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At least 181 records · Page 10

From the Great Wave of Translation to the Force between Quarks

Here, the chance observation of a novel traveling wave in a canal led over time to the formulation of a nonlinear wave equation—the Korteweg–de Vries equation—that describes strikingly robust disturbances now called solitons. The figure of an isolated soliton corresponds to a reflectionless potential that supports a single bound state in the one-dimensional Schrödinger equation. An appropriate combination of individual solitons yields a symmetric reflectionless potential that supports multiple bound states. Thus, the KdV equation opens the path to solving the inverse scattering problem for a collection of bound states. Applied to the quarkonium spectra, this formalism allows the construction of reflectionless approximations to the confining potentials that account for the force between quarks, and to tests of the flavor-independence of the interquark interaction.

Inverse Scattering↗

Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity

Here, the damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter $\kappa$ is analyzed, when the external force is periodic in space and given by $\mathcal{f(x) = r}$ cos(Kx), both numerically and in a variational approximation using five collective coordinates (time dependent shape parameters of the wave function). Our variational approximation satisfies exactly the low-order moment equations. Because of competition between the spatial period of the external force λ = 2π/K , and the soliton width $l_s$, which is a function of the nonlinearity $\kappa$ as well as the initial frequency ω 0 of the solitary wave, there is a transition (at fixed ω 0 ) from trapped to unbound behavior of the soliton, which depends on the parameters $\mathcal{r}$ and K of the external force and the nonlinearity parameter $\kappa$. We previously studied this phenomena when $\kappa$ = 1 where we showed that for λ $\gg l_s$ the soliton oscillates in an effective potential, while forλ $\ll l_s$ it moves uniformly as a free particle. In this paper we focus on the $\kappa$ dependence of the transition from oscillatory to particle behavior and explicitly compare the curves of the transition regime found in the collective coordinate approximation as a function of $\mathcal{r}$ and K when $\kappa$ = 1/2,1,2 at fixed value of the frequency ω 0 . Since the solitary wave gets narrower for fixed ω 0 as a function of $\kappa$, we expect and indeed find that the regime where the solitary wave is trapped is extended as we increase $\kappa$.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

An attractive model: simulating fuzzy dark matter with attractive self-interactions

ABSTRACT Fuzzy dark matter (FDM), comprised of ultralight ($m \sim 10^{-22}\,{\rm eV}$) boson particles, has received significant attention as a viable alternative to cold dark matter (CDM), as it approximates CDM on large scales (${\gtrsim}1$ Mpc) while potentially resolving some of its small-scale problems via kiloparsec-scale quantum interference. However, the most basic FDM model, with one free parameter (the boson mass), is subject to a tension: small boson masses yield the desired cores of dwarf galaxies but underpredict structure in the Lyman-α forest, while large boson masses render FDM effectively identical to CDM. This Catch-22 problem may be alleviated by considering an axion-like particle with attractive particle self-interactions. We simulate an idealized FDM halo with self-interactions parametrized by an energy decay constant $f \sim 10^{15}~\rm {GeV}$ related to the axion symmetry-breaking conjectured to solve the strong-CP problem in particle physics. We observe solitons, a hallmark of FDM, condensing within a broader halo envelope, and find that the density profile and soliton mass depend on self-interaction strength. We propose generalized formulae to extend those from previous works to include self-interactions. We also investigate a critical mass threshold predicted for strong interactions at which the soliton collapses into a compact, unresolved state. We find that the collapse happens quickly, and its effects are initially contained to the central region of the halo.

Painter, Connor A. (ORCID:0000000235314806)↗

Experimental observation of linear and nonlinear ion acoustic phenomena in a cylindrical geometry

Ion acoustic phenomena are studied in a cylindrical geometry for two distinct cases. A large amplitude compressive pulse is seen to evolve into solitons. The evolution of these solitons and their dependence on initial conditions show a similarity to previous work on one dimensional solitons. Dimensionless scaling arguments are used to distinguish the two cases. In the presence of a steady state uniform cylindrical beam, approximated by a ring in V sub r, V sub phi, an ion-ion beam instability is observed. This instability exists for a limited range of beam velocities and shows a marked similarity to the strictly one dimensional ion-ion beam instability. Solution of the appropriate dispersion relation shows agreement with the observed phenomenon.

