Funnel Potential Research Articles

Continuation of the Stieltjes series to the large regime by finite-part integration

We devise a prescription to use a novel convergent expansion in the strong-asymptotic regime for the Stieltjes integral and its generalizations (Galapon EA. 2017 Proc. R. Soc A 473 , 20160567) to sum the associated divergent series of Stieltjes across all asymptotic regimes. The novel expansion makes use of the divergent negative-power moments, which we treated as Hadamard’s finite part integrals. The result allowed us to compute the ground state energy of the quartic, sextic anharmonic oscillators as well as the P T symmetric cubic oscillator, and the funnel potential across all perturbation regimes from a single expansion that is built from the divergent weak-coupling perturbation series and incorporates the known leading-order strong-coupling behaviour of the spectra.

Clogging, diode and collective effects of skyrmions in funnel geometries

Using a particle-based model, we examine the collective dynamics of skyrmions interacting with a funnel potential under dc driving as the skyrmion density and relative strength of the Magnus and damping terms are varied. For driving in the easy direction, we find that increasing the skyrmion density reduces the average skyrmion velocity due to jamming of skyrmions near the funnel opening, while the Magnus force causes skyrmions to accumulate on one side of the funnel array. For driving in the hard direction, there is a critical skyrmion density below which the skyrmions become trapped. Above this critical value, a clogging effect appears with multiple depinning and repinning states where the skyrmions can rearrange into different clogged configurations, while at higher drives, the velocity-force curves become continuous. When skyrmions pile up near the funnel opening, the effective size of the opening is reduced and the passage of other skyrmions is blocked by the repulsive skyrmion–skyrmion interactions. We observe a strong diode effect in which the critical depinning force is higher and the velocity response is smaller for hard direction driving. As the ratio of Magnus force to dissipative term is varied, the skyrmion velocity varies in a non-linear and non-monotonic way due to the pile up of skyrmions on one side of the funnels. At high Magnus forces, the clogging effect for hard direction driving is diminished.

Symmetry breaking in Bose-Einstein condensates confined by a funnel potential

In this paper we consider a Bose-Einstein condensate in self-attraction regime, confined transversely by a funnel-like potential and axially by a double-well potential formed by the combination of two inverted Pöschl-Teller potentials. The system is well described by a one-dimensional nonpolynomial Schrödinger equation, for which we analyze the symmetry break of the wave function that describes the particle distribution of the condensate. The symmetry break was observed for several interaction strength values as a function of the minimum potential well. In addition, we analyzed the symmetric and asymmetric solutions using a real-time evolution method, in which it was possible to confirm the stability of the results. Finally, a comparison with the cubic nonlinear Schrödinger equation and the full Gross-Pitaevskii equation were performed to check the accuracy of the effective equation used here.

Geometrically constrained path planning for robotic grasping with Differential Evolution and Fast Marching Square

AbstractThis paper presents a new approach for geometrically constrained path planning applied to the field of robotic grasping. The method proposed in this paper is based on the Fast Marching Square (FM $\, ^2$ ) and a path calculation approach based on an optimization evolutionary filter named Differential Evolution (DE). The geometric restrictions caused by the link lengths of the kinematic chain composed by the robot arm and hand are introduced in the path calculation phase. This phase uses both the funnel potential of the surroundings created with FM $\, ^2$ and the kinematic constraints of the robot as cost functions to be minimized by the evolutionary filter. The use of an optimization filter allows for a near-optimal solution that satisfies the kinematic restrictions, while preserving the characteristics of a path computed with FM $\, ^2$ . The proposed method is tested in a simulation using a robot composed by a mobile base with two arms.

Quasi-one-dimensional approximation for Bose–Einstein condensates transversely trapped by a funnel potential

Starting from the standard three-dimensional (3D) Gross–Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schrödinger equation (1D-NPSE) governing the axial dynamics of atomic Bose–Einstein condensates (BECs) under the action of a singular but physically relevant funnel-shaped transverse trap, i.e. an attractive 2D potential ∼−1/r (where r is the radial coordinate in the transverse plane), in combination with the repulsive self-interaction. Wave functions of the trapped BEC are regular, in spite of the potential’s singularity. The model applies to a condensate of particles (small molecules) carrying a permanent electric dipole moment in the field of a uniformly charged axial thread, as well as to a quantum gas of magnetic atoms pulled by an axial electric current. By means of numerical simulations, we verify that the effective 1D-NPSE provides accurate static and dynamical results, in comparison to the full 3D GPE, for both repulsive and attractive signs of the intrinsic nonlinearity.

