Special Symmetry Research Articles

Systematic design of Cauchy symmetric structures through Bayesian optimization

Using a new Bayesian Optimization algorithm to guide the design of mechanical metamaterials, we design nonhomogeneous 3D structures possessing the Cauchy symmetry, which dictates the relationship between continuum and atomic deformations. Recent efforts to merge optimization techniques with the design of mechanical metamaterials has resulted in a concentrated effort to tailor their elastic and post elastic properties. Even though these properties of either individual unit cells or homogenized continua can be simulated using multi-physics solvers and well established optimization schemes, they are often computationally expensive and require many design iterations, rendering the validation stage a significant obstacle in the design of new metamaterial designs. This study aims to provide a framework on how to utilize miniscule computational cost to control the elastic properties of metamaterials such that specific symmetries can be accomplished. Using the Cauchy symmetry as a design objective, we engineer structures through the strategic arrangement of 5 different unit cells in a 5×5×5 cubic symmetric microlattice structure. This lattice design, despite constituting a design space with 510 3D lattice configurations, can converge to an effective solution in only 69 function calls as a result of the efficiency of the new Bayesian optimization scheme. To validate the mechanical behavior of the design, the lattice structures were fabricated using multiphoton lithography and mechanically tested, revealing a close correlation between experiments and simulated results in the elastic regime. Ultimately, a similar methodology can be utilized to design metamaterials with other material properties, aspiring to control properties at different length scales, an endeavor that requires inordinate computation cost.

General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

The inverse scattering transformation for a novel nonlocal Lakshmanan–Porsezian–Daniel (LPD) equation with rapidly decaying initial data is studied in the framework of Riemann–Hilbert problem. Firstly, a novel integrable nonlocal LPD equation corresponding to a \(3\times 3\) Lax pair is proposed. Secondly, the inverse scattering process with a novel left-right \(3\times 3\) matrix Riemann–Hilbert(RH) problem is constructed. The analytical properties and symmetry relations for the Jost functions and scattering data are considerably different from the local ones. Due to the special symmetry properties for the nonlocal LPD equation, the zeros of the RHP problem are purely imaginary or occur in pairs. With different types and configuration of zeros, the soliton formula is provided and the rich dynamical behaviors for the three kinds of multi-solitons for the novel nonlocal LPD equation are demonstrated. Third, by a technique of adding perturbed parameters and limiting process, the formula of higher-order solitons for the nonlocal LPD equation is exhibited. Lastly, the plots of diverse higher-order solitons and various solutions corresponding to different combinations of the following zeros: purely imaginary higher-order zeros, purely imaginary simple zeros, pairs of non-purely imaginary simple zeros and pairs of non-purely imaginary higher-order zeros are displayed.

Symmetry-Breaking Bifurcations of the Information Bottleneck and Related Problems.

In this paper, we investigate the bifurcations of solutions to a class of degenerate constrained optimization problems. This study was motivated by the Information Bottleneck and Information Distortion problems, which have been used to successfully cluster data in many different applications. In the problems we discuss in this paper, the distortion function is not a linear function of the quantizer. This leads to a challenging annealing optimization problem, which we recast as a fixed-point dynamics problem of a gradient flow of a related dynamical system. The gradient system possesses an symmetry due to its invariance in relabeling representative classes. Its flow hence passes through a series of bifurcations with specific symmetry breaks. Here, we show that the dynamical system related to the Information Bottleneck problem has an additional spurious symmetry that requires more-challenging analysis of the symmetry-breaking bifurcation. For the Information Bottleneck, we determine that when bifurcations occur, they are only of pitchfork type, and we give conditions that determine the stability of the bifurcating branches. We relate the existence of subcritical bifurcations to the existence of first-order phase transitions in the corresponding distortion function as a function of the annealing parameter, and provide criteria with which to detect such transitions.

