Spatial Symmetry Research Articles

Impacts of spatial symmetries on stimulated Brillouin scatterings in nanoscale silicon waveguides: a theoretical and numerical study considering material anisotropies.

Fully considering the mechanical and photoelastic anisotropies of monocrystalline silicon, the impacts of spatial symmetries on the stimulated Brillouin scatterings (SBSs) in nanoscale suspended silicon waveguides are studied theoretically and numerically based on group theory. First, starting from an assumption that the principal material coordinate system can be arbitrarily orientated in a waveguide with fixed geometry, the silicon waveguides are systematically classified into a number of point groups according to their spatial symmetry features. Thereafter, the symmetry characteristics of physical fields and SBS opto-mechanical coupling characteristics in the silicon waveguides belonging to different point groups are further examined, and the major new findings can be summarized as follows: The SBS opto-mechanical couplings in several kinds of silicon waveguides with certain nontrivial symmetry features exhibit relatively predictable behaviors in that the opto-mechanical coupling coefficients can be deterministically vanishing or nonvanishing under very few constraints, which can thus serve as general symmetry selection rules for SBSs in suspended silicon waveguides. The results obtained in the present study could be a useful theoretical reference for the design of novel SBS-active silicon photonic devices.

Normal mode description of phases of matter: Application to heat capacity

Understanding thermodynamics in liquids at the atomic level is challenging because of strong atomic interactions and lack of spatial symmetry. Recent prior theoretical works have focused on describing heat capacity of liquids in terms of phonon-like excitations but often rely on fitting factors and assumptions. In this work, we propose characterizing various phases in terms of instantaneous normal modes (INMs) of structural snapshots from molecular dynamics simulations of single-element systems over wide ranges of temperature and pressure. We use the INMs to build a mode-level microscopic description of heat capacity and demonstrate that heat capacity of liquids can be described by a combination of both solidlike and gaslike degrees of freedom, leading to a more unified framework to fundamentally describe heat capacity of all three phases of matter: solid, liquid, and gas. Published by the American Physical Society 2024

Analytical exploration of generic undamped mass–spring chains: A comprehensive study

Analysis of structural vibrations presents challenges due to the coupling between different degrees of freedom, often preventing the derivation of analytical expressions for quantities such as poles, vibration amplitude, etc. While numerical methods are commonly employed to tackle such challenges, their purely numerical nature prevents achieving a comprehensive understanding of the system behaviour. This paper builds on a novel recursive transfer function formulation recently proposed by the authors to analytically characterise the dynamics of generic undamped mass-chain systems. This approach provides fundamental properties and analytical insights that cannot be obtained through current numerical approaches, representing a significant breakthrough in the understanding of vibrations and offering valuable insights for analysing complex vibrating systems. These results presented in this paper allow for a rapid assessment of the minimum phase nature of the vibration system through straightforward stability assessment, and present analytical expressions for sums and multiplications of natural frequencies squared by induction and Vieta’s formulas. Furthermore, it derives conditions for existence of repeated roots using direct analytical derivation of the characteristics equations, including purely imaginary roots and repeated roots at the origin, showing that repeated roots can only occur when some forms of spatial symmetries exist, and confirms bounds for the arithmetic mean of natural frequencies by using inequalities between geometric, arithmetic and quadratic means. Additionally, analytical conditions are established for systems with different degrees of freedom to share the same roots, providing a theoretical foundation for eigenvalue assignment in the time domain or pole placement in the frequency domain. This foundation enables the determination of desired natural frequencies from scratch using transparent analytical conditions, without relying on complex algorithms typically required by current inverse methodologies involving passive structural modifications or active controllers. Moreover, this paper also explores the relationship between independent and coupled vibrations, providing insights for comparing natural frequencies. Overall, this paper contributes to a deeper understanding of structural vibrations through analytical exploration and offers practical guidance for eigenvalue assignment and natural frequency analysis.

