Multistability and Self-Similarity in the Parameter-Space of a Vibro-Impact System

The dynamics of a dissipative vibro-impact system called impact-pair is investigated. This system is similar to Fermi-Ulam accelerator model and consists of an oscillating one-dimensional box containing a point mass moving freely between successive inelastic collisions with the rigid walls of the box. In our numerical simulations, we observed multistable regimes, for which the corresponding basins of attraction present a quite complicated structure with smooth boundary. In addition, we characterize the system in a two-dimensional parameter space by using the largest Lyapunov exponents, identifying self-similar periodic sets. Copyright (C) 2009 Silvio L.T. de Souza et al.

Hidden vorticity in binary Bose-Einstein condensates

We consider a binary Bose-Einstein condensate (BEC) described by a system of two-dimensional (2D) Gross-Pitaevskii equations with the harmonic-oscillator trapping potential. The intraspecies interactions are attractive, while the interaction between the species may have either sign. The same model applies to the copropagation of bimodal beams in photonic-crystal fibers. We consider a family of trapped hidden-vorticity (HV) modes in the form of bound states of two components with opposite vorticities S(1,2) = +/- 1, the total angular momentum being zero. A challenging problem is the stability of the HV modes. By means of a linear-stability analysis and direct simulations, stability domains are identified in a relevant parameter plane. In direct simulations, stable HV modes feature robustness against large perturbations, while unstable ones split into fragments whose number is identical to the azimuthal index of the fastest growing perturbation eigenmode. Conditions allowing for the creation of the HV modes in the experiment are discussed too. For comparison, a similar but simpler problem is studied in an analytical form, viz., the modulational instability of an HV state in a one-dimensional (1D) system with periodic boundary conditions (this system models a counterflow in a binary BEC mixture loaded into a toroidal trap or a bimodal optical beam coupled into a cylindrical shell). We demonstrate that the stabilization of the 1D HV modes is impossible, which stresses the significance of the stabilization of the HV modes in the 2D setting.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroumldinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ""ship-wave"" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Precise measurements of direct CP violation, CPT symmetry, and other parameters in the neutral kaon system

We present precise tests of CP and CPT symmetry based on the full data set of K -> pi pi decays collected by the KTeV experiment at Fermi National Accelerator Laboratory during 1996, 1997, and 1999. This data set contains 16 x 10(6) K -> pi(0)pi(0) and 69 x 10(6) K -> pi(+)pi(-) decays. We measure the direct CP violation parameter Re(epsilon'/epsilon) = (19.2 +/- 2.1) x 10(-4). We find the K(L) -> K(S) mass difference Delta m = (5270 +/- 12) x 10(6) (h) over tilde s(-1) and the K(S) lifetime tau(S) = (89.62 +/- 0.05) x 10(-12) s. We also measure several parameters that test CPT invariance. We find the difference between the phase of the indirect CP violation parameter epsilon and the superweak phase: phi(epsilon) - phi(SW) =(0.40 +/- 0.56)degrees. We measure the difference of the relative phases between the CP violating and CP conserving decay amplitudes for K -> pi(+)pi(-) (phi(+-)) and for K -> pi(0)pi(0) (phi(00)): Delta phi = (0.30 +/- 0.35)degrees. From these phase measurements, we place a limit on the mass difference between K(0) and (K) over bar (0): Delta M < 4.8 x 10(-19) GeV/c(2) at 95% C.L. These results are consistent with those of other experiments, our own earlier measurements, and CPT symmetry.

Generalized Sznajd model for opinion propagation

In the last decade the Sznajd model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a version of the Sznajd model with a generalized bounded confidence rule-a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabaacutesi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.

Physical approximations for the nonlinear evolution of perturbations in inhomogeneous dark energy scenarios

The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation of state of dark energy, which parametrizes the smooth component of its pressure, but also to the sound speed of dark energy, which determines the amount of pressure in inhomogeneous and collapsed structures. Since the evolution of these structures must be followed well into the nonlinear regime, and a fully relativistic framework for this regime does not exist yet, we compare two approximate schemes: the widely used spherical collapse model and the pseudo-Newtonian approach. We show that both approximation schemes convey identical equations for the density contrast, when the pressure perturbation of dark energy is parametrized in terms of an effective sound speed. We also make a comparison of these approximate approaches to general relativity in the linearized regime, which lends some support to the approximations.

