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

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

Pseudo-classical theory for fidelity of nearly resonant quantum rotors

Using a semiclassical ansatz we analytically predict for the fidelity of delta-kicked rotors the occurrence of revivals and the disappearance of intermediate revival peaks arising from the breaking of a symmetry in the initial conditions. A numerical verification of the predicted effects is given and experimental ramifications are discussed.Comment: Shortened and improved versio

The undesired fellow traveller

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Double butterfly spectrum for two interacting particles in the Harper model

We study the effect of interparticle interaction $U$ on the spectrum of the Harper model and show that it leads to a pure-point component arising from the multifractal spectrum of non interacting problem. Our numerical studies allow to understand the global structure of the spectrum. Analytical approach developed permits to understand the origin of localized states in the limit of strong interaction $U$ and fine spectral structure for small $U$.Comment: revtex, 4 pages, 5 figure

Quantum Diffusion in Separable d-Dimensional Quasiperiodic Tilings

We study the electronic transport in quasiperiodic separable tight-binding models in one, two, and three dimensions. First, we investigate a one-dimensional quasiperiodic chain, in which the atoms are coupled by weak and strong bonds aligned according to the Fibonacci chain. The associated d-dimensional quasiperiodic tilings are constructed from the product of d such chains, which yields either the square/cubic Fibonacci tiling or the labyrinth tiling. We study the scaling behavior of the mean square displacement and the return probability of wave packets with respect to time. We also discuss results of renormalization group approaches and lower bounds for the scaling exponent of the width of the wave packet.Comment: 6 pages, 4 figures, conference proceedings Aperiodic 2012 (Cairns

Upper bounds on wavepacket spreading for random Jacobi matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.Comment: final version, to appear in CM

[OP.2D.05] RELATIONSHIP OF OXIDATIVE STRESS WITH CARDIAC HYPERTROPHY IN HYPERTENSIVE PATIENTS

OBJECTIVE: Left ventricular hypertrophy is common in hypertensive patients. In these subjects increased oxidative stress has been observed. Our aim was to evaluate the association of biomarkers of both oxidative stress and inflammation with markers of cardiovascular damage in a large group of hypertensives with different stages of renal function. DESIGN AND METHOD: In 517 hypertensives we analyzed left ventricular mass indexed for body surface area, and we assayed plasma levels of 8-isoprostaglandin F2alpha and high sensitivity C reactive protein. RESULTS: Multivariate analysis carried out considering left ventricular mass as dependent variable, and including 8-isoprostaglandin F2alpha, high sensitivity C reactive protein, age, sex, body mass index, estimated glomerular filtration rate, serum glucose, (log)triglycerides, hemoglobin, pulse pressure or systolic blood pressure, mean or diastolic blood pressure, and antihypertensive treatment showed that in hypertensives plasma levels of 8-isoprostaglandin F2alpha were correlated with left ventricular mass (beta=0.269, p\u200a<\u200a0.0001).The bivariate relationship of left ventricular mass with 8-isoprostaglandin F2alpha in hypertensives with estimated glomerular filtration rate higher and lower than 60\u200aml/min/1.73m2 was also calculated separately, demonstrating no significant differences in both correlations coefficients and slopes of the regression lines (r\u200a=\u200a0.254, p\u200a<\u200a0.001 and r\u200a=\u200a0.226, p\u200a<\u200a0.002; respectively).In the overall group, receiver operating characteristic curves showed that 8-isoprostaglandin F2alpha and high sensitivity C reactive protein were predictors of left ventricular hypertrophy, p\u200a<\u200a0.0001. CONCLUSIONS: To the best of our knowledge, this is the first demonstration that in hypertensives oxidative stress is correlated to left ventricular hypertrophy independently of other confounding factors. Oxidative stress might participate in the development of hypertensive cardiac hypertrophy