Number Of Symmetries Research Articles

Identification of Langmuir wave turbulence-supercontinuum transition by application of von Neumann entropy

A transition from Langmuir wave turbulence (LWT) to coherent Langmuir wave supercontinuum (LWSC) is identified in one-dimensional particle-in-cell simulations as the emergence of a broad frequency band showing significant temporal coherence of a wave field accompanied by a decrease in the von Neumann entropy of classical wave fields. The concept of the von Neumann entropy is utilized for evaluation of the phase-randomizing degree of the classical wave fields, together with introduction of the density matrix of the wave fields. The transition from LWT to LWSC takes place when the energy per one plasmon (one wave quantum) exceeds a certain threshold. The coherent nature, which Langmuir wave systems acquire through the transition, is created by four wave mixings of the plasmons. The emergence of temporal coherence and the decrease in the phase randomization are considered as the development of long-range order and spontaneous symmetry breaking, respectively, indicating that the LWT-LWSC transition is a secon...

Magnetic hexadecapole order and magnetopiezoelectric metal state in Ba1−xKxMn2As2

We study an odd-parity magnetic multipole order in Ba$_{1-x}$K$_x$Mn$_2$As$_2$ and related materials. Although BaMn$_2$As$_2$ is a seemingly conventional Mott insulator with G-type antiferromagnetic order, we identify the ground state as a magnetic hexadecapole ordered state accompanied by simultaneous time-reversal and space-inversion symmetry breaking. A symmetry argument and microscopic calculations reveal the ferroic ordering of leading magnetic hexadecapole moment and admixed magnetic quadrupole moment. Furthermore, we clarify electromagnetic responses characterizing the magnetic hexadecapole state of semiconducting BaMn$_2$As$_2$ and doped metallic systems. A magnetoelectric effect and antiferromagnetic Edelstein effect are shown. Interestingly, a counter-intuitive currentinduced nematic order occurs in the metallic state. The electric current along the \textit{z}-axis induces the \textit{xy}-plane nematicity in sharp contrast to the spontaneous nematic order in superconducting Febased 122-compounds. Thus, the magnetic hexadecapole state of doped BaMn$_2$As$_2$ is regarded as a magnetopiezoelectric metal. The anomalous responses stem from the peculiar symmetry of the parity-violating magnetic order. Other candidate materials for magnetic hexadecapole order are proposed.

Nanocross: A Highly Tunable Plasmonic System

With the help of electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) and boundary element method (BEM) simulations, we have shown that silver nanocross can be used to tune the plasmon modes and especially the higher order modes in a very controlled manner. Morphing a nanorod to a nanocross by growing another arm along the perpendicular bisector of a nanorod can lead to a spectacular evolution of various order modes in the EEL spectra. One can keep a mode fixed in energy while bringing the next higher order mode close to it, or even make it cross. This allows one to control the relative separation of energy of the plasmon modes. Hybridization of individual nanocross plasmon modes have also been studied by bringing two nanocrosses close together along one of their arms. An analytical approach based on first order perturbation theory and symmetry arguments based on group theory aptly fits the experimental observations.

Design of circular antenna arrays of circular subarrays exploiting rotational symmetry

This paper presents a design of fractal antenna arrays based on circular arrays of circular subarrays for scannable pattern using rotational symmetry properties of the complex feeding excitations for a maximum performance in terms of side lobe level (SLL) and directivity (DIR). This fractal array design considers the optimization of the amplitude and phase excitations exploiting the fractal characteristics of the geometry (rotational symmetry) in order to generate a scannable pattern. The synthesis process is carried out by the method of Differential Evolution (DE). The main advantages of using rotational symmetry are that the optimal excitations for a particular beam steering angle could be applied to other beam steering angles remaining in the same array factor characteristics (SLL and directivity) for every beam steering angle. This design of fractal antenna arrays provides a complete scanning of the azimuth plane with optimal characteristics of the radiation pattern using just one optimal design vector of amplitude and phase excitations. Furthermore, the performance of the fractal antenna array optimized with DE is compared with respect to the cases of Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and the conventional progressive phase for the same array geometry.

Invariant Functions, Symmetries and Primary Branch Solutions of First Order Autonomous Systems**Supported by the National Natural Science Foundations of China under Grant Nos. 11435005, 11471004, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things No. ZF1213 and K. C. Wong Magna Fund in Ningbo University

An invariant function (IF) is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary (1+1)-dimensional first order autonomous systems. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions.