Topotaxis of active particles across long distances by sliding along obstacles

Many biological active agents respond to gradients of environmental cues by redirecting their motion. In addition to the well-studied prominent examples such as phototaxis and chemotaxis, there has been considerable recent interest in topotaxis, i.e., the ability to sense and follow topographic environmental cues. A trivial topotaxis is achievable through a spatial gradient of obstacle density, though over limited length scales. Here, we introduce a type of topotaxis based on sliding of particles along obstacles—as observed, e.g., in bacterial dynamics near surfaces. We numerically demonstrate how imposing a gradient in the angle of sliding along pillars breaks the spatial symmetry and biases the direction of motion, resulting in an efficient topotaxis in a uniform pillar park. By repeating blocks of pillars with a strong gradient of sliding angle, we propose an efficient method for guiding particles over arbitrary long distances. We provide an explanation for this spectacular phenomenon based on effective reflection at the borders of neighboring blocks. Our results are of technological and medical importance for design of efficient taxis devices for living agents. Published by the American Physical Society 2024

Local Markers for Crystalline Topology.

Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches currently used to classify bulk topological crystalline phases cannot predict the existence, localization, or spectral isolation of any resulting boundary-localized modes. While interfaces between materials in different crystalline phases must have topological states at some energy, these states need not appear within the band gap, and thus may not be useful for applications. Here, we derive a class of local markers for identifying material topology due to crystalline symmetries, as well as a corresponding measure of topological protection. As our real-space-based approach is inherently local, it immediately reveals the existence and robustness of topological boundary-localized states, yielding a predictive framework for designing topological crystalline heterostructures. Beyond enabling the optimization of device geometries, we anticipate that our framework will also provide a route forward to deriving local markers for other classes of topology that are reliant upon spatial symmetries.

In-plane strain-induced structural phase transition and interlayer antiferromagnetic skyrmions in 2H-VSe2 bilayer

The sliding and manipulation of interlayer magnetism and magnetic topological textures in two-dimensional (2D) layered materials have recently received tremendous attention. In this work, using first-principles calculations, we report a structural phase transition induced by manipulating the interlayer distance using an in-plane biaxial strain in a 2H-VSe2 bilayer. This structural phase transition is accompanied by a semiconductor-to-metal transition, in-plane-to-out-of-plane magnetization switching, and a reversal in the chirality of the Dzyaloshinskii–Moriya interaction (DMI). The binding strength of the interlayer Se2–Se3 atoms and charge density difference can serve as indicators for this structural phase transition. Furthermore, the interlayer distance of Se2–Se3 atoms can be employed as a descriptor that perfectly characterizes the degree of symmetry breaking and the magnitude of the DMI resulting from the broken spatial symmetry due to sliding. In addition, using atomistic simulations, we identify magnetic topological textures such as interlayer antiferromagnetic (AFM) frustrated bimerons and interlayer AFM skyrmions with strain. These results are beneficial for understanding and manipulating the interlayer properties of 2D layered materials through in-plane biaxial strain. In addition, the interlayer AFM frustrated bimerons and skyrmions in bilayer VSe2, which can suppress the skyrmion Hall effect due to the canceled Magnus forces in the top and bottom layers, highlight the promising applications of VSe2 in next-generation information storage devices.

Spatiotemporal lower-limb asymmetries during stair descent in athletes following anterior cruciate ligament reconstruction

PurposeThis study evaluated motor control recovery at different times following anterior cruciate ligament reconstruction (ACLR) by investigating lower-limb spatiotemporal symmetry during stair descent performances. MethodsWe used a cross-sectional design to compare asymptomatic athletes (Controls, n = 18) with a group of people with ACLR (n = 49) divided into three time-from-ACLR subgroups (Early: <6 months, n = 17; Mid: 6–18 months, n = 16; Late: ≥18 months, n = 16). We evaluated: “temporal symmetry” during the stance subphases (single-support, first and second double-support) and “spatial symmetry” for hip-knee-ankle intra-joint angular displacements during the stance phase using a dissimilarity index applied on superimposed 3D phase plots. ResultsWe found significant between-group differences in temporal variables (p ≤ 0.001). Compared to Controls, both Early and Mid (p ≤ 0.05) showed asymmetry in the first double-support time (longer for their injured vs. non-injured leg), while Early generally also showed longer durations in all other phases, regardless of stepping leg. No statistically significant differences were found for spatial intra-joint symmetry between groups. ConclusionTemporal but not spatial asymmetry in stair descent is often present early after ACLR; it may remain for up to 18 months and may underlie subtle intra- and inter-joint compensations. Spatial asymmetry may need further exploration.

