Arbitrary Potential Research Articles

Topological contribution to magnetism in the Kane-Mele model: An explicit wave-function approach

In our previous publication [Ozaki and Ogata, Phys. Rev. Res. 3, 013058 (2021)], the quantization of the orbital-Zeeman (OZ) cross term in the magnetic susceptibility, or the cross term of spin Zeeman and orbital effect, was shown for the Kane-Mele model using the expansion around the Dirac points. In the present study, we accurately evaluate the orbital, spin-Zeeman, and OZ cross term of the Kane-Mele model using a recently developed formulation. This method uses the explicit real-space Bloch wave functions and enables us to accurately evaluate each contribution taking into account an infinite number of high-energy bands and core electron contribution at arbitrary chemical potential. We find that the effect beyond the previous formulations does not change the quantization of the OZ cross term. We also study the OZ cross term in the metalic case, and the sum rule of the OZ cross term with respect to the chemical potential is found. The possibility of experimental detection of the quantization is also discussed.

Symmetry Analysis of the Square Well Potential

Symmetry considerations are taken into account when a particle in a square well potential is studied. This system may display natural degeneracy, accidental degeneracy or systematic accidental degeneracy depending on the depth of the potential. In order to obtain the solutions associated with an arbitrary potential an algebraic discrete variable representation approach based on Pöschl-Teller functions is proposed. It is proved that the geometrical group C 4v is the symmetry group of the system for the case of a finite potential barrier. A similar analysis is carried out for the rectangular square well potential with commensurate sides. In both cases the symmetry projection is crucial to simplify the calculations.

On the collective properties of quantum media

We discuss the hydrodynamic representation of a wide class of quantum media exhibiting similar elementary excitations and dispersion properties. The representation covers quantum systems characterized by any type of (long-range) self-interaction, associated with an arbitrary potential. It also accounts for possible nonlinearities, which may arise, e.g., due to short-range interactions (collisions) in the case of bosons, or from the Pauli exclusion principle for fermions. The approach equally applies to various physical scenarios, such as self-gravitating quantum media (e.g., dark matter), quantum plasmas, Bose–Einstein condensates, and non-condensed cold atomic clouds. We discuss the formal analogies that can be drawn between these different systems and how they can be used to realize laboratory experiments emulating gravitational phenomena, especially in the context of alternative theories of gravity. To substantiate our point, we elaborate more closely on the case of non-minimal matter-curvature coupling gravity theories.

Computation of the thermal elastic constants for arbitrary manybody potentials in LAMMPS using the stress-fluctuation formalism

This paper describes the implementation of the stress-fluctuation technique into the LAMMPS code to compute the anisotropic thermal elastic constants tensor of materials. The implementation provides both methods for computing the analytical fluctuation expressions and also a generic numerical derivative method. The former makes the extension to new potentials straightforward, as it requires writing code only for the second derivatives of each energy term w.r.t. distance, angle, etc. The latter provides a generic interface to compute an accurate approximation of the elastic constants for any potential already implemented in LAMMPS. We show how both methods compare with the direct deformation computation in several test cases and discuss the implementation advantages and limitations.

On the spectrum of the Landau Hamiltonian perturbed by a periodic electric potential

We study the spectrum of the Landau Hamiltonian perturbed by a periodic electric potential $V\in L^2_{\mathrm{loc}}(\mathbb R^2;\mathbb R)$ assuming that the magnetic flux of the homogeneous magnetic field $B>0$ satisfies the condition $(2\pi)^{-1}Bv(K)=Q^{-1}$, $Q\in \mathbb N $, where $v(K)$ is the area of the unit cell $K$ of the period lattice of the potential $V$. For arbitrary periodic potentials $V\in L^2_{\mathrm {loc}}(\mathbb R^2;\mathbb R)$ with zero mean $V_0=0$ we show that the spectrum has no eigenvalues different from Landau levels. For periodic potentials $V\in L^2_{\mathrm{loc}}(\mathbb R^2;\mathbb R)\setminus C^{\infty}(\mathbb R^2;\mathbb R)$ we also show that the spectrum is absolutely continuous. Bibliography: 23 titles.