Approximations of the Homoclinic Orbits Near a Double-Zero Bifurcation with Symmetry of Order Two

The two-dimensional system of differential equations corresponding to the normal form of the double-zero bifurcation with symmetry of order two is considered. This is a codimension two bifurcation. The associated dynamical system exhibits, among others, a homoclinic bifurcation. In this paper, we obtain second order approximations both for the curve of parametric values of homoclinic bifurcation and for the homoclinic orbits. To perform this task, we reduce first the normal form to a perturbed Hamiltonian system, using a blow-up technique. Then, by means of a perturbation method, we determine explicit first and second order approximations of the homoclinic orbits. The solutions obtained theoretically are compared with those obtained numerically for several cases. Finally, an application of the obtained results is presented.

Neutrinoless Double Beta Decay and Lepton Flavour Violation in Broken μ − τ Symmetric Neutrino Mass Models

We have studied neutrinoless double beta decay and charged lepton flavour violation in broken $\mu-\tau$ symmetric neutrino masses in a generic left-right symmetric model (LRSM). The leading order $\mu-\tau$ symmetric mass matrix originates from the type I (II) seesaw mechanism, whereas the perturbations to $\mu-\tau$ symmetry in order for generation of non-zero reactor mixing angle $\theta_{13}$, as required by latest neutrino oscillation data, originates from the type II (I) seesaw mechanism. In our work, we considered four different realizations of $\mu-\tau$ symmetry, viz. Tribimaximal Mixing (TBM), Bimaximal Mixing (BM), Hexagonal Mixing (HM) and Golden Ratio Mixing (GRM). We then studied the new physics contributions to neutrinoless double beta decay (NDBD) ignoring the left-right gauge boson mixing and the heavy-light neutrino mixing within the framework of LRSM. We have considered the mass of the gauge bosons and scalars to be around TeV and studied the effects of the new physics contributions on the effective mass and the NDBD half life and compared with the current experimental limit imposed by KamLAND-Zen. We further extended our analysis by correlating the lepton flavour violation of the decay processes, $\left(\mu\rightarrow 3e\right)$ and $\left(\mu\rightarrow e\gamma\right)$ with the lightest neutrino mass and atmospheric mixing angle $\theta_{23}$ respectively.

Directing clinical care using lower extremity biomechanics in patients with ankle osteoarthritis and ankle arthroplasty.

Ankle osteoarthritis is a debilitating disease with approximately 50,000 new cases per year leading to skeletal deformity, severe and recurrent pain, cartilage breakdown, and gait dysfunction limiting patient mobility and well-being. Although many treatments (total ankle arthroplasty [TAA], ankle fusion [arthrodesis], and ankle distraction arthroplasty) relieve pain, it is not clear that these procedures significantly improve patient mobility. The goal of the research presented here is to summarize what is presently known about lower extremity gait mechanics and outcomes and to quantify the impact of ankle osteoarthritis and TAA have on these measures using an explicitly holistic and mechanistic approach. Our recent studies have explored physical performance and energy recovery and revealed unexpected patterns and sequelae to treatment including incomplete restoration of gait function. These studies demonstrated for the first time the extreme levels and range of gait and balance dysfunction present in ankle osteoarthritis patients as well as quantifying the ways in which the affected joint alters movement and loading patterns not just in the painful joint, but throughout both the ipsilateral and contralateral lower extremity. Through this work, we determined that relieving pain alone through TAA is not enough to restore normal walking mechanics and balance due to underlying causes including limited ankle range of motion and balance deficits leading to long-term disability despite treatment. The results indicate the need to consider additional therapeutic interventions aimed at restoring balance, ankle range of motion, and movement symmetry in order to improve long-term health and function. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2345-2355, 2017.

Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

We study aspects of Heterotic/F-theory duality for compactifications with Abelian discrete gauge symmetries. We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group {mathbb{Z}}_n . Such models are obtained by studying first a specific toric set-up whose associated Heterotic vector bundle has structure group {mathbb{Z}}_n . By employing a conjectured Heterotic/F-theory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compactifications to six dimensions. We provide explicit constructions of mirror-pairs for symmetric examples with {mathbb{Z}}_2 and {mathbb{Z}}_3 , in six dimensions. The Heterotic models with symmetric discrete symmetries are related in field theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stückelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of fibrations with torsional sections and those with multi-sections.

