Showing papers on "Antisymmetric relation published in 2022"
TL;DR: The stability of symmetric and antisymmetric solitons in the fractional nonlinear Schrödinger equation with the defocused saturable nonlinearity and the PT-symmetric potential was investigated in this paper .
22 citations
TL;DR: In this paper , the second-order nonlinear conductivity on a two-dimensionalally stacked zigzag chain based on the nonlinear Kubo formula was analyzed and it was shown that an effective coupling between the magnetic toroidal moment and the antisymmetric spin-orbit interaction is an essential source of the secondorder conductivity, and the nonreciprocal longitudinal current and nonlinear transverse current in a multi-band system are largely enhanced just below the transition temperature of the antiferromagnetic ordering.
Abstract: A magnetic toroidal moment is a fundamental electronic degree of freedom in the absence of both spatial inversion and time-reversal symmetries and gives rise to novel multiferroic and transport properties. We elucidate essential model parameters of the nonlinear transport in the space-time ($\mathcal{PT}$) symmetric collinear antiferromagnetic metals accompanying a magnetic toroidal moment. By analyzing the longitudinal and transverse components of the second-order nonlinear conductivity on a two-dimensionally stacked zigzag chain based on the nonlinear Kubo formula, we show that an effective coupling between the magnetic toroidal moment and the antisymmetric spin-orbit interaction is an essential source of the nonlinear conductivity. Moreover, we find that the nonreciprocal longitudinal current and nonlinear transverse current in a multi-band system are largely enhanced just below the transition temperature of the antiferromagnetic ordering. We also discuss the relevance of the nonlinear conductivity to the linear magnetoelectric coefficient and conductivity. Our result serves as a guide for exploring microscopic essence and clarifying the parameter dependence of the nonlinear conductive phenomena in ferrotoroidal metals.
13 citations
TL;DR: In this article, antisymmetrical laminates are introduced into the transition elements to reduce the area of transition elements and also have good applicability to various deformation elements.
Abstract: Multistable structures are known for their high adaptability and are thereby used in various applications in the fields of aerospace, biomedical, and in packaging industries. In this paper, novel multistable structures composed of different deformation elements and new transition elements are presented. Inspired by the shape of the transition region, antisymmetrical laminates are introduced into the transition elements. Samples with different deformation elements in series and parallel are manufactured experimentally, and their properties are found to be in good agreement with the simulation results. The results demonstrate that these new methods not only reduce the area of transition elements but also have good applicability to various deformation elements. Finite element simulations and experiments were conducted to explore the deformations and trigger forces. The influence of the width and thickness of transition elements on multistable structures, as well as the relationship between the laminate angles of deformed elements and the shape of multistable structures, are discussed. The results show that the maximum number of stable states obtained by the experiment is 16. Comparison with other multistable structures demonstrate that deformability is improved, offering a large degree of design freedom for a variety of morphing applications.
12 citations
TL;DR: In this paper , antisymmetrical laminates are introduced into the transition elements to reduce the area of transition elements and also have good applicability to various deformation elements.
Abstract: Multistable structures are known for their high adaptability and are thereby used in various applications in the fields of aerospace, biomedical, and in packaging industries. In this paper, novel multistable structures composed of different deformation elements and new transition elements are presented. Inspired by the shape of the transition region, antisymmetrical laminates are introduced into the transition elements. Samples with different deformation elements in series and parallel are manufactured experimentally, and their properties are found to be in good agreement with the simulation results. The results demonstrate that these new methods not only reduce the area of transition elements but also have good applicability to various deformation elements. Finite element simulations and experiments were conducted to explore the deformations and trigger forces. The influence of the width and thickness of transition elements on multistable structures, as well as the relationship between the laminate angles of deformed elements and the shape of multistable structures, are discussed. The results show that the maximum number of stable states obtained by the experiment is 16. Comparison with other multistable structures demonstrate that deformability is improved, offering a large degree of design freedom for a variety of morphing applications.
