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In this study, a method is proposed to systematically generate solutions of the two-dimensional Toda lattice equation in terms of previously known solutions ϕ(x,y) of the two-dimensional Laplace's equation. The solitonic solution of Nakamura's [J. Phys. Soc. Jpn. 52 (1983) 380] is shown to correspond to one particular choice of ϕ(x,y).
Recently a variety of nonlocal integrable systems has been introduced that besides fields located at particular space-time points simultaneously also contain fields that are located at different, but symmetrically related, points. Here we investigate different types of soliton solutions with regard to their stability against linear perturbations obtained for the nonlocal version of the Hirota/nonlinear Schrödinger equation and the so-called Alice and Bob versions of the Korteweg-de Vries and Bousinesq equations. In this work, we encounter different types of scenarios: Solition solutions that are linearly stable or unstable and also solutions that change their stability properties depending on the parameter regime they are in.
The formation of a Raman-induced temporal waveguide is demonstrated by launching short pump and probe pulses inside a photonic crystal fiber. The pump pulse creates a fundamental soliton whose speed changes continuously owing to its deceleration through the Raman-induced red shift of its spectrum. The spectrum of the probe pulse is blue-shifted to ensure that the two pulses move at the same speed and follow the same trajectory over the entire length of the fiber. Furthermore, the output wavelengths of the pump and probe pulses depend on the peak power of input pump pulses and their measured values agree with the predictions based on the dispersion data. Numerical modeling also shows good agreement with the experimental results.
Based on the nontrivial topology of buckled antimonene, we propose two conceptual device designs based on breaking the inversion symmetry which can be achieved by gating. The first one is a quantized topological switch obtained by breaking the degeneracy of the fractionalized charge conducting edge states, inducing a metal-insulator transition. In the second one, using local gating with different polarity in different areas, a domain wall is created at their interface, which hosts a soliton type electronic gap state in which transport could be accessed by doping and shown to be robust over a wide range of disorder.
We investigate the condensation time of self-interacting axionlike particles in a gravitational well, extending the prior work which showed that the Wigner formalism is a good analytic approach to describe a condensing scalar field. In the present work, we use this formalism to affirm that $\phi$4 self-interactions will take longer than necessary to support the time scales associated with structure formation, making gravity a necessary part of the process to bring axion dark matter into a solitonic form. Here we show that when the axions’ virial velocity is taken into account, the time scale associated with self-interactions will scale as λ2. This is consistent with recent numerical estimates, and it confirms that the Wigner formalism described in prior work is a helpful analytic framework to check computational work for potential numerical artifacts.
Here, we compute the gravitational form factor D(t) of various nuclei in the generalized Skyrme model where nuclei are described as solitonic field configurations each with a definite baryon number B. We separately discuss the cases B = 1 (nucleons), B = 2 (deuteron), B = 3 (helium-3 and tritium), and extrapolate to larger B-values. Configurations with B > 1 are in general not spherically symmetric, and we demonstrate how group theory helps to extract the form factor. Numerical results are presented for the configurations with B = 1, 2, 3, 4, 5, 6, 7, 8, 32, 108. We find that the B-dependence is consistent with a power-law D(0) ∝ B β with β = 1.7–1.8. Other gravitational form factors can be calculated in the same framework, and we show the result for the J(t) form factor associated with the angular momentum for the B = 3 solution.
Hopfions, three-dimensional topological solitons characterized by nontrivial Hopf indices, represent a fundamental class of field configurations that emerge across diverse areas of physics. Despite extensive studies of isolated hopfions, a framework for constructing spatially ordered arrays of hopfions, i.e., hopfion crystals, has been lacking. Here, we present a systematic approach for generating hopfion crystals with cubic symmetry by combining the Hopf map with rational mapping techniques. By superposing helical waves in ℝ 4 , we construct hopfion crystals with tunable Hopf indices and controllable topology. We demonstrate simple cubic, face-centered cubic, and body-centered cubic hopfion crystals and extend our framework to create crystals of more complex topological structures, including axially symmetric tori, torus links, and torus knots with higher Hopf indices. Our results provide a foundation for searching hopfions in real materials and studying their collective phenomena.
The rotation velocity curves of stars in galaxies, the motions of pairs of galaxies, and the behavior of galaxies in clusters and super-clusters all indicate that there is a lack of mass on different scales in the universe. In this paper, we derive the expression for rotational velocity using the nonlinear density wave theory considering only stellar components and we show that such theory can support the observed flat rotational velocity curve due to the main property of the soliton wave, which is a constant group velocity of the wave. The surface mass density (SMD) function, used to derive gravitational potential gradient and rotational velocity, is not assumed but rather derived as a solution of the nonlinear Srödinger equation, on the contrary to the widely used, in the literature, exponential disk approximation. Three parameters relevant to the curve shape are the intensities of equilibrium SMD, the amplitude of the wave, and total angular velocity or differential rotation, equivalently. Since the shape of the rotational velocity is highly sensitive to the mentioned parameters, this theory eventually provides a method for a very accurate estimation of galaxy mass and angular velocity as well.