Chickpea Aquafaba-Based Emulsions as a Fat Replacer in Pound Cake: Impact on Cake Properties and Sensory Analysis.

This study evaluates the use of chickpea aquafaba (CA)-based emulsions as a potential substitute for palm oil (PO), using pound cake as a case study. The CA was characterized in terms of pH (6.38 ± 0.01), density (1.02 g mL−1 ± 0.01), color, total soluble solids (6.3 ± 0.2 °Bx), total solids (5.7 ± 0.2%), thermal properties through DSC, and apparent viscosity (2.5 cPa·s−1 ± 0.02 at 300 s−1). Emulsions containing 35, 30, and 25% of CA were produced and applied to cake formulation C1, C2, and C3, respectively. The cake batter was evaluated in terms of apparent density (0.87–1.04 g1 cm−3), rheology, and pH (6.6–6.8). The cakes were evaluated for specific volume, baking loss (8.9–9.5%), color, and symmetry index on day 1, and firmness, water activity (aw), and moisture content (%), after 14 days of storage. The cakes produced with the emulsions were found to have slightly higher specific volume (2.3 cm3 g−1) when compared to the control (C4) produced with PO (2.2 cm3 g−1). The moisture and aw decreased and firmness increased during storage. In terms of formulation (i.e., day 1 for C1, C2, C3, and C4), there was no significant difference for moisture. As for aw, the C4 (0.90) was significantly different from the cakes produced with emulsions (0.91–0.92). The results from the sensory evaluation, carried out with 120 panelists, showed no statistically significant difference between C3 and C4 for the attributes of aroma, color, texture, flavor, and overall impression. Based on our results, it appears that the CA-based emulsions have the potential to replace PO in pound-cake recipes, reducing total and saturated fat.

Non‐Hermitian Hartman Effect

AbstractThe Hartman effect refers to the rather paradoxical result that the time spent by a quantum mechanical particle or a photon to tunnel through an opaque potential barrier becomes independent of barrier width for long barriers. Such an effect, which has been observed in different physical settings, raised a lively debate and some controversies, owing to the correct definition and interpretation of tunneling times and the apparent superluminal transmission. A rather open question is whether (and under which conditions) the Hartman effect persists for inelastic scattering, that is, when the potential becomes non‐Hermitian and the scattering matrix is not unitary. Here, tunneling through a heterojunction barrier in the tight‐binding picture is considered, where the barrier consists of a generally non‐Hermitian finite‐sized lattice attached to two semi‐infinite nearest‐neighbor Hermitian lattice leads. A simple and general condition is derived for the persistence of the Hartman effect in non‐Hermitian barriers, showing that it can be found rather generally when non‐Hermiticity arises from nonreciprocal couplings, that is, when the barrier displays the non‐Hermitian skin effect, without any special symmetry in the system.

Subwavelength Chiral Spiral Acoustic Metamaterials for a Robust Topological Acoustic Insulator

Topological acoustic insulators enable sound waves to transmit along the surface without backscattering, which builds a new pathway towards sound wave control. However, a large share of topological acoustic insulators are realized based on special point group symmetry and Bragg scattering mechanism. This method not only exerts a restriction on the unit cell design but also requires the lattice constant to be comparable with the wavelength. In this paper, the chiral spiral acoustic metamaterials are constructed based on an Archimedean spiral structure. This structure enjoys subwavelength characteristics and is easy to construct. Taking advantage of the chirality of the spiral structure topological phases with opposite energy flow direction can be constructed. The edge state is formed at the interface composed of the spiral units sharing different chirality, which does not depend on point group symmetry. The topological transportation on the interfaces shows strong robustness despite sharp corners verified by straight and zigzag waveguides. The topological acoustic insulator with a chiral spiral structure provides a novel strategy for small acoustic devices with robust sound transmission.

