2,776 research outputs found
Anderson localization or nonlinear waves? A matter of probability
In linear disordered systems Anderson localization makes any wave packet stay
localized for all times. Its fate in nonlinear disordered systems is under
intense theoretical debate and experimental study. We resolve this dispute
showing that at any small but finite nonlinearity (energy) value there is a
finite probability for Anderson localization to break up and propagating
nonlinear waves to take over. It increases with nonlinearity (energy) and
reaches unity at a certain threshold, determined by the initial wave packet
size. Moreover, the spreading probability stays finite also in the limit of
infinite packet size at fixed total energy. These results are generalized to
higher dimensions as well.Comment: 4 pages, 3 figure
Weed Control in Chickpea Crops in Lower Volga
Chickpea is a cheap source of nutrients and does not require special soil conditions of growth. In addition, the properties of the symbiotic relationship of nitrogen-containing bacteria in its root system make it a valuable crop for agriculture. Due to its droughtresistant properties, it is one of the most dynamically developing cultures in export potential, which allows producers making profitable trading operations in foreign food markets and improving their financial condition. The climatic conditions of the Russian Federation make it possible to grow chickpeas and produce its seeds. The cultivated areas of chickpea in Russia in 2018, according to Russian Statistic Agency, amounted to 851.2 thousand hectares. Over the year, they increased by 71.6 %, from 2013 – by 26.5 %. Volgograd region in the all-Russian chickpea field occupies 22.5 % after the Saratov region, on yield it occupies the seventh position after the Stavropol Territory – 7.7 c/ha. Chickpea is a valuable crop, the cultivation of which will make it possible to obtain grain beans that are valuable for human food and to engage Russian agricultural producers in export operations. However, weed vegetation reduces the efficiency of chickpea production. The article describes a method of dealing with weed vegetation in chickpea crops in dry conditions. This will allow the use of tank mixtures of herbicides, which are cheaper in cost and effective in combating weeds in chickpea crops. Using this method, it is possible to get a crop without spending extra funds and achieve a profitability of 15 and 25.6 %
Collective oscillations in spatially modulated exciton-polariton condensate arrays
We study collective dynamics of interacting centers of exciton-polariton
condensation in presence of spatial inhomogeneity, as modeled by diatomic
active oscillator lattices. The mode formalism is developed and employed to
derive existence and stability criteria of plane wave solutions. It is
demonstrated that wave number mode with the binary elementary cell on a
diatomic lattice possesses superior existence and stability properties.
Decreasing net on-site losses (balance of dissipation and pumping) or
conservative nonlinearity favors multistability of modes, while increasing
frequency mismatch between adjacent oscillators detriments it. On the other
hand, spatial inhomogeneity may recover stability of modes at high
nonlinearities. Entering the region where all single-mode solutions are
unstable we discover subsequent transitions between localized quasiperiodic,
chaotic and global chaotic dynamics in the mode space, as nonlinearity
increases. Importantly, the last transition evokes the loss of synchronization.
These effects may determine lasing dynamics of interacting exciton-polariton
condensation centers.Comment: 9 pages, 3 figure
Localization in periodically modulated speckle potentials
Disorder in a 1D quantum lattice induces Anderson localization of the
eigenstates and drastically alters transport properties of the lattice. In the
original Anderson model, the addition of a periodic driving increases, in a
certain range of the driving's frequency and amplitude, localization length of
the appearing Floquet eigenstates. We go beyond the uncorrelated disorder case
and address the experimentally relevant situation when spatial correlations are
present in the lattice potential. Their presence induces the creation of an
effective mobility edge in the energy spectrum of the system. We find that a
slow driving leads to resonant hybridization of the Floquet states, by
increasing both the participation numbers and effective widths of the states in
the strongly localized band and decreasing values of these characteristics for
the states in the quasi-extended band. Strong driving homogenizes the bands, so
that the Floquet states loose compactness and tend to be spatially smeared. In
the basis of the stationary Hamiltonian, these states retain localization in
terms of participation number but become de-localized and spectrum-wide in term
of their effective widths. Signatures of thermalization are also observed.Comment: 6 pages, 3 figure
Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method
Quantum systems out of equilibrium are presently a subject of active
research, both in theoretical and experimental domains. In this work we
consider time-periodically modulated quantum systems which are in contact with
a stationary environment. Within the framework of a quantum master equation,
the asymptotic states of such systems are described by time-periodic density
operators. Resolution of these operators constitutes a non-trivial
computational task. To go beyond the current size limits, we use the quantum
trajectory method which unravels master equation for the density operator into
a set of stochastic processes for wave functions. The asymptotic density matrix
is calculated by performing a statistical sampling over the ensemble of quantum
trajectories, preceded by a long transient propagation. We follow the ideology
of event-driven programming and construct a new algorithmic realization of the
method. The algorithm is computationally efficient, allowing for long 'leaps'
forward in time, and is numerically exact in the sense that, being given the
list of uniformly distributed (on the unit interval) random numbers, , one could propagate a quantum trajectory (with 's
as norm thresholds) in a numerically exact way. %Since the quantum trajectory
method falls into the class of standard sampling problems, performance of the
algorithm %can be substantially improved by implementing it on a computer
cluster. By using a scalable -particle quantum model, we demonstrate that
the algorithm allows us to resolve the asymptotic density operator of the model
system with states on a regular-size computer cluster, thus reaching
the scale on which numerical studies of modulated Hamiltonian systems are
currently performed
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