Symmetric Dispersion Research Articles

Reconfigurable spin-wave properties in two-dimensional magnonic crystals formed of diamond and triangular shaped nanomagnets

Two-dimensional ferromagnetic nanodot structures exhibit intriguing magnetization dynamics and hold promise for future magnonic devices. In this study, we present a comparative experimental investigation into the reconfigurable magnetization dynamics of non-ellipsoidal diamond and triangular-shaped nanodot structures, employing broadband ferromagnetic resonance spectroscopy. Our findings reveal substantial variations in the spin wave (SW) spectra of these structures under different bias field strengths (H) and angles (φ). Notably, the diamond nanodot structure exhibits a variation from nearly symmetric W-shaped dispersion to a skewed dispersion and subsequent transition to a discontinuous dispersion with subtle variation in bias field angle. On the other hand, in the triangular nanodot array a SW mode anti-crossing appears at φ = 15° which is starkly modified with the increase in φ to 30°. By analyzing the static magnetic configurations, we unveil the nature of the SW spectra in these two shapes. We reinforce our observations with simulated spatial power and phase maps. This study underscores the critical impact of dot shape and inversion symmetry on SW dynamical response, highlighting the significance of selecting appropriate structures and bias field strength and orientation for required functionalities. The remarkable tunability demonstrated by the magnonic crystals underscores their potential suitability for future magnonic devices.

Field Theory Expansions of String Theory Amplitudes.

Motivated by quantum field theory (QFT) considerations, we present new representations of the Euler-Beta function and tree-level string theory amplitudes using a new two-channel, local, crossing symmetric dispersion relation. Unlike standard series representations, the new ones are analytic everywhere except at the poles, sum over poles in all channels, and include contact interactions, in the spirit of QFT. This enables us to consider mass-level truncation, which preserves all the features of the original amplitudes. By starting with such expansions for generalized Euler-Beta functions and demanding QFT-like features, we single out the open superstring amplitude. We demonstrate the difficulty in deforming away from the string amplitude and show that a class of such deformations can be potentially interesting when there is level truncation. Our considerations also lead to new QFT-inspired, parametric representations of the Zeta function and π, which show fast convergence.

Bootstrapping high-energy observables

In this paper, we set up the numerical S-matrix bootstrap by using the crossing symmetric dispersion relation (CSDR) to write down Roy equations for the partial waves. As a motivation behind examining the local version of the CSDR, we derive a new crossing symmetric, 3-channels-plus-contact-terms representation of the Virasoro-Shapiro amplitude in string theory that converges everywhere except at the poles. We then focus on gapped theories and give novel analytic and semi-analytic derivations of several bounds on low-energy data. We examine the high-energy behaviour of the experimentally measurable rho-parameter, introduced by Khuri and Kinoshita and defined as the ratio of the real to the imaginary part of the amplitude in the forward limit. Contrary to expectations, we find numerical evidence that there could be multiple changes in the sign of this ratio before it asymptotes at high energies. We compare our approach with other existing numerical methods and find agreement, with improvement in convergence.

Modal displacement analyses of Lamb waves in micro/nano-plates based on the consistent couple stress theory

In micro-scale structures, the influence of scale effects on the mechanical properties cannot be ignored, and the continuum mechanics theory cannot effectively describe guided wave propagation. This paper studies modal displacements in an isotropic micro/nano-scale plate — an essential factor for the mode selection of Lamb waves in non-destructive testing technology. To achieve this, the consistent couple stress theory, which additionally accounts for the impact of scale effects on wave propagation, has to be employed. A mathematical derivation method with singular value decomposition is proposed, and the excitation amplitude is computed by applying a normal stress source to evaluate the in-plane and out-of-plane displacements. The results indicate that the in-plane displacement vanishes on the plate surface for anti-symmetric modes when the phase velocity equals the velocity of shear waves. Moreover, the intersections of symmetric and anti-symmetric dispersion curves identify specific frequencies at which the out-of-plane displacement vanishes on the free surface. These findings highlight the difference in modal displacement characteristics between micro-scale and macro-scale structures. The results from this study may furnish theoretical guidance for ultrasonic non-destructive testing of microstructures.

Kinetic gases in static spherically symmetric modified dispersion relations

We study the dynamics of a collisionless kinetic gas in the most general static, spherically symmetric dispersion relation. For a static, spherically symmetric kinetic gas, we derive the most general solution to these dynamics, and find that any solution is given by a one-particle distribution function which depends on three variables. For two particular solutions, describing a shell of monoenergetic orbiting particles and a purely radial inflow, we calculate the particle density as a function of the radial coordinate. As a particular example, we study a κ-Poincaré modification of the Schwarzschild metric dispersion relation and derive its influence on the particle density. Our results provide a possible route towards quantum gravity phenomenology via the observation of matter dynamics in the vicinity of massive compact objects.

