Showing papers on "Dispersion relation published in 2020"

Dispersion tuning and route reconfiguration of acoustic waves in valley topological phononic crystals.

Abstract: The valley degree of freedom in crystals offers great potential for manipulating classical waves, however, few studies have investigated valley states with complex wavenumbers, valley states in graded systems, or dispersion tuning for valley states. Here, we present tunable valley phononic crystals (PCs) composed of hybrid channel-cavity cells with three tunable parameters. Our PCs support valley states and Dirac cones with complex wavenumbers. They can be configured to form chirped valley PCs in which edge modes are slowed to zero group velocity states, where the energy at different frequencies accumulates at different designated locations. They enable multiple functionalities, including tuning of dispersion relations for valley states, robust routing of surface acoustic waves, and spatial modulation of group velocities. This work may spark future investigations of topological states with complex wavenumbers in other classical systems, further study of topological states in graded materials, and the development of acoustic devices. The valley degree of freedom gives additional flexibility to tunable phononic and photonic crystals. Here, the authors realise a honeycomb phononic structure where both the size of the cavities and of the air channel can be actively tuned, allowing several functionalities in a broad frequency range.

A Conformal Dispersion Relation: Correlations from Absorption

Abstract: We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its “absorptive part”, defined as a double discontinuity, times a theory-independent kernel which we compute explicitly. The kernel is found by resumming the data obtained by the Lorentzian inversion formula. For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios. We perform various checks of the dispersion relation (generalized free fields, holographic theories at tree-level, 3D Ising model), and get perfect matching. Finally, we derive an integral relation that relates the “inverted” conformal block with the ordinary conformal block.

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Abstract: We investigate non-Hermitian elastic lattices characterized by non-local feedback control interactions. In one-dimensional lattices, we show that the proportional control interactions produce complex dispersion relations characterized by gain and loss in opposite propagation directions. Depending on the non-local nature of the control interactions, the resulting non-reciprocity occurs in multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is also investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional dependent wave amplification. Moreover, the non-Hermitian skin effect manifests as modes localized at the boundaries of finite lattice strips, whose combined effect in two directions leads to the presence of bulk modes localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and open new possibilities for the design of metamaterials with novel functionalities related to selective wave filtering, amplification and localization. The results also suggest that feedback interactions may be a useful strategy to investigate topological phases of non-Hermitian systems.

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 ω ∼ 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.

A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation.

Abstract: The description of strong interaction physics of low-lying resonances is out of the valid range of perturbative QCD. Chiral effective field theories have been developed to tackle the issue. Partial wave dynamics is the systematic tool to decode the underlying physics and reveal the properties of those resonances. It is extremely powerful and helpful for our understanding of the non-perturbative regime, especially when dispersion techniques are utilized simultaneously. Recently, plenty of exotic/ordinary hadrons have been reported by experiment collaborations, e.g. LHCb, Belle, and BESIII, etc.. In this review, we summarize the recent progress on the applications of partial wave dynamics combined with chiral effective field theories and dispersion relations, on related topics, with emphasis on $\pi\pi$, $\pi K$, $\pi N$ and $\bar{K}N$ scatterings.

Quasinormal modes in charged fluids at complex momentum

Abstract: We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordstrom black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics.

Differential Sensor Based on Electroinductive Wave Transmission Lines for Dielectric Constant Measurements and Defect Detection

Abstract: A differential-mode sensor based on a pair of electroinductive wave transmission lines (EIW-TLs) is proposed in this article. The EIW-TLs are implemented by etching a chain of complementary split-ring resonators (CSRRs) in a metallic plate. Such metallic plate acts as the ground plane of the microstrip (access) lines, necessary for feeding each EIW-TL and collecting the transmitted power at the output ports. The working principle of the sensor is mode conversion, caused when the EIW-TLs are asymmetrically loaded. Thus, one of the lines is loaded with the reference (REF) sample, whereas the other one is loaded with the sample under test (SUT). If both samples are identical and the pair of EIW-TLs is fed by a common-mode signal, a pure common-mode signal is collected at the differential output port. Conversely, mode conversion arises when the lines are unequally loaded, due to the different propagation characteristics (particularly the phase velocity) of the lines. Due to the typical dispersion relation of the EIW-TLs, with strong variation in the phase velocity (or phase constant) with frequency, the structure is very sensitive to dielectric constant differences between the REF and SUT samples. Thus, the proposed structure is useful for the accurate measurement of dielectric constants (sensor functionality) and the detection of tiny differences between the REF and SUT samples (comparator functionality).