Microwave Zero-Resistance States in a Bilayer Electron System

Magnetotransport measurements on a high-mobility electron bilayer system formed in a wide GaAs quantum well reveal vanishing dissipative resistance under continuous microwave irradiation. Profound zero-resistance states (ZRS) appear even in the presence of additional intersubband scattering of electrons. We study the dependence of photoresistance on frequency, microwave power, and temperature. Experimental results are compared with a theory demonstrating that the conditions for absolute negative resistivity correlate with the appearance of ZRS.

Quantum Hall Effect near the Charge Neutrality Point in a Two-Dimensional Electron-Hole System

We study the transport properties of HgTe-based quantum wells containing simultaneously electrons and holes in a magnetic field B. At the charge neutrality point (CNP) with nearly equal electron and hole densities, the resistance is found to increase very strongly with B while the Hall resistivity turns to zero. This behavior results in a wide plateau in the Hall conductivity sigma(xy) approximate to 0 and in a minimum of diagonal conductivity sigma(xx) at nu = nu(p) - nu(n) = 0, where nu(n) and nu(p) are the electron and hole Landau level filling factors. We suggest that the transport at the CNP point is determined by electron-hole ""snake states'' propagating along the nu = 0 lines. Our observations are qualitatively similar to the quantum Hall effect in graphene as well as to the transport in a random magnetic field with a zero mean value.

Role of dipolar interactions in a system of Ni nanoparticles studied by magnetic susceptibility measurements

The role of dipolar interactions among Ni nanoparticles (NPs) embedded in an amorphous SiO(2)/C matrix with different concentrations has been studied performing ac magnetic susceptibility chi(ac) measurements. For very diluted samples, with Ni concentrations < 4 wt % Ni or very weak dipolar interactions, the data are well described by the Neacuteel-Arrhenius law. Increasing Ni concentration to values up to 12.8 wt % Ni results in changes in the Neacuteel-Arrhenius behavior, the dipolar interactions become important, and need to be considered to describe the magnetic response of the NPs system. We have found no evidence of a spin-glasslike behavior in our Ni NP systems even when dipolar interactions are clearly present.

Classical and quantum magnetoresistance in a two-subband electron system

We observe a large positive magnetoresistance in a bilayer electron system (double quantum well) as the latter is driven by the external gate from double to single layer configuration. Both classical and quantum contributions to magnetotransport are found to be important for explanation of this effect. We demonstrate that these contributions can be separated experimentally by studying the magnetic-field dependence of the resistance at different gate voltages. The experimental results are analyzed and described by using the theory of low-field magnetotransport in the systems with two occupied subbands.

Nonlinear transport and oscillating magnetoresistance in double quantum wells

The nonlinear regime of low-temperature magnetoresistance of double quantum wells in the region of magnetic fields below 1 T is studied both experimentally and theoretically. The observed inversion of the magnetointersubband oscillation peaks with increasing electric current and splitting of these peaks are described by the theory based on the kinetic equation for the isotropic nonequilibrium part of electron distribution function. The inelastic-scattering time of electrons is determined from the current dependence of the inversion field.

Critical behavior of the magnetization in the spin-gapped system NiCl(2)-4SC (NH(2))(2)

We report accurate magnetization measurements on the spin-gap compound NiCl(2)-4SC (NH(2))(2) around the low portion of the magnetic induced phase ordering. The critical density of the magnetization at the phase boundary is analyzed in terms of a Bose-Einstein condensation (BEC) of bosonic particles, and the boson interaction strength is obtained as upsilon(0)=0.61 meV. The detailed analysis of the magnetization data across the transition leads to the conclusion for the preservation of the U(1) symmetry, as required for BEC. (c) 2009 American Institute of Physics. [DOI: 10.1063/1.3055265]