Nonlocal effective medium theory for phononic temporal metamaterials

We have developed a nonlocal effective medium theory (EMT) for phononic temporal metamaterials using the multiscale technique. Our EMT yields closed-form expressions for effective constitutive parameters and reveals these materials as reciprocal media with symmetric band dispersion. Even without spatial symmetry breaking, nonzero Willis coupling coefficients emerge with time modulation and broken time-reversal symmetry, when the nonlocal effect is taken into account. Compared to the local EMT, our nonlocal version is more accurate for calculating the bulk band at high wavenumbers and essential for understanding nonlocal effects at temporal boundaries. This nonlocal EMT can be a valuable tool for studying and designing phononic temporal metamaterials beyond the long-wavelength limit.

Symmetrically dispersion-engineered microcombs

Normal-dispersion microcombs have gained significant attention for their features, including high conversion efficiency, deterministic generation, and thermal management-free operation. However, most of the demonstrated microcombs in the normal-dispersion regime heavily rely on asymmetric local dispersion anomalies, which introduce odd-order dispersion components and originate asymmetric spectral characteristics. In this study, we present a scheme that employs two symmetrically positioned local dispersion alterations on either side of the pump mode. This configuration enables direct mode-locked microcombs, referred to as ‘dark pulses’ or ‘platicons’, while preserving spectral symmetry. The platicon microcombs exhibit efficient conversion, spectral symmetry, and can be generated with high repeatability. Furthermore, we demonstrate the deterministic generation of perfect platicon crystals with highly symmetric spectra by precisely controlling the position of the two symmetric dispersion alterations relative to the pump mode. Our proposed method offers a reliable approach for achieving power-efficient microcombs with highly symmetric spectra, and can be transferred to other integrated nonlinear platforms.

AI-algorithm-assisted 895-nm praseodymium laser emitting sub-100-fs pulses.

Praseodymium (Pr) lasers have achieved outstanding pico- and sub-picosecond pulsations covering the near-infrared (NIR) and visible spectral range in recent years. However, it has been a stagnant task for more than two decades to leapfrog into the sub-100 femtosecond (fs) regime as the Pr gain bandwidths are too narrow for their major transition lines. Although the wide tunability at the NIR bands in the Pr:YLF crystals has been explored, the spectral tails in these transitions suffer severely from weak gains for mode locking, combined with the intricate dispersion control to achieve transform-limit formation. In this work, we target the Pr:YLF's 895-nm line with a specially designed edge-pass filter to balance the gain bandwidth and transitional strength. By deploying a symmetric dispersion scheme and tuning with the soft actor-critic artificial intelligence (AI) algorithm, we have achieved the pulse duration down to sub-100-fs in a Pr laser for the first time. This work also enriches the AI-assisted methodology for ultrafast solid-state laser realizations.

Asymmetric Directional Control of Thermal Emission.

Control over the directionality of thermal emission plays a fundamental role in efficient heat transport. Although nanophotonic technologies have demonstrated the capability for angular-selective thermal emission, achieving asymmetric directional thermal emission in reciprocal systems with energy directed to a single output angle remains challenging due to symmetric band dispersion. In this work, wepresent a general strategy for achieving asymmetric directional thermal emission in reciprocal systems. With periodic perturbation and broken mirror symmetry, metasurfaces behave as resonant metagratings whose resonances can be diffracted to symmetric output angles with distinct efficiency, allowing for high emissivity towards a single direction. The asymmetric directional thermal emitter is experimentally demonstrated at mid-infrared wavelengths with high emissivity (ε = 0.61) at the observation angle of +30°, and low emissivity (ε<0.3) at other angles. This work highlights the potential for manipulating the directionality of thermal emission, which holds promise for developing ultrathin customized thermal sources and impacts on various thermal-engineering applications. This article is protected by copyright. All rights reserved.

Compensation of the Distorted WDM Signals by Symmetric Dispersion Map with Nonuniform Zero-Crossing Place of Accumulated Dispersion in Midway-OPC System

The nonlinear Kerr effect and chromatic dispersion are the fundamental causes of optical signal degradation in single-mode fiber (SMF) and erbium-doped fiber-amplification (EDFA)-based wavelength division multiplexing (WDM) transmission. Dispersion management combined with a midway optical phase conjugator among the technologies for compensating for such optical signal distortion is known to not be limited by the modulation format and multiplexing technology. Optimization of the dispersion map can partially alleviate the capacity and maximum transmission distance limitations of the SMF and EDFA system. In this paper, we propose various types of symmetric dispersion maps in which the position of zero-crossing place of the cumulative dispersion is not constant, and analyze the effect of each dispersion map configuration on 40 Gb/s × 24-channel WDM signal distortion compensation. When designed with the residual dispersion per span (RDPS) around 400 ps/nm, it is confirmed that most of the proposed dispersion maps are more effective in compensating the distorted WDM signal than conventional dispersion map. In particular, we confirm that, among the proposed dispersion maps, the dispersion map in which the RDPS is designed uniformly for all fiber spans can increase the power margin of WDM channel and expand the range of the total residual dispersion in the dispersion-managed link.