Romesser, T. E.↗

Inhomogeneities in the early universe

The paper investigates certain nonlinear processes that are viable candidates for the mechanisms which produced large-scale inhomogeneities in the early Universe. Several nonlinear Lagrangians are presented for matter, the Korteweg-de Vries equation is analyzed, and the existence of solitons among its solutions is noted. A model based on the possibility of generating a cascade of solitons from an initial perturbation is proposed, and it is shown how large-scale inhomogeneities can be generated when an initial soliton fragments into many others through the nonlinear action of the terms in the Korteweg-de Vries equation. A second model is examined which is based on the interaction of matter with a strong radiation field (an almost monochromatic photon gas) and which involves changes in the refractive index of the vacuum. It is found that matter and radiation will not mix if the radiation field has a nonuniform intensity and that the matter will separate into dense portions or 'cosmological protogalaxies'. The evolution of these portions of matter is studied, and it is found that conditions would be appropriate for the interface between them and the surrounding radiation field to become unstable, giving rise to a turbulent layer.

Canuto, V.↗

On the production and interaction of planetary solitary waves - Applications to the Jovian atmosphere

Further evidence is presented that strengthens the case for the interpretation of many features in the Jovian atmosphere as solitary Rossby waves (solitons). These include: a mechanism whereby such waves can evolve from the instability of the basic shear flows; further interpretation of the interaction between observed features, and comparison with calculations of the interaction between planetary solitons of a restricted class; and calculations of soliton morphology for a type of shear flow other than the type considered originally by Maxworthy and Redekopp (1976).

Maxworthy, T.↗

Numerical comparison of strong Langmuir turbulence models

Two models of Langmuir turbulence, the nonlinear Schroedinger equation and the Zakharov equations, are solved numerically for an initial value problem in which the electric field evolves from an almost flat initial condition via the modulational instability and finally saturates into a set of solitons. The two models agree well with each other only when the initial dimensionless electric field has an amplitude less than unity. An analytic soliton gas model consisting of equal-amplitude, randomly spaced, zero-speed solitons is remarkably good at reproducing the time-averaged Fourier spectra in both cases.

Shen, Mei-Mei↗

Application of the sine-Poisson equation in solar magnetostatics

Solutions of the sine-Poisson equations are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model (j) is directed along the x-axis, where x is the horizontal ignorable coordinate; (j) varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. Solutions for the magnetostatic potential A corresponding to the one-soliton, two-soliton, and breather solutions of the sine-Gordon equation are studied. Depending on the values of the free parameters in the soliton solutions, horizontally periodic magnetostatic structures are obtained possessing either a single X-type neutral point, multiple neural X-points, or solutions without X-points.

Webb, G. M.↗

Evolution of Nonlinear Internal Waves in China Seas

Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.

Liu, Antony K.↗

High precision computing with charge domain devices and a pseudo-spectral method therefor

The present invention enhances the bit resolution of a CCD/CID MVM processor by storing each bit of each matrix element as a separate CCD charge packet. The bits of each input vector are separately multiplied by each bit of each matrix element in massive parallelism and the resulting products are combined appropriately to synthesize the correct product. In another aspect of the invention, such arrays are employed in a pseudo-spectral method of the invention, in which partial differential equations are solved by expressing each derivative analytically as matrices, and the state function is updated at each computation cycle by multiplying it by the matrices. The matrices are treated as synaptic arrays of a neural network and the state function vector elements are treated as neurons. In a further aspect of the invention, moving target detection is performed by driving the soliton equation with a vector of detector outputs. The neural architecture consists of two synaptic arrays corresponding to the two differential terms of the soliton-equation and an adder connected to the output thereof and to the output of the detector array to drive the soliton equation.

Barhen, Jacob↗

Testing multiflavored ULDM models with SPARC

We perform maximum likelihood estimates (MLEs) for single and double flavor ultralight dark matter (ULDM) models using the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. These estimates are compared to MLEs for several commonly used cold dark matter (CDM) models. By comparing various CDM models we find, in agreement with previous studies, that the Burkert and Einasto models tend to perform better than other commonly used CDM models. We focus on comparisons between the Einasto and ULDM models and analyze cases for which the ULDM particle masses are: free to vary; and fixed. For each of these analyses, we perform fits assuming the soliton and halo profiles are: summed together; and matched at a given radius. When we let the particle masses vary, we find a negligible preference for any particular range of particle masses, within $10^{-25}\,\text{eV}\leq m\leq10^{-19}\,\text{eV}$, when assuming the summed models. For the matched models, however, we find that almost all galaxies prefer particles masses in the range $10^{-23}\,\text{eV}\lesssim m\lesssim10^{-20}\,\text{eV}$. For both double flavor models we find that most galaxies prefer approximately equal particle masses. We find that the summed models give much larger variances with respect to the soliton-halo (SH) relation than the matched models. When the particle masses are fixed, the matched models give median and mean soliton and halo values that fall within the SH relation bounds, for most masses scanned. When the particle masses are fixed in the fitting procedure, we find the best fit results for the particle mass $m=10^{-20.5}\,\text{eV}$ (for the single flavor models) and $m_1=10^{-20.5}\,\text{eV}$, $m_2=10^{-20.2}\,\text{eV}$ for the double flavor, matched model. We discuss how our study will be furthered using a reinforcement learning algorithm.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Application of neural networks to determine the discrete spectrum of the direct Zakharov – Shabat problem