Naturally light Dirac neutrino in Left-Right Symmetric Model

We study the possibility of generating tiny Dirac masses of neutrinos in Left-Right Symmetric Model (LRSM) without requiring the existence of any additional symmetries. The charged fermions acquire masses through a universal seesaw mechanism due to the presence of additional vector like fermions. The neutrinos acquire a one-loop Dirac mass from the same additional vector like charged leptons without requiring any additional discrete symmetries. The model can also be extended by an additional Z2 symmetry in order to have a scotogenic version of this scenario predicting a stable dark matter candidate. We show that the latest Planck upper bound on the effective number of relativistic degrees of freedom Neff=3.15 ± 0.23 tightly constrains the right sector gauge boson masses to be heavier than 3.548 TeV . This bound on gauge boson mass also affects the allowed values of right scalar doublet dark matter mass from the requirement of satisfying the Planck bound on dark matter relic abundance. We also discuss the possible implications of such a scenario in charged lepton flavour violation and generating observable electric dipole moment of leptons.

Field dependence of the magnetic correlations of the frustrated magnetSrDy2O4

The frustrated magnet SrDy$_2$O$_4$ exhibits a field-induced phase with a magnetization plateau at $1/3$ of the saturation value for magnetic fields applied along the $b$-axis. We report here a neutron scattering study of the nature and symmetry of the magnetic order in this field-induced phase. Below $T\approx 0.5$ K, there are strong hysteretic effects, and the order is short or long ranged for zero-field and field cooling, respectively. We find that the long-range ordered magnetic structure within the zig-zag chains is identical to that expected for the one-dimensional axial next-nearest neighbour Ising (ANNNI) model in longitudinal field. The long-range ordered structure in field contrasts with the short-range order found at zero field, and is probably reached through enhanced quantum fluctuations with increasing fields.

How is the presence of horizons and localized matter encoded in the entanglement entropy?

Motivated by the new theoretical paradigm that views space–time geometry as emerging from the entanglement of a pre-geometric theory, we investigate the issue of the signature of the presence of horizons and localized matter on the entanglement entropy (EE) [Formula: see text] for the case of three-dimensional AdS (AdS3) gravity. We use the holographically dual two-dimensional CFT on the torus and the related modular symmetry in order to treat bulk black holes and conical singularities (sourced by pointlike masses not shielded by horizons) on the same footing. In the regime where boundary tori can be approximated by cylinders, we are able to give universal expressions for the EE of black holes and conical singularities. We argue that the presence of horizons/localized matter in the bulk is encoded in the EE in terms of (i) enhancement/reduction of the entanglement of the AdS3 vacuum, (ii) scaling as area/volume of the leading term of the perturbative expansion of [Formula: see text], (iii) exponential/periodic behavior of [Formula: see text] and (iv) presence of unaccessible regions in the noncompact/compact dimension of the boundary cylinder. In particular, we show that the reduction effect of matter on the entanglement of the vacuum found by Verlinde for the de Sitter vacuum extends to the AdS3 vacuum.

Phonon-like Hydrogen-Bond Modes in Protic Ionic Liquids

Gigahertz- to terahertz-frequency infrared and Raman spectra contain a wealth of information concerning the structure, intermolecular forces, and dynamics of ionic liquids. However, these spectra generally have a large number of contributions ranging from slow diffusional modes to underdamped librations and intramolecular vibrational modes. This makes it difficult to isolate effects such as the role of Coulombic and hydrogen-bonding interactions. We have applied far-infrared and ultrafast optical Kerr effect spectroscopies on carefully selected ions with a greater or lesser degree of symmetry in order to isolate spectral signals of interest. This has allowed us to demonstrate the presence of longitudinal and transverse optical phonon modes and a great similarity of alkylammonium-based protic ionic liquids to liquid water. The data show that such phonon modes will be present in all ionic liquids, requiring a reinterpretation of their spectra.

Insulators and metals with topological order and discrete symmetry breaking

Numerous experiments have reported discrete symmetry breaking in the high temperature pseudogap phase of the hole-doped cuprates, including breaking of one or more of lattice rotation, inversion, or time-reversal symmetries. In the absence of translational symmetry breaking or topological order, these conventional order parameters cannot explain the gap in the charged fermion excitation spectrum in the anti-nodal region. Zhao et al. (1601.01688) and Jeong et al. (arXiv:1701.06485) have also reported inversion and time-reversal symmetry breaking in insulating Sr2IrO4 similar to that in the metallic cuprates, but co-existing with Neel order. We extend an earlier theory of topological order in insulators and metals, in which the topological order combines naturally with the breaking of these conventional discrete symmetries. We find translationally-invariant states with topological order co-existing with both Ising-nematic order and spontaneous charge currents. The link between the discrete broken symmetries and the topological-order-induced pseudogap explains why the broken symmetries do not survive in the confining phases without a pseudogap at large doping. Our theory also connects to the O(3) non-linear sigma model and CP1 descriptions of quantum fluctuations of the Neel order. In this framework, the optimal doping criticality of the cuprates is primarily associated with the loss of topological order.