A refined quasi-3D isogeometric model for dynamic instability of graphene nanoplatelets-reinforced porous sandwich plates

This study pays attention to the dynamic instability behavior of advanced sandwich plate structures subjected to periodic in-plane compressive loads. By utilizing a powerful and efficient computational approach based on a four-variable refined quasi-3D plate theory and NURBS-based isogeometric analysis (IGA), the dynamic behavior of structures can be accurately evaluated while accounting adequately for the thickness stretching effect of normal deformation. To investigate the dynamic instability behavior, this study examines sandwich plate models that consist of two graphene nanoplatelets (GNPs)-reinforced skin layers and a porous core layer with two typical distributions of internal porosity: uniform and symmetric dispersion. Bolotin's method is applied in this study to solve the Mathieu–Hill equation and obtain the boundary of dynamic instability zones. Numerical examples are performed to examine the influence of various input parameters on the instability regions, as well as to provide new insights into the dynamic instability behavior of advanced sandwich plates under compressive loading which has not been comprehensively studied in the literature. The findings of this study suggest that the thickness stretching effect should be carefully evaluated for moderate to thick plate structures, such as sandwich plates.

A Celestial route to AdS bulk locality

We prove a precise form of AdS bulk locality by deriving analytical two-sided bounds on bulk Wilson coefficients. Our bounds are on the Wilson coefficients themselves, rather than their ratios, as is typically found in the literature. Inspired by the Celestial amplitudes program in flat space, we perform a Celestial transform of the CFT Mellin amplitude of four identical scalars. Using the crossing symmetric dispersion relation (CSDR), we express the resulting amplitude in terms of crossing symmetric conformal partial waves. The partial waves satisy remarkable positivity properties which along with the unitarity of the CFT prove sufficient to derive the bounds. We then employ our methods in the limit of large AdS radius and recover known bounds on flat space Wilson coefficients and new bounds on their large radius corrections. We check that the planar Mellin amplitude of four stress-tensor multiplets in mathcal{N} = 4 SYM satisfies our bounds. Finally, using null constraints, we derive a form of low-spin dominance in AdS EFTs. We find that the low-spin dominance is strongest in flat space and weakens as we move away from flat space towards higher AdS curvature.

Positivity, low twist dominance and CSDR for CFTs

We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly symmetric under the cross-ratios u,vu,v interchange. This representation has several features in common with the CSDR for quantum field theories. It enables a study of the expansion of the correlation function around u=v=1/4u=v=1/4, which is used in the numerical conformal bootstrap program. We elucidate several remarkable features of the dispersive representation using the four point correlation function of \Phi_{1,2}Φ1,2 operators in 2d minimal models as a test-bed. When the dimension of the external scalar operator (\Delta_\sigmaΔσ) is less than \frac{1}{2}12, the CSDR gets contribution from only a single tower of global primary operators with the second tower being projected out. We find that there is a notion of low twist dominance (LTD) which, as a function of \Delta_\sigmaΔσ, is maximized near the 2d Ising model as well as the non-unitary Yang-Lee model. The CSDR and LTD further explain positivity of the Taylor expansion coefficients of the correlation function around the crossing symmetric point and lead to universal predictions for specific ratios of these coefficients. These results carry over to the epsilon expansion in 4-\epsilon4−ϵ dimensions. We also conduct a preliminary investigation of geometric function theory ideas, namely the Bieberbach-Rogosinski bounds.

New economic geography model with natural capital and migration congestion effect

This paper constructs the economic model to consider the economy in cities from the waste management perspective. Specifically, we analyze the link between migration, natural capital, and waste management by applying the new economic geography model. We show the results; the population distribution pattern in the long run varies depending on the congestion effect of natural capital and waste management’s technological level. In particular, a full agglomeration equilibrium realizes in the long run for higher technological levels of waste management (lower congestion effects), an interior asymmetric equilibrium does for intermediate technological levels (intermediate congestion effects), and the symmetric dispersion equilibrium realizes for the lower technological levels (higher congestion effects).