12 citations
28 Jan 2022
TL;DR: In this article , the authors investigated the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles (circular unitary, orthogonal, and symplectic) and obtained insights into the interplay between the local entenglement generation by the gates and the entunglement reduction by the measurements.
Abstract: We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson’s three circular ensembles (circular unitary, orthogonal, and symplectic ensembles; CUE, COE and CSE). We utilise the established model of a one-dimensional circuit evolving under alternating local random unitary gates and projective measurements performed with tunable rate, which for gates drawn from the CUE is known to display a transition from extensive to intensive entanglement scaling as the measurement rate is increased. By contrasting this case to the COE and CSE, we obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements. For this, we combine exact analytical random-matrix results for the entanglement generated by the individual gates in the different ensembles, and numerical results for the complete quantum circuit. These considerations include an efficient rephrasing of the statistical entangling power in terms of a characteristic entanglement matrix capturing the essence of Cartan’s KAK decomposition, and a general result for the eigenvalue statistics of antisymmetric matrices associated with the CSE.
11 citations
TL;DR: In this paper , the statistical properties of fluctuations in active systems that are governed by nonsymmetric responses are investigated. And the authors find that the antisymmetric parts of the time-correlation functions can exist and that they are proportional to either the odd resistance coefficient or the odd elastic constant.
Abstract: We investigate the statistical properties of fluctuations in active systems that are governed by nonsymmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd elastic tensor are studied. For a system in thermal equilibrium, the time-correlation functions should satisfy time-reversal symmetry and the antisymmetric parts of the correlation functions should vanish. For the odd Langevin systems, however, we find that the antisymmetric parts of the time-correlation functions can exist and that they are proportional to either the odd resistance coefficient or the odd elastic constant. This means that the time-reversal invariance of the correlation functions is broken due to the presence of odd responses in active systems. Using the short-time asymptotic expressions of the time-correlation functions, one can estimate an odd elastic constant of an active material such as an enzyme or a motor protein.
10 citations
TL;DR: In this paper , the antisymmetric component of the thermopolarization tensor becomes nonzero due to the ferrotype order for electric-toroidal dipole moments.
Abstract: We investigate electric polarizations that emerge perpendicular to an applied thermal gradient in insulating systems. The thermally induced electric polarization, known as thermopolarization, has been studied conventionally in the case where an electric polarization appears along the thermal gradient. Here, we focus on the antisymmetric component of the thermopolarization tensor, and we reveal that it becomes nonzero due to the ferrotype order for electric-toroidal dipole moments. To describe local electric polarizations originating from the disproportionation of localized electronic clouds, we introduce a two-dimensional three-orbital model with localized $s$ and two $p$ orbitals, where the electric polarization at each site interacts with the neighboring one as dipole-dipole interactions. We find that a vortex-type configuration of local electric polarizations appears as a mean-field ground state, corresponding to a ferrotype electric-toroidal dipole order. By taking account of collective modes from this ordered state, we calculate the coefficient of the thermopolarization based on the linear-response theory. The antisymmetric component is nonzero in the presence of the electric-toroidal dipole order. We clarify that fluctuations in the $p$ orbitals are crucial in enhancing the antisymmetric thermopolarization. We discuss the appearance conditions based on the symmetry argument and the relevance to real materials.
10 citations
TL;DR: In this paper, the authors investigate the microscopic and macroscopic instabilities developing in magneto-active elastomer (MAE) composites undergoing large deformations in the presence of an external magnetic field.
10 citations
TL;DR: In this paper , the authors investigate the microscopic and macroscopic instabilities developing in magneto-active elastomer composites undergoing large deformations in the presence of an external magnetic field.
10 citations
TL;DR: In this article , the authors proposed the three-directional functional graded materials (3D FGMs) to carry out the composition of slender beams to meet the requirements of the hygro-thermal distribution in the multi-directions and improve the endural ability so that catastrophic failure is refrained due to large deflections.
