Summary: 1. Introduction; 2. Quasi-Crossing and Chaos; 3. Molecular
Spectroscopy; 4. Nuclear Models; 4.1 Zirnbauer-Verbaashot-Weidenmuller Model;
4.2 Lipkin-Meshow-Glick Model; 5. Particle Physics and Field Theory; 6.
Conclusions.Comment: 26 pages, Latex, 9 figures, to be published in International Journal
of Modern Physics
Quantal Overlapping Resonance Criterion in the Pullen Edmonds Model
In order to highlight the onset of chaos in the Pullen-Edmonds model a
quantal analog of the resonance overlap criterion has been examined. A quite
good agreement between analytical and numerical results is obtained.Comment: 12 pages, LATEX, 2 figures available upon request to the Authors,
submitted to Mod. Phys. Lett.
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