Revisiting longitudinal plasmon-axion conversion in external magnetic fields

Abstract: In the presence of an external magnetic field, the axion and the photon mix. In particular, the dispersion relation of a longitudinal plasmon always crosses the dispersion relation of the axion (fo ...

Magnetophonons & type-B Goldstones from hydrodynamics to holography

Abstract: We perform a detailed analysis of a large class of effective holographic models with broken translations at finite charge density and magnetic field. We exhaustively discuss the dispersion relations of the hydrodynamic modes at zero magnetic field and successfully match them to the predictions from charged hydrodynamics. At finite magnetic field, we identify the presence of an expected type-B Goldstone boson Re[ω] ∼ k2, known as magnetophonon and its gapped partner — the magnetoplasmon. We discuss their properties in relation to the effective field theory and hydrodynamics expectations. Finally, we compute the optical conductivities and the quasinormal modes at finite magnetic field. We observe that the pinning frequency of the magneto-resonance peak increases with the magnetic field, in agreement with experimental data on certain 2D materials, revealing the quantum nature of the holographic pinning mechanism.

Active control for acoustic wave propagation in nonlinear diatomic acoustic metamaterials

Abstract: Wave propagation through nonlinear acoustic metamaterials has generated numerous scientific interests for their enormous potential in practical applications these years. This study focuses on the effects of nonlinearity on the band properties of diatomic mass-in-mass chain with active control. By applying the Lindestedt–Poincare (L–P) perturbation method, analytical dispersion relations of the linear and nonlinear diatomic mass-in-mass system have been established and investigated by numerical simulation. Different from the monatomic mass-in-mass chain, this two mass-in-mass units forming a unit cell of the periodic structure results in four branches of the dispersion relation. The effects of nonlinearity on the band gaps of the system have been exhaustively illustrated. By only tuning the nonlinear constitutive relation parameter of the spring, the fourth branch and the third gap are found to be more sensitive compared to the other branches and gaps. It is concluded that closing and re-opening of the band-folding-induced gap in this nonlinear system is still possible. Here, a piezoelectric spring model is applied to the diatomic mass-in-mass to make the system available for wider applications. With the negative proportional control, a new stop band is generated which can be also captured in the monatomic nonlinear system. The new results here will help better analyze the band gap properties in nonlinear mechanical metamaterials and emphasize the great potentials of the topological analysis of such a nonlinear local resonance system that induces band-folding-induced band gaps.

On the wave dispersion in microstructured solids

Abstract: In this paper, elastic wave propagation in a one-dimensional micromorphic medium characterized by two internal variables is investigated. The evolution equations are deduced following two different approaches, namely using: (i) the balance of linear momentum and the Clausius–Duhem inequality, and (ii) an assumed Lagrangian functional (including a gyroscopic coupling) together with a variational principle. The dispersion relation is obtained and the possibility of the emerging band gaps is shown in such microstructured materials. Some numerical simulations are also performed in order to highlight the dispersive nature of the material under study.

Spectro-spatial analyses of a nonlinear metamaterial with multiple nonlinear local resonators

Abstract: Recent focus has been given to spectro-spatial analysis of nonlinear metamaterials since they can predict interesting nonlinear phenomena not accessible by spectral analysis (i.e., dispersion relations). However, current studies are limited to a nonlinear chain with single linear resonator or linear chain with nonlinear resonator. There is no work that examines the combination of nonlinear chain with nonlinear resonators. This paper investigates the spectro-spatial properties of wave propagation through a nonlinear metamaterials consisting of nonlinear chain with multiple nonlinear local resonators. Different combinations of softening and hardening nonlinearities are examined to reveal their impact on the traveling wave features and the band structure. The method of multiple scales is used to obtain closed-form expressions for the dispersion relations. Our analytical solution is validated via the numerical simulation and results from the literature. The numerical simulation is based on spectro-spatial analysis using signal processing techniques such as spatial spectrogram, wave filtering, and contour plots of 2D Fourier transform. The spectro-spatial analysis provides a detailed information about wave distortion due to nonlinearity and classify the distortion into different features. The observations suggest that nonlinear chain with multiple nonlinear resonators can affect the waveform at all wavelength limits. Such nonlinear metamaterials are suitable for broadband vibration control and energy harvesting, as well as other applications such as acoustic switches, diodes, and rectifiers, allowing wave propagation only in a pre-defined direction.

