Symmetry Analysis Research Articles

Lattice Hamiltonian for adjoint QCD2

We introduce a Hamiltonian lattice model for the (1 + 1)-dimensional SU(Nc) gauge theory coupled to one adjoint Majorana fermion of mass m. The discretization of the continuum theory uses staggered Majorana fermions. We analyze the symmetries of the lattice model and find lattice analogs of the anomalies of the corresponding continuum theory. An important role is played by the lattice translation by one lattice site, which in the continuum limit involves a discrete axial transformation. On a lattice with periodic boundary conditions, the Hilbert space breaks up into sectors labeled by the Nc-ality p = 0, … Nc − 1. Our symmetry analysis implies various exact degeneracies in the spectrum of the lattice model. In particular, it shows that, for m = 0 and even Nc, the sectors p and p′ are degenerate if |p − p′| = Nc/2. In the Nc = 2 case, we explicitly construct the action of the Hamiltonian on a basis of gauge-invariant states, and we perform both a strong coupling expansion and exact diagonalization for lattices of up to 12 lattice sites. Upon extrapolation of these results, we find good agreement with the spectrum computed previously using discretized light-cone quantization. One of our new results is the first numerical calculation of the fermion bilinear condensate.

Lie symmetry analysis of time fractional nonlinear partial differential equations in Hilfer sense

Lie symmetry analysis of time fractional nonlinear partial differential equations in Hilfer sense

Exact solutions, wave dynamics and conservation laws of a generalized geophysical Korteweg de Vries equation in ocean physics using Lie symmetry analysis

An evolution equation is a partial diferential equation that describes the time evolution of a physical system starting from given initial data. Evolution equations arise from many areas of applied and engineering sciences. To this end, this article investigates the analytical studies of a generalized geophysical Korteweg-de Vries equation in ocean physics. The examination of this model is conducted via the Lie group theory of diferential equations. In the first place, point symmetries, which are constituent elements of a four-dimensional Lie algebra, are systematically computed. Thereafter, one-parameter transformation groups for the algebra are calculated. Besides, going forward, a one-dimensional optimal system of subalgebras is derived in a procedural manner. Sequel to this, the subalgebras and combination of the achieved symmetries are invoked in the reduction proces which enables the derivation of nonlinear ordinary diferential equations associated with the generalized geophysical Korteweg-de Vries equation under study. Most of the achieved nonlinear ordinary diferential equations are further solved either via direct integration or using a power series approach. Furthermore, travelling wave solutions are initially obtained. This is attained via direct integration and the use of Jacobi elliptic function approach. These techniques enable the attainment of various exact soliton solutions, including non-topological soliton solutions as well as general periodic function solutions of note, such as cosine amplitude, sine amplitude, and delta amplitude solutions of the model. Furthermore, numerical simulations of the solutions are invoked to gain a gross knowledge of the physical phenomena represented by the under-study generalized geophysical Korteweg-de Vries equation in ocean physics. In the end, the investigation further gives attention to the calculation of conserved vectors for the model using Ibragimov's theorem for conservation laws, as well as Noether's theorem.

Predictable Gate-Field Control of Spin in Altermagnets with Spin-Layer Coupling.

Spintronics, a technology harnessing electron spin for information transmission, offers a promising avenue to surpass the limitations of conventional electronic devices. While the spin directly interacts with the magnetic field, its control through the electric field is generally more practical, and has become a focal point in the field. Here, we propose a mechanism to realize static and almost uniform effective magnetic field by gate-electric field. Our method employs two-dimensional altermagnets with valley-mediated spin-layer coupling (SLC), in which electronic states display valley-contrasted spin and layer polarization. For the low-energy valley electrons, a uniform gate field is approximately identical to a uniform magnetic field, leading to predictable control of spin. Through symmetry analysis and abinitio calculations, we predict altermagnetic monolayer Ca(CoN)_{2} and its family materials as potential candidates hosting SLC. We show that an almost uniform magnetic field (B_{z}) indeed is generated by gate field (E_{z}) in Ca(CoN)_{2} with B_{z}∝E_{z} in a wide range, and B_{z} reaches as high as about 10^{3} T when E_{z}=0.2 eV/Å. Furthermore, owing to the clean band structure and SLC, one can achieve perfect and switchable spin and valley currents and significant tunneling magnetoresistance in Ca(CoN)_{2} solely using the gate field. Our work provides new opportunities to generate predictable control of spin and design spintronic devices that can be controlled by purely electric means.