Magnetic structure and spin dynamics of the quasi-two-dimensional antiferromagnet Zn-doped copper pyrovanadate

Magnetic properties of the antiferromagnet Zn$_{0.15}$Cu$_{1.85}$V$_2$O$_7$ (ZnCVO) have been thoroughly investigated on powder and single-crystal samples. The crystal structure determination using powder x-ray and neutron diffraction confirms that ZnCVO with Zn = 0.15 is isostructural with $\beta$-Cu$_{2}$V$_2$O$_7$ ($\beta$-CVO) with small deviation in the lattice parameters. Macroscopic magnetic properties measurements also confirm the similarity between the two compounds. The Cu$^{2+}$ spins were found to align along the crystallographic $c$-axis, antiparallel to their nearest neighbors connected by the leading exchange interaction $J_1$. Spin dynamics reveals a typical symmetric spin-wave dispersion with strong interactions in the $bc$-plane and weak interplane coupling. The exchange interaction analysis indicates that the spin network of ZnCVO is topologically consistent with the previous DFT prediction but the values of leading exchange interactions are contradictory. Furthermore, rather than the predicted 2D honeycomb structure, the spin network in ZnCVO could be better described by the anisotropic 2D spin network composing of $J_1$, $J_5$, and $J_6$ interactions, four bonds per one spin site, coupled by weak interplane interactions.

Dispersion relations, knots polynomials, and the q -deformed harmonic oscillator

We show that the crossing symmetric dispersion relation (CSDR) for 2-2 scattering leads to a fascinating connection with knot polynomials and q-deformed algebras. In particular, the dispersive kernel can be identified naturally in terms of the generating function for the Alexander polynomials corresponding to the torus knot $(2,2n+1)$ arising in knot theory. Certain linear combinations of the low energy expansion coefficients of the amplitude can be bounded in terms of knot invariants. Pion S-matrix bootstrap data respects the analytic bounds so obtained. We correlate the $q$-deformed harmonic oscillator with the CSDR-knot picture. In particular, the scattering amplitude can be thought of as a $q$-averaged thermal two point function involving the $q$-deformed harmonic oscillator. The low temperature expansion coefficients are precisely the $q$-averaged Alexander knot polynomials.

Locality and analyticity of the crossing symmetric dispersion relation

This paper discusses the locality and analyticity of the crossing symmetric dispersion relation (CSDR). Imposing locality constraints on the CSDR gives rise to a local and fully crossing symmetric expansion of scattering amplitudes, dubbed as Feynman block expansion. A general formula is provided for the contact terms that emerge from the expansion. The analyticity domain of the expansion is also derived analogously to the Lehmann-Martin ellipse. Our observation of type-II super-string tree amplitude suggests that the Feynman block expansion has a bigger analyticity domain and better convergence.

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy Wilson coefficients. We consider scattering of photons, gravitons in weakly coupled effective field theories. We provide general expressions for the locality/null constraints. Consideration of the positivity of the absorptive part leads to an interesting connection with the recently conjectured weak low spin dominance. We also construct the crossing symmetric amplitudes and locality constraints for the massive neutral Majorana fermions and parity violating photon and graviton theories. The techniques developed in this paper will be useful for considering numerical S-matrix bootstrap in the future.

Celestial insights into the S-matrix bootstrap

We consider 2-2 scattering in four spacetime dimensions in Celestial variables. Using the crossing symmetric dispersion relation (CSDR), we recast the Celestial amplitudes in terms of crossing symmetric partial waves. These partial waves have spurious singularities in the complex Celestial variable, which need to be removed in local theories. The locality constraints (null constraints) admit closed form expressions, which lead to novel bounds on partial wave moments. These bounds allow us to quantify the degree of low spin dominance(LSD) for scalar theories. We study a new kind of positivity that seems to be present in a wide class of theories. We prove that this positivity arises only in theories with a spin-0 dominance. The crossing symmetric partial waves with spurious singularities removed, dubbed as Feynman blocks, have remarkable properties in the Celestial variable, namely typically realness, in the sense of Geometric Function Theory (GFT). Using GFT techniques we derive non-projective bounds on Wilson coefficients in terms of partial wave moments.

Particle–hole asymmetry and quantum confinement effects on the magneto-optical response of topological insulator thin-films

Intrinsically broken symmetries in the bulk of topological insulators (TIs) are manifested in their surface states. Despite particle–hole asymmetry in TIs, it has often been assumed that their surface states are characterized by a particle–hole symmetric Dirac energy dispersion. In this work, we demonstrate that the effect of particle–hole asymmetry is essential to correctly describe the energy spectrum and the magneto-optical response in TIs thin-films. In thin-films of TIs with a substantial degree of particle–hole symmetry breaking, such as Sb2Te3, the longitudinal optical conductivity displays absorption peaks arising from optical transitions between bulk and surface Landau levels for low photon energies. The transition energies between the bulk and surface Landau levels exhibit clearly discernable signatures from those between surface Landau levels due to their distinct magnetic field dependence. Bulk contributions to the magneto-optical conductivity in a TI thin-film are enhanced via one type of doping while being suppressed by the other. This asymmetric dependence on the type of doping aids in revealing the particle–hole asymmetry in TI thin-films.