4,538 research outputs found
Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier
In quantum mechanics some properties are maximally incompatible, such as the
position and momentum of a particle or the vertical and horizontal projections
of a 2-level spin. Given any definite state of one property the other property
is completely random, or unbiased. For N-level systems, the 6-level ones are
the smallest for which a tomographically efficient set of N+1 mutually unbiased
bases (MUBs) has not been found. To facilitate the search, we numerically
extend the classification of unbiased bases, or Hadamards, by incrementally
adjusting relative phases in a standard basis. We consider the non-unitarity
caused by small adjustments with a second order Taylor expansion, and choose
incremental steps within the 4-dimensional nullspace of the curvature. In this
way we prescribe a numerical integration of a 4-parameter set of Hadamards of
order 6.Comment: 5 pages, 2 figure
A nonpolynomial Schroedinger equation for resonantly absorbing gratings
We derive a nonlinear Schroedinger equation with a radical term, in the form
of the square root of (1-|V|^2), as an asymptotic model of the optical medium
built as a periodic set of thin layers of two-level atoms, resonantly
interacting with the electromagnetic field and inducing the Bragg reflection. A
family of bright solitons is found, which splits into stable and unstable
parts, exactly obeying the Vakhitov-Kolokolov criterion. The soliton with the
largest amplitude, which is |V| = 1, is found in an explicit analytical form.
It is a "quasi-peakon", with a discontinuity of the third derivative at the
center. Families of exact cnoidal waves, built as periodic chains of
quasi-peakons, are found too. The ultimate solution belonging to the family of
dark solitons, with the background level |V| = 1, is a dark compacton, also
obtained in an explicit analytical form. Those bright solitons which are
unstable destroy themselves (if perturbed) attaining the critical amplitude,
|V| = 1. The dynamics of the wave field around this critical point is studied
analytically, revealing a switch of the system into an unstable phase.
Collisions between bright solitons are investigated too. The collisions between
fast solitons are quasi-elastic, while slowly moving ones merge into breathers,
which may persist or perish (in the latter case, also by attaining |V| = 1).Comment: Physical Review A, in pres
Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation
We consider an extended Korteweg-de Vries (eKdV) equation, the usual
Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity.
We investigate the statistical behaviour of flat-top solitary waves described
by an eKdV equation in the presence of weak dissipative disorder in the linear
growth/damping term. With the weak disorder in the system, the amplitude of
solitary wave randomly fluctuates during evolution. We demonstrate numerically
that the probability density function of a solitary wave parameter
which characterizes the soliton amplitude exhibits loglognormal divergence near
the maximum possible value.Comment: 8 pages, 4 figure
New way to achieve chaotic synchronization in spatially extended systems
We study the spatio-temporal behavior of simple coupled map lattices with
periodic boundary conditions. The local dynamics is governed by two maps,
namely, the sine circle map and the logistic map respectively. It is found that
even though the spatial behavior is irregular for the regularly coupled
(nearest neighbor coupling) system, the spatially synchronized (chaotic
synchronization) as well as periodic solution may be obtained by the
introduction of three long range couplings at the cost of three nearest
neighbor couplings.Comment: 5 pages (revtex), 7 figures (eps, included
Green consumer markets in the fight against climate change
Climate change has become one of the greatest threats to environmental security, as attested by the growing frequency of severe flooding and storms, extreme temperatures and droughts. Accordingly, the European Unionâs (EU) 6th Environment Action Programme (2010) lists tackling climate change as its first priority. A key aim of the EU has been to cut CO2 emissions, a major factor in climate change, by 8% until 2012 and 20% until 2020. The European Commission has proposed the encouragement of private consumer market for green products and services as one of several solutions to this problem. However, existing research suggests that the market share of these products has been only 3%, although 30% of individuals favour environmental and ethical goods. This article uses Public Goods Theory to explain why the contribution of the green consumer market to fighting climate change has been and possibly may remain limited without further public intervention
Corn Yield Response to Water Availability
Drought-tolerant technologies have become popular in hybrids for low-yielding corn environments across central and western Kansas and are marketed for their ability to produce higher grain yields with less water. The objective of this study was to compare water use, yield, and water use efficiency (WUE) of two types of drought-tolerant (DT) corn hybrids and a high-yielding non-DT hybrid. Water use and yield of two DT and one non-DT, high-yielding hybrid were compared in both dryland and irrigated situations. The average yield for the irrigated corn was 217 bu/a, and the average was 127 bu/a in dryland, representing a yield increase of 90 bu/a. The irrigated corn received a total of 10 in. more water than the dryland corn over the course of the growing season, resulting in 9 bu for each additional inch of water use averaged across the three hybrids. The irrigated corn used a mean of 20.85 in. of water, and the dryland corn used a mean of 11.66 in. of water. The WUE was 10.71 bu/in. and 10.43 bu/in. for dryland and irrigated corn, respectively. Although hybrid yields differed in the irrigated environment, water use and WUE were similar for all hybrids in both dryland and irrigated environments. One DT hybrid exhibited more stable yields across dryland and irrigated environments compared with the other DT hybrid and the non-DT hybrid
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Two-Component 3D Atomic Bose-Einstein Condensates Support Complex Stable Patterns
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schrödinger type. While our computations relate to two-component atomic Bose-Einstein condensates in parabolic traps, our methods can be broadly applied to high-dimensional, nonlinear systems of partial differential equations. The combination of the so-called deflation technique with a careful selection of initial guesses enables the computation of an unprecedented breadth of patterns, including ones combining vortex lines, rings, stars, and âvortex labyrinthsâ. Despite their complexity, they may be dynamically robust and amenable to experimental observation, as confirmed by Bogolyubov-de Gennes spectral analysis and numerical evolution simulations
Reflectionless analytic difference operators I. algebraic framework
We introduce and study a class of analytic difference operators admitting
reflectionless eigenfunctions. Our construction of the class is patterned after
the Inverse Scattering Transform for the reflectionless self-adjoint
Schr\"odinger and Jacobi operators corresponding to KdV and Toda lattice
solitons
Zeros of Rydberg-Rydberg Foster Interactions
Rydberg states of atoms are of great current interest for quantum
manipulation of mesoscopic samples of atoms. Long-range Rydberg-Rydberg
interactions can inhibit multiple excitations of atoms under the appropriate
conditions. These interactions are strongest when resonant collisional
processes give rise to long-range C_3/R^3 interactions. We show in this paper
that even under resonant conditions C_3 often vanishes so that care is required
to realize full dipole blockade in micron-sized atom samples.Comment: 10 pages, 4 figures, submitted to J. Phys.
"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded Lie algebras
Using special quasigraded Lie algebras we obtain new hierarchies of
integrable nonlinear vector equations admitting zero-curvature representations.
Among them the most interesting is extension of the generalized Landau-Lifshitz
hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This
hierarchy can be also interpreted as an anisotropic vector generalization of
"modified" Sine-Gordon hierarchy or as a very special vector generalization of
so(3) anisotropic chiral field hierarchy.Comment: 16 pages, no figures, submitted to Journal of Physics
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