164 research outputs found

    ``Critical'' phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams

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    The phonon modes of the Frenkel-Kontorova model are studied both at the pinning transition as well as in the pinned (cantorus) phase. We focus on the minimal frequency of the phonon spectrum and the corresponding generalized eigenfunction. Using an exact decimation scheme, the eigenfunctions are shown to have nontrivial scaling properties not only at the pinning transition point but also in the cantorus regime. Therefore the phonons defy localization and remain critical even where the associated area-preserving map has a positive Lyapunov exponent. In this region, the critical scaling properties vary continuously and are described by a line of renormalization limit cycles. Interesting renormalization bifurcation diagrams are obtained by monitoring the cycles as the parameters of the system are varied from an integrable case to the anti-integrable limit. Both of these limits are described by a trivial decimation fixed point. Very surprisingly we find additional special parameter values in the cantorus regime where the renormalization limit cycle degenerates into the above trivial fixed point. At these ``degeneracy points'' the phonon hull is represented by an infinite series of step functions. This novel behavior persists in the extended version of the model containing two harmonics. Additional richnesses of this extended model are the one to two-hole transition line, characterized by a divergence in the renormalization cycles, nonexponentially localized phonons, and the preservation of critical behavior all the way upto the anti-integrable limit.Comment: 10 pages, RevTeX, 9 Postscript figure

    Localization and Fluctuations in Quantum Kicked Rotors

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    We address the issue of fluctuations, about an exponential lineshape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical localization. An exact renormalization scheme establishes the fractal character of the fluctuations and provides a new method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuations are independent of the kicking parameter kk and exhibit self-similarity for certain values of the quasienergy. For given kk, the asymptotic localization length is a good characteristic of the localized lineshapes for all quasienergies. This is in stark contrast to the quadratic rotor, where the fluctuations depend upon the strength of the kicking and exhibit local "resonances". These resonances result in strong deviations of the localization length from the asymptotic value. The consequences are particularly pronounced when considering the time evolution of a packet made up of several quasienergy states.Comment: REVTEV Document. 9 pages, 4 figures submitted to PR

    Undersown cover crops have limited weed suppression potential when reducing tillage intensity in organically grown cereals

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    The possibilities to reduce primary tillage by introducing CCs to maintain weed infestation at a level that does not substantially jeopardize crop yield were studied in a field experiment in southern Finland during 2015–2017. Eight different CC mixtures were undersown in cereals and the response in weed occurrence was consecutively assessed in spring barley, winter wheat, and finally, as a subsequent effect, in spring wheat. Growth of CCs was too slow to prevent the flush of early emerging weeds in spring barley whereas in winter wheat, CCs succeeded in hindering the growth of weeds

    Kevätviljapeltojen rikkakasvien runsauden muutokset

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    Self-Similarity and Localization

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    The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is characterized by a single strong coupling fixed point of the renormalization equations. This fixed point also describes the generalized Harper model with next nearest neighbor interaction below a certain threshold. Above the threshold, the fluctuations in the generalized Harper model are described by a strange invariant set of the renormalization equations.Comment: 4 pages, RevTeX, 2 figures include
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