Discrete surface solitons in two dimensions

We investigate fundamental localized modes in 2D lattices with an edge (surface). Interaction with the edge expands the stability area for ordinary solitons, and induces a difference between perpendicular and parallel dipoles; on the contrary, lattice vortices cannot exist too close to the border. Furthermore, we show analytically and numerically that the edge stabilizes a novel wave species, which is entirely unstable in the uniform lattice, namely, a "horseshoe" soliton, consisting of 3 sites. Unstable horseshoes transform themselves into a pair of ordinary solitons.Comment: 6 pages, 4 composite figure

The Hurricane Exposure, Adversity, and Recovery Tool (HEART): Developing and Validating a Risk Screening Instrument for Youth Exposed to Hurricane Harvey

Given the increasing regularity with which severe (named) hurricanes arise, there is a need for valid, practically useful measures that facilitate child-centered post-hurricane situation analysis and needs assessment. Measures that accurately assess the most potent hurricane-related risk factors are essential to identifying youth at risk for developing posttraumatic stress reactions and providing them with effective post-disaster support. With feedback from community stakeholders (e.g., school personnel, physicians and hospital staff, community clinicians), we developed the Hurricane Exposure, Adversity, and Recovery Tool (HEART), a 29-item self-report measure of hurricane risk factors. Test development procedures included: (1) Reviewing the literature regarding hurricane exposure-related risk factors in youth; (2) Generating a developmentally-informed test item pool; (3) Conducting interviews with clinicians, as well as youth impacted by Hurricane Harvey, to evaluate the comprehensibility and acceptability of candidate items; and (4) evaluating endorsement rates for hurricane exposure-related risk factors among (N = 107) youth in an outpatient clinic specializing in the treatment of childhood trauma and loss. Disaster-related exposure, pre-existing indicators of risk, and ongoing post-disaster adversities were correlated with posttraumatic stress and depressive symptoms. These results provide support for an integrative approach to post-hurricane screening for both hurricane-specific (e.g., witnessing injuries) and non-specific (e.g., prior trauma) factors

Slow 4He^{4}He Quenches Produce Fuzzy, Transient Vortices

We examine the Zurek scenario for the production of vortices in quenches of liquid $^{4}He$ in the light of recent experiments. Extending our previous results to later times, we argue that short wavelength thermal fluctuations make vortices poorly defined until after the transition has occurred. Further, if and when vortices appear, it is plausible that that they will decay faster than anticipated from turbulence experiments, irrespective of quench rates.Comment: 4 pages, Revtex file, no figures Apart from a more appropriate title, this paper differs from its predecessor by including temperature, as well as pressure, quenche

Nonlinear Lattice Dynamics of Bose-Einstein Condensates

The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in non-metallic solids and develop ``experimental'' techniques for studying nonlinear problems, continues to yield a wealth of results in the theory and applications of nonlinear Hamiltonian systems with many degrees of freedom. Inspired by the studies of this seminal model, solitary-wave dynamics in lattice dynamical systems have proven vitally important in a diverse range of physical problems--including energy relaxation in solids, denaturation of the DNA double strand, self-trapping of light in arrays of optical waveguides, and Bose-Einstein condensates (BECs) in optical lattices. BECS, in particular, due to their widely ranging and easily manipulated dynamical apparatuses--with one to three spatial dimensions, positive-to-negative tuning of the nonlinearity, one to multiple components, and numerous experimentally accessible external trapping potentials--provide one of the most fertile grounds for the analysis of solitary waves and their interactions. In this paper, we review recent research on BECs in the presence of deep periodic potentials, which can be reduced to nonlinear chains in appropriate circumstances. These reductions, in turn, exhibit many of the remarkable nonlinear structures (including solitons, intrinsic localized modes, and vortices) that lie at the heart of the nonlinear science research seeded by the FPU paradigm.Comment: 10 pages, revtex, two-columns, 3 figs, accepted fpr publication in Chaos's focus issue on the 50th anniversary of the publication of the Fermi-Pasta-Ulam problem; minor clarifications (and a couple corrected typos) from previous versio

Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed minimal models. As a significant example we consider the Ising model in a magnetic field. We check that the results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.Comment: 20 pages; v2: some misprints, textual inaccuracies and references corrected; some references and remarks adde

On the dispersionless Kadomtsev-Petviashvili equation in n+1 dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking

We study the (n+1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quasi one dimensional waves in n+1 dimensions, and arising in several physical contexts, like acoustics, plasma physics and hydrodynamics. For n=2, this equation is integrable, and it has been recently shown to be a prototype model equation in the description of the two dimensional wave breaking of localized initial data. We construct an exact solution of the n+1 dimensional model containing an arbitrary function of one variable, corresponding to its parabolic invariance, describing waves, constant on their paraboloidal wave front, breaking simultaneously in all points of it. Then we use such solution to build a uniform approximation of the solution of the Cauchy problem, for small and localized initial data, showing that such a small and localized initial data evolving according to the (n+1)-dimensional dKP equation break, in the long time regime, if and only if n=1,2,3; i.e., in physical space. Such a wave breaking takes place, generically, in a point of the paraboloidal wave front, and the analytic aspects of it are given explicitly in terms of the small initial data.Comment: 20 pages, 10 figures, few formulas adde

Unitary Gate Synthesis for Continuous Variable Systems

We investigate the synthesis of continuous-variable two-mode unitary gates in the setting where two modes A and B are coupled by a fixed quadratic Hamiltonian H. The gate synthesis consists of a sequence of evolutions governed by Hamiltonian H interspaced by local phase shifts applied to A and B. We concentrate on protocols that require the minimum necessary number of steps and we show how to implement the beam splitter and the two-mode squeezer in just three steps. Particular attention is paid to the Hamiltonian x_A p_B that describes the effective off-resonant interaction of light with the collective atomic spin.Comment: 7 pages, minor text modifications, references adde

Geroch--Kinnersley--Chitre group for Dilaton--Axion Gravity

Kinnersley--type representation is constructed for the four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times possessing two non--null commuting Killing symmetries. New representation essentially uses the matrix--valued $SL(2,R)$ formulation and effectively reduces the construction of the Geroch group to the corresponding problem for the vacuum Einstein equations. An infinite hierarchy of potentials is introduced in terms of $2\times 2$ real symmetric matrices generalizing the scalar hierarchy of Kinnersley--Chitre known for the vacuum Einstein equations.Comment: Published in ``Quantum Field Theory under the Influence of External Conditions'', M. Bordag (Ed.) (Proc. of the International Workshop, Leipzig, Germany, 18--22 September 1995), B.G. Teubner Verlagsgessellschaft, Stuttgart--Leipzig, 1996, pp. 228-23