10 citations
TL;DR: In this article , an antisymmetric spin split band structure under spin density waves with finite ordering wave vectors in centrosymmetric systems without the relativistic spin-orbit coupling was investigated.
Abstract: We investigate how to engineer an antisymmetric spin-split band structure under spin density waves with finite ordering wave vectors in centrosymmetric systems without the relativistic spin-orbit coupling. On the basis of a perturbative analysis for the spin-charge coupled model in centrosymmetric itinerant magnets, we show that nonzero chiral-type bilinear and biquadratic spin cross products in momentum space under the magnetic orderings are related to an antisymmetric spin polarization in the electronic band structure. We apply the derived formula to the single-$Q$ cycloidal spiral and double-$Q$ noncoplanar states including the meron-antimeron and skyrmion crystals. Our results present a clue to realize a giant antisymmetric spin splitting driven by magnetic phase transitions in the centrosymmetric lattice structures without the spin-orbit coupling.
TL;DR: In this paper , a geometrical interpretation of frequency in electric circuits is presented, where the frequency is defined as a multivector with symmetric and antisymmetric components.
Abstract: The letter provides a geometrical interpretation of frequency in electric circuits. According to this interpretation, the frequency is defined as a multivector with symmetric and antisymmetric components. The conventional definition of frequency is shown to be a special case of the proposed theoretical framework. Several examples serve to show the features, generality as well as practical aspects of the proposed approach.
TL;DR: In this paper , the authors show that on-site interaction strengths can be widely tuned by the magnetic field and confinement strength but collapse onto a universal single-parameter curve when rescaled by the harmonic energy and length scales of a single lattice site.
Abstract: Exchange-antisymmetric pair wavefunctions in fermionic systems can give rise to unconventional superconductors and superfluids with non-trivial transport properties. The realisation of these states in controllable quantum systems, such as ultracold gases, could enable new types of quantum simulations, topological quantum gates, and exotic few-body states. However, p-wave and other antisymmetric interactions are weak in naturally occurring systems, and their enhancement via Feshbach resonances in ultracold systems has been limited by three-body loss. In this work, we create isolated pairs of spin-polarised fermionic atoms in a multi-orbital three-dimensional optical lattice. We spectroscopically measure elastic p-wave interaction energies of strongly interacting pairs of atoms near a magnetic Feshbach resonance and find pair lifetimes to be up to fifty times larger than in free space. We demonstrate that on-site interaction strengths can be widely tuned by the magnetic field and confinement strength but collapse onto a universal single-parameter curve when rescaled by the harmonic energy and length scales of a single lattice site. Since three-body processes are absent within our approach, we are able to observe elastic unitary p-wave interactions for the first time. We take the first steps towards coherent temporal control via Rabi oscillations between free-atom and interacting-pair states. All experimental observations are compared both to an exact solution for two harmonically confined atoms interacting via a p-wave pseudopotential, and to numerical solutions using an ab-initio interaction potential. The understanding and control of on-site p-wave interactions provides a necessary component for the assembly of multi-orbital lattice models, and a starting point for investigations of how to protect such a system from three-body recombination even in the presence of tunnelling.
TL;DR: In this article , the effect of varying temperature on the GW propagation characteristics in a carbon fiber-reinforced composite plate is studied under a varying temperature condition, representative of the aeronautics application, and a temperature independent averaged time compensation factor is proposed to mitigate the numerical data dependency on excitation frequency and propagation angle.
TL;DR: In this paper , a quantum version of the Monge-Kantorovich optimal transport problem is analyzed, where the transport cost is minimized over the set of all bipartite coupling states such that both of its reduced density matrices of dimension N are fixed.
