Showing papers on "Dispersion relation published in 2019"

Magnon Spintronics : Fundamentals of Magnon-Based Computing

Abstract: This chapter addresses a selection of fundamental topics that form the basis of the magnon-based computing and are of primary importance for the further development of theconcept. It examines the transport of spin-wave-carried information in one and two dimensions that is required for the realization of logic elements and integrated magnon circuits is covered. The chapter discusses the converters between spin waves and electron currents. It provides a basic knowledge of spin waves in the most commonly used structure, a spin-wave waveguide in the form of a narrow strip. The main spin-wave characteristics can be obtained from the analysis of its dispersion relation, that is, the dependence of the wave frequency on its wavenumber k. Spin waves are usually studied in nanometer-thick and micrometer-wide waveguides and, several additional factors, which define spin-wave properties, should be considered. The fabrication of high-quality spin-wave waveguides in the form of magnetic strips is also one of the primary tasks in the field of magnonics.

Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides.

Abstract: Spin waves are investigated in yttrium iron garnet waveguides with a thickness of 39 nm and widths ranging down to 50 nm, i.e., with an aspect ratio thickness over width approaching unity, using Brillouin light scattering spectroscopy. The experimental results are verified by a semianalytical theory and micromagnetic simulations. A critical width is found, below which the exchange interaction suppresses the dipolar pinning phenomenon. This changes the quantization criterion for the spin-wave eigenmodes and results in a pronounced modification of the spin-wave characteristics. The presented semianalytical theory allows for the calculation of spin-wave mode profiles and dispersion relations in nanostructures.

Convergence of the Gradient Expansion in Hydrodynamics.

Abstract: Hydrodynamic excitations corresponding to sound and shear modes in fluids are characterized by gapless dispersion relations. In the hydrodynamic gradient expansion, their frequencies are represented by power series in spatial momenta. We investigate the analytic structure and convergence properties of the hydrodynamic series by studying the associated spectral curve in the space of complexified frequency and complexified spatial momentum. For the strongly coupled $\mathcal{N}=4$ supersymmetric Yang-Mills plasma, we use the holographic duality methods to demonstrate that the derivative expansions have finite nonzero radii of convergence. Obstruction to the convergence of hydrodynamic series arises from level crossings in the quasinormal spectrum at complex momenta.

Dispersion relation of the fast neutrino oscillation wave

Abstract: A dense neutrino medium can support flavor oscillation waves which are coherent among different momentum modes of the neutrinos. The dispersion relation (DR) branches of such a wave with complex frequencies and/or wave numbers can lead to the exponential growth of the wave amplitude which in turn will engender a collective flavor transformation in the neutrino medium. In this work, we propose that the complex DR branches of the neutrino oscillation wave should be bound by the critical points of the DR. We demonstrate how this theory can be applied to the neutrino medium with an (approximate) axial symmetry about the propagation direction of the neutrino oscillation wave. We also show how the flavor instabilities in this medium can be identified by tracing the critical points of the DR as the electron lepton number distribution of the neutrino medium is changed continuously.

Three-dimensional Simulations of Massive Stars. I. Wave Generation and Propagation

Abstract: We present the first three-dimensional (3D), hydrodynamic simulations of the core convection zone (CZ) and extended radiative zone spanning from 1% to 90% of the stellar radius of an intermediate mass (3 $\mathrm{M}_\odot$) star. This allows us to self-consistently follow the generation of internal gravity waves (IGWs) at the convective boundary and their propagation to the surface. We find that convection in the core is dominated by plumes. The frequency spectrum in the CZ and that of IGW generation is a double power law as seen in previous two-dimensional (2D) simulations. The spectrum is significantly flatter than theoretical predictions using excitation through Reynolds stresses induced by convective eddies alone. It is compatible with excitation through plume penetration. An empirically determined distribution of plume frequencies generally matches the one necessary to explain a large part of the observed spectrum. We observe waves propagating in the radiation zone and excited standing modes, which can be identified as gravity and fundamental modes. They show similar frequencies and node patterns to those predicted by the stellar oscillation code GYRE. The continuous part of the spectrum fulfills the IGW dispersion relation. A spectrum of tangential velocity and temperature fluctuations close to the surface is extracted, which are directly related to observable brightness variations in stars. Unlike 2D simulations we do not see the high frequencies associated with wave breaking, likely because these 3D simulations are more heavily damped.

Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals

Abstract: Anisotropic crystals have recently attracted considerable attention because of their ability to support polaritons with a variety of unique properties, such as hyperbolic dispersion, negative phase velocity, or extreme confinement. Particularly, the biaxial crystal $\ensuremath{\alpha}\ensuremath{-}{\mathrm{MoO}}_{3}$ has been demonstrated to support phonon polaritons, light coupled to lattice vibrations, with in-plane anisotropic propagation and unusually long lifetime. However, the lack of theoretical studies on electromagnetic modes in biaxial crystal slabs impedes a complete interpretation of the experimental data, as well as an efficient design of nanostructures supporting such highly anisotropic polaritons. Here, we derive the dispersion relation of electromagnetic modes in biaxial slabs surrounded by semi-infinite isotropic dielectric half-spaces with arbitrary dielectric permittivities. Apart from a general dispersion relation, we provide very simple analytical expressions in typical experiments in nano-optics: the limits of short polaritonic wavelength and/or very thin slabs. The results of our study will allow for an in-depth analysis of anisotropic polaritons in novel biaxial van der Waals materials.

Diffusion and universal relaxation of holographic phonons

Abstract: In phases where translations are spontaneously broken, new gapless degrees of freedom appear in the low energy spectrum (the phonons). At long wavelengths, they couple to small fluctuations of the conserved densities of the system. This mixing is captured by new diffusive transport coefficients, as well as qualitatively different collective modes, such as shear sound modes. We use Gauge/Gravity duality to model such phases and analytically compute the corresponding diffusivities in terms of data of the dual background black hole solution. In holographic quantum critical low temperature phases, we show that these diffusivities are governed by universal relaxation of the phonons into the heat current when the dynamical critical exponent z > 2. Finally, we compute the spectrum of transverse collective modes and show that their dispersion relation matches the dispersion relation of the shear sound modes of the hydrodynamic theory of crystalline solids.

Hydrodynamics of broken global symmetries in the bulk.

Abstract: We consider holographic theories at finite temperature in which a continuous global symmetry in the bulk is spontaneously broken. We study the linear response of operators in a regime which is dual to time dependent, long wavelength deformations of solutions generated by the symmetry. By computing the boundary theory retarded Green’s function we show the existence of a gapless mode with a diffusive dispersion relation. The diffusive character of the mode is compatible with the absence of a conserved charge from the field theory point of view. We give an analytic expression for the corresponding diffusion constant in terms of thermodynamic data and a new transport coefficient σb which is fixed by the black hole horizon data. After adding a perturbative source on the boundary, we compute the resulting gap δωg as a simple function of σb and of data of the thermal state.

Measuring the Berry phase of graphene from wavefront dislocations in Friedel oscillations

Abstract: Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore crucial for technological applications. Although the spectral distribution in energy bands is routinely measured by various techniques1, it is more difficult to access the topological properties of band structures such as the quantized Berry phase, γ, which is a gauge-invariant geometrical phase accumulated by the wavefunction along an adiabatic cycle2. In graphene, the quantized Berry phase γ = π accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect4,5. It is usually thought that measuring the Berry phase requires the application of external electromagnetic fields to force the charged particles along closed trajectories3. Contradicting this belief, here we demonstrate that the Berry phase of graphene can be measured in the absence of any external magnetic field. We observe edge dislocations in oscillations of the charge density ρ (Friedel oscillations) that are formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry6 in describing these topological defects as phase singularities of complex fields, we show that the number of additional wavefronts in the dislocation is a real-space measure of the Berry phase of graphene. Because the electronic dispersion relation can also be determined from Friedel oscillations7, our study establishes the charge density as a powerful observable with which to determine both the dispersion relation and topological properties of wavefunctions. This could have profound consequences for the study of the band-structure topology of relativistic and gapped phases in solids. The Berry phase of graphene is measured in the absence of an applied magnetic field by observing dislocations in the Friedel oscillations formed at a hydrogen atom adsorbed on graphene.

Low frequency propagating shear waves in holographic liquids

Abstract: Recently, it has been realized that liquids are able to support solid-like transverse modes with an interesting gap in momentum space developing in the dispersion relation. We show that this gap is also present in simple holographic bottom-up models, and it is strikingly similar to the gap in liquids in several respects. Firstly, the appropriately defined relaxation time in the holographic models decreases with temperature in the same way. More importantly, the holographic k-gap increases with temperature and with the inverse of the relaxation time. Our results suggest that the Maxwell-Frenkel approach to liquids, involving the additivity of liquid hydrodynamic and solid-like elastic responses, can be applicable to a much wider class of physical systems and effects than thought previously, including relativistic models and strongly-coupled quantum field theories. More precisely, the dispersion relation of the propagating shear waves is in perfect agreement with the Maxwell-Frenkel approach. On the contrary the relaxation time appearing in the holographic models considered does not match the Maxwell prediction in terms of the shear viscosity and the instantaneous elastic modulus but it shares the same temperature dependence.

