31,048 research outputs found
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
- …