Fractal Spectrum of a Quasi_periodically Driven Spin System

We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time behaviour of various dynamical quantities, such as the moments of the distribution of the wave packet. Our data suggest a close similarity between the information dimension of the spectrum and the exponent ruling the algebraic growth of the 'entropic width' of wavepackets.Comment: 17 pages, RevTex, 5 figs. available on request from [email protected]

Distribution of resonance widths in localized tight-binding models

We numerically analyze the distribution of scattering resonance widths in one- and quasi-one dimensional tight binding models, in the localized regime. We detect and discuss an algebraic decay of the distribution, similar, though not identical, to recent theoretical predictions.Comment: 18 pages, 6 eps figures, to be published in `The European Physical Journal B

Chaos and Thermalization in a Dynamical Model of Two Interacting Particles

A quantum dynamical model of two interacting spins, with chaotic and regular components, is investigated using a finite two-particles symmetrized basis. Chaotic eigenstates give rise to an equilibrium occupation number distribution in close agreement with the Bose-Einstein distribution despite the small number of particles ($n=2$). However, the corresponding temperature differs from that derived from the standard Canonical Ensemble. On the other side, an acceptable agreement with the latter is restored by artificially randomizing the model. Different definitions of temperature are then discussed and compared .Comment: RevteX, 4 pages, 2 figures postscrip

On the Spectrum of the Resonant Quantum Kicked Rotor

It is proven that none of the bands in the quasi-energy spectrum of the Quantum Kicked Rotor is flat at any primitive resonance of any order. Perturbative estimates of bandwidths at small kick strength are established for the case of primitive resonances of prime order. Different bands scale with different powers of the kick strength, due to degeneracies in the spectrum of the free rotor.Comment: Description of related published work has been expanded in the Introductio

Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers

It is shown that correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number $Ra \sim 10^{11}$) exhibits exponential decay with a very long correlation time, while corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail

What determines the spreading of a wave packet?

The multifractal dimensions D2^mu and D2^psi of the energy spectrum and eigenfunctions, resp., are shown to determine the asymptotic scaling of the width of a spreading wave packet. For systems where the shape of the wave packet is preserved the k-th moment increases as t^(k*beta) with beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound. Furthermore, we show that in d dimensions asymptotically in time the center of any wave packet decreases spatially as a power law with exponent D_2^psi - d and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure

Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.Comment: 5 pages Late

Analytical Results for Multifractal Properties of Spectra of Quasiperiodic Hamiltonians near the Periodic Chain

The multifractal properties of the electronic spectrum of a general quasiperiodic chain are studied in first order in the quasiperiodic potential strength. Analytical expressions for the generalized dimensions are found and are in good agreement with numerical simulations. These first order results do not depend on the irrational incommensurability.Comment: 10 Pages in RevTeX, 2 Postscript figure