7,980 research outputs found
PT-symmetric sine-Gordon breathers
In this work, we explore a prototypical example of a genuine continuum
breather (i.e., not a standing wave) and the conditions under which it can
persist in a -symmetric medium. As our model of interest, we
will explore the sine-Gordon equation in the presence of a -
symmetric perturbation. Our main finding is that the breather of the
sine-Gordon model will only persist at the interface between gain and loss that
-symmetry imposes but will not be preserved if centered at the
lossy or at the gain side. The latter dynamics is found to be interesting in
its own right giving rise to kink-antikink pairs on the gain side and complete
decay of the breather on the lossy side. Lastly, the stability of the breathers
centered at the interface is studied. As may be anticipated on the basis of
their "delicate" existence properties such breathers are found to be
destabilized through a Hopf bifurcation in the corresponding Floquet analysis
Thresholds for breather solutions on the Discrete Nonlinear Schr\"odinger Equation with saturable and power nonlinearity
We consider the question of existence of periodic solutions (called breather
solutions or discrete solitons) for the Discrete Nonlinear Schr\"odinger
Equation with saturable and power nonlinearity. Theoretical and numerical
results are proved concerning the existence and nonexistence of periodic
solutions by a variational approach and a fixed point argument. In the
variational approach we are restricted to DNLS lattices with Dirichlet boundary
conditions. It is proved that there exists parameters (frequency or
nonlinearity parameters) for which the corresponding minimizers satisfy
explicit upper and lower bounds on the power. The numerical studies performed
indicate that these bounds behave as thresholds for the existence of periodic
solutions. The fixed point method considers the case of infinite lattices.
Through this method, the existence of a threshold is proved in the case of
saturable nonlinearity and an explicit theoretical estimate which is
independent on the dimension is given. The numerical studies, testing the
efficiency of the bounds derived by both methods, demonstrate that these
thresholds are quite sharp estimates of a threshold value on the power needed
for the the existence of a breather solution. This it justified by the
consideration of limiting cases with respect to the size of the nonlinearity
parameters and nonlinearity exponents.Comment: 26 pages, 10 figure
Subharmonic gap structure in short ballistic graphene junctions
We present a theoretical analysis of the current-voltage characteristics of a
ballistic superconductor-normal-superconductor (SNS) junction, in which a strip
of graphene is coupled to two superconducting electrodes. We focus in the
short-junction regime, where the length of the strip is much smaller than
superconducting coherence length. We show that the differential conductance
exhibits a very rich subharmonic gap structure which can be modulated by means
of a gate voltage. On approaching the Dirac point the conductance normalized by
the normal-state conductance is identical to that of a short diffusive SNS
junction.Comment: revtex4, 4 pages, 4 figure
Nonlinear switching and solitons in PT-symmetric photonic systems
One of the challenges of the modern photonics is to develop all-optical
devices enabling increased speed and energy efficiency for transmitting and
processing information on an optical chip. It is believed that the recently
suggested Parity-Time (PT) symmetric photonic systems with alternating regions
of gain and loss can bring novel functionalities. In such systems, losses are
as important as gain and, depending on the structural parameters, gain
compensates losses. Generally, PT systems demonstrate nontrivial
non-conservative wave interactions and phase transitions, which can be employed
for signal filtering and switching, opening new prospects for active control of
light. In this review, we discuss a broad range of problems involving nonlinear
PT-symmetric photonic systems with an intensity-dependent refractive index.
