Repulsive Case Research Articles

Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions

We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space, and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for \textit{subfundamental solitons} (SFSs) is found in the second finite bandgap. For the existence of gap solitons (GSs) under the attractive DD interaction, the contact repulsion must be strong enough. In the opposite case of the DD repulsion, GSs exist if the contact attraction is not too strong. Collisions between solitons in the free space are studied too. In the case of the local attraction, they merge or pass through each other at small and large velocities, respectively. In the presence of the local repulsion, slowly moving solitons bounce from each other.

Small traveling clusters in attractive and repulsive Hamiltonian mean-field models

Long-lasting small traveling clusters are studied in the Hamiltonian mean-field model by comparing between attractive and repulsive interactions. Nonlinear Landau damping theory predicts that a Gaussian momentum distribution on a spatially homogeneous background permits the existence of traveling clusters in the repulsive case, as in plasma systems, but not in the attractive case. Nevertheless, extending the analysis to a two-parameter family of momentum distributions of Fermi-Dirac type, we theoretically predict the existence of traveling clusters in the attractive case; these findings are confirmed by direct N -body numerical simulations. The parameter region with the traveling clusters is much reduced in the attractive case with respect to the repulsive case.

Infinite Cycles in Boson Lattice Models

We study the relationship between long cycles and Bose-Einstein condensation (BEC) in the case of several models. A convenient expression for the density of particles on cycles of length $q$ is obtained, in terms of $q$ unsymmetrised particles coupled with a boson field. Using this formulation we reproduce known results on the Ideal Bose Gas, Mean-Field and Perturbed Mean-Field Models, where the condensate density exactly equals the long cycle density. Then we consider the Infinite-Range-Hopping Bose-Hubbard model, with and without hard-cores. For the hard-core case, we find we can disregard the hopping contribution of the q unsymmetrised particles to obtain an exact expression for the density of particles on long cycles. It is shown that only the cycle of length one contributes to the cycle density. We conclude that while the existence of a non-zero long cycle density coincides with the occurrence of Bose-Einstein condensation, the respective densities are not necessarily equal. For the case of a finite on-site repulsion, we obtain an expression for the cycle density by neglecting the $q$ unsymmetrised hop. Inspired by the Approximating Hamiltonian method we conjecture a simplified expression for the short cycle density as a ratio of single-site partition functions. In the absence of condensation we prove that this simplification is exact and find that in this case the long-cycle density vanishes. In the presence of condensation we justify this simplification when a gauge-symmetry breaking term is introduced in the Hamiltonian. Assuming our conjecture is correct, we compare numerically the long-cycle density with the condensate and again find that though they coexist, in general they are not equal.

Influence of surface affinity of planar walls on effective interaction between the wall and colloids

Abstract Using density functional theory, we investigate the effective interaction between a big colloid immersed in a sea of small colloids and a wall which has different affinity to the small colloids. Steele 10-4-3 potential is introduced to mimic both short-range repulsive and long-range attractive interactions between the wall and the small colloids. It is found that the surface affinity of the wall has a significant influence on the effective interaction. In the short-range repulsive case, the repulsion greatly enhances the big colloid-wall effective attraction, which sensitively depends on the concentration of small colloids, and is not sensitive to the repulsive strength. In the long-range attractive case, both the concentration of small colloids and the attractive strength have great effect on the effective interaction, and with an increase of the attractive strength, a strong repulsion may be induced when the big colloid is close to the wall. In low density limit of small colloids, the present results agree well with those of the Asakura and Oosawa(AO) approximation.

Static properties of trapped bose gases at finite temperature: Thomas-Fermi limit

We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit for the repulsive case. We derive simple analytic expressions for the condensate properties at finite temperature. The noncondensate and anomalous density profiles are also analyzed in terms of the condensate fraction. The results are quite encouraging owing to the simplicity of the formalism.

Dynamics of Bose–Einstein condensates with atomic pumping and dissipative processes

In the dynamics of condensed systems described by a nonconservative non-linear Schrödinger equation, we investigate numerically the role of atomic feeding and inelastic collisions where dipolar relaxation is the dominant process. By analyzing the range of possible values of the nonconservative parameters to have stable (or unstable) solutions, we verify that spatio-temporal chaos patterns, known for attractive two-body systems due to collapsing effects, can also occur in the repulsive case when the term corresponding to the linear atomic feeding dominates the nonconservative contributions.

