Perturbation Of Symmetry Research Articles

All-dielectric ellipsoidal tetramer metasurface sensor with multi-resonances from the bound states in the continuum.

We demonstrate an all-dielectric tetramer metasurface that achieves high-precision refractive index sensing through the excitation of toroidal dipole, magnetic dipole, and electric quadrupole modes, driven by bound states in the continuum (BIC). The metasurface exhibits exceptional performance, with a quality factor of 4.65 × 104, a sensitivity parameter of 649 nm/RIU, and a figure of merit of 1.51 × 104 RIU-1, achieved by optimizing symmetry and lattice perturbations in periodic silicon tetramer ellipsoidal nanodisks on a SiO2 substrate. Additionally, the sensor effectively distinguishes analytes with extinction coefficient differences as small as 0.01 through enhanced broadband absorption. This innovation demonstrates substantial potential for label-free sensing applications in microfluidic chip integration.

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.

Electronic Band Structure of Heavy Fermion Compound Cecoge2

The following article provides a thorough examination of the electronic band structure observed in heavy fermion compounds, which are a type of material that has received considerable interest within the realm of condensed matter physics. The compounds under consideration exhibit significantly high charge carrier masses, which give rise to intriguing electronic phenomena when subjected to low temperatures. Through the analysis of electronic band structures, valuable insights can be obtained regarding the distinctive characteristics displayed by these captivating materials. The research centers on the distinctive attributes and theoretical frameworks employed to elucidate the electronic properties of the subjects under investigation. In this study, we present an introduction to heavy fermions and their experimental manifestations, including the observation of enhanced specific heat and low-temperature resistivity. The present study delves into the theoretical examination of the Kondo effect, which involves the emergence of heavy quasi-particles resulting from the hybridization process between localized f-electrons and conduction electrons. This paper examines the utilization of band structure calculations and various spectroscopic techniques, including angle-resolved photoemission spectroscopy (ARPES), inelastic neutron scattering, and transport measurements. The experimental results demonstrate the presence of hybridization gaps, the characteristics of the Fermi surface topology, and the occurrence of spin fluctuations. This study investigates the effects of crystal symmetry, spin-orbit coupling, and external perturbations on the electronic band structure. Specifically, it explores how these factors influence hybridization strength, Fermi surface topology, and quantum phase transitions. The abstract provides a concise overview of the existing knowledge, acknowledges the obstacles encountered, and proposes potential avenues for further investigation. The significance of this research lies in its ability to elucidate the fundamental principles of heavy fermion compounds, as well as explore their potential practical implications.

Metal-organic framework as high-order topological insulator with protected corner modes

The capacity to design and manipulate the chemical characteristics of metal-organic frameworks (MOFs) presents a promising approach for developing functional materials, particularly with regard to their topological properties. Here, based on first-principles calculations, we predict Ni3(C6S6)2 as a two-dimensional (2D) higher-order topological insulator (HOTI) with protected corner modes, which is the first material example of such topological phase in MOFs reported so far. The non-trivial topology of the material is identified by two different classes of bulk topological invariants: the real Chen number induced by spacetime inversion symmetry, and the fractional corner charge induced by rotational symmetry. The presence of corner states can serve as a diagnostic of its nontrivial topology. Moreover, the HOTI natural is demonstrated to be robust against symmetry perturbations and spin-orbit coupling. Inspired by the topological properties of Ni3(C6S6)2, we can explore regulating organic ligands or metal atoms in metal-organic frameworks to realize other 2D HOTIs, thereby expanding the family of 2D HOTIs. Our findings not only broaden the understanding of physical properties of metal-organic materials, but also extend the study of high-order topological insulators to organic platforms.

Bound states at disclinations: an additive rule of real and reciprocal space topology

Focusing on the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model, we propose an additive rule between the real-space topological invariant s of disclinations (related to the Burgers vector B) and the reciprocal-space topological invariant p of bulk wave functions (the vectored Zak phase). The disclination-induced bound states in the 2D SSH model appear only if (s + p/2π) is nonzero modulo the lattice constant. These disclination-bound states are robust against perturbations respecting C4 point group symmetry and other perturbations within an amplitude determined by p. Besides the disclination-bound states, the proposed additive rule also suggests that a half-bound state extends over only half of a sample and a hybrid-bound state, which always have a nonvanishing component of s + p/2π.