Nonlinearity in such PT symmetric systems provides a basis for many effects
such as the formation of localized modes, nonlinearly-induced PT-symmetry
breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve
as powerful building blocks for the development of novel photonic devices
targeting an active light control.Comment: 33 pages, 33 figure
Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model
A collective coordinate theory is develop for soliton ratchets in the damped
discrete sine-Gordon model driven by a biharmonic force. An ansatz with two
collective coordinates, namely the center and the width of the soliton, is
assumed as an approximated solution of the discrete non-linear equation. The
evolution of these two collective coordinates, obtained by means of the
Generalized Travelling Wave Method, explains the mechanism underlying the
soliton ratchet and captures qualitatively all the main features of this
phenomenon. The theory accounts for the existence of a non-zero depinning
threshold, the non-sinusoidal behaviour of the average velocity as a function
of the difference phase between the harmonics of the driver, the non-monotonic
dependence of the average velocity on the damping and the existence of
non-transporting regimes beyond the depinning threshold. In particular it
provides a good description of the intriguing and complex pattern of subspaces
corresponding to different dynamical regimes in parameter space
Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction
On the elementary level, electronic current consists of individual electron
tunnelling events that are separated by random time intervals. The waiting time
distribution is a probability to observe the electron transfer in the detector
electrode at time given that an electron was detected in the same
electrode at earlier time . We study waiting time distribution for quantum
transport in a vibrating molecular junction. By treating the electron-vibration
interaction exactly and molecule-electrode coupling perturbatively, we obtain
master equation and compute the distribution of waiting times for electron
transport. The details of waiting time distributions are used to elucidate
microscopic mechanism of electron transport and the role of electron-vibration
interactions. We find that as nonequilibrium develops in molecular junction,
the skewness and dispersion of the waiting time distribution experience
stepwise drops with the increase of the electric current. These steps are
associated with the excitations of vibrational states by tunnelling electrons.
In the strong electron-vibration coupling regime, the dispersion decrease
dominates over all other changes in the waiting time distribution as the
molecular junction departs far away from the equilibrium
Length-dependent conductance and thermopower in single-molecule junctions of dithiolated oligophenylene derivatives
We study theoretically the length dependence of both conductance and
thermopower in metal-molecule-metal junctions made up of dithiolated
oligophenylenes contacted to gold electrodes. We find that while the
conductance decays exponentially with increasing molecular length, the
thermopower increases linearly as suggested by recent experiments. We also
analyze how these transport properties can be tuned with methyl side groups.
Our results can be explained by considering the level shifts due to their
electron-donating character as well as the tilt-angle dependence of conductance
and thermopower. Qualitative features of the substituent effects in our
density-functional calculations are explained using a tight-binding model. In
addition, we observe symmetry-related even-odd transmission channel
degeneracies as a function of molecular length.Comment: 7 pages, 9 figures; submitted to Phys. Rev.
A Review of Soil-Improving Cropping Systems for Soil Salinization
A major challenge of the Sustainable Development Goals linked to Agriculture, Food Security, and Nutrition, under the current global crop production paradigm, is that increasing crop yields often have negative environmental impacts. It is therefore urgent to develop and adopt optimal soil-improving cropping systems (SICS) that can allow us to decouple these system parameters. Soil salinization is a major environmental hazard that limits agricultural potential and is closely linked to agricultural mismanagement and water resources overexploitation, especially in arid climates. Here we review literature seeking to ameliorate the negative effect of soil salinization on crop productivity and conduct a global meta-analysis of 128 paired soil quality and yield observations from 30 studies. In this regard, we compared the effectivity of different SICS that aim to cope with soil salinization across 11 countries, in order to reveal those that are the most promising. The analysis shows that besides case-specific optimization of irrigation and drainage management, combinations of soil amendments, conditioners, and residue management can contribute to significant reductions of soil salinity while significantly increasing crop yields. These results highlight that conservation agriculture can also achieve the higher yields required for upscaling and sustaining crop production
Breather Statics and Dynamics in Klein--Gordon Chains with a Bend
In this communication, we examine a nonlinear model with an impurity
emulating a bend. We justify the geometric interpretation of the model and
connect it with earlier work on models including geometric effects. We focus on
both the bifurcation and stability analysis of the modes that emerge as a
function of the strength of the bend angle, but we also examine dynamical
effects including the scattering of mobile localized modes (discrete breathers)
off of such a geometric structure. The potential outcomes of such numerical
experiments (including transmission, trapping within the bend as well as
reflection) are highlighted and qualitatively explained. Such models are of
interest both theoretically in understanding the interplay of breathers with
curvature, but also practically in simple models of photonic crystals or of
bent chains of DNA.Comment: 14 pages, 16 figure
Lower and upper estimates on the excitation threshold for breathers in DNLS lattices
We propose analytical lower and upper estimates on the excitation threshold
for breathers (in the form of spatially localized and time periodic solutions)
in DNLS lattices with power nonlinearity. The estimation depending explicitly
on the lattice parameters, is derived by a combination of a comparison argument
on appropriate lower bounds depending on the frequency of each solution with a
simple and justified heuristic argument. The numerical studies verify that the
analytical estimates can be of particular usefulness, as a simple analytical
detection of the activation energy for breathers in DNLS lattices.Comment: 10 pages, 3 figure
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