Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrodinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport. (C) 2010 Elsevier B.V. All rights reserved.

Notes on beta-deformations of the pure spinor superstring in AdS(5) x S(5)

We study the properties of the vertex operator for the beta-deformation of the superstring in AdS(5) x S(5) in the pure spinor formalism. We discuss the action of supersymmetry on the infinitesimal beta-deformation, the application of the homological perturbation theory, and the relation between the worldsheet description and the spacetime supergravity description. (C) 2011 Elsevier B.V. All rights reserved.

Finite temperature effective actions

We present, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background held at finite temperature, which can be used to determine the finite temperature effective action for the system. As applications, we determine the complete one loop finite temperature effective actions for (0 + 1)-dimensional QED as well as the Schwinger model. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories. (C) 2009 Elsevier B.V. All rights reserved.

Borel-Leroy summability of a nonpolynomial potential

We investigate the perturbation series for the spectrum of a class of Schrodinger operators with potential V = 1/2 x(2) + g(m-1)x(2m)/(1 + alpha gx(2)) which generalize particular cases investigated in the literature in connection with models in laser theory and quantum field theory of particles and fields. It is proved that the series obey a modified strong asymptotic condition of order (m - 1) and have an order (m - 1) strong asymptotic series in g which are shown to be summable in the sense of Borel-Leroy method.

Pion: space-like structure

The scalar form factor describes modifications induced by the pion over the quark condensate. Assuming that representations produced by chiral perturbation theory can be pushed to high values of negative-t, a region in configuration space is reached (r < R similar to 0.5 fm) where the form factor changes sign, indicating that the condensate has turned into empty space. A simple model for the pion incorporates this feature into density functions. When supplemented by scalar-meson excitations, it yields predictions close to empirical values for the mean square radius (< r(2)>(pi)(S) = 0.59 fm(2)) and for one of the low energy constants ((l) over bar (4) = 4.3), with no adjusted parameters.

Scalar form factors and nuclear interactions

The scalar-isoscalar term in the two-pion exchange NN potential is abnormally large and does not respect the hierarchy of effects predicted by chiral perturbation theory. We argue that this anomaly is associated with non-perturbative effects, which are also present in the pi N scalar form factor.

NUCLEAR INTERACTIONS: THE CHIRAL PICTURE

Chiral expansions of the two-pion exchange components of both two- and three-nucleon forces are reviewed and a discussion is made of the predicted pattern of hierarchies. The strength of the scalar-isoscalar central potential is found to be too large and to defy expectations from the symmetry. The causes of this effect can be understood by studying the nucleon scalar form factor.

Large Changes of Static Electric Properties Induced by Hydrogen Bonding: An ab Initio Study of Linear HCN Oligomers

We report the partitioning of the interaction-induced static electronic dipole (hyper)polarizabilities for linear hydrogen cyanide complexes into contributions arising from various interaction energy terms. We analyzed the nonadditivities of the studied properties and used these data to predict the electric properties of an infinite chain. The interaction-induced static electric dipole properties and their nonadditivities were analyzed using an approach based on numerical differentiation of the interaction energy components estimated in an external electric field. These were obtained using the hybrid variational-perturbational interaction energy decomposition scheme, augmented with coupled-cluster calculations, with singles, doubles, and noniterative triples. Our results indicate that the interaction-induced dipole moments and polarizabilities are primarily electrostatic in nature; however, the composition of the interaction hyperpolarizabilities is much more complex. The overlap effects substantially quench the contributions due to electrostatic interactions, and therefore, the major components are due to the induction and exchange induction terms, as well as the intramolecular electron-correlation corrections. A particularly intriguing observation is that the interaction first hyperpolarizability in the studied systems not only is much larger than the corresponding sum of monomer properties, but also has the opposite sign. We show that this effect can be viewed as a direct consequence of hydrogen-bonding interactions that lead to a decrease of the hyperpolarizability of the proton acceptor and an increase of the hyperpolarizability of the proton donor. In the case of the first hyperpolarizability, we also observed the largest nonadditivity of interaction properties (nearly 17%) which further enhances the effects of pairwise interactions.

Fermion perturbations in string theory black holes

In this paper we study fermion perturbations in four-dimensional black holes of string theory, obtained either from a non-extreme configuration of three intersecting five-branes with a boost along the common string or from a non-extreme intersecting system of two two-branes and two five-branes. The Dirac equation for the massless neutrino field, after conformal re-scaling of the metric, is written as a wave equation suitable to study the time evolution of the perturbation. We perform a numerical integration of the evolution equation, and with the aid of Prony fitting of the time-domain profile, we calculate the complex frequencies that dominate the quasinormal ringing stage, and also determine these quantities by the semi-analytical sixth-order WKB method. We also find numerically the decay factor of fermion fields at very late times, and show that the falloff is identical to those showing for massless fields in other four-dimensional black hole spacetimes.