A primary model of THz and far-infrared signal generation and conduction in neuron systems based on the hypothesis of the ordered phase of water molecules on the neuron surface I: signal characteristics

Abstract: In this paper, we use the theory of quantum optics and electrodynamics to study the electromagnetic field problem in the nervous system based on the assumption of an ordered arrangement of water molecules on the neuronal surface. Using the Lagrangian of the water molecule-field ion, the dynamic equations for neural signal generation and transmission are derived. Perturbation theory and the numerical method are used to solve the dynamic equations, and the characteristics of high-frequency signals (the dispersion relation, the time domain of the field, the frequency domain waveform, etc.) are discussed. This model predicts some intrinsic vibration modes of electromagnetic radiation on the neuronal surface. The frequency range of these vibration modes is in the THz and far-infrared ranges.

Multiband Hypersound Filtering in Two-Dimensional Colloidal Crystals: Adhesion, Resonances, and Periodicity.

Abstract: The hypersonic phonon propagation in large-area two-dimensional colloidal crystals is probed by spontaneous micro Brillouin light scattering. The dispersion relation of thermally populated Lamb waves reveals multiband filtering due to three distinct types of acoustic band gaps. We find Bragg gaps accompanied by two types of hybridization gaps in both sub- and superwavelength regimes resulting from contact-based resonances and nanoparticle eigenmodes, respectively. The operating GHz frequencies can be tuned by particle size and depend on the adhesion at the contact interfaces. The experimental dispersion relations are well represented by a finite element method model enabling identification of observed modes. The presented approach also allows for contactless study of the contact stiffness of submicrometer particles, which reveals size effect deviating from macroscopic predictions.

Dispersion Relation for CFT Four-Point Functions

Abstract: We present a dispersion relation in conformal field theory which expresses the four point function as an integral over its single discontinuity. Exploiting the analytic properties of the OPE and crossing symmetry of the correlator, we show that in perturbative settings the correlator depends only on the spectrum of the theory, as well as the OPE coefficients of certain low twist operators, and can be reconstructed unambiguously. In contrast to the Lorentzian inversion formula, the validity of the dispersion relation does not assume Regge behavior and is not restricted to the exchange of spinning operators. As an application, the correlator 〈ϕϕϕϕ〉 in ϕ4 theory at the Wilson-Fisher fixed point is computed in closed form to order є2 in the E expansion.

Dispersion Engineering With Photonic Inverse Design

Abstract: Dispersion engineering, such as the design of slow light waveguide systems, is an effective tool for a wide range of photonic applications, but presents a difficult optical design challenge. Most applications require a slow light waveguide design that mitigates group velocity dispersion, and efficient coupling solutions over the slow light operating bandwidth. In this work, we optimize the slow light dispersion relation of a photonic crystal waveguide with three dimensional (3D) inverse design methods. In addition, we design mode couplers for the photonic crystal waveguide. The optimized waveguide supports a slow light mode with a group index of $\mathbf {n_g = 25}$ and a normalized bandwidth group index product of $\mathbf {0.38}$ . A compact mode coupler to a strip waveguide is designed with an average efficiency of 92.7% within the slow light operating bandwidth. Lastly, we design a fully etched grating which couples directly to the slow light mode with a 32.5% average efficiency.

