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.

One-dimensional trapped atoms: critical coupling parameter and critical number of particles

In this paper we consider the case of a Bose gas in low dimension in order to illustrate the applicability of a method that allows us to construct analytical relations, valid for a broad range of coupling parameters, for a function which asymptotic expansions are known. The method is well suitable to investigate the problem of stability of a collection of Bose particles trapped in one- dimensional configuration for the case where the scattering length presents a negative value. The eigenvalues for this interacting quantum one-dimensional many particle system become negative when the interactions overcome the trapping energy and, in this case, the system becomes unstable. Here we calculate the critical coupling parameter and apply for the case of Lithium atoms obtaining the critical number of particles for the limit of stability.

Synchronization and Basins of Synchronized in Two-Dimensional Piecewise Maps Via Coupling Three Pieces of One-Dimensional Maps

This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.

C-H and C-D interbond coupling in CHDCl2

Laser photoacoustic spectra of vapour phase CHDCl2 reveal the presence of an interaction which has been ascribed to interbond coupling between C-H and C-D local modes. The absolute value of the interbond coupling parameter for the CHD group, determined from a fit of a model local mode hamiltonian to the experimental data, is shown to be given approximately by the geometric mean of the interbond coupling parameters of the CH2 and CD2 groups recently derived from similar studies of CH2Cl2 and CD2Cl2. Such behaviour is understood in terms of a simple analysis in which kinetic coupling effects dominate. It is suggested that C-H stretch/bend Fermi resonance is responsible for some weaker features in the spectra and modelling calculations are described which allow an order of magnitude estimate of the size of the coupling parameter involved.

Time-dependent orientation coupling in equilibrium polymer melts

The motion in concentrated polymer systems is described by either the Rouse or the reptation model, which both assume that the relaxation of each polymer chain is independent of the surrounding chains. This, however, is in contradiction with several experiments. In this Letter, we propose a universal description of orientation coupling in polymer melts in terms of the time-dependent coupling parameter κ(t). We use molecular dynamics simulations to show that the coupling parameter increases with time, reaching about 50% at long times, independently of the chain length or blend composition. This leads to predictions of component dynamics in mixtures of different molecular weights from the knowledge of monodisperse dynamics for unentangled melts. Finally, we demonstrate that entanglements do not play a significant role in the observed coupling. © 2010 The American Physical Society

Electrochemical single-molecule transistors with optimized gate coupling

Electrochemical gating at the single molecule level of viologen molecular bridges in ionic liquids is examined. Contrary to previous data recorded in aqueous electrolytes, a clear and sharp peak in the single molecule conductance versus electrochemical potential data is obtained in ionic liquids. These data are rationalized in terms of a two-step electrochemical model for charge transport across the redox bridge. In this model the gate coupling in the ionic liquid is found to be fully effective with a modeled gate coupling parameter, ξ, of unity. This compares to a much lower gate coupling parameter of 0.2 for the equivalent aqueous gating system. This study shows that ionic liquids are far more effective media for gating the conductance of single molecules than either solid-state three-terminal platforms created using nanolithography, or aqueous media.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

Ligand K-edge X-ray absorption spectroscopy and DFT calculations on [Fe3S4]0,+ clusters: delocalization, redox, and effect of the protein environment