Testing de Broglie’s Double Solution in the Mesoscopic Regime

We present here solutions of a non-linear Schrödinger equation in presence of an arbitrary linear external potential. The non-linearity expresses a self-focusing interaction. These solutions are the product of the pilot wave with peaked solitons the velocity of which obeys the guidance equation derived by Louis de Broglie in 1926. The degree of validity of our approximations increases when the size of the soliton decreases and becomes negligible compared to the typical size over which the pilot wave varies. We discuss the possibility to reveal their existence by implementing a humpty-dumpty Stern-Gerlach interferometer in the mesoscopic regime.

Interference Phenomenon in Electron-Molecule Collisions

This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combination of a plane wave and two spherical s-waves propagating freely throughout space. The asymptotic behavior of this function determines the amplitude of elastic particle scattering in closed form. It is demonstrated that this amplitude can be represented as a partial expansion in a set of the orthonormal functions Zλ(r) other than spherical harmonics Ylm(r). General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion into a series of functions Zλ(r) and determine the scattering phases ηλ(k) for the considered two- atomic target. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.

Combined effects of temperature-dependent properties and magnetic field on electro-osmotic mobility at arbitrary zeta potentials

ABSTRACT We analyze the thermo-electroosmotic mobility of power-law electrolyte solution under the action of a magnetic field in a wavy pattern micro-channel. The flow is driven by the combined effect of the pressure gradient and the electric potential applied externally in the axial direction. The variable properties such as the viscosity, zeta potential, electrical and thermal conductivity of electro-thermal flow are assumed to vary with temperature. The entire flow phenomena have been solved by employing the finite difference method. We have presented the variation of electroosmotic mobility with the effect of Joule heating and applied magnetic field. We have examined the coupling effects of axial velocity, thermal energy, and electric potential function for various values of the temperature-dependent properties. These temperature-dependent property variations lead to developing volumetric flow rates associated with the behavior of the power-law index. The Nusselt number is drastically influenced by the temperature-dependent zeta potential variation in comparison with the Newtonian and shear-thickening fluids. The numerical and analytical solutions are validated with the existing literature and obtained a good agreement.

Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle.

The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general expression for the Laplace transform of the transient electrophoretic mobility, we present an approximation method to avoid the numerical inverse Laplace transformation and derive a simple approximate analytic mobility expression for a weakly charged particle without involving numerical inverse Laplace transformations. The transient electrophoretic mobility can be obtained directly from this approximate mobility expression without recourse to the numerical inverse Laplace transformation. The results are found to be in excellent agreement with the exact numerical results obtained by Huang and Keh.

Relic gravitational waves in verified inflationary models based on the generalized scalar–tensor gravity

In this work, we consider the models of cosmological inflation based on generalized scalar–tensor theories of gravity with quadratic connection between the Hubble parameter and coupling function. For such a class of the models, we discuss the correspondence between well-known versions of the scalar–tensor gravity theories and physically motivated potentials of a scalar field. It is shown that this class of models corresponds to the Planck observational constraints on the cosmological perturbation parameters for an arbitrary potential of a scalar field and arbitrary version of a scalar–tensor gravity theory. The spectrum of relict gravitational waves is analyzed, and the frequency range corresponding to maximal energy density is determined. The possibility of direct detection of the relic gravitational waves, predicted in such a class of models, by satellite and ground-based detectors is discussed as well.