Abstract: A quantum version of the Monge-Kantorovich optimal transport problem is analyzed. The transport cost is minimized over the set of all bipartite coupling states ρ^{AB} such that both of its reduced density matrices ρ^{A} and ρ^{B} of dimension N are fixed. We show that, selecting the quantum cost matrix to be proportional to the projector on the antisymmetric subspace, the minimal transport cost leads to a semidistance between ρ^{A} and ρ^{B}, which is bounded from below by the rescaled Bures distance and from above by the root infidelity. In the single-qubit case, we provide a semianalytic expression for the optimal transport cost between any two states and prove that its square root satisfies the triangle inequality and yields an analog of the Wasserstein distance of the order of 2 on the set of density matrices. We introduce an associated measure of proximity of quantum states, called swap fidelity, and discuss its properties and applications in quantum machine learning.
TL;DR: In this article , the authors considered the almost circular regime of the Ginibre process on the plane, where most of the points lie in a thin annulus of width O 1N$O\left(\frac{1}{N}\right)$ as N→∞$N \rightarrow \infty$ .
Abstract: We consider the symplectic‐induced Ginibre process, which is a Pfaffian point process on the plane. Let N be the number of points. We focus on the almost‐circular regime where most of the points lie in a thin annulus SN$\mathcal {S}_{N}$ of width O1N$O\left(\frac{1}{N}\right)$ as N→∞$N \rightarrow \infty$ . Our main results are the bulk scaling limits of all correlation functions near the real axis, and also away from the real axis. Near the real axis, the limiting correlation functions are Pfaffians with a new correlation kernel, which interpolates the limiting kernels in the bulk of the symplectic Ginibre ensemble and of the antisymmetric Gaussian Hermitian ensemble of odd size. Away from the real axis, the limiting correlation functions are determinants, and the kernel is the same as the one appearing in the bulk limit of almost‐Hermitian random matrices. Furthermore, we obtain precise large N asymptotics for the probability that no points lie outside SN$\mathcal {S}_{N}$ , as well as of several other “semi‐large” gap probabilities.
TL;DR: In this paper , the authors theoretically investigate the microscopic conditions for emergent non-reciprocal magnons toward unified understanding on the basis of a microscopic model analysis, and they show that the products of the Bogoliubov Hamiltonian obtained within the linear spin wave approximation is enough to obtain the momentum-space functional form and the key ingredients in the non-rewarded magnon dispersions in an analytical way even without solving the eigenvalue problems.
Abstract: We theoretically investigate the microscopic conditions for emergent nonreciprocal magnons toward unified understanding on the basis of a microscopic model analysis. We show that the products of the Bogoliubov Hamiltonian obtained within the linear spin wave approximation is enough to obtain the momentum-space functional form and the key ingredients in the nonreciprocal magnon dispersions in an analytical way even without solving the eigenvalue problems. We find that the odd order of an effective antisymmetric Dzyaloshinskii-Moriya interaction and/or the even order of an effective symmetric anisotropic interaction in the spin rotated frame can be a source of the antisymmetric dispersions. We present possible kinetic paths of magnons contributing to the antisymmetric dispersions in the one- to four-sublattice systems with the general exchange interactions. We also test the formula for both ferromagnetic and antiferromagnetic orderings in the absence of spatial inversion symmetry.
TL;DR: In this paper , a novel layup design of a multistable morphing structure was proposed, and the difference between the two types of multi-stable configurations was systematically investigated by numerical simulations and experiments.
TL;DR: In this article , the authors show that a crossing antisymmetric function can be expanded in terms of manifestly crossing antsy objects, which they call the "+ type Polyakov blocks", which are built from AdS$d+1$ Witten diagrams.
Abstract: Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call the '+ type Polyakov blocks'. These blocks are built from AdS$_{d+1}$ Witten diagrams. In 1d they encode the '+ type' analytic functionals which act on crossing antisymmetric functions. In general d we establish this Witten diagram basis from a crossing antisymmetric dispersion relation in Mellin space. Analogous to the crossing symmetric case, the dispersion relation imposes a set of independent 'locality constraints' in addition to the usual CFT sum rules given by the 'Polyakov conditions'. We use the Polyakov blocks to simplify more general analytic functionals in $d > 1$ and global symmetry functionals.