Digitalized Geometric Phases for Parallel Optical Spin and Orbital Angular Momentum Encoding

Geometric phases have attracted considerable attention in recent years, due to their capability of arbitrary beam shaping in a most efficient and compact way, while traditional geometric phases are usually limited to handling single-structured beams and lack the capability of parallel manipulation. Here, we propose a digitalized geometric phase enabling parallel optical spin and orbital angular momentum encoding. The concept is demonstrated in inhomogeneous anisotropic media by imprinting a particularly designed binary phase into a space-variant geometric phase. We theoretically analyze its spin–orbit interaction of light and experimentally created higher-order Poincare sphere beam lattices, the order number and symmetry of which can be flexibly manipulated. Special lattices of cylindrical vector beams and orbital angular momentum modes with square and hexagonal symmetry are presented. This work discloses a new insight in programming geometric phases for tailoring the optical field and inspires various ph...

Antiferroquadrupolar Order and Rotational Symmetry Breaking in a Generalized Bilinear-Biquadratic Model on a Square Lattice.

The magnetic and nematic properties of the iron chalcogenides have recently been the subject of intense interest. Motivated by the proposed antiferroquadrupolar and Ising-nematic orders for the bulk FeSe, we study the phase diagram of an S=1 generalized bilinear-biquadratic model with multineighbor interactions. We find a large parameter regime for a (π, 0) antiferroquadrupolar phase, showing how quantum fluctuations stabilize it by lifting an infinite degeneracy of certain semiclassical states. Evidence for this C_{4}-symmetry-breaking quadrupolar phase is also provided by an unbiased density matrix renormalization group analysis. We discuss the implications of our results for FeSe and related iron-based superconductors.

A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7.

Strong electron interactions can drive metallic systems toward a variety of well-known symmetry-broken phases, but the instabilities of correlated metals with strong spin-orbit coupling have only recently begun to be explored. We uncovered a multipolar nematic phase of matter in the metallic pyrochlore Cd2Re2O7 using spatially resolved second-harmonic optical anisotropy measurements. Like previously discovered electronic nematic phases, this multipolar phase spontaneously breaks rotational symmetry while preserving translational invariance. However, it has the distinguishing property of being odd under spatial inversion, which is allowed only in the presence of spin-orbit coupling. By examining the critical behavior of the multipolar nematic order parameter, we show that it drives the thermal phase transition near 200 kelvin in Cd2Re2O7 and induces a parity-breaking lattice distortion as a secondary order.

Lie symmetries, symmetry reductions and conservation laws of time fractional modified Korteweg–de Vries (mkdv) equation

In this work, we study Lie symmetry analysis for fractional order differential equations that is one of the applications of symmetries. This study deals with Lie symmetry of fractional order modified Korteweg–de Vries (mKdV) equation. We found Lie symmetries of this equation and then we reduced fractional order modified Korteweg–de Vries (mKdV) equation to fractional order ordinary differential equation with Erdelyi–Kober fractional differential operator. Then we used characteristic method for fractional order differential equations and help of founded these Lie symmetries for finding solutions for given equation. Then we obtained infinite and finite conservation laws of fractional order modified Korteweg–de Vries (mKdV) equation.

Superelliptic Josephson Tunnel Junctions

The most important practical characteristic of a Josephson junction is its critical current. The shape of the junction determines the specific form of the magnetic-field dependence of the its Josephson current. Here we address the magnetic diffraction patterns of specially shaped planar Josephson tunnel junctions. We focus on a wide ensemble of generalized ellipses, called superellipses, which retain the second order symmetry. We analyze the implications of this type of isometry and derive the explicit expressions for the threshold curves of superelliptic Josephson junctions. A detailed study is made of their magnetic patterns with emphasis on the rate of decay of the sidelobes amplitudes for large field amplitudes.

Dynamic characteristics of azimuthally correlated structures of axial instability of wire-array Z pinches

Particular attention was placed on observations of dynamic properties of the azimuthally correlated structures of axial instability of wire-array Z pinches, which were conducted at 10-MA (for short circuit load) pulsed power generator-the Primary Test Stand facility. Not well fabricated loads, which were expected to preset bubble or spike in plasma, were used to degrade the implosion symmetry in order to magnify the phenomenon of instability. The side-view sequence of evolution of correlation given by laser shadowgraphy clearly demonstrates the dynamic processes of azimuthal correlation of the bubble and spike. A possible mechanism presented here suggests that it is the substantial current redistribution especially in regions surrounding the bubble/spike resulting from change of inductance due to the presence of the bubble/spike that plays an essential part in establishment of azimuthal correlation of wire array and liner Z pinches.