Topological solitary fields, such as magnetic and polar skyrmions, are envisioned to revolutionize microelectronics. These configurations have been stabilized in solid-state materials with a global inversion symmetry breaking, which translates in magnetic materials into a vector spin exchange known as the Dzyaloshinskii-Moriya interaction (DMI), as well as spin chirality selection and isotropic solitons. This work reports experimental evidence of 3D chiral spin textures, such as helical spins and skyrmions with different chirality and topological charge, stabilized in amorphous Fe-Ge thick films. Overall, these results demonstrate that structurally and chemically disordered materials with a random DMI can resemble inversion symmetry broken systems with similar magnetic properties, moments, and states. Disordered systems are distinguished from systems with global inversion symmetry breaking by their degenerate spin chirality that allows for forming isotropic and anisotropic topological spin textures at remanence, while offering greater flexibility in materials synthesis, voltage, and strain manipulation.
Topological solitary fields, such as magnetic and polar skyrmions, are envisioned to revolutionize microelectronics. These configurations have been stabilized in solid-state materials with a global inversion symmetry breaking, which translates in magnetic materials into a vector spin exchange known as the Dzyaloshinskii–Moriya interaction (DMI), as well as spin chirality selection and isotropic solitons. This work reports experimental evidence of 3D chiral spin textures, such as helical spins and skyrmions with different chirality and topological charge, stabilized in amorphous Fe–Ge thick films. These results demonstrate that structurally and chemically disordered materials with a random DMI can resemble inversion symmetry broken systems with similar magnetic properties, moments, and states. In conclusion, disordered systems are distinguished from systems with global inversion symmetry breaking by their degenerate spin chirality that allows for forming isotropic and anisotropic topological spin textures at remanence, while offering greater flexibility in materials synthesis, voltage, and strain manipulation.
Topological spin configurations, such as soliton-like spin texture and Dirac electron assemblies, have recently emerged in fundamental science and technology. Achieving stable topological spin textures at room temperature is crucial for their use as long-range information carriers. However, their creation and manipulation are hindered by multi-step field training and competing interactions. Thus, a spontaneous ground state for multidimensional topological spin textures is desirable, with skyrmions forming swirling, hedgehog-like spin structures in two dimensions and hopfions as their twisted 3D counterparts. Here, the first observation of robust and reproducible topological spin textures of hopfions and skyrmions observed at room temperature and in zero magnetic field is reported, which are stabilized by geometric confinement and protected by interfacial magnetism in a ferromagnet/topological insulator/ferromagnet trilayer heterostructure. These skyrmion-hopfion configurations are directly observed at room temperature with Lorenz transmission electron microscopy. Using micromagnetic modeling, the experimental observations of hopfion-skyrmion assemblies are reproduced. This model reveals a complete picture of how spontaneously organized skyrmion lattices encircled by hopfion rings are controlled by surface electrons, uniaxial anisotropy, and Dzyaloshinskii-Moriya interaction. This study provides evidence that topological chiral spin textures can facilitate the development of magnetic topological carriers, paving the way for ultralow-power and high-density information processing.
Janus transition metal dichalcogenides are an emerging class of atomically thin materials with engineered broken mirror symmetry that gives rise to long‐lived dipolar excitons, Rashba splitting, and topologically protected solitons. They hold great promise as a versatile nonlinear optical platform due to their broadband harmonic generation tunability, ease of integration on photonic structures, and nonlinearities beyond the basal crystal plane. Here, second and third harmonic generation in MoSSe and WSSe Janus monolayers is studied. Polarization‐resolved spectroscopy is used to map the full second‐order susceptibility tensor of MoSSe, including its out‐of‐plane components. In addition, the effective third‐order susceptibility and the second‐order nonlinear dispersion close to exciton resonances for both MoSSe and WSSe are measured at room and cryogenic temperatures. This work sets a bedrock for understanding the nonlinear optical properties of Janus transition metal dichalcogenides and probing their use in the next‐generation on‐chip multifaceted photonic devices.
The class of chiral-polar magnets has recently captured significant interest in scientific study due to their intriguing physical phenomena. Among all the chiral-polar magnets, Ni 2 InSbO 6 stands out because of its unique attributes, such as the emergence of the topological chiral soliton lattice in the presence of an external magnetic field perpendicular to the chiral-polar axis. However, the magnetic structure of Ni 2 InSbO 6 at zero field has not been well understood yet. This work presents an analysis including polarized optical microscopy and polarized neutron diffraction on a carefully chosen Ni 2 InSbO 6 crystal. Here, results confirm the predominance of a single chiral-polar domain within the crystal and indicate the likelihood of cycloidal magnetic ordering under zero magnetic field, alongside the observation of net magnetic helicity. The existence of both a dominant chiral-polar domain and a dominant cycloidal magnetic domain within Ni 2 InSbO 6 provides an excellent platform for further exploration of its unconventional physical attributes.