Room-temperature sub-100 nm Néel-type skyrmions in non-stoichiometric van der Waals ferromagnet Fe3-xGaTe2 with ultrafast laser writability

Realizing room-temperature magnetic skyrmions in two-dimensional van der Waals ferromagnets offers unparalleled prospects for future spintronic applications. However, due to the intrinsic spin fluctuations that suppress atomic long-range magnetic order and the inherent inversion crystal symmetry that excludes the presence of the Dzyaloshinskii-Moriya interaction, achieving room-temperature skyrmions in 2D magnets remains a formidable challenge. In this study, we target room-temperature 2D magnet Fe3GaTe2 and unveil that the introduction of iron-deficient into this compound enables spatial inversion symmetry breaking, thus inducing a significant Dzyaloshinskii-Moriya interaction that brings about room-temperature Néel-type skyrmions with unprecedentedly small size. To further enhance the practical applications of this finding, we employ a homemade in-situ optical Lorentz transmission electron microscopy to demonstrate ultrafast writing of skyrmions in Fe3-xGaTe2 using a single femtosecond laser pulse. Our results manifest the Fe3-xGaTe2 as a promising building block for realizing skyrmion-based magneto-optical functionalities.

Open-Endedness in Genelife.

We explore the open-ended nature of evolution in Genelife, an evolutionary extension of Conway's Game of Life cellular automaton in which "live" cell states are endowed at birth with a genome that affects their local dynamics and can be inherited. Both genetic sequences and locally connected spatial patterns are analyzed for novelty, keeping track of all new structures, and innovation is quantified using activity statistics. The impacts of both spatial symmetry breaking with nontotalistic rules and superimposed density regulation of the live state proliferation on the open-ended nature of the evolution are explored. Conditions are found where both genetic and spatial patterns exhibit open-ended innovation. This innovation appears to fall short of functional biological innovation, however, and potential reasons for this are discussed.

Linear instability and weakly nonlinear effects in eastward dipoles

The linear instability and weakly nonlinear dynamics of eastward-propagating, steady-state Larichev–Reznik vortex dipoles are explored in terms of two-dimensional normal-mode analysis. To extract the fastest growing normal modes, we apply both breeding methodology based on solving the initial-value problem, as well as a direct-solution approach through the full-spectrum eigenproblem involving large matrices. We find that the amplification rate of dipole instability decreases with respect to increase in dipole intensity. In our study, both approaches yield consistent results and are systematically compared to provide guidance for further studies of vortex structures.We consider nonlinear self-interaction of the fastest growing mode, along with the induced eddy fluxes, their divergence and mechanical energy balance. Through this analysis, we find that the unstable mode leads to weakening of the dipole by extracting its energy and exchanging potential vorticity content in the down-gradient sense, thus, providing a nonlinear physical mechanism for the dipole destruction. In particular, we highlight the fundamental importance of the west-east asymmetry of the normal mode for destruction to be realized. In summary, we consider this work to be a foundational demonstration of useful methodology for future studies of dynamics and stability of isolated vortices without simplifying spatial symmetries, such as ubiquitous vortices in geophysical fluids.

Tunable pure spin current realized by photogalvanic effect in triangulene dimer based nano-devices

The unique magnetic properties of triangulene and its homologues have generated a great deal of interest in recent years. Triangulene dimers, with their magnetic ground states and the detection of singlet-triplet spin excitations, have been synthesized on-surface by Mishra, and shown to be suitable for spintronics applications. In our study, we use first-principles calculations to investigate the photogalvanic effect (PGE) of triangulene dimers based nano-devices. The devices are constructed by two graphene nanoribbon electrodes and a triangulene dimer molecule connected by carbon chains, which has a spatial inversion symmetry. We find that when light irradiation is applied to the device, there are both spin-up and spin-down current induced with the same magnitude and opposite flowing directions. In this case, there is no accompanying charge current, but a finite pure spin current arises. Furthermore, we find that the currents generated by PGE can be tuned by impurity states. When nitrogen atoms are doped into the triangulene dimer molecule, we observe the emergence of impurity states, which supply other electron transition modes and result in a photo-current under different photon energy. Our findings provide a useful insight into the real application of tunable photoelectric carbon-based nano-devices. The PGE properties of triangulene dimers can be applied in the development of efficient spintronics devices.

Topological Nodal-Point Superconductivity in Two-Dimensional Ferroelectric Hybrid Perovskites.

Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) with enhanced stability, high tunability, and strong spin-orbit coupling have shown great potential in vast applications. Here, we extend the already rich functionality of 2D HOIPs to a new territory, realizing topological superconductivity and Majorana modes for fault-tolerant quantum computation. Especially, we predict that room-temperature ferroelectric BA2PbCl4 (BA for benzylammonium) exhibits topological nodal-point superconductivity (NSC) and gapless Majorana modes on selected edges and ferroelectric domain walls when proximity-coupled to an s-wave superconductor and an in-plane Zeeman field, attractive for experimental verification and application. Since NSC is protected by spatial symmetry of 2D HOIPs, we envision more exotic topological superconducting states to be found in this class of materials due to their diverse noncentrosymmetric space groups, which may open a new avenue in the fields of HOIPs and topological superconductivity.

Robust elastic shear wave transport in membrane-type topological metamaterials induced by material difference

Novel membrane-type topological metamaterials induced by material difference are investigated in this work. Different from previous common method to break spatial inversion symmetry and realize topological phase transition, choosing different materials is more convenient and shows more complex topological properties. Not all combinations of different materials can open the topological band gap. Interestingly, not only the topological interface modes but also the conventional interface modes are found in this system. Although strong energy localization capacity is found near the interface, both kinds of interface modes show different robustness against defects. To further enhance adaptability to environmental variations and broaden the working frequency range, the thermal field is introduced in membrane-type topological metamaterials to tune the dispersion relations. Fortunately, not only interface modes can be tuned to a lower frequency range, but also the energy localization of interface modes can be remained at a high level. The temperature can act as a switch to turn on/off the robust shear wave transport in membrane-type topological metamaterials. Given that, novel temperature-controlled topological metamaterials are expected to open new avenues for active elastic multifunctional devices.

A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-3 He2 @C60.

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two 3 He atoms encapsulated in C60 . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-3 He2 @C60 ) and triplet (ortho-3 He2 @C60 ) nuclear spin configurations, respectively. The ortho-3 He2 @C60 ground state is 5.69 cm-1 higher in energy than the para-3 He2 @C60 ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C60 embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of 3 He2 @C60 .

Spatial inversion symmetry breaking of vortex current in a biased-ladder superfluid

We investigate the quench dynamics of interacting bosons on a two-leg ladder in the presence of a uniform Abelian gauge field. The model hosts a variety of emergent quantum phases, and we focus on the superfluid biased-ladder phase breaking the Z2 symmetry of two legs. We observe an asymmetric spreading of vortex current and particle density, i.e., the vortices propagate ballistically on the right and dissolve during the propagation on the left, indicating spontaneous breaking of the spatial inversion symmetry. By decreasing the repulsion strength, it is found that the ballistic propagating vortices are more robust than the dissolving ones on the other side. Published by the American Physical Society 2024

Programmable flip-metasurface with dynamically tunable reflection and broadband undistorted transmission

Abstract We introduce a programmable flip-metasurface that can dynamically control the reflection while leaving the transmitted wavefront undistorted in an ultra-broad spectrum, i.e., the same as that of the incidence. This metasurface is constructed by unique meta-atoms that can be dynamically switched between two flip states, which correspond to the spatial inversion of each other. Due to the reciprocity principle and spatial inversion symmetry, the transmission is independent of the flip states, regardless of the frequency. While the reflection can be conveniently controlled by tuning the flip states. Dynamical steering of the reflected waves, such as diffuse reflection, focusing, and beam-splitting, is numerically and experimentally validated along with unaffected transmission. Our finding opens an approach to dynamically modulate reflections without affecting transmission, which could have broad potential applications ranging from wireless communications to stealth technology.

QuadGridSIM: A quadrilateral grid‐based method for high‐performance and robust trajectory similarity analysis

AbstractMeasuring trajectory similarity is a fundamental algorithm in trajectory data mining, playing a key role in trajectory clustering, pattern mining, and classification, for instance. However, existing trajectory similarity measures based on vector representation have challenges in achieving both fast and accurate similarity measurements. On one hand, most existing methods have a high computational complexity of O(n × m), resulting in low efficiency. On the other hand, many of them are sensitive to trajectory sampling rates and lack of accuracy. This article proposes QuadGridSIM, a quadrilateral grid‐based method for trajectory similarity analysis, which enables high‐performance trajectory similarity measure without the cost of low effectiveness. Specifically, we first realize the multiscale coding representation of trajectory data based on quadrilateral discrete grids. Then, a novel trajectory similarity measure is defined to reduce the computational complexity of O(n). Several effectiveness properties of QuadGridSIM are further optimized, including the spatial overlap, directionality, symmetry, and robustness to sampling rate variations. Experimental results based on real‐world and simulated taxi trajectory data indicate that QuadGridSIM outperforms most of the other tested algorithms developed previously in terms of effectiveness, particularly in its robustness regarding trajectory sampling rates. Furthermore, QuadGridSIM exhibits superior performance and is approximately one order of magnitude faster than previous methods in the literature. QuadGridSIM provides a solution to the low‐efficiency problem of massive trajectory similarity analysis and can be applied in many application scenarios, such as route recommendation and suspect detection.