Dispersion relations for γ ∗ γ ∗ → ππ: helicity amplitudes, subtractions, and anomalous thresholds

Abstract: We present a comprehensive analysis of the dispersion relations for the doubly-virtual process γ∗γ∗ → ππ. Starting from the Bardeen-Tung-Tarrach amplitudes, we first derive the kernel functions that define the system of Roy-Steiner equations for the partial-wave helicity amplitudes. We then formulate the solution of these partial-wave dispersion relations in terms of Omnes functions, with special attention paid to the role of subtraction constants as critical for the application to hadronic light-by-light scattering. In particular, we explain for the first time why for some amplitudes the standard Muskhelishvili-Omnes solution applies, while for others a modified approach based on their left-hand cut is required unless subtractions are introduced. In the doubly-virtual case, the analytic structure of the vector-resonance partial waves then gives rise to anomalous thresholds, even for space-like virtualities. We develop a strategy to account for these effects in the numerical solution, illustrated in terms of the D-waves in γ∗γ∗ → ππ, which allows us to predict the doubly-virtual responses of the f2(1270) resonance. In general, our results form the basis for the incorporation of two-meson intermediate states into hadronic light-by-light scattering beyond the S-wave contribution.

Holographic plasmon relaxation with and without broken translations

Abstract: We study the dynamics and the relaxation of bulk plasmons in strongly coupled and quantum critical systems using the holographic framework. We analyze the dispersion relation of the plasmonic modes in detail for an illustrative class of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we entangle the complicated interplay between the three least damped modes and shed light on the underlying physical processes. Such as the dependence of the plasma frequency and the effective relaxation time in terms of the electromagnetic coupling, the charge and the temperature of the system. Introducing momentum dissipation, we then identify its additional contribution to the damping. Finally, we consider the spontaneous symmetry breaking (SSB) of translational invariance. Upon dialing the strength of the SSB, we observe an increase of the longitudinal sound speed controlled by the elastic moduli and a decrease in the plasma frequency of the gapped plasmon. We comment on the condensed matter interpretation of this mechanism.

Engineering terahertz surface magnon-polaritons in hyperbolic antiferromagnets

Abstract: Magnetic crystals were recently studied as a route to hyperbolic dispersion and the effects associated with it. These studies, however, concentrated on bulk waves and frequencies where transmission is possible and where negative refraction occurs. Here, in contrast, we concentrate on geometries which sample regions of the dispersion relations where bulk propagation is not possible. This is done by controlling the orientation of the uniaxial anisotropy axis with respect to the surface of the crystal. Furthermore, we find that new magnetic surface polaritons exist in these regions, and we investigate the nature of these waves. In addition, significant tunability can be introduced by applying an external field perpendicular to the easy axes of a uniaxial antiferromagnet, creating a canted structure and generally shifting the frequencies to higher values. This externally applied field dramatically changes the nature of both surface and bulk polaritons, making them highly nonreciprocal.

Detection of Rossby Waves in the Sun using Normal-mode Coupling

Abstract: Rossby waves play a fundamental role in angular momentum processes in rotating fluids. In addition to the potential to shed light on physical mechanisms operating in the solar convection zone, the recent detection of Rossby waves in the Sun (Loptien et al. 2018; Liang et al. 2018) also serves as a means of comparison between different helioseismic methods. Time-distance helioseismology, ring-diagram analysis and other techniques have all proven successful in recovering the Rossby-wave dispersion relation from analyses of Helioseismic and Magnetic Imager data (HMI; Schou et al. 2012). In this article, we demonstrate that analyses of two years of HMI global-mode-oscillation data using the technique of normal-mode coupling also show signatures of Rossby waves. In addition to providing an independent means of inferring Rossby waves, this detection lends credence to the methodology of mode coupling and encourages a more complete exploration of its possibilities.

Band gap and experimental study in phononic crystals with super-cell structure

Abstract: The phononic crystals (PCs) have the wide application prospects in the field of regulating sound waves and vibration reduction due to their unique band gaps (BGs) characteristics. In this paper, a new phononic crystal of which the super-cell is composed of a simple combination of traditional PCs is proposed to open BGs in low frequency range. The dispersion relations, displacement fields of eigenmodes and transmission spectra are obtained by the finite element method. Both theoretical and experimental results verify that the improved PCs obtained low-frequency BGs range from 153 Hz to 196 Hz, which is generated by the rigid body resonance. The effect of the geometrical parameters and shapes on the dispersion relations are further analysed and discussed. Finally, the experimental transmission spectrum of the improved PCs is presented by a hammer test. This study might provide theoretical and practical support to the design of PCs components in the field of low-frequency vibration reduction.