TL;DR: In this article , a method for microcrack localization based on cross-shaped sensor clusters in a plate is proposed by combining nonlinear ultrasonic Lamb wave technology and time difference of arrival (TDOA) technology.
TL;DR: In this paper , the authors reported the observation of a magnetic-field-antisymmetric Seebeck effect in a tilted Weyl semimetal, Co$_3$Sn$_2$S $_2$.
Abstract: Tilting the Weyl cone breaks the Lorentz invariance and enriches the Weyl physics. Here, we report the observation of a magnetic-field-antisymmetric Seebeck effect in a tilted Weyl semimetal, Co$_3$Sn$_2$S$_2$. Moreover, it is found that the Seebeck effect and the Nernst effect are antisymmetric in both the in-plane magnetic field and the magnetization. We attribute these exotic effects to the one-dimensional chiral anomaly and phase space correction due to the Berry curvature. The observation is further reproduced by a theoretical calculation, taking into account the orbital magnetization.
23 May 2022
TL;DR: In this paper , the least-mean-square (LMS) and normalized LMS (NLMS) algorithms with symmetric/antisymmetric properties (termed here LMS-SAS and NLMS -SAS) are proposed.
Abstract: In applications involving system identification problems, some characteristics of the impulse response of the system to be identified are usually exploited to design adaptive algorithms with improved performance. In this context, this paper focuses on the identification of systems that own intrinsic symmetric or antisymmetric properties, which can be further formulated by using a combination of bilinear forms. Based on such an approach, the least-mean-square (LMS) and normalized LMS (NLMS) algorithms with symmetric/antisymmetric properties (termed here LMS-SAS and NLMS-SAS) are proposed. Simulation results are shown confirming the improved convergence speed achieved by the proposed algorithms as compared to the conventional LMS and NLMS counterparts for different operating scenarios.
TL;DR: In this paper , the dispersion of a flexural edge wave (FEW) is analyzed in a plate with its free edge structured by an array of grooves, revealing the essence of a kind of modulated FEW.
TL;DR: In this article , the authors investigated the effect of nonlinear damping on energy harvesting and vibration isolation under harmonic inputs and introduced the concept of power transmissibility, which can increase the harvested energy and reduce the vibration over both the resonant and higher frequency ranges.
Abstract: Abstract Beneficial effects of nonlinear damping on energy harvesting and vibration isolation under harmonic inputs have been investigated showing that the introduction of nonlinear damping can increase the harvested energy and reduce the vibration over both the resonant and higher frequency ranges. However, the scenario becomes more complicated when the loading inputs are of more general form such as multi-tone and random inputs, which can produce system responses that are induced by an interaction of system input components of different frequencies. In the present study, by introducing the concept of power transmissibility, the study of the beneficial effects of nonlinear damping is extended to the systems subject to general inputs including both multi-tone and random inputs. A rigorous analysis is conducted based on single degree of freedom systems subject to general inputs. The analysis reveals the conditions under which the antisymmetric nonlinear damping is beneficial for improving energy harvester performance and reducing of the power of system output in vibration isolation. Moreover, the beneficial effects are demonstrated by two case studies.
TL;DR: In this article , a lattice study of SU (4) gauge theory with two Dirac fermions in the fundamental and two in the two-index antisymmetric representation is presented.
Abstract: Abstract We present a lattice study of the SU (4) gauge theory with two Dirac fermions in the fundamental and two in the two-index antisymmetric representation, a model close to a theory of partial compositeness proposed by G. Ferretti. Focus of this work are the methodologies behind the computation of the spectrum and the extrapolation of the chiral point for a theory with matter in multiple representations. While being still technical, this study provides important steps towards a non-perturbative understanding of the spectrum of theories of partial compositeness, which present a richer dynamics compared to single-representation theories. The multi-representation features are studied first in perturbation theory, and then non-perturbatively by adopting a dual outlook on lattice data through a joint analysis of time-momentum correlation functions and smeared spectral densities.
TL;DR: In this article , the exact solutions for the plate type piezoelectric bimorph energy harvesters composed of laminated cross-ply or angle-ply substrate plate were derived.