Subwavelength and broadband tunable topological interface state for flexural wave in one-dimensional locally resonant phononic crystal

Abstract: The topological interface state for an elastic wave in a one-dimensional system, as reported in the literature, mainly occurs through Bragg scattering, making it difficult to achieve subwavelength wave control and flexible tunability. Here, inspired by the band-folding mechanism, this paper confirms that an interface state can likewise be excited by local resonance. The topological phase transition is accomplished by purposely arranging the locations of local resonators. The system is composed of a uniform thin beam with periodically attached local resonators made from an electrorheological elastomer subjected to adjustable electric fields. By simply doubling the primitive unit cell, the passing bands in the dispersion relation are folded and a folding point falls below the locally resonant bandgap, which can be lifted up by simply tuning the distance between two local resonators to realize a topological phase transition. Furthermore, we demonstrate the dynamic tunability of the working frequency of the topological interface state by using an external electric field to adjust the starting frequency of the local resonance. Since the excited frequency of the interface mode is lower than the resonance frequency, this work overcomes the ineffectiveness of the Bragg topological phononic crystal at low frequencies. Moreover, the use of an electroactive resonator whose parameters are readily tuned also enables the flexible design of a frequency-variable topological system without requiring a geometrical modification of the base structure. This technique may have potential applications, such as vibration isolation or in fabricating a robust waveguide.

Geometric Control of Collective Spontaneous Emission.

Abstract: Dipole spin-wave states of atomic ensembles with wave vector k(ω) mismatched from the dispersion relation of light are difficult to access by far-field excitation but may support rich phenomena beyond the traditional phase-matched scenario in quantum optics. We propose and demonstrate an optical technique to efficiently access these states. In particular, subnanosecond laser pulses shaped by a home-developed wideband modulation method are applied to shift the spin wave in k space with state-dependent geometric phase patterning, in an error-resilient fashion and on timescales much faster than spontaneous emission. We verify this control through the redirection, switch off, and recall of collectively enhanced emission from a ^{87}Rb gas with ∼75% single-step efficiency. Our work represents a first step toward efficient control of electric dipole spin waves for studying many-body dissipative dynamics of excited gases, as well as for numerous quantum optical applications.

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Abstract: We investigate non-Hermitian elastic lattices characterized by non-local feedback control interactions. In one-dimensional lattices, we show that the proportional control interactions produce complex dispersion relations characterized by gain and loss in opposite propagation directions. Depending on the non-local nature of the control interactions, the resulting non-reciprocity occurs in multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is also investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional dependent wave amplification. Moreover, the non-Hermitian skin effect manifests as modes localized at the boundaries of finite lattice strips, whose combined effect in two directions leads to the presence of bulk modes localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and open new possibilities for the design of metamaterials with novel functionalities related to selective wave filtering, amplification and localization. The results also suggest that feedback interactions may be a useful strategy to investigate topological phases of non-Hermitian systems.

Novel analytical model of anisotropic multi-layer cylindrical waveguides incorporating graphene layers

Abstract: We propose a novel analytical model for anisotropic multi-layer cylindrical structures containing graphene layers. The general structure is formed by the aperiodic repetition of a three-layer sub-structure, where a graphene layer with isotropic surface conductivity of σ is sandwiched between two adjacent magnetic materials. Each anisotropic material has permittivity and permeability tensors of e and μ , respectively. An external magnetic bias is applied in the axial direction. The general matrix representation is obtained for our proposed analytical model to determine the dispersion relation. The relation is used to find the effective index of the structure and its other propagation parameters. Two special exemplary structures are introduced and employed to illustrate the richness of the proposed general structure in terms of the related specific plasmonic wave phenomena and effects. Several simulations were conducted to demonstrate the notable wave-guiding properties of the structure in the 10–40 THz band. Very good agreement was obtained between the analytical and simulation results. The proposed structure can be utilized to design novel plasmonic devices, such as absorbers, modulators, plasmonic sensors, and tunable antennas in the THz frequencies.

Derivation of the homogeneous kinetic wave equation: longer time scales

Abstract: We consider the nonlinear Schrodinger equation set on a flat torus, in the regime which is conjectured to lead to the kinetic wave equation; in particular, the data are random, and spread up to high frequency in a weakly nonlinear regime We pursue the investigations of our previous paper, and show that, in the case where the torus is the standard one, only the scaling considered there allows convergence of the Dyson series up to the kinetic time scale We also show that, for generic quadratic dispersion relations (non rectangular tori), the Dyson series converges on significantly longer time scales; we are able to reach the kinetic time up to an arbitrarily small polynomial error for a larger set of scalings These results show the importance of the exact structure of the dispersion relation, more specifically of equidistribution properties of some bilinear quantities akin to pair correlations derived from it