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.

A multistream model for quantum plasmas

The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schroedinger-Poisson system. Here, we consider a multistream model representing a statistical mixture of N pure states, each described by a wavefunction. The one-stream and two-stream cases are investigated. We derive the dispersion relation for the two-stream instability and show that a new, purely quantum, branch appears. Numerical simulations of the complete Schroedinger-Poisson system confirm the linear analysis, and provide further results in the strongly nonlinear regime. The stationary states of the Schroedinger-Poisson system are also investigated. These can be viewed as the quantum mechanical counterpart of the classical Bernstein-Greene-Kruskal modes, and are described by a set of coupled nonlinear differential equations for the electrostatic potential and the stream amplitudes.Comment: 20 pages, 10 figure

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

Load distribution in small world networks

In this paper we introduce a new model of data packet transport, based on a stochastic approach with the aim of characterizing the load distribution on complex networks. Moreover we analyze the load standard deviation as an index of uniformity of the distribution of packets within the network, to characterize the effects of the network topology. We measure such index on the model proposed by Watts and Strogatz as the redirection probability is increased. We find that the uniformity of the load spread is maximized in the intermediate region, at which the small world effect is observed and both global and local efficiency are high. Moreover we analyze the relationship between load centrality and degree centrality as an approximate measure of the load at the edges. Analogous results are obtained for the load variance computed at the edges as well as at the vertices.Comment: 6 pages, 5 figures. Included in conference proceedings International Conference PhysCon 2005 August 24-26, 2005, Saint Petersburg, RUSSI

Spectral Statistics in Large Shell Model Calculations

The spectral statistics of low--lying states of $fp$ shell nuclei are studied by performing large shell--model calculations with a realistic nuclear interaction. For $Ca$ isotopes, we find deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.Comment: 9 pages, LaTex, 3 figures available upon request, to appear in Proceedings of the V International Spring Seminar on Nuclear Physics, Ed. by A. Covello (World Scientific

Large Shell Model Calculations for Calcium Isotopes: Spectral Statistics and Chaos

We perform large shell model calculations for Calcium isotopes in the full fp shell by using the realistic Kuo-Brown interaction. The Calcium isotopes are especially interesting because the nearest-neighbour spacing distribution P(s) of low-lying energy levels shows significant deviations from the predictions of the Gaussian Orthogonal Ensemble of random--matrix theory. This contrasts with other neighbouring nuclei which show fully chaotic spectral distributions. We study the chaotic behaviour as a function of the excitation energy. In addition, a clear signature of chaos suppression is obtained when the single-particle spacings are increased. In our opinion the relatively weak strength of the neutron-neutron interaction is unable to destroy the regular single-particle mean-field motion completely. In the neighbouring nuclei with both protons and neutrons in valence orbits, on the other hand, the stronger proton-neutron interaction would appear to be sufficient to destroy the regular mean-field motion.Comment: Latex, 7 pages, 2 postscript figures, to be published in the Proceedings 'Highlights of Modern Nuclear Structure', S. Agata sui due Golfi (italy), Ed. A. Covello (World Scientific

Characteristics of Candida isolates from patients with diabetes mellitus.

The present research has investigated the molecular characterization of oral yeasts in healthy individuals from different dental clinical settings in the United Kingdom, and patients from the UK and Italy who were affected by diabetes mellitus (DM) to determine the impact of DM upon candidal infection of the mouth. In the present study of patients with DM from the UK and Italy a lower than expected incidence of oral candidal infections (7/249, 2.8%) was observed. The presence of oral yeasts and genotypic diversity of C. albicans was also not influenced by DM. There was no significant difference between the presence of oral yeasts in Italian and UK DM patients. However, more (p=0.04) C. dubliniensis isolates were found in non-DM individuals. Higher levels of Candida adhesion to fibronectin-coated paramagnetic beads were observed in isolates from DM patients. Isolates from patients with low oral yeast loads adhered significantly (p=0.0T) more than those from patients with high oral yeast loads. In general, there was no difference in proteolytic activity of isolates from DM or control patients. Candida isolates from UK DM patients had significantly greater in vitro resistance to azole antifungal agents (miconazole p<0.0001 fluconazole p=0.02 ketoconazole p=0.01) than those from Italian DM patients. In addition, C. albicans isolates from all examined patients were more susceptible to fluconazole (p=0.0008) and miconazole (p=0.01) than non-C. albicans strains. PCR fingerprinting and subsequent phylogenetic analysis revealed that C. albicans isolates from UK DM patients were the most diverse (p<0.0001) in comparison to those from Italian DM patients or from healthy subjects. Finally, it was observed that the activity of a rat IgM monoclonal anti-idiotypic antibody (mAbKlO) and a synthetic decapeptide (KP) had a significant dose- dependant fungicidal activity upon a wide spectrum of C. albicans and non-C albicans isolates from patients with and without DM