Exact solutions, conservation laws, and shock wave propagation of two-lanes traffic flow model via Lie symmetry

In this study, we consider a hyperbolic system of quasi-linear partial differential equations, governed by the traffic flow model on two lanes. We employ symmetry analysis and establish one-dimensional optimal subalgebras. Subsequently, we reduce the model into a system of ordinary differential equations for each optimal subalgebra and construct some new exact solutions; some of them are presented graphically. Further, by imposing the traveling wave transformation, we derive solutions including peakon-type solitons and upward parabola solitons. Furthermore, we demonstrate the existence of the nonlinear self-adjointness property of the model and formulate conservation laws. Finally, we discussed the evolutionary behavior of C1-waves, characteristic shock, and their interactions through one of the obtained exact solutions.

Group foliations of the β-plane barotropic vorticity equation

Despite the large number of publications on symmetry analysis of the barotropic vorticity equation on the β-plane, its group foliations have not been considered previously. The present publication aims to address this shortcoming. Group foliations are constructed for the equation, and based on them, invariant solutions are derived, some of which generalize previously known exact analytical solutions. There is also a discussion of the pros and cons of the group foliation approach including consideration of some numerical issues.

Hydrogen Bonding Analysis of Structural Transition-Induced Symmetry Breaking and Spin Splitting in a Hybrid Perovskite Employing a Synergistic Diffraction-DFT Approach.

Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) offer an outstanding opportunity for spin-related technologies owing in part to their tunable structural symmetry breaking and distortions driven by organic-inorganic hydrogen (H) bonds. However, understanding how H-bonds tailor inorganic symmetry and distortions and therefore enhance spin splitting for more effective spin manipulation remains imprecise due to challenges in measuring H atom positions using X-ray diffraction. Here, we report a thermally induced structural transition (at ∼209 K) for a 2D HOIP, (2-BrPEA)2PbI4 [2-BrPEA = 2-(2-bromophenyl)ethylammonium], which induces inversion asymmetry and a strong spin splitting (ΔE > 30 meV). While X-ray diffraction generally establishes heavy atom coordinates, we utilize neutron diffraction for accurate H atom position determination, demonstrating that the structural transition-induced rearrangement of H-bonds with distinct bond strengths asymmetrically shifts associated iodine atom positions. Consequences of this shift include an increased structural asymmetry, an enhanced difference between adjacent interoctahedra distortions (i.e., Pb-I-Pb bond angles), and therefore significant spin splitting. We further show that H-only density-functional theory (DFT) relaxation of the X-ray structure shifts H atoms to positions that are consistent with the neutron experimental data, validating a convenient pathway to more generally improve upon HOIP H-bonding analyses derived from quicker/less-expensive X-ray data.

Symmetry group detection of point clouds in 3D via a decomposition method

Analyzing the symmetries present in point clouds, which represent sets of 3D coordinates, is important for understanding their underlying structure and facilitating various applications. In this paper, we propose a novel decomposition-based method for detecting the entire symmetry group of 3D point clouds. Our approach decomposes the point cloud into simpler shapes whose symmetry groups are easier to find. The exact symmetry group of the original point cloud is then derived from the symmetries of these individual components. The method presented in this paper is a direct extension of the approach recently formulated in Bizzarri et al. (2022a) for discrete curves in plane. The method can be easily modified also for perturbed data. This work contributes to the advancement of symmetry analysis in point clouds, providing a foundation for further research and enhancing applications in computer vision, robotics, and augmented reality.

Symmetry analysis, conservation laws and exact soliton solutions for the $$(n+1)$$-dimensional modified Zakharov–Kuznetsov equation in plasmas with magnetic fields

Symmetry analysis, conservation laws and exact soliton solutions for the $$(n+1)$$-dimensional modified Zakharov–Kuznetsov equation in plasmas with magnetic fields

Alternating spin splitting of electronic and magnon bands in two-dimensional altermagnetic materials

Abstract Unconventional antiferromagnetism dubbed as altermagnetism was firstly discovered in rutile structured magnets, which is featured by spin splitting even without the spin-orbit coupling effect. This interesting phenomenon has led to the discovery of more altermagnetic materials. In this work, we explore two-dimensional altermagnetic materials by studying two series of two-dimensional magnets, including MF4 with M covering all 3d and 4d transition metal elements, as well as TS2 with T = V, Cr, Mn, Fe. Through the magnetic symmetry operation of the RuF4 and MnS2, it was verified that breaking the time inversion is a necessary condition for spin splitting. Based on symmetry analysis and first-principles calculations, we found that the electronic bands and magnon dispersion experience alternating spin splitting along the same path. This work paves the way for exploring altermagnetism in two-dimensional materials.