Simulation of substrate contact effects on heavy ion-induced current transient in SiGe HBT

This paper presents an investigation into the impact of substrate contact structure on the heavy ion-induced current transient in silicon‑germanium heterojunction bipolar transistor (SiGe HBT) based on Technology Computer Aided Design (TCAD) simulation. The results show that the size of the heavily doped ring wall used for substrate contact extraction has a significant impact on the collector current transient features. In addition, the impact of the ring size is position-dependent. For the strike positions inside or near the collector-substrate (CS) junction, the variation of transient features is attributed to the shape and volume of the funnel potential. While for the strike positions far from the CS junction, the variation is dominated by the diffusion process of the ion-induced electrons.

Mass Specta of Heavy Quarkonium with Screened Potential in Momentum Space

In this paper we have solved the homogeneous Lippmann-Schwinger integral equation in the momentum space by using a screened funnel potential which is suggested by unquenched lattice calculations. As an application the mass spectra of heavy quarkonia \(\mathrm {\Upsilon }(b\bar {b})\) and \(\psi (c\bar {c}))\), have been calculated. The results have been compared with non screened potentials and experimental data.

Characteristics of an ion funnel as ion guide in an inductively coupled plasma mass spectrometer

The characteristics of an electrodynamic ion funnel as an alternative ion optics element for inductively coupled plasma mass spectrometry (ICPMS) were investigated in this work. Therefore the ion lens of a conventional ICPMS system has been removed and a custom made ion funnel was installed instead. The effects of the radiofrequency-amplitude and frequency and the axial funnel potential on the ion transmission have been investigated for different configurations. Under optimum conditions the ion current was in average 10-fold lower than with the un-modified instrument, while CeO+/Ce+ ratios increased ten-fold. Nonetheless, confinement of atomic ions from the ICP inside the ion funnel could be achieved by optimizing radiofrequency and DC potentials at the funnel electrodes as indicated by an increase in the ion signal intensities relative to the field-free case. With the ion funnel being partially enclosed, gases, such as N2 and H2, could be introduced which can reduce the abundance of Ar+ and Ar-based polyatomic ions by one (H2) to three (N2) orders of magnitude. Based on these experiments, however H2 would be more favorable since it did not affect the transmission of low m/z analyte ions to a great extent.

Energy eigenvalues of spherical symmetric potentials with relativistic corrections: analytic results

Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including the relativistic corrections. The energy eigenvalues of spherical symmetric potentials for two-particle bound state systems with relativistic corrections are analytically derived. The energy spectra of linear and funnel potentials with orbital and radial excitations are determined. The energy spectrum of a superposition of Coulomb and Yukawa potentials is also determined. Our result shows that the energy spectrum with the relativistic corrections for the linear, harmonic oscillator and funnel potentials is smaller than the upper boundaries for the energy spectrum established in the framework of the spinless Salpeter equation for the orbital and radial excited states. The relativistic corrections to the energy spectrum of a superposition of the attractive Coulomb potential and the Yukawa (exponentially screened Coulomb) potentials are very small.

Effective potential between two transverse gluons from lattice QCD

Modeling glueballs as bound states of transverse constituent gluons allows to understand the main features of the lattice QCD glueball spectrum. In particular it has been shown in previous works that the lightest C-even glueballs can be seen as bound states of two transverse constituent gluons interacting via a funnel potential. In the present study we show that such an effective potential emerges from the available lattice QCD data. Starting from the scalar glueball mass and wave function computed in lattice QCD, we indeed compute the equivalent local potential between two transverse constituent gluons in the scalar channel and show that it is compatible with a funnel shape, where standard values of the parameters are used and where a negative constant has to be added to reproduce the absolute height of the potential. Such a constant could be related to instanton-induced effects in glueballs.

Study of dynamical behaviour and fermionization of a bosonic gas in funnel potential

This paper presents a funnel external potential model to investigate dynamic properties of ultracold Bose gas. By using variational method, we obtain the ground-state energy and density properties of ultracold Bose atoms. The results show that the ultracold Bose gas confined in a funnel potential experiences the transition from three-dimensional regime to quasi-one-dimensional regime in a small aspect ratio, and undergoes fermionization process as the aspect ratio increases.

Connectivity graph: Multiple connectivity on potential energy surface does affect the dynamics

A mapping called a connectivity graph is proposed to visualize the complicated networks between local minima via saddles on many-dimensional potential energy surfaces. With this mapping, the effect of the topography of a complex potential energy surface on the dynamics is studied in model funnel potentials and a Lennard-Jones cluster. We present strong evidence that energetically expensive but dynamically relevant saddles are indispensable for kinetic dynamics. The results show that the connectivity graphs provide a sound basis for understanding nonequilibrium dynamics.

Accurate analytic presentation of solution of the Schrödinger equation with arbitrary physical potential

High precision approximate analytic expressions of the ground state energies and wave functions for the arbitrary physical potentials are found by first casting the Schrödinger equation into the nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. The choice of zero iteration is based on general features of exact solutions near the boundaries. The approach is illustrated on the examples of the Yukawa, Woods–Saxon and funnel potentials. For the latter potential, solutions describing charmonium, bottonium and topponium are analyzed. Comparison of our approximate analytic expressions for binding energies and wave functions with the exact numerical solutions demonstrates their high accuracy in the wide range of physical parameters. The accuracy ranging between 10−4 and 10−8 for the energies and, correspondingly, 10−2 and 10−4 for the wave functions is reached. The derived formulas enable one to make accurate analytical estimates of how variation of different interactions parameters affects correspondent physical systems.