Analysis of different boundary types on wave velocity in bedded piezo-structure with flexoelectric effect

Abstract: This research article manifests the influence of mechanically and dielectrically conducting interface on the characteristics of surface wave transmission in a piezo-structure with flexoelectric effect at the nanoscale level. The considered model consists a piezoelectric (Lithium Niobate (LiNbO3)) layer resting on piezoelectric (lead zirconate titanate (PZT-5H)) half-space. The imperfect interface includes mechanically compliment and dielectrically weakly conducting interface, mechanically compliment and dielectrically highly conducting interface, mechanically debond interface and dielectrically insulating interface. Complex dispersion relations are obtained analytically in determinant form corresponding to electrically open and short circuit cases. A numerical example has been provided to highlight the influences of different affecting parameters (like layer thickness, flexoelectric parameter, degree of dielectric and mechanically imperfect interface) on the phase velocity curve. Salient outcomes of the present study have been shown graphically.

Horizon constraints on holographic Green's functions

Abstract: We explore a new class of general properties of thermal holographic Green's functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green's functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these `pole-skipping' points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green's function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales $\omega\sim T$ are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved $U(1)$ current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of pole-skipping points as real wavenumber is increased. We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems.

Nonlinear dynamics of a spin-orbit-coupled Bose-Einstein condensate

Abstract: Single-particle dynamics of a spin-orbit-coupled Bose-Einstein condensate has recently been investigated in experiments that explore the physics of Landau-Zener tunneling and of the Zitterbewegung. In this paper, we study the influence of a nonlinearity due to interactions on these dynamics and show that the dispersion relation develops interesting loop structures. The atoms can move along the nonlinear dispersion curve in the presence of a weak acceleration force, and we show that the loops lead to straightforward nonlinear Landau-Zener tunneling. However, we find that for the Zitterbewegung, induced by a sudden quench in the spin-orbit-coupling parameters, the nonlinear dispersion is irrelevant.

Modulational instability in a full‐dispersion shallow water model

Abstract: We propose a shallow water model which combines the dispersion relation of water waves and the Boussinesq equations, and which extends the Whitham equation to permit bidirectional propagation. We establish that its sufficiently small, periodic wave train is spectrally unstable to long wavelength perturbations, provided that the wave number is greater than a critical value, like the Benjamin-Feir instability of a Stokes wave. We verify that the asso- ciated linear operator possesses infinitely many collisions of purely imaginary eigenvalues, but they do not contribute to instability away from the origin in the spectral plane to the leading order in the amplitude parameter. We discuss the effects of surface tension on the modulational instability. The results agree with those from formal asymptotic expansions and numerical computations for the physical problem.

Diffusion and universal relaxation of holographic phonons

Abstract: In phases where translations are spontaneously broken, new gapless degrees of freedom appear in the low energy spectrum (the phonons). At long wavelengths, they couple to small fluctuations of the conserved densities of the system. This mixing is captured by new diffusive transport coefficients, as well as qualitatively different collective modes, such as shear sound modes. We use Gauge/Gravity duality to model such phases and analytically compute the corresponding diffusivities in terms of data {of the dual background black hole solution}. In holographic quantum critical low temperature phases, we show that these diffusivities are governed by universal relaxation of the phonons into the heat current when the dynamical critical exponent $z>2$. Finally, we compute the spectrum of transverse collective modes and show that their dispersion relation matches the dispersion relation of the shear sound modes of the hydrodynamic theory of crystalline solids.

Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases.

Abstract: We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors. At zero temperature, we analytically continue the equation on the collective mode energy in Anderson's Random Phase Approximation or Gaussian fluctuations through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. The branch exists as long as the chemical potential μ is positive and the wave number below sqrt[2mμ]/ℏ (with m the fermion mass). In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically for an arbitrary interaction strength.

Cauchy formalism for Lamb waves in functionally graded plates

Abstract: Propagation of harmonic Lamb waves in plates made of functionally graded materials with transverse inhomogeneity is analyzed by applying Cauchy six-dimensional formalism previously developed for the study of Lamb wave propagation in homogeneous or stratified anisotropic plates. For anisotropic plates with arbitrary transverse inhomogeneity a closed form implicit solution for the dispersion equation is derived and analyzed.