164 research outputs found
``Critical'' phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams
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
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 and exhibit
self-similarity for certain values of the quasienergy. For given , 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
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
Self-Similarity and Localization
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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