Multiple quasibound states in the continuum of permittivity-asymmetric all-dielectric metasurface: Group-theoretical description

Symmetry-protected bound states in the continuum (BICs) allow for high-efficiency light-matter interactions. Multi-channel BICs supported by a single nanophotonic-based device capable of further enriching the trapping and manipulation of light. It is well established that by breaking the in-plane geometrically symmetry, BICs can be transformed into quasi-BICs (qBICs). In this work, we propose and theoretically demonstrate that such optical states can also be accessed in metasurfaces with symmetric geometric parameters by breaking the in-plane symmetry in the permittivity of the comprising materials. We show that multiband qBICs with exquisitely high quality (Q) factors are excited under different polarization light incidence at near-infrared range, where a strong modulation of the optical response can be obtained by a small perturbation of the permittivity symmetry of the system. The group-theoretical methods and the representation theory are used to uncover the physical mechanism of qBICs and their polarization dependence. The full-wave and eigenfrequency simulations confirm the theoretical analysis.The results of near-field distributions and detailed multipole decompositions reveal that these qBICs present different optical characteristics. The polarization-multiplexed all-dielectric metasurfaces with high Q factors have great potential for applications in integrated multi-channel optical devices.

Phase control of localization in the nonlinear two-mode system from harmonic mixing driving: Perturbative analysis and symmetry consideration

In this paper, we present a rigorous analysis of symmetry and underlying physics of the nonlinear two-mode system driven by a harmonic mixing field, by means of multiple scale asymptotic analysis method. The effective description in the framework of the second-order perturbative theory provides an accurate picture for understanding the Floquet eigenspectrum and dynamical features of the nonlinear two-mode system, showing full agreement with the prediction of symmetry considerations. We find that two types of symmetries play significant role in the dynamical features of this model, the mechanism behind which can be interpreted in terms of the effective description. The results are of relevance for the phase control of the atomic localization in Bose–Einstein condensates or switch of the optical signals in nonlinear mediums.

Controlling Tunneling Oscillation and Quantum Localization in an Asymmetric Double-Well Potential: A Bohmian Perspective.

The roles of spatial symmetry and strength of external time-dependent perturbation on the dynamics of a quantum particle, initially localized in one of the wells of an asymmetric double-well potential are studied using the recently developed techniques incorporating quantum theory of motion and time-dependent Fourier grid Hamiltonian methods. The model used here includes a mimic of the related experimental situations which is considered as a perturbation to the static double-well potential. Analysis of localized and delocalized phase space structures and corresponding time-profile of tunneling probability reveal the recipe toward controlling the tunneling oscillations by modulating the parameters of applied perturbation. A study on a stochastic pulsating potential also reveals the root to the quantum localization, even in moderate field strength.

Perturbative Symmetry Approach for Differential–Difference Equations

We propose a new method to tackle the integrability problem for evolutionary differential–difference equations of arbitrary order. It enables us to produce necessary integrability conditions, to determine whether a given equation is integrable or not, and to advance in classification of integrable equations. We define and develop symbolic representation for the difference polynomial ring, difference operators and formal series. In order to formulate necessary integrability conditions, we introduce a novel quasi-local extension of the difference ring. We apply the developed formalism to solve the classification problem of integrable equations for anti-symmetric quasi-linear equations of order (-3,3) and produce a list of 17 equations satisfying the necessary integrability conditions. For every equation from the list we present an infinite family of integrable higher order relatives. Some of the equations obtained are new.

Natural Chain Inflation

In Chain Inflation the universe tunnels along a series of false vacua of ever-decreasing energy. The main goal of this paper is to embed Chain Inflation in high energy fundamental physics. We begin by illustrating a simple effective formalism for calculating Cosmic Microwave Background (CMB) observables in Chain Inflation. Density perturbations seeding the anisotropies emerge from the probabilistic nature of tunneling (rather than from quantum fluctuations of the inflation). To obtain the correct normalization of the scalar power spectrum and the scalar spectral index, we find an upper limit on the scale of inflation at horizon crossing of CMB scales, V⁎1/4<1012 GeV. We then provide an explicit realization of chain inflation, in which the inflaton is identified with an axion in supergravity. The axion enjoys a perturbative shift symmetry which is broken to a discrete remnant by instantons. The model, which we dub ‘natural chain inflation’ satisfies all cosmological constraints and can be embedded into a standard ΛCDM cosmology. Our work provides a major step towards the ultraviolet completion of chain inflation in string theory.