Nonreciprocal propagation of bending waves in spatiotemporally modulated prestressed beam

Breaking time or/and spatial symmetry can lead to unprecedent mechanical responses of a structure, the design of which is usually very intricate. This paper proposes a simple design of a beam structure with spatiotemporal modulation. In fact, a time-varying axial load applied to the ends of an elastic beam will induce space-time dependent axial force propagating in the form of longitudinal wave in the beam, which can modulate spatiotemporally the propagation of transverse bending waves. The governing equation is derived, of which the Floquet solution leads to a quadratic eigenvalue problem that can be solved for the frequency as a function of the wavenumber. Theoretical results show the existence of asymmetric wavenumber bandgaps and the unique dispersion diagram which is not periodic with respect to time or space. The breaking of temporal symmetry enables nonreciprocal propagation of transverse bending waves, which is confirmed by the finite element simulations. This modulation method offers promise for applications in the fields of elastic wave filter, frequency converter and magnitude amplifier.

Nonsequential double ionization of Ar atoms in counter-rotating two-color elliptically polarized laser fields

Electron correlation behaviors and recollision dynamics in nonsequential double ionization (NSDI) of Ar atoms in counter-rotating two-color elliptically polarized (TCEP) laser fields are investigated by using the classical ensemble model. The combined electric field in counter-rotating TCEP laser pulses traces out a trefoil pattern, i.e. the waveform in a period shows three leaves in different directions, and each leaf is called a lobe. Unlike counter-rotating two-color circularly polarized laser field, the combined electric field has no spatial symmetry. The amplitudes of the three field lobes and the angles between them are different. Thus, the returning electron mainly returns to the parent ion from one direction, and the electron momentum distributions show strong asymmetry. Numerical results show that the NSDI yield gradually decreases as the ellipticity increases, and the correlated behavior of the correlated electron momentum along the long axis of the laser polarization plane gradually evolves from correlation behavior mainly located in the first quadrant and the third quadrant to anti-correlation behavior mainly located in the second quadrant and fourth quadrant. In order to further understand the correlation behaviors of electron pairs, different characteristic times in the NSDI processes are discussed, respectively. It is found that single ionization events and recollision events gradually decrease, but single ionization time and recollision time change slightly. This may be the main reason for the decrease in NSDI yield. And as the ellipticity increases, the traveling time and the recollision energy gradually decrease, while the delay time increases. Therefore, we can conclude that ellipticity may be responsible for the NSDI process. In addition, further analysis finds that the shape of the trajectory becomes more and more triangular as the ellipticity increases due to the counter-rotating TCEP laser fields of the specific dynamical symmetries of the total net electric field. And it is found that whether it is a “short trajectory” or a “long trajectory”, more populations move to the second quadrant and the fourth quadrant as the ellipticity increases. The results show that increasing the ellipticity will gradually change the two electrons from emitting in the same direction to emitting in the opposite direction. This well demonstrates that both ellipticity and travelling time are responsible for the formation of the electron momentum distribution at the recollision time, meaning that both of them affect the emitted directions of both electrons.

Building spatial symmetries into parameterized quantum circuits for faster training

Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much research has been devoted to devising adequate gate-sets, typically respecting some symmetries of the problem, very little is known about how their parameters should be structured. In this work, we show that an ideal parameter structure naturally emerges when carefully considering spatial symmetries (i.e. the symmetries that are permutations of parts of the system under study). Namely, we consider the automorphism group of the problem Hamiltonian, leading us to develop a circuit construction that is equivariant under this symmetry group. The benefits of our novel circuitstructure, called ORB, are numerically probed in several ground-state problems. We find a consistent improvement (in terms of circuit depth, number of parameters required, and gradient magnitudes) compared to literature circuit constructions.