A neural network architecture is proposed to determine the number of solitons generated by random processes in optical wavelength-division multiplexed telecommunication systems with QPSK, 16-QAM, 64-QAM, and 1024-QAM modulation. The dependence of the prediction quality of a neural network with a special architecture on the number of soliton modes in the signal and the parameters of this signal is studied. (paper)

97 MATHEMATICS AND COMPUTING↗

Mechanics of a ferromagnetic domain wall

Abstract This paper gives a pedagogical introduction to the mechanics of ferromagnetic solitons. We start with the dynamics of a single spin and develop all the tools required for the description of the dynamics of solitons in a ferromagnet.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Singularities in nearly uniform one-dimensional condensates due to quantum diffusion

Dissipative systems often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to k 2 (k being the wavevector) and vanishing at long wavelengths as k→0. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly uniform condensate—a dispersive analog to the Kardar-Parisi-Zhang equation—which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

74 ATOMIC AND MOLECULAR PHYSICS↗

Bicrystallography-informed Frenkel–Kontorova model for interlayer dislocations in strained 2D heterostructures

In recent years, van der Waals (vdW) heterostructures and homostructures, which consist of stacks of two-dimensional (2D) materials, have risen to prominence due to their association with exotic quantum phenomena originating from correlated electronic states harbored by them. Atomistic scale relaxation effects play an extremely important role in the electronic scale quantum physics of these systems, providing means of manipulation of these materials and allowing them to be tailored for emergent technologies. We investigate such structural relaxation effects in this work using atomistic and mesoscale models, within the context of twisted bilayer graphene — a well-known heterostructure system that features moiré patterns arising from the lattices of the two graphene layers. For small twist angles, atomic relaxation effects in this system are associated with the natural emergence of interface dislocations or strain solitons, which result from the cyclic nature of the generalized stacking fault energy (GSFE), that measures the interface energy based on the relative movement of the two layers. Here, in this work, we first demonstrate using atomistic simulations that atomic reconstruction in bilayer graphene under a large twist also results from interface dislocations, although the Burgers vectors of such dislocations are considerably smaller than those observed in small-twist systems. To reveal the translational invariance of the heterointerface responsible for the formation of such dislocations, we derive the translational symmetry of the GSFE of a 2D heterostructure using the notions of coincident site lattices (CSLs) and displacement shift complete lattices (DSCLs). The workhorse for this exercise is a recently developed Smith normal form bicrystallography framework. Next, we construct a bicrystallography-informed and frame-invariant Frenkel–Kontorova model, which can predict the formation of strain solitons in arbitrary 2D heterostructures, and apply it to study a heterostrained, large-twist bilayer graphene system. Our mesoscale model is found to produce results consistent with atomistic simulations. We anticipate that the model will be invaluable in predicting structural relaxation and for providing insights into various heterostructure systems, especially in cases where the fundamental unit cell is large and therefore, atomistic simulations are computationally expensive.

2D heterostructures↗

Electrically writing a magnetic heliknoton in a chiral magnet

A magnetic heliknoton is the three-dimensional counterpart to the two-dimensional magnetic skyrmion, and serves as a pivotal topological soliton for extending topological magnetism into three dimensions. However, its experimental realization remains elusive. Here we report the controlled nucleation of a magnetic heliknoton in the chiral magnet FeGe at zero magnetic field, achieved through nanoscale current-pulse excitation. By combining angle-dependent quantitative electron holography with micromagnetic simulations, we resolve the three-dimensional spin texture of the heliknoton. In particular, the heliknoton exhibits current-driven collinear motion without the Hall effect. Furthermore, our findings establish a readily accessible experimental platform for further exploration of three-dimensional topological solitons and highlight their potential for practical applications.

Magnetic properties and materials↗

Liquid crystal torons in Poiseuille-like flows

Three-dimensional (3D) simulations of the structure of liquid crystal (LC) torons, topologically protected distortions of the LC director field, under material flows are rare but essential in microfluidic applications. Here, we show that torons adopt a steady-state configuration at low flow velocity before disintegrating at higher velocities, in line with experimental results. Furthermore, we show that under partial slip conditions at the boundaries, the flow induces a reversible elongation of the torons, also consistent with the experimental observations. These results are in contrast with previous simulation results for 2D skyrmions under similar flow conditions, highlighting the need for a 3D description of this LC soliton in relation to its coupling to the material flow. These findings pave the way for future studies of other topological solitons, like hopfions and heliknotons, in flowing soft matter systems.

Science & Technology - Other Topics↗

The 2020 Skyrmionics Roadmap

The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purpose- design broad-band spin dynamic and logic devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