Revisiting the linear instabilities of plane channel flow between compliant walls

By revisiting the linear dynamics of plane channel flow between compliant walls it is shown that the instability is mainly dominated by perturbations of varicose symmetry. The prevailing modes are of traveling-wave-flutter type and governed by the reduced velocity, a nondimensional control parameter measuring the response of the flexible wall to hydrodynamic loading. Analysis of the energy transfer mechanisms reveals that a stabilizing effect for one class of modes is often accompanied by a destabilizing effect for another class. Thus it seems impossible to significantly delay instability onset by wall compliance.

Phase Control of Localization in the Nonlinear Two-Mode System from Harmonic Mixing Driving: Perturbative Analysis and Symmetry Consideration

Phase Control of Localization in the Nonlinear Two-Mode System from Harmonic Mixing Driving: Perturbative Analysis and Symmetry Consideration

Dissipation in holographic superfluids

We study dissipation in holographic superfluids at finite temperature and zero chemical potential. The zero overlap with the heat current allows us to isolate the physics of the conserved current corresponding to the broken global U(1). By using analytic techniques we write constitutive relations including the first non-trivial dissipative terms. The corresponding transport coefficients are determined in terms of thermodynamic quantities and the black hole horizon data. By analysing their behaviour close to the phase transition we show explicitly the breakdown of the hydrodynamic expansion. Finally, we study the pseudo-Goldstone mode that emerges upon introducing a perturbative symmetry breaking source and we determine its resonant frequency and decay rate.

Epitaxial Growth of Quasi-One-Dimensional Bismuth-Halide Chains with Atomically Sharp Topological Non-Trivial Edge States.

Quantum spin Hall insulators (QSHIs) have one-dimensional (1D) spin-momentum locked topological edge states (ES) inside the bulk band gap, which can serve as dissipationless channels for the practical applications in low consumption electronics and high performance spintronics. However, obtaining the clean and atomically sharp ES which serves as ideal 1D spin-polarized nondissipative conducting channels is demanding and still a challenge. Here, we report the formation of the quasi-1D Bi4I4 nanoribbons on the surface of Bi(111) with the support of the graphene-terminated 6H-SiC(0001) and the direct observation of the topological ES at the step edges by the scanning tunneling microscopy (STM) and spectroscopic-imaging results. The ES reside surround the edge of Bi4I4 nanoribbons and exhibits noteworthy robustness against nontime reversal symmetry (non-TRS) perturbations. The theoretical simulations verify the topological nontriviality of 1D ES, which is retained after considering the presence of the underlying Bi(111). Our study supports the existence of topological ES in Bi4I4 nanoribbons, benefiting to engineer the topological features by using the 1D nanoribbons as building blocks.

Viscocapillary instability in cellular spheroids

We describe a viscocapillary instability that can perturb the spherical symmetry of cellular aggregates in culture, also called multicellular spheroids. In the condition where the cells constituting the spheroid get their necessary metabolites from the immediate, outer microenvironment, a permanent cell flow exists within the spheroid from its outer rim where cells divide towards its core where they die. A perturbation of the spherical symmetry induces viscous shear stresses within the tissue that can destabilise the aggregate. The proposed instability is viscocapillary in nature and does not rely on external heterogeneities, such as a pre-existing pattern of blood vessels or the presence of a substrate on which the cells can exert pulling forces. It arises for sufficiently large cell–cell adhesion strengths, cell-renewal rates, and metabolite supplies, as described by our model parameters. Since multicellular spheroids in culture are good model systems of small, avascular tumours, mimicking the metabolite concentration gradients found in vivo, we can speculate that our description applies to microtumour instabilities in cancer progression.