Exploring symmetries in photoelectron holography with two-color linearly polarized fields

We investigate photoelectron holography in bichromatic linearly polarized fields of commensurate frequencies rω and sω, with emphasis on the existing symmetries and for which values of the relative phase between the two driving waves they are kept or broken. Using group-theoretical methods, we show that, additionally to the well-known half-cycle symmetry, which is broken for r + s odd, there are reflection symmetries around the field zero crossings and maxima, which may or may not be kept, depending on how both waves are dephased. The three symmetries are always present for monochromatic fields, while for bichromatic fields this is not guaranteed, even if r + s is even and the half-cycle symmetry is retained. Breaking the half-cycle symmetry automatically breaks one of the other two, while, if the half-cycle symmetry is retained, the other two symmetries are either both kept or broken. We analyze how these features affect the ionization times and saddle-point equations for different bichromatic fields. We also provide general expressions for the relative phases ϕ which retain specific symmetries. As an application, we compute photoelectron momentum distributions for ω − 2ω fields with the Coulomb quantum orbit strong-field approximation and assess how holographic structures such as the fan, the spider and interference carpets behave, focusing on the reflection symmetries. The features encountered can be traced back to the field gradient and amplitude affecting ionization probabilities and quantum interference in different momentum regions.

Phase diagram of chiral magnets via Green’s function method

In this paper, Green’s function method is applied to study the ferromagnetic system with Dzyaloshinkii–Moriya (DM) interaction in both two-dimension (2D) and three-dimension chiral magnets. Relevant properties in 2D magnets are calculated, such as the susceptibility, correlation function and analytical expressions of phase boundary. Based on the theoretical results, a new phase is predicted in the window of strong DM interaction characterized by a negative winding number. In addition, helical state in pure 2D material only appears at zero temperature. The analysis on correlation function shows a special symmetry of transverse spin correlation, which corresponds to the skyrmion phase. The results also prove the instability of helical state and its lifetime is numerically computed. Different from 2D magnets, helical state in 3D exists in the window of a lower Zeeman energy and has a long lifetime. DM interaction also reduces Curie temperature because of the spatial symmetry breaking.

Zeeman-type energy level splittings controlled by an electric field

Two-level systems are at the heart of quantum information and quantum computation based on qubits. The manipulation of Zeeman-type energy-level splittings is crucial for utilizing two-level systems hosted by electronic spin or pseudospin in crystalline materials. Of particular interest are Zeeman-type energy level splittings controlled by the electric field, most of which were realized in materials involving both spin and nonspin degrees of freedom that are entangled strongly via spin-orbital interaction. Here, we provide a strategy enabling the electric-field control of Zeeman-type energy-level splitting rooted in the nonspin degree of freedom of electrons---essentially from sublattice/atomic orbitals---in materials containing nonsymmorphic symmetry elements (e.g., glide plane or screw axis). The physical origin of such a Zeeman-type splitting is revealed as the breakdown of the specific nonsymmorphic symmetry elements by electric field. We further propose, via first-principles simulations, a platform system of $\mathrm{Ca}\mathrm{Ti}{\mathrm{O}}_{3}$ under tensile strain (ferroelectric compound) that accommodates a large Zeeman-type energy-level splitting of $\ensuremath{\sim}124\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$, controllable by the electric field.

Existence of weakly quasisymmetric magnetic fields without rotational transform in asymmetric toroidal domains

A quasisymmetry is a special symmetry that enhances the ability of a magnetic field to trap charged particles. Quasisymmetric magnetic fields may allow the realization of next generation fusion reactors (stellarators) with superior performance when compared with tokamak designs. Nevertheless, the existence of such magnetic configurations lacks mathematical proof due to the complexity of the governing equations. Here, we prove the existence of weakly quasisymmetric magnetic fields by constructing explicit examples. This result is achieved by a tailored parametrization of both magnetic field and hosting toroidal domain, which are optimized to fulfill quasisymmetry. The obtained solutions hold in a toroidal volume, are smooth, possess nested flux surfaces, are not invariant under continuous Euclidean isometries, have a non-vanishing current, exhibit a vanishing rotational transform, and fit within the framework of anisotropic magnetohydrodynamics. Due to the vanishing rotational transform, these solutions are however not suitable for particle confinement.