We show that interactions between axion-like particles (ALPs) and co-dimension one defects, such as phase-transition bubble walls and solitonic domain walls, can lead to important changes in the evolution of both walls and ALPs. The leading effect arises from the change in the ALP decay constant across the interface, which naturally follows from shift-symmetric interactions with the corresponding order parameter. Specifically, we show that for thin walls moving relativistically, an ALP background — such as e.g. axion dark matter — gives rise to a frictional force on the interface that is proportional to γ 2 , with γ the Lorentz factor of the wall, and that this effect is present in both the oscillating and frozen axion regimes. We explore the broader consequences of this effect for bubble and domain walls in the early universe, and show that this source of friction can be present even in the absent of a conventional medium such as radiation or matter. Possible implications include modifications to the dynamics of bubble and domain walls and their corresponding gravitational wave signatures, as well as the generation of a dark radiation component of ALPs in the form of ultra-relativistic ‘axion shells’ with Lorentz factor γ shell ≃ 2γ 2 ≫ 1 that may remain relativistic until the present day.
Massive scalar fields provide excellent dark matter candidates, whose dynamics are often explored analytically and numerically using nonrelativistic Schrödinger-Poisson (SP) equations in a cosmological context. In this paper, starting from the nonlinear and fully relativistic Klein-Gordon-Einstein (KGE) equations in an expanding universe, we provide a systematic framework for deriving the SP equations, as well as relativistic corrections to them, by integrating out ‘fast modes’ and including nonlinear metric and matter contributions. We provide explicit equations for the leading-order relativistic corrections, which provide insight into deviations from the SP equations as the system approaches the relativistic regime. Upon including the leading-order corrections, our equations are applicable beyond the domain of validity of the SP system, and are simpler to use than the full KGE case in some contexts. As a concrete application, we calculate the mass-radius relationship of solitons in scalar dark matter and accurately capture the deviations of this relationship from the SP system towards the KGE one.
Abstract Microstrata are the non-extremal analogues of superstrata: they are smooth, non-extremal (non-BPS) solitonic solutions to IIB supergravity whose deep-throat limits approximate black holes. Using perturbation theory and numerical methods, we construct families of solutions using a consistent truncation to three-dimensional supergravity. The most general families presented here involve two continuous parameters, or amplitudes, and four quantized parameters that set the angular momenta and energy levels. Our solutions are asymptotic to the vacuum of the D1-D5 system: AdS 3 ×S 3 × 𝕋 4 . Using holography, we show that the they are dual to multi-particle states in the D1-D5 CFT involving a large number of mutually non-BPS supergravitons and we determine the anomalous dimensions of these states from the binding energies in supergravity. These binding energies are uniformly negative and depend non-linearly on the amplitudes of the states. In one family of solutions, smoothness restricts some of the fields to lie on a special locus of the parameter space. Using precision holography we show that this special locus can be identified with the multi-particle states constructed via the standard OPE of the single-particle constituents. Our numerical analysis shows that microstrata are robust at large amplitudes and the solutions can be obtained to very high precision.
This paper introduces an explicit material point method designed specifically for simulating the micropolar continuum dynamics in the finite deformation and finite microrotation regime. The material point method enables us to simulate large deformation problems while circumventing the potential mesh distortion without remeshing. To eliminate rotational motion damping and loss of angular momentum during the projection, we introduce the mapping for microinertia and angular momentum between particles and grids through the affine particle-in-cell approach. The microrotation and the curvature at each particle are updated through zero-order forward integration of the microgyration and its spatial gradient. We show that the microinertia and the angular momentum are conserved during the projections between particles and grids in our formulation. We verify the formulation and implementation by comparing with the analytical dispersion relation of micropolar waves under the small strain and small microrotation, as well as the analytical soliton solution for solids undergoing large deformation and large microrotation. Additionally we also demonstrate the capacity of the proposed computational framework to handle a wide spectrum of simulations that exhibit size effects in the geometrical nonlinear regime through three representative numerical examples, i.e., a cantilever beam torsion problem, a fragment-impact penetration problem, and a micropolar fluid discharging problem.
The generalized parton distributions for transitions between baryon states with different masses have a forward limit in which they behave as parton densities (light-front momentum transfer Δ + , Δ T = 0, energy transfer Δ - ≠ 0). These "transition parton densities" can realize spin/isospin quantum numbers not accessible in the ground-state nucleon. The N → Δ transition gives rise to a new parton density proportional to the 1/2 → 3/2 spin transition tensor. Its properties are derived, and its magnitude is estimated in the chiral quark-soliton model based on the large-N c limit of QCD.