Nonlinear orbital and spin Edelstein effect in centrosymmetric metals

Nonlinear spintronics combines nonlinear dynamics with spintronics, opening up new possibilities beyond linear responses. A recent theoretical work [Xiao et al. Phys. Rev. Lett.130, 166302 (2023)] predicts the nonlinear generation of spin density [nonlinear spin Edelstein effect (NSEE)] in centrosymmetric metals based on symmetry analysis combined with first-principle calculation. This paper focuses on the fundamental role of orbital degrees of freedom for the nonlinear generation in centrosymmetric systems. Using a combination of tight-binding model and density functional theory calculations, we demonstrate that nonlinear orbital density can arise independently of spin–orbit coupling. In contrast, spin density follows through spin–orbit coupling. We further elucidate the microscopic mechanism responsible for this phenomenon, which involves the NSEE induced by electric-field-induced orbital Rashba texture. In addition, we also explore the potential applications of the nonlinear orbital and spin Edelstein effect for magnetic-field-free switching of magnetization.

Noether symmetry analysis in f(T,TG) gravity theory: A study of classical cosmology

This work deals with [Formula: see text] gravity in the background of homogeneous and isotropic flat Friedmann–Lemaître–Robertson–Walker (FLRW) space-time model. The main aim of this work is to examine whether the model supports the observational data or not. By using the Noether symmetry analysis, not only the symmetry vector is obtained, but also the coupling function [Formula: see text] in the Lagrangian has been determined. Also, the symmetry analysis identifies a transformation from [Formula: see text] to [Formula: see text] in such a way that one of the new variables become cyclic along the direction symmetry vector and as a result the field equations become solvable. Then the solution is analyzed from the observational point of view. Finally, quantum cosmology has been formulated for the present model and the wave function of the universe has been evaluated by solving the Wheeler–DeWitt equation with some assumptions.

Symmetry Analysis in Construction Two Dynamic Lightweight S-Boxes Based on the 2D Tinkerbell Map and the 2D Duffing Map

The lack of an S-Box in some lightweight cryptography algorithms, like Speck and Tiny Encryption Algorithm, or the presence of a fixed S-Box in others, like Advanced Encryption Standard, makes them more vulnerable to attacks. This proposal presents a novel approach to creating two dynamic 8-bit S-Boxes (16 × 16). The generation process for each S-Box consists of two phases. Initially, the number initialization phase involves generating sequence numbers 1, sequence numbers 2, and shift values for S-Box1 using the 2D Tinkerbell map. Additionally, sequence numbers 3, sequence numbers 4, and shift values for S-Box2 are generated using the 2D Duffing map. Subsequently, the S-Box construction phase involves the construction of S-Box1 and S-Box2. The effectiveness of the newly proposed S-Boxes was evaluated based on various criteria, including the bijective property, balance, fixed points, and strict avalanche criteria. It was observed that S-Box1 achieved a remarkable linear and differential branch number of 4, surpassing any previous studies. Furthermore, it exhibited a non-linearity of 105.50, a differential uniformity of 12, and an algebraic degree of 7. Similarly, S-Box2 also achieved a linear and differential branch number of 4, a non-linearity of 105.25, a differential uniformity of 14, and an algebraic degree of 7. Moreover, the reduction in the number of linear and nonlinear operations for both S-Boxes makes them suitable for lightweight algorithms. The architecture of the proposed S-Boxes demonstrates robustness, with a total of 3.35 × 10504 possible S-Boxes, providing protection against algebraic attacks.

On integrability of a new dynamical system associated with the BBM‐type hydrodynamic flow

This article explores the exceptional integrability property of a family of higher‐order Benjamin–Bona–Mahony (BBM)‐type nonlinear dispersive equations. Here, we highlight its deep relationship with a generalized infinite hierarchy of the integrable Riemann‐type hydrodynamic equations. A previous Lie symmetry analysis revealed a particular case which was conjectured to be integrable. Namely, a Lie–Bäcklund symmetry exists, thus highlighting another associated dynamical system. Here, we investigate these two equations using the gradient‐holonomic integrability scheme. Moreover, we construct their infinite hierarchy of conservation laws analytically, using three compatible Poisson structures to prove the complete integrability of both dynamical systems. We investigate these two equations using the so‐called gradient‐holonomic integrability scheme. Based on this scheme, applied to the equation under consideration, we have analytically constructed its infinite hierarchy of conservation laws, derived two compatible Poisson structures, and proved its complete integrability.

Matching constraint extraction for analog integrated circuits layout via edge classify

Achieving matching constraints between various components is important in analog integrated circuit (IC) layout design, as it can reduce the impact of layout parasitics on the performance of IC. When automating analog integrated circuit layout design, identifying accurate matching constraints is an essential step before placement and routing. The matching relationship between devices strongly depends on circuit's topology and design expertise. This work focuses on differential circuits with various topologies and proposes a supervised learning framework that incorporates symmetry analysis. The heterogeneous multi-relationship graph representation is proposed to capture circuit's topology and extract matching constraints. Additionally, a symmetry analysis algorithm and filtering method based on matching levels are investigated to enhance the model's performance. The experimental results demonstrate that this work maintains a low false alarm rate and outperforms other matching constraint detection algorithms in terms of F1 score and accuracy.

