Bell's Theorem and Nonlinear Systems

For all Einstein-Podolsky-Rosen-type experiments on deterministic systems the Bell inequality holds, unless non-local interactions exist between certain parts of the setup. Here we show that in nonlinear systems the Bell inequality can be violated by non-local effects that are arbitrarily weak. Then we show that the quantum result of the existing Einstein-Podolsky-Rosen-type experiments can be reproduced within deterministic models that include arbitrarily weak non-local effects.Comment: Accepted for publication in Europhysics Letters. 14 pages, no figures. In the Appendix (not included in the EPL version) the author says what he really thinks about the subjec

SUSY QCD one-loop effects in (un)polarized top-pair production at hadron colliders

We study the effects of O(alpha_s) supersymmetric QCD (SQCD) corrections on the total production rate and kinematic distributions of polarized and unpolarized top-pair production in pp and p anti-p collisions. At the Fermilab Tevatron p anti-p collider, top-quark pairs are mainly produced via quark-antiquark annihilation, q anti-q -> t anti-t, while at the CERN LHC pp collider gluon-gluon scattering, g g -> t anti-t, dominates. We compute the complete set of O(alpha_s) SQCD corrections to both production channels and study their dependence on the parameters of the Minimal Supersymmetric Standard Model. In particular, we discuss the prospects for observing strong, loop-induced SUSY effects in top-pair production at the Tevatron Run II and the LHC.Comment: 56 pages, 29 figures, RevTeX

Direct transformations yielding the knight's move pattern in 3x3x3 arrays

Three-way arrays (or tensors) can be regarded as extensions of the traditional two-way data matrices that have a third dimension. Studying algebraic properties of arrays is relevant, for example, for the Tucker three-way PCA method, which generalizes principal component analysis to three-way data. One important algebraic property of arrays is concerned with the possibility of transformations to simplicity. An array is said to be transformed to a simple form when it can be manipulated by a sequence of invertible operations such that a vast majority of its entries become zero. This paper shows how 3 × 3 × 3 arrays, whether symmetric or nonsymmetric, can be transformed to a simple form with 18 out of its 27 entries equal to zero. We call this simple form the “knight's move pattern” due to a loose resemblance to the moves of a knight in a game of chess. The pattern was examined by Kiers, Ten Berge, and Rocci. It will be shown how the knight's move pattern can be found by means of a numeric–algebraic procedure based on the Gröbner basis. This approach seems to work almost surely for randomly generated arrays, whether symmetric or nonsymmetric

Observations of the Crab Nebula with H.E.S.S. Phase II

The High Energy Stereoscopic System (H.E.S.S.) phase I instrument was an array of four $100\,\mathrm{m}^2$ mirror area Imaging Atmospheric Cherenkov Telescopes (IACTs) that has very successfully mapped the sky at photon energies above $\sim 100\,$GeV. Recently, a $600\,\mathrm{m}^2$ telescope was added to the centre of the existing array, which can be operated either in standalone mode or jointly with the four smaller telescopes. The large telescope lowers the energy threshold for gamma-ray observations to several tens of GeV, making the array sensitive at energies where the Fermi-LAT instrument runs out of statistics. At the same time, the new telescope makes the H.E.S.S. phase II instrument. This is the first hybrid IACT array, as it operates telescopes of different size (and hence different trigger rates) and different field of view. In this contribution we present results of H.E.S.S. phase II observations of the Crab Nebula, compare them to earlier observations, and evaluate the performance of the new instrument with Monte Carlo simulations.Comment: In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherland

Dielectrophoresis-Driven Spreading of Immersed Liquid Droplets

In recent years electrowetting-on-dielectric (EWOD) has become an effective tool to control partial wetting. EWOD uses the liquid−solid interface as part of a capacitive structure that allows capacitive and interfacial energies to adjust by changes in wetting when the liquid−solid interface is charged due to an applied voltage. An important aspect of EWOD has been its applications in micro fluidics in chemistry and biology and in optical devices and displays in physics and engineering. Many of these rely on the use of a liquid droplet immersed in a second liquid due to the need either for neutral buoyancy to overcome gravity and shield against impact shocks or to encapsulate the droplet for other reasons, such as in microfluidic-based DNA analyses. Recently, it has been shown that nonwetting oleophobic surfaces can be forcibly wetted by nonconducting oils using nonuniform electric fields and an interface-localized form of liquid dielectrophoresis (dielectrowetting). Here we show that this effect can be used to create films of oil immersed in a second immiscible fluid of lower permittivity. We predict that the square of the thickness of the film should obey a simple law dependent on the square of the applied voltage and with strength dependent on the ratio of difference in permittivity to the liquid-fluid interfacial tension, Δε/γLF. This relationship is experimentally confirmed for 11 liquid−air and liquid−liquid combinations with Δε/γLF having a span of more than two orders of magnitude. We therefore provide fundamental understanding of dielectrowetting for liquid-in-liquid systems and also open up a new method to determine liquid−liquid interfacial tensions

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schr\"odinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct PDE and ODE simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.Comment: 4 pages, 3 figures, Submitted to Phys. Rev.

Sfermion Pair Production in Polarized and Unpolarized γγ\gamma\gamma Collisions

We calculate total and differential cross sections for the production of sfermion pairs in photon-photon collisions, including contributions from resolved photons and arbitrary photon polarization. Sfermion production in photon collisions depends only on the sfermion mass and charge. It is thus independent of the details of the SUSY breaking mechanism, but highly sensitive to the sfermion charge. We compare the total cross sections for bremsstrahlung, beamstrahlung, and laser backscattering photons to those in $e^+e^-$ annihilation. We find that the total cross section at a polarized photon collider is larger than the $e^+e^-$ annihilation cross section up to the kinematic limit of the photon collider.Comment: 19 pages, Latex, 18 (e)ps-figure

Walking vector soliton caging and releasing

We address the formation and propagation of vector solitons in optical lattices in the presence of anisotropy-induced walk-off between ordinary and extraordinary polarized field components. Stable vector solitons trapped by the lattice form above a threshold power, while decreasing the lattice depth below a critical value results in the abrupt release of the caged solitons, that then move across the lattice and may get trapped in a desired lattice channel.Comment: 13 pages, 4 figures, to appear in Optics Letter

Similarity transformations for Nonlinear Schrodinger Equations with time varying coefficients: Exact results

In this paper we use a similarity transformation connecting some families of Nonlinear Schrodinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrodinger equation. This transformation allows one to apply all known results for that equation to the non-autonomous case with the additional dynamics introduced by the transformation itself. In particular, using stationary solutions of the autonomous nonlinear Schrodinger equation we can construct exact breathing solutions to multidimensional non-autonomous nonlinear Schrodinger equations. An application is given in which we explicitly construct time dependent coefficients leading to solutions displaying weak collapse in three-dimensional scenarios. Our results can find physical applicability in mean field models of Bose-Einstein condensates and in the field of dispersion-managed optical systems

Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs

We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in these networks belongs to a given set of motifs (generalization of the configuration model). These networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs. Here a hypergraph is a generalization of a graph, where a hyperedge can connect any number of vertices. These uncorrelated hypergraphs are tree-like (hypertrees), which crucially simplify the problem and allow us to apply the belief-propagation algorithm to these loopy networks with arbitrary motifs. As natural examples, we consider motifs in the form of finite loops and cliques. We apply the belief-propagation algorithm to the ferromagnetic Ising model on the resulting random networks. We obtain an exact solution of this model on networks with finite loops or cliques as motifs. We find an exact critical temperature of the ferromagnetic phase transition and demonstrate that with increasing the clustering coefficient and the loop size, the critical temperature increases compared to ordinary tree-like complex networks. Our solution also gives the birth point of the giant connected component in these loopy networks.Comment: 9 pages, 4 figure