Glueball and hybrid mass and decay with string tension below Casimir scaling

Lattice computations with excited SU(3) representations suggest that the confining gluon–gluon interaction complies with the Casimir scaling. The constituent gluon models have also assumed the Casimir scaling. Nevertheless, inspired by type-II superconductors, we explore a new scenario for the gluon–gluon interaction where the adjoint string is replaced by a pair of fundamental strings, resulting in a factor of 2, smaller than the Casimir scaling factor of 9/4. To test our proposal we construct a simple constituent gluon model, extrapolated from the funnel potential for quarkonium, and apply it to compute the wavefunction of glueballs and of hybrid gluelumps. From the decay widths of quarkonium, we also extrapolate the decay widths of the glueballs. Our predictions apply to charmonia, lightonia, glueballs and hybrid gluelumps with large angular momentum J.Communicated by Professor S Kabana

WKB method for the Dirac equation with a scalar-vector coupling

We outline a recursive method for obtaining WKB expansions of solutions of the Dirac equation in an external centrally symmetric field with a scalar-vector Lorentz structure of the interaction potentials. We obtain semiclassical formulas for radial functions in the classically allowed and forbidden regions and find conditions for matching them in passing through the turning points. We generalize the Bohr-Sommerfeld quantization rule to the relativistic case where a spin-1/2 particle interacts simultaneously with a scalar and an electrostatic external field. We obtain a general expression in the semiclassical approximation for the width of quasistationary levels, which was earlier known only for barrier-type electrostatic potentials (the Gamow formula). We show that the obtained quantization rule exactly produces the energy spectrum for Coulomb- and oscillatory-type potentials. We use an example of the funnel potential to demonstrate that the proposed version of the WKB method not only extends the possibilities for studying the spectrum of energies and wave functions analytically but also ensures an appropriate accuracy of calculations even for states with nr ∼ 1.

Electromagnetic splittings for hadrons with dressed constituent quarks

Electromagnetic splittings for hadrons are calculated in a formalism where the constituent quarks are considered as dressed quasiparticles. The electromagnetic interaction, which contains coulomb, contact and hyperfine terms, is folded with the quark electrical density. The strong potential is a modification of the well known funnel potential. Our model contains only one free parameter and the agreement with experimental data is reasonable although it seems very difficult to obtain a perfect description in any case.

On the summation of divergent perturbation series in quantum mechanics and field theory

The possibility of recovering the Gell-Mann–Low function in the asymptotic strong-coupling regime by known first-order perturbation-theory (PT) terms βn and their asymptotics as \(\tilde \beta _n \) as n → ∞ is investigated. Conditions are formulated that are necessary for recovering the required function at the physical level of rigor: (1) a large number of PT coefficients are known whose asymptotics has already been established, and (2) there is no intermediate asymptotics. Higher orders of PT, their asymptotic behavior, and power corrections are calculated in quantum mechanical problems that involve divergent PT series (including series for a funnel potential, the ϕ (0) 4 model, and the Stark effect in a strong field). The scalar field theory ϕ (4) 4 is considered in the \(\overline {MS} \) and MOM regularization schemes. It is shown that one cannot make any definite conclusion about the asymptotics of the Gell-Mann–Low function as g → ∞ on the basis of information available for the above theory.

Semiclassical model of light mesons

The dominantly orbital state description is applied to the study of light mesons. The effective Hamiltonian is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement. The influence of two different finite quark masses and potential parameters on Regge and vibrational trajectories is discussed.

Quasiclassical approximation with the centrifugal potential excluded

We develop a modification of the WKB method (the modified quantization method, or MQM) for finding the radial wave functions. The method is based on excluding the centrifugal potential from the quasiclassical momentum and changing correspondingly the phase in the Bohr-Sommerfeld quantization condition. MQM is used to calculate the asymptotic coefficients at zero and at infinity. We use the examples of power-law and funnel potentials to show that MQM not only dramatically broadens the possibilities of studying the energy spectrum and the wave functions analytically but also ensures accuracy to within a few percent even when one calculates states with a radial quantum number n r ∼1, provided that the angular momentum l is not too large. We also briefly discuss the possibility of generalizing MQM to the relativistic case (the spinless Salpeter equation).

Universality of Regge and vibrational trajectories in a semiclassical model

The orbital and radial excitations of light-light mesons are studied in the framework of the dominantly orbital state description. The equation of motion is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement. The influence of finite quark masses and potential parameters on Regge and vibrational trajectories is discussed. The case of heavy-light mesons is also presented.