Predictions from an anisotropic inflationary era

This paper investigates the predictions of an inflationary phase starting from a homogeneous and anisotropic universe of the Bianchi I type. After discussing the evolution of the background spacetime, focusing on the number of e-folds and the isotropization, we solve the perturbation equations and predict the power spectra of the curvature perturbations and gravity waves at the end of inflation. The main features of the early anisotropic phase is (1) a dependence of the spectra on the direction of the modes, (2) a coupling between curvature perturbations and gravity waves and (3) the fact that the two gravity wave polarizations do not share the same spectrum on large scales. All these effects are significant only on large scales and die out on small scales where isotropy is recovered. They depend on a characteristic scale that can, but a priori must not, be tuned to some observable scale. To fix the initial conditions, we propose a procedure that generalizes the one standardly used in inflation but that takes into account the fact that the WKB regime is violated at early times when the shear dominates. We stress that there exist modes that do not satisfy the WKB condition during the shear-dominated regime and for which the amplitude at the end of inflation depends on unknown initial conditions. On such scales, inflation loses its predictability. This study paves the way for the determination of the cosmological signature of a primordial shear, whatever the Bianchi I spacetime. It thus stresses the importance of the WKB regime to draw inflationary predictions and demonstrates that, when the number of e-folds is large enough, the predictions converge toward those of inflation in a Friedmann-Lemaitre spacetime but that they are less robust in the case of an inflationary era with a small number of e-folds.

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.

Sensitivity of complex networks measurements

Complex networks obtained from real-world networks are often characterized by incompleteness and noise, consequences of imperfect sampling as well as artifacts in the acquisition process. Because the characterization, analysis and modeling of complex systems underlain by complex networks are critically affected by the quality and completeness of the respective initial structures, it becomes imperative to devise methodologies for identifying and quantifying the effects of the sampling on the network structure. One way to evaluate these effects is through an analysis of the sensitivity of complex network measurements to perturbations in the topology of the network. In this paper, measurement sensibility is quantified in terms of the relative entropy of the respective distributions. Three particularly important kinds of progressive perturbations to the network are considered, namely, edge suppression, addition and rewiring. The measurements allowing the best balance of stability (smaller sensitivity to perturbations) and discriminability (separation between different network topologies) are identified with respect to each type of perturbation. Such an analysis includes eight different measurements applied on six different complex networks models and three real-world networks. This approach allows one to choose the appropriate measurements in order to obtain accurate results for networks where sampling bias cannot be avoided-a very frequent situation in research on complex networks.

The effect of the negative coupling parameter on the spectrum of a trapped Bose gas

The interest in attractive Bose-Einstein Condensates arises due to the chemical instabilities generate when the number of trapped atoms is above a critical number. In this case, recombination process promotes the collapse of the cloud. This behavior is normally geometry dependent. Within the context of the mean field approximation, the system is described by the Gross-Pitaevskii equation. We have considered the attractive Bose-Einstein condensate, confined in a nonspherical trap, investigating numerically and analytically the solutions, using controlled perturbation and self-similar approximation methods. This approximation is valid in all interval of the negative coupling parameter allowing interpolation between weak-coupling and strong-coupling limits. When using the self-similar approximation methods, accurate analytical formulas were derived. These obtained expressions are discussed for several different traps and may contribute to the understanding of experimental observations.

Generation of Vortices and Observation of Quantum Turbulence in an Oscillating Bose-Einstein Condensate

We report on the experimental observation of vortex formation and production of tangled vortex distribution in an atomic BEC of (87)Rb atoms submitted to an external oscillatory perturbation. The oscillatory perturbations start by exciting quadrupolar and scissors modes of the condensate. Then regular vortices are observed finally evolving to a vortex tangle configuration. The vortex tangle is a signature of the presence of a turbulent regime in the cloud. We also show that this turbulent cloud has suppression of the aspect ratio inversion typically observed in quantum degenerate bosonic gases during free expansion.

Number of particle creation and decoherence in the nonideal dynamical Casimir effect at finite temperature

In this work we investigate the dynamical Casimir effect in a nonideal cavity by deriving an effective Hamiltonian. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary, under the only restriction of small velocities. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of a slow moving boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. Since our results were obtained in the framework of the perturbation theory, they are restricted, under resonant conditions, to a short-time approximation. (C) 2009 Elsevier Inc. All rights reserved.