Fock-space WKB method for the boson Josephson model describing a Bose-Einstein condensate trapped in a double-well potential

We develop a Fock-space WKB method for a Bose-Einstein condensate (BEC) in a double-well trap, using an analogy with a single particle of either positive or negative mass in a quantum potential. The usual mean-field approach is the classical limit, and the inverse number of atoms plays the role of Planck constant. The ground state of positive-mass particles corresponds to the mean-field fixed point of lower energy, while that of negative mass to the excited fixed point. In the case of attractive BECs above the threshold for symmetry breaking, the ground state is the Schr\"odinger cat state and we relate this to the double-well shape of the potential in Fock space. In the repulsive case, we identify the quantum states corresponding to the mean-field macroscopic self-trapping phenomenon. In particular, the phase-locked ($\ensuremath{\pi}$ phase) macroscopic quantum self-trapping of BECs is related to the double-well shape of the potential in Fock space. The running-phase macroscopic quantum self-trapping state is found to be subject to quantum collapses and revivals. The phase dispersion grows exponentially, reaching the absolute maximum just before the first collapse of the running phase, which may explain the growth of the phase fluctuations seen in the experiment on macroscopic quantum self-trapping.

Non-collision periodic solutions of second order singular dynamical systems

We study the existence of non-collision periodic solutions for second order singular dynamical systems. The repulsive case and the attractive case are dealt with using a unified topological approach. The proof is based on a well-known fixed point theorem for completely continuous operators, involving a new type of cone. We do not need to consider so-called strong force conditions. Moreover, for the repulsive case, the critical case can be covered. Recent results in the literature, even in the scalar case, are complemented, generalized and improved.

Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity

In this paper we analyze the existence, stability, dynamical formation, and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schrödinger equation with a linear point defect. We consider both attractive and repulsive defects in a focusing lattice. Among our main findings are (a) the destabilization of the on-site mode centered at the defect in the repulsive case, (b) the disappearance of localized modes in the vicinity of the defect due to saddle-node bifurcations for sufficiently strong defects of either type, (c) the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects, and (d) the detailed elucidation as a function of initial speed and defect strength of the different regimes (trapping, trapping and reflection, pure reflection, and pure transmission) of interaction of a moving localized mode with the defect.

Symbiotic gap and semigap solitons in Bose-Einstein condensates

Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case of interspecies repulsion, while the intraspecies interaction may be either repulsive or attractive. Several types of gap solitons are found: symmetric or asymmetric; unsplit or split, if centers of the components coincide or separate; intragap (with both chemical potentials falling into a single band gap) or intergap, otherwise. In the case of the intraspecies attraction, a smooth transition takes place between solitons in the semi-infinite gap, those in the first finite band gap, and semigap solitons (with one component in a band gap and the other in the semi-infinite gap).

Thermodynamic and structural properties of mixed colloids represented by a hard-core two-Yukawa mixture model fluid: Monte Carlo simulations and an analytical theory

The interaction between colloidal particles is well represented by a hard-core two-Yukawa potential. In order to assess the accuracy of theoretical predictions for the thermodynamic and structural properties of mixed colloids, standard Monte Carlo simulations are carried out for the hard-core two-Yukawa mixtures. In the simulations, one range parameter in the two-Yukawa potential is taken as 1.8 or 2.8647, and another is taken as 4, 8, or 13.5485. Both attractive and repulsive dominant cases of the potential outside the hard core are considered. The effects of temperature, density, composition, size and energy parameter ratios on internal energy, compressibility factor, and radial distribution function are investigated extensively. Theoretical calculations are performed in the framework of analytical solution for the Ornstein-Zernike equation with the first-order mean spherical approximation (FMSA). Our analysis shows that the FMSA is very accurate for the prediction of the compressibility factor of the hard-core two-Yukawa mixtures at all conditions studied. The FMSA generally predicts accurate internal energy, but overestimates the internal energy of the systems at lower temperatures. Furthermore, we found that a simplified exponential version of the FMSA predicts fairly good radial distribution function at contact for the mixed two-Yukawa fluids. The comparison of the theoretical compressibility factor with that from the Monte Carlo simulations suggests that the FMSA can be used to investigate the fluid-fluid equilibria of hard-core two-Yukawa mixtures.