TL;DR: In this paper , the effects of the extended constitutive relations on the propagation of electromagnetic waves in bi-isotropic and bi-anisotropic media using a classical general approach based on the evaluation of dispersion relations and refractive indices were investigated.
Abstract: The Maxwell equations and the constitutive relations describe the classical propagation of electromagnetic waves in continuous matter. Here, we investigate the effects stemming from extended constitutive relations on the propagation of waves in bi-isotropic and bi-anisotropic media using a classical general approach based on the evaluation of dispersion relations and refractive indices. For the bi-anisotropic media, we specify two classes of magnetoelectric parameters represented by symmetric and antisymmetric tensors. The three cases examined have provided real and distinct refractive indices for two propagating modes, which implies birefringence. The propagating modes were also carried out in all cases. The anisotropy or birefringence effect, given by the rotatory power or phase difference, was evaluated in terms of the magnetoelectric parameters of the theory in each case. The propagation orthogonal to the vectors used to parametrize the symmetric and antisymmetric magnetoelectric tensors is described by distinct modes, representing a route to identify the kind of bi-anisotropic medium examined. The group velocity and Poynting vector were also evaluated for all the cases examined to discuss the energy propagation in these anisotropic media.
TL;DR: In this paper , a new model is proposed based on a single periodic structure, where arrays of asymmetric and symmetric interfacial delaminations are intentionally introduced into the top and bottom part of a stack of periodic elastic layers, respectively.
Abstract: Unidirectional nonreciprocal wave propagation is an unprecedented phenomenon, which has attracted much research interest. Connecting a phononic crystal with an asymmetric structure to break the spatial inversion symmetry is a popular manner to realize this phenomenon using the wave mode transformation. In this paper, a new model is proposed based on a single periodic structure. The arrays of asymmetric and symmetric interfacial delaminations are intentionally introduced into the top and the bottom part of a stack of periodic elastic layers, respectively. So, the structural spatial inversion symmetry can be broken and the guided waves can pass through the whole structure only from the top side with the changed mode generated by the array of asymmetric interfacial delaminations. Thus, it is indispensable for the part of phononic crystal that the partial band-gaps of symmetric and antisymmetric guided waves have to be separated, which is the reason why we introduce the array of symmetric central or side interfacial delaminations into the stack of periodic elastic layers. The transmission spectra of the guided waves and the dispersion curves for the unit cell imposed by the Bloch–Floquet boundary condition are both calculated by the spectral element method. Then, the interfacial delamination-induced unidirectional propagation of guided waves in the finite stack of periodic elastic layers is numerically confirmed. This paper provides a new concept to control the waves propagating in phononic crystals via the insertion of some interfacial delaminations or cracks.
TL;DR: Within the electrostatic formulation of holographic duals to (balanced) conformal quivers in five and three dimensions, the authors derived general expressions for various quantities participating in the formalism and applied these to examples, connecting some results present in the bibliography.
TL;DR: In this article , a unified semianalytical model based on the extensible deformation assumption and nonlinear theory of plates and shells was proposed to predict bistability of two types of bistable polymer composite structures.
Abstract: Bistable polymer composite structures are morphing shells that can change shape and maintain two stable configurations. At present, mainly two types of bistable polymer composite structures are being studied: cross-ply laminates and antisymmetric cylindrical shells. This paper proposes a unified semianalytical model based on the extensible deformation assumption and nonlinear theory of plates and shells to predict bistability. Moreover, the higher-order theoretical model is extended for better prediction accuracy, while the number of degrees of freedom is not increased; this ensures a lower computational cost. Finally, based on these theoretical models, the main factors affecting the stable characteristic of the two bistable polymer composite structures are determined by comparing the models of various orders. The main challenges in describing the bistable behavior, such as bifurcation points and the curvatures of stable states, are addressed through prediction of the corner transversal displacement in stable configurations. The results obtained from the theoretical model are validated through nonlinear finite element analysis.