Optimal conditions for the numerical calculation of the largest Lyapunov exponent for systems of ordinary differential equations

A general indicator of the presence of chaos in a dynamical system is the largest Lyapunov exponent. This quantity provides a measure of the mean exponential rate of divergence of nearby orbits. In this paper, we show that the so-called two-particle method introduced by Benettin et al. could lead to spurious estimations of the largest Lyapunov exponent. As a comparator method, the maximum Lyapunov exponent is computed from the solution of the variational equations of the system. We show that the incorrect estimation of the largest Lyapunov exponent is based on the setting of the renormalization time and the initial distance between trajectories. Unlike previously published works, we here present three criteria that could help to determine correctly these parameters so that the maximum Lyapunov exponent is close to the expected value. The results have been tested with four well known dynamical systems: Ueda, Duffing, R\"ossler and Lorenz.Comment: 12 pages, 8 figures. Accepted in the International Journal of Modern Physics

Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals

Ultracold fermions trapped in a honeycomb optical lattice constitute a versatile setup to experimentally realize the Haldane model [Phys. Rev. Lett. 61, 2015 (1988)]. In this system, a non-uniform synthetic magnetic flux can be engineered through laser-induced methods, explicitly breaking time-reversal symmetry. This potentially opens a bulk gap in the energy spectrum, which is associated with a non-trivial topological order, i.e., a non-zero Chern number. In this work, we consider the possibility of producing and identifying such a robust Chern insulator in the laser-coupled honeycomb lattice. We explore a large parameter space spanned by experimentally controllable parameters and obtain a variety of phase diagrams, clearly identifying the accessible topologically non-trivial regimes. We discuss the signatures of Chern insulators in cold-atom systems, considering available detection methods. We also highlight the existence of topological semi-metals in this system, which are gapless phases characterized by non-zero winding numbers, not present in Haldane's original model.Comment: 30 pages, 12 figures, 4 Appendice

Novel Scintillating Materials Based on Phenyl-Polysiloxane for Neutron Detection and Monitoring

Neutron detectors are extensively used at many nuclear research facilities across Europe. Their application range covers many topics in basic and applied nuclear research: in nuclear structure and reaction dynamics (reaction reconstruction and decay studies); in nuclear astrophysics (neutron emission probabilities); in nuclear technology (nuclear data measurements and in-core/off-core monitors); in nuclear medicine (radiation monitors, dosimeters); in materials science (neutron imaging techniques); in homeland security applications (fissile materials investigation and cargo inspection). Liquid scintillators, widely used at present, have however some drawbacks given by toxicity, flammability, volatility and sensitivity to oxygen that limit their duration and quality. Even plastic scintillators are not satisfactory because they have low radiation hardness and low thermal stability. Moreover organic solvents may affect their optical properties due to crazing. In order to overcome these problems, phenyl-polysiloxane based scintillators have been recently developed at Legnaro National Laboratory. This new solution showed very good chemical and thermal stability and high radiation hardness. The results on the different samples performance will be presented, paying special attention to a characterization comparison between synthesized phenyl containing polysiloxane resins where a Pt catalyst has been used and a scintillating material obtained by condensation reaction, where tin based compounds are used as catalysts. Different structural arrangements as a result of different substituents on the main chain have been investigated by High Resolution X-Ray Diffraction, while the effect of improved optical transmittance on the scintillation yield has been elucidated by a combination of excitation/fluorescence measurements and scintillation yield under exposure to alpha and {\gamma}-rays.Comment: InterM 2013 - International Multidisciplinary Microscopy Congres

Non-relativistic limit in the 2+1 Dirac Oscillator: A Ramsey Interferometry Effect

We study the non-relativistic limit of a paradigmatic model in Relativistic Quantum Mechanics, the two-dimensional Dirac oscillator. Remarkably, we find a novel kind of Zitterbewegung which persists in this non-relativistic regime, and leads to an observable deformation of the particle orbit. This effect can be interpreted in terms of a Ramsey Interferometric phenomenon, allowing an insightful connection between Relativistic Quantum Mechanics and Quantum Optics. Furthermore, subsequent corrections to the non-relativistic limit, which account for the usual spin-orbit Zitterbewegung, can be neatly understood in terms of a Mach-Zehnder interferometer.Comment: RevTex4 file, color figures, submitted for publicatio