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing-wave solution is stable in H rad 1 ( R ) and unstable in H 1 ( R ) under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the nonradial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.

Strength of Cα−H···OC Hydrogen Bonds in Transmembrane Proteins

A large number of Calpha-H...O contacts are present in transmembrane protein structures, but contribution of such interactions to protein stability is still not well understood. According to previous ab initio quantum calculations, the stabilization energy of a Calpha-H...O contact is about 2-3 kcal/mol. However, experimental studies on two different Calpha-H...O hydrogen bonds present in transmembrane proteins lead to conclusions that one contact is only weakly stabilizing and the other is not even stabilizing. We note that most previous computational studies were on optimized geometries of isolated molecules, but the experimental measurements were on those in the structural context of transmembrane proteins. In the present study, 263 Calpha-H...O=C contacts in alpha-helical transmembrane proteins were extracted from X-ray crystal structures, and interaction energies were calculated with quantum mechanical methods. The average stabilization energy of a Calpha-H...O=C interaction was computed to be 1.4 kcal/mol. About 13% of contacts were stabilizing by more than 3 kcal/mol, and about 11% were destabilizing. Analysis of the relationships between energy and structure revealed four interaction patterns: three types of attractive cases in which additional Calpha-H...O or N-H...O contact is present and a type of repulsive case in which repulsion between two carbonyl oxygen atoms occur. Contribution of Calpha-H...O=C contacts to protein stability is roughly estimated to be greater than 5 kcal/mol per helix pair for about 16% of transmembrane helices but for only 3% of soluble protein helices. The contribution would be larger if Calpha-H...O contacts involving side chain oxygen were also considered.

Jamming in attractive granular media

AbstractThe jamming transition is studied numerically in systems of particles with attraction. Unlike the purely repulsive case where a single transition separates the jammed from unjammed phase, the presence of even an infinitesimal amount of attraction yields two distinct transitions: connectivity and rigidity percolation. We measure critical exponents of these two percolation transitions and find that they are different than the corresponding lattice values. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamical instability and dispersion management of an attractive condensate in an optical lattice

We investigate the stability of an attractive Bose-Einstein condensate in a one-dimensional lattice in the presence of radial confinement. We find that the system is dynamically unstable for low quasimomenta and becomes stable near the band edge, in a specular fashion with respect to the repulsive case. For low interactions the instability occurs via long-wavelength excitations that produce an oscillating density pattern in both real and momentum space instead of spoiling the condensate coherence. This behavior is illustrated by simulations for the expansion of the condensate in a moving lattice.

Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Effects of atomic interactions on quantum accelerator modes

We consider the influence of the inclusion of interatomic interactions on the $\ensuremath{\delta}$-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modeled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.

Dynamical Heterogeneity and Nonlinear Susceptibility in Supercooled Liquids with Short-Range Attraction

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here we study in detail the behavior of nonlinear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard nonlinear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids.

Lexical repulsion between sense-related pairs

This paper builds on the groundwork and setting up of methods for an innovative approach to analysing text. We have proposed that there is a hitherto unexplored textual feature, which we call ‘repulsion’, which operates on the construction of meaning in an opposing way to that of word collocation. To illustrate, we do not say cheerfully happy even though we say blissfully happy. We focus on ‘lexical repulsion’, by which we mean the intuitively-observed tendency in conventional language use for certain pairs of words not to occur together, for no apparent reason other than convention. Our goal is to establish how repulsion as a whole operates and whether it can be assigned the status of an objectively measurable ‘force’. It is anticipated that this approach will have wide implications for corpus linguistics and NLP. In this paper, we take the particular case of repulsion between sense-related word pairs.

Translation-Invariance of Two-Dimensional Gibbsian Point Processes

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general.