Multiple positive solutions for coupled Schrödinger equations with perturbations

For coupled Schrodinger equations with nonhomogeneous perturbations we give several results on the existence of multiple positive solutions. In particular in one case we consider perturbations of the permutation symmetry.

The projective core of symmetric games with externalities

The purpose of this paper is to study which coalition structures have stable distributions. We employ the projective core as a stability concept. Although the projective core is often defined only for the grand coalition, we define it for every coalition structure. We apply the core notion to a variety of economic models including the public goods game, the Cournot and Bertrand competition, and the common pool resource game. We use a partition function to formulate these models. We argue that symmetry is a common property of these models in terms of a partition function. We offer some general results that hold for all symmetric partition function form games and discuss their implications in the economic models. We also provide necessary and sufficient conditions for the projective core of the models to be nonempty. In addition, we show that our results hold even in the presence of small perturbations of symmetry.

Broken democracy with intermediate [formula omitted] residual symmetry and random perturbations

The democratic mass matrix is an intriguing possibility for explaining the observed fermion mixings due to its inherent hierarchical mass eigenvalues and large mixing angles. Nevertheless, two of the three mass eigenvalues are zero if the flavor democracy is exact, in obvious contradiction with the experimental observations. One possibility is breaking the flavor democracy with anarchical perturbations as we proposed in an earlier work. However, even within the first two generations, the charged fermion masses are also hierarchical which may not be a coincidence. The democratic S3L×S3R symmetry of the three generations may first be broken down to an intermediate S2L×S2R symmetry among the first two generations to regulate the sequential hierarchies, followed by random perturbations, that generate the correct size of all measured observables. Unique predictions for neutrinoless double beta decay are also found.

Lie symmetry and invariants for a generalized Birkhoffian system on time scales

Abstract The Lie symmetry and invariants for a generalized Birkhoffian system on time scales are studied, which include exact invariants and adiabatic invariants. First, the generalized Pfaff-Birkhoff principle on time scales is established, and by using Dubois-Reymond lemma the generalized Birkhoff’s equations on time scale are derived. Secondly, the determining equations of Lie symmetry for the generalized Birkhoffian system on time scales are established. We prove that if the Lie symmetry satisfies the structural equation, it leads to a conserved quantity, which is an exact invariant of the system. Again, the perturbation of Lie symmetry under the action of small disturbance is considered, the determining equations and the structural equations of disturbed system are established, and the adiabatic invariants led by the Lie symmetry perturbation for the generalized Birkhoffian system on time scales are given. Because of the arbitrariness of selecting time scales and the generality of the generalized Birkhoffian system, the results of this paper are of universal significance. The results of this paper contain the corresponding results for Birkhoffian system on time scales and classical generalized Birkhoffian system as its special cases. At the end of the paper, an example is given to illustrate the validity of the method and the results.

Changes in the symmetry of external perturbations affect patterns of muscle activity during gait initiation

BackgroundGait initiation is associated with changes in the steady state and experiencing an external perturbation during initiation of gait could further threaten balance stability. Research questionThe aim of the study was to investigate if changes in the symmetry of the perturbations affect patterns of muscle activity during gait initiation. MethodsEleven young health participants were instructed to stand on the force platform and wait for the instruction of taking a right step, left step or stand still while experiencing a pendulum perturbation applied to the back of both shoulders (symmetric), back of the right shoulder (asymmetric) or no perturbations. Bilateral electromyographic activity (EMG) of dorsal and ventral muscles, moments of the pendulum release and perturbation impact, center of pressure (COP) displacements and pelvic movements were recorded and analyzed before and after the onset of the perturbation. ResultsTaking the right/left step in presence of symmetric perturbation did not affect the temporal sequence of COP and pelvic movements. The onset of COP and pelvic movement occurred before the perturbation impact at the shoulder levels. The factors of step and perturbation did not significantly affect integrals of bilateral muscles at the pendulum release. After the pendulum release, ventral and dorsal EMG integrals of the trunk, thigh, and shank segments increased or decreased corresponding to the swing and stance leg. Changes in muscle activities were also associated with the symmetric or asymmetric perturbations before and after the perturbation impact. SignificanceThe outcome of the study provides information about strategies used to coordinate the activity of muscles while body perturbations are induced during gait initiation.