Physical symmetries and gauge choices in the Landau problem

Due to a special nature of the Landau problem, in which the magnetic field is uniformly spreading over the whole two-dimensional plane, there necessarily exist three conserved quantities, i.e. two conserved momenta and one conserved orbital angular momentum for the electron, independently of the choice of the gauge potential. Accordingly, the quantum eigen-functions of the Landau problem can be obtained by diagonalizing the Landau Hamiltonian together with one of the above three conserved operators with the result that the quantum mechanical eigen-functions of the Landau problem can be written down for arbitrary gauge potential. The purpose of the present paper is to clarify the meaning of gauge choice in the Landau problem based on this gauge-potential-independent formulation, with a particular intention of unraveling the physical significance of the concept of gauge-invariant-extension of the canonical orbital angular momentum advocated in recent literature on the nucleon spin decomposition problem. At the end, our analysis is shown to disclose a physically vacuous side face of the gauge symmetry.

New inflationary exact solution from Lie symmetries

For the inflaton field, we determine a new exact solution by using the Lie symmetry analysis. Specifically, we construct a second-order differential master equation for arbitrary scalar field potential by assuming that the spectral indices for the density perturbations [Formula: see text] and the scalar-to-tensor ratio [Formula: see text] are related as [Formula: see text]. Function [Formula: see text] is classified according to the admitted Lie symmetries for the master equation. The possible admitted Lie symmetries form the [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] Lie algebras. The new inflationary solution is recovered by the Lie symmetries of the [Formula: see text] algebra. Scalar field potential is derived explicitly, while we compare the resulting spectral indices with the observations.

Ricci-like Solitons with Arbitrary Potential and Gradient Almost Ricci-like Solitons on Sasaki-like Almost Contact B-metric Manifolds

Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. A manifold of this type can be considered as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. The soliton under study is characterized and proved that its Ricci tensor is equal to the vertical component of both B-metrics multiplied by a constant. Thus, the scalar curvatures with respect to both B-metrics are equal and constant. In the 3-dimensional case, it is found that the special sectional curvatures with respect to the structure are constant. Gradient almost Ricci-like solitons on Sasaki-like almost contact B-metric manifolds have been proved to have constant soliton coefficients. Explicit examples are provided of Lie groups as manifolds of dimensions 3 and 5 equipped with the structures under study.

Smart: A program to automatically compute accelerations and variational equations

Modern astronomical potentials modelling galaxies or stellar systems can be rather involved, and deriving their first derivatives (accelerations) and second derivatives (variational equations) in order to compute orbits and their chaoticity may be a formidable task. We present here a fully automated routine, dubbed Smart, with which the accelerations and the variational equations of an arbitrary potential that has been written in the Fortran 77 language can be computed. Almost any Fortran 77 statement is admitted in the potential, and the output are standard Fortran 77 routines ready to use. We validate our algorithm with a set of potentials including time-dependent, velocity-dependent and very complex potentials that even involve auxiliary routines. We also describe with some detail a realistic seven-component Galactic potential, MilkyWayHydra, which yields very involved derivatives, thus being a good test bed for Smart.

Quasi-symmetry protected topology in a semi-metal.

The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we call 'quasi-symmetry'. This is the situation where a Hamiltonian has an exact symmetry at lower-order that is broken by higher-order perturbation terms. This enforces finite but parametrically small gaps at some low-symmetry points in momentum space. Untethered from the restraints of symmetry, quasi-symmetries eliminate the need for fine-tuning as they enforce that sources of large Berry curvature will occur at arbitrary chemical potentials. We demonstrate that a quasi-symmetry in the semi-metal CoSi stabilizes gaps below 2 meV over a large near-degenerate plane that can be measured in the quantum oscillation spectrum. The application of in-plane strain breaks the crystal symmetry and gaps the degenerate point, observable by new magnetic breakdown orbits. The quasi-symmetry, however, does not depend on spatial symmetries and hence transmission remains fully coherent. These results demonstrate a class of topological materials with increased resilience to perturbations such as strain-induced crystalline symmetry breaking, which may lead to robust topological applications as well as unexpected topology beyond the usual space group classifications.

Electrophoresis of a highly charged fluid droplet in dilute electrolyte solutions: Analytical Hückel-type solution.