Controlling Noncollinear Ferromagnetism in van der Waals Metal-Organic Magnets.

Van der Waals (vdW) magnets both allow exploration of fundamental 2D physics and offer a route toward exploiting magnetism in next generation information technology, but vdW magnets with complex, noncollinear spin textures are currently rare. We report here the syntheses, crystal structures, magnetic properties and magnetic ground states of four bulk vdW metal-organic magnets (MOMs): FeCl2(pym), FeCl2(btd), NiCl2(pym), and NiCl2(btd), pym = pyrimidine and btd = 2,1,3-benzothiadiazole. Using a combination of neutron diffraction and bulk magnetometry we show that these materials are noncollinear magnets. Although only NiCl2(btd) has a ferromagnetic ground state, we demonstrate that low-field hysteretic metamagnetic transitions produce states with net magnetization in zero-field and high coercivities for FeCl2(pym) and NiCl2(pym). By combining our bulk magnetic data with diffuse scattering analysis and broken-symmetry density-functional calculations, we probe the magnetic superexchange interactions, which when combined with symmetry analysis allow us to suggest design principles for future noncollinear vdW MOMs. These materials, if delaminated, would prove an interesting new family of 2D magnets.

Dynamical Symmetry-Reduction-Induced Giant Anharmonicity in IV-VI Compounds: Role of Cation Lone-Pair s Electrons.

The low thermal conductivity of group IV-VI semiconductors is often attributed to the soft phonons and giant anharmonicity observed in these materials. However, there is still no broad consensus on the fundamental origin of this giant anharmonic effect. Utilizing first-principles calculations and group symmetry analysis, we find that the cation lone-pairs s electrons in IV-VI materials cause a significant coupling between occupied cation s orbitals and unoccupied cation p orbitals due to the symmetry reduction when atoms vibrate away from their equilibrium positions under heating. This leads to an electronic energy gain, consequently flattening the potential energy surface and causing soft phonons and strong anharmonic effects. Our findings provide an intrinsic understanding of the low thermal conductivity in IV-VI compounds by connecting the anharmonicity with the dynamical electronic structures, and can also be extended to a large family of hybrid systems with lone-pair electrons, for promising thermoelectric applications and predictive designs.

Lie symmetry analysis of cubic–quartic optical solitons having cubic–quintic–septic–nonic form of self-phase modulation structure

AbstractThe present study examines optical solitons characterized by cubic–quartic dynamics and featuring a self-phase modulation structure encompassing cubic, quintic, septal, and nonic terms. Soliton solutions are obtained through Lie symmetry analysis, followed by integration of the resulting ordinary differential equations using Kudryashov’s auxiliary equation method and a hyperbolic function approach. A comprehensive range of optical soliton solutions has been recovered, alongside the revelation of their criteria for existence.

Sliding Ferroelectricity Engineered Coupling between Spin Hall Effect and Layertronics in 2D Lattice.

Coupling the spin Hall effect with novel degrees of freedom of electrons is central to the rich phenomena observed in condensed-matter physics. Here, using symmetry analysis and a low-energy k·p model, we report the sliding ferroelectricity engineered coupling between spin Hall effect and emerging layertronics, thereby generating the layer spin Hall effect (LSHE), in a 2D lattice. The physics is rooted in a pair of T-symmetry connected valleys, which experience spin splitting accompanied by large Berry curvature under spin-orbit coupling. The interaction between the out-of-plane ferroelectricity and electronic properties gives rise to the layer-locked Berry curvature and thus layer-polarized spin Hall effect (LP-SHE) in the bilayers. Such LP-SHE is strongly coupled with sliding ferroelectricity, enabling it to be ferroelectrically reversible. Using first-principles calculations, the mechanism is further demonstrated in a series of real bilayer systems, including MoS2, MoTe2, WSe2, MoSi2P4, and MoSi2As4. These phenomena and insights open a new direction for spin Hall effect.

Group Classification of Second-Order Linear Neutral Differential Equations

In this paper, we shall extend the method of obtaining symmetries of ordinary differential equations to second-order non-homogeneous functional differential equations with variable coefficients. The existing research for delay differential equations defines a Lie-Bäcklund operator and uses the invariant manifold theorem to obtain the infinitesimal generators of the Lie group. However, we shall use a different approach that requires Taylor’s theorem for a function of several variables to obtain a Lie invariance condition and the determining equations for second-order functional differential equations. Certain standard results from the theory of ordinary differential equations have been employed to simplify the equation under study. The symmetry analysis of this equation was found to be non-trivial for arbitrary variable coefficients. In such cases, by selecting certain specific functions, arising in most practical models, we find the symmetries that are seen to be in terms of Bessel’s functions, Mathieu functions, etc. We then make a complete group classification of the second-order linear neutral differential equation, for which there is no existing literature.