Two-dimensional Bloch electrons in perpendicular magnetic fields: an exact calculation of the Hofstadter butterfly spectrum

The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's Butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the strong field limiting cases. Here we report calculations of the full spectrum of the single-particle Schr\"{o}dinger equation without further approximations. Our method is exact, up to numerical precision, for any combination of potential and uniform field strength. We first study a situation that corresponds to the strong potential limit, and compare the exact results to the predictions of a Hofstadter-like model. We then go on to analyze the evolution of the fractal spectrum from a Landau-like nearly-free electron system to the Hofstadter tight-binding limit by tuning the amplitude of the modulation potential

Numerical Study of a Lyapunov Functional for the Complex Ginzburg-Landau Equation

We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional decreases monotonically in time towards the plane wave attractors, as expected for a Lyapunov functional, provided that no phase singularities are encountered. In the phase turbulence region the potential relaxes towards a value characteristic of the phase turbulent attractor, and the dynamics there approximately preserves a constant value. There are however very small but systematic deviations from the theoretical predictions, that increase when going deeper in the phase turbulence region. In more disordered chaotic regimes characterized by the presence of phase singularities the functional is ill-defined and then not a correct Lyapunov potential.Comment: 20 pages,LaTeX, Postcript version with figures included available at http://formentor.uib.es/~montagne/textos/nep

Synchronization of Chaotic Systems by Common Random Forcing

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough intensity, to different trajectories which start from different initial conditions, leads eventually to the perfect synchronization of the trajectories. The largest Lyapunov exponent becomes negative due to the presence of the noise terms.Comment: 5 pages, uses aipproc.cls and aipproc.sty (included). Five double figures are provided as ten separate gif files. Version with (large) postscript figures included available from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

Anomalous melting behavior of solid hydrogen at high pressures

Hydrogen is the most abundant element in the universe, and its properties under conditions of high temperature and pressure are crucial to understand the interior of of large gaseous planets and other astrophysical bodies. At ultra high pressures solid hydrogen has been predicted to transform into a quantum fluid, because of its high zero point motion. Here we report first principles two phase coexistence and Z method determinations of the melting line of solid hydrogen in a pressure range spanning from 30 to 600 GPa. Our results suggest that the melting line of solid hydrogen, as derived from classical molecular dynamics simulations, reaches a minimum of 367 K at about 430 GPa, at higher pressures the melting line of the atomics Cs IV phase regain a positive slope. In view of the possible importance of quantum effects in hydrogen at such low temperatures, we also determined the melting temperature of the atomic CsIV phase at pressures of 400, 500, 600 GPa, employing Feynman path integral simulations. These result in a downward shift of the classical melting line by about 100 K, and hint at a possible secondary maximum in the melting line in the region between 500 and 600 GPa, testifying to the importance of quantum effects in this system. Combined, our results imply that the stability field of the zero temperature quantum liquid phase, if it exists at all, would only occur at higher pressures than previously thought.Comment: Submitted to JC

Electromagnetic radiation produced by avalanches in the magnetization reversal of Mn12-Acetate

Electromagnetic radiation produced by avalanches in the magnetization reversal of Mn12-Acetate has been measured. Short bursts of radiation have been detected, with intensity significantly exceeding the intensity of the black-body radiation from the sample. The model based upon superradiance from inversely populated spin levels has been suggested

Quantum dynamics of vortices in mesoscopic magnetic disks

Model of quantum depinning of magnetic vortex cores from line defects in a disk geometry and under the application of an in-plane magnetic field has been developed within the framework of the Caldeira-Leggett theory. The corresponding instanton solutions are computed for several values of the magnetic field. Expressions for the crossover temperature Tc and for the depinning rate \Gamma(T) are obtained. Fitting of the theory parameters to experimental data is also presented.Comment: 8 page