An analytical formula is presented here for the electrophoresis of a dielectric or perfectly conducting fluid droplet with arbitrary surface potentials suspended in a very dilute electrolyte solution. In other words, when the Debye length (κ-1 ) is very large, or κa 1, where κ is the electrolyte strength and a stands for the droplet radius. This formula can be regarded as an extension of the famous Hückel solution valid for weakly charged rigid particles to arbitrarily charged fluid droplets. The formula reduces successfully to the ones obtained by Booth for a dielectric droplet, and Ohshima for a perfectly conducting droplet, both under Debye-Hückel approximation valid for weakly charged droplets. Moreover, the formula is valid for a gas bubble and a rigid solid particle as well. Classic results obtained by Hückel for a rigid particle are reproduced as well. We found that for a dielectric droplet, the more viscous the droplet is, the faster it moves regardless of its surface potential, contrary to the intuition based on the purely hydrodynamic consideration. For a perfectly conducting liquid droplet, on the other hand, the situation is reversed: The less viscous the droplet is, the faster it moves. The presence or absence of the spinning electric driving force tangent to the droplet surface is found to be responsible for it. As a result, an axisymmetric exterior vortex flow surrounding the droplet is always present for a dielectric liquid droplet, and never there for a conducting liquid droplet.

Schrödinger operators on Lie groups with purely discrete spectrum

On a Lie group G, we investigate the discreteness of the spectrum of Schrödinger operators of the form L+V, where L is a subelliptic sub-Laplacian on G and the potential V is a locally integrable function which is bounded from below. We prove general necessary and sufficient conditions for arbitrary potentials, and we obtain explicit characterizations when V is a polynomial on G or belongs to a local Muckenhoupt class. We finally discuss how to transfer our results to weighted sub-Laplacians on G.

Programmable particles patterning by multifrequency excitation radiation force of acoustic resonance modes

Acoustic radiation force has been extensively investigated to trap and spatially manipulate particles into various patterns. Existing acoustical methods for particles manipulation are developed by designing the acoustic structures or modulating the transducers arrays. These patterns and trajectories manipulation of particles have been limited to nodal lines by the prefabricated acoustic structures. Additionally, the acoustic potential field is limited by the wavelength due to the excitation of narrow frequency band, which is only suitable for local trapping and translation of particles. It is challenging to accomplish various programmable particles patterning by acoustic radiation force. In this work, we theoretically and numerically investigate the mechanisms for multifrequency excitation radiation force of acoustic resonance modes. The acoustic potential field can be programmed to arbitrary functional distributions by simultaneously exciting multiple resonance modes. Thus, we propose the programmable algorithm for arbitrary acoustic radiation potential, particles are trapped at the minima, forming a wide variety of patterns. Further, the selective manipulation of particles is realized by the programmable localized maximum of the acoustic radiation potential. Finally, the temporally modulated patterns of particles are achieved through modulating the positions of the localized maximum of acoustic radiation potential. This work paves the way for manipulation of arbitrary functional acoustic potential field, thereby opening up the realm of programmable particles patterning.

Para-Ricci-like Solitons with Arbitrary Potential on Para-Sasaki-like Riemannian Π-Manifolds

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian Π-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of both metrics. Thus, the corresponding scalar curvatures of both considered metrics are equal and constant. An explicit example of the Lie group as the manifold under study is presented.

Neural network approaches for solving Schr\xf6dinger equation in arbitrary quantum wells

In this work we approach the Schrödinger equation in quantum wells with arbitrary potentials, using the machine learning technique. Two neural networks with different architectures are proposed and trained using a set of potentials, energies, and wave functions previously generated with the classical finite element method. Three accuracy indicators have been proposed for testing the estimates given by the neural networks. The networks are trained by the gradient descent method and the training validation is done with respect to a large training data set. The two networks are then tested for two different potential data sets and the results are compared. Several cases with analytical potential have also been solved.