Ligand K-edge XAS of an [Fe3S4]0 model complex is reported. The pre-edge can be resolved into contributions from the í2Ssulfide, í3Ssulfide, and Sthiolate ligands. The average ligand-metal bond covalencies obtained from these pre-edges are further distributed between Fe3+ and Fe2.5+ components using DFT calculations. The bridging ligand covalency in the [Fe2S2]+ subsite of the [Fe3S4]0 cluster is found to be significantly lower than its value in a reduced [Fe2S2] cluster (38% vs 61%, respectively). This lowered bridging ligand covalency reduces the superexchange coupling parameter J relative to its value in a reduced [Fe2S2]+ site (-146 cm-1 vs -360 cm-1, respectively). This decrease in J, along with estimates of the double exchange parameter B and vibronic coupling parameter ì2/k-, leads to an S ) 2 delocalized ground state in the [Fe3S4]0 cluster. The S K-edge XAS of the protein ferredoxin II (Fd II) from the D. gigas active site shows a decrease in covalency compared to the model complex, in the same oxidation state, which correlates with the number of H-bonding interactions to specific sulfur ligands present in the active site. The changes in ligand-metal bond covalencies upon redox compared with DFT calculations indicate that the redox reaction involves a two-electron change (one-electron ionization plus a spin change of a second electron) with significant electronic relaxation. The presence of the redox inactive Fe3+ center is found to decrease the barrier of the redox process in the [Fe3S4] cluster due to its strong antiferromagnetic coupling with the redox active Fe2S2 subsite.

Search for new light gauge bosons in Higgs boson decays to four-lepton final states in pp collisions at s√=8TeV with the ATLAS detector at the LHC

This paper presents a search for Higgs bosons decaying to four leptons, either electrons or muons, via one or two light exotic gauge bosons Zd, H→ZZd→4ℓ or H→ZdZd→4ℓ. The search was performed using pp collision data corresponding to an integrated luminosity of about 20 fb−1 at the center-of-mass energy of s√=8TeV recorded with the ATLAS detector at the Large Hadron Collider. The observed data are well described by the Standard Model prediction. Upper bounds on the branching ratio of H→ZZd→4ℓ and on the kinetic mixing parameter between the Zd and the Standard Model hypercharge gauge boson are set in the range (1--9)×10−5 and (4--17)×10−2 respectively, at 95% confidence level assuming the Standard Model branching ratio of H→ZZ∗→4ℓ, for Zd masses between 15 and 55 GeV. Upper bounds on the effective mass mixing parameter between the Z and the Zd are also set using the branching ratio limits in the H→ZZd→4ℓ search, and are in the range (1.5--8.7)×10−4 for 15coupling parameter, controlling the strength of the coupling of the Higgs boson to dark vector bosons, are set in the range (2--3)×10−5 and (1--10)×10−4 respectively, at 95 % confidence level assuming the Standard Model Higgs boson production cross sections, for Zd masses between 15 and 60 GeV.

Structural and optical properties of dilute InAsN grown by molecular beam epitaxy

We perform a structural and optical characterization of InAs1¿xNx epilayers grown by molecular beam epitaxy on InAs substrates x 2.2% . High-resolution x-ray diffraction HRXRD is used to obtain information about the crystal quality and the strain state of the samples and to determine the N content of the films. The composition of two of the samples investigated is also obtained with time-of-flight secondary ion mass spectroscopy ToF-SIMS measurements. The combined analysis of the HRXRD and ToF-SIMS data suggests that the lattice parameter of InAsN might significantly deviate from Vegard"s law. Raman scattering and far-infrared reflectivity measurements have been carried out to investigate the incorporation of N into the InAsN alloy. N-related local vibrational modes are detected in the samples with higher N content. The origin of the observed features is discussed. We study the compositional dependence of the room-temperature band gap energy of the InAsN alloy. For this purpose, photoluminescence and optical absorption measurements are presented. The results are analyzed in terms of the band-anticrossing BAC model. We find that the room-temperature coupling parameter for InAsN within the BAC model is CNM=2.0 0.1 eV.

Dynamical aspects of coupled Rossler systems: effects of noise

Nonlinear time series analysis is employed to study the complex behaviour exhibited by a coupled pair of Rossler systems. Dimensional analysis with emphasis on the topological correlation dimension and the Kolmogorov entropy of the system is carried out in the coupling parameter space. The regime of phase synchronization is identified and the extent of synchronization between the systems constituting the coupled system is quantified by the phase synchronization index. The effect of noise on the coupling between the systems is also investigated. An exhaustive study of the topological, dynamical and synchronization properties of the nonlinear system under consideration in its characteristic parameter space is attempted.

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.