404 research outputs found
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]
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 ) 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
Decay of Quantum Accelerator Modes
Experimentally observable Quantum Accelerator Modes are used as a test case
for the study of some general aspects of quantum decay from classical stable
islands immersed in a chaotic sea. The modes are shown to correspond to
metastable states, analogous to the Wannier-Stark resonances. Different regimes
of tunneling, marked by different quantitative dependence of the lifetimes on
1/hbar, are identified, depending on the resolution of KAM substructures that
is achieved on the scale of hbar. The theory of Resonance Assisted Tunneling
introduced by Brodier, Schlagheck, and Ullmo [9], is revisited, and found to
well describe decay whenever applicable.Comment: 16 pages, 11 encapsulated postscript figures (figures with a better
resolution are available upon request to the authors); added reference for
section
Quantum Return Probability for Substitution Potentials
We propose an effective exponent ruling the algebraic decay of the average
quantum return probability for discrete Schrodinger operators. We compute it
for some non-periodic substitution potentials with different degrees of
randomness, and do not find a complete qualitative agreement with the spectral
type of the substitution sequences themselves, i.e., more random the sequence
smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics
Arnol'd Tongues and Quantum Accelerator Modes
The stable periodic orbits of an area-preserving map on the 2-torus, which is
formally a variant of the Standard Map, have been shown to explain the quantum
accelerator modes that were discovered in experiments with laser-cooled atoms.
We show that their parametric dependence exhibits Arnol'd-like tongues and
perform a perturbative analysis of such structures. We thus explain the
arithmetical organisation of the accelerator modes and discuss experimental
implications thereof.Comment: 20 pages, 6 encapsulated postscript figure
Distinct roles for strigolactones in cyst nematode parasitism of Arabidopsis roots
Phytohormones play an essential role in different stages of plant-nematode interactions. Strigolactones (SLs) are a novel class of plant hormones which play an important role in plant development. Furthermore, certain soil-inhabiting organisms exploit this plant molecule as allelochemical. However, whether SLs play a role in plant parasitism by nematodes is as yet unknown. This prompted us to investigate the potential role of SLs in different stages of the nematode life cycle using the beet cyst nematode Heterodera schachtii and Arabidopsis as a model system. We analyzed the effect of SLs on cyst nematode hatching, host attraction and invasion, and the establishment of a feeding relation upon infection of the SL deficient mutant max4-1 and the SL signaling mutant max2-1. In addition, infection assays were performed under phosphate shortage to enhance SL production and in the presence of the synthetic SL analog GR24. From this study, we can conclude that SLs do not contribute to cyst nematode hatching at the levels tested but that they do play a role in host attraction and subsequent invasion in a MAX2 dependent manner. Furthermore, we observed that increased levels of exogenous and endogenous SLs change the root invasion zone. Upon root infection, cyst nematode development was enhanced in both the max2-1 and max4-1 mutants due to the formation of enlarged feeding cells. These data provide evidence for distinct roles of SLs during cyst nematode parasitism of plant roots
Fractal fluctuations in quantum integrable scattering
We theoretically and numerically demonstrate that completely integrable
scattering processes may exhibit fractal transmission fluctuations, due to
typical spectral properties of integrable systems.
Similar properties also occur with scattering processes in the presence of
strong dynamical localization, thus explaining recent numerical observations of
fractality in the latter class of systems.Comment: revtex, 4 pages, 3 eps figure
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