Random Tensor Theory for Tensor Decomposition

We propose a new framework for tensor decomposition based on trace invariants, which are particular cases of tensor networks. In general, tensor networks are diagrams/graphs that specify a way to "multiply" a collection of tensors together to produce another tensor, matrix or scalar. The particularity of trace invariants is that the operation of multiplying copies of a certain input tensor that produces a scalar obeys specific symmetry constraints. In other words, the scalar resulting from this multiplication is invariant under some specific transformations of the involved tensor. We focus our study on the O(N)-invariant graphs, i.e. invariant under orthogonal transformations of the input tensor. The proposed approach is novel and versatile since it allows to address different theoretical and practical aspects of both CANDECOMP/PARAFAC (CP) and Tucker decomposition models. In particular we obtain several results: (i) we generalize the computational limit of Tensor PCA (a rank-one tensor decomposition) to the case of a tensor with axes of different dimensions (ii) we introduce new algorithms for both decomposition models (iii) we obtain theoretical guarantees for these algorithms and (iv) we show improvements with respect to state of the art on synthetic and real data which also highlights a promising potential for practical applications.

Arbitrary higher-order optical spatial state generation by using spontaneously broken degeneracy modes in helically twisted ring-core hole assisted fibers.

A helically twisted ring-core hole assisted fiber (HAF) is proposed for an arbitrary higher-order spatial state generation. In usual circular core fibers, HE and EH modes are degenerate and have vector field distributions. We will show the degeneracy of these modes having specific azimuthal mode order is lifted by periodically placing air-holes around the core with specific symmetry while preserving their vector field distributions. It is called spontaneously broken degeneracy (SBD) in this paper. Azimuthal order of the SBD modes can be changed with the arrangement of surrounding air-holes. By using this SBD modes, it is shown that arbitrary higher-order spatial state generation, including orbital angular momentum (OAM) state, is possible based on a geometric phase existing in twisted fibers. Furthermore, by using periodically inverted twisting, efficient OAM state generation is possible by accumulating the geometric phase. The topological charge can be changed by changing the arrangement of surrounding air-holes. Since the mechanism does not depend on a phase matching, such as a long-period grating, but on a topological effect, the wavelength dependence is very small, leading to novel and efficient mechanism for the manipulation of the spatial state of the light.

Electric double layers with modulated surface charge density: exact 2D results

Electric double layers (EDL) with counterions only, say electrons with the elementary charge −e, in thermal equilibrium at the inverse temperature β are considered. In particular, we study the effect of the surface charge modulation on the particle number density profile and the pressure. The mobile particles are constrained to the surface of a 2D cylinder and immersed in vacuum (no dielectric image charges). An EDL corresponds to the end-circle of the cylinder which carries a (fixed) position-dependent line charge density. The geometries of one single EDL and two EDLs at distance d are considered; the particle density profile is studied for both geometries, the effective interaction of two EDLs is given by the particle pressure on either of the line walls. For any coupling constant Γ ≡ βe 2 = 2 × integer, there exists a mapping of the 2D one-component Coulomb system onto the 1D interacting anticommuting-field theory defined on a chain of sites. Using specific transformation symmetries of anticommuting variables, the contact value theorem is generalized to the EDL with modulated line charge density. For the free-fermion coupling Γ = 2 it is shown that, under certain conditions, the matrix of interaction strengths between anticommuting variables diagonalizes itself which permits one to obtain exact formulas for the particle density profile as well as the pressure. The obtained results confirm the previous indications of weak-coupling and Monte Carlo observations that the surface charge inhomogeneity implies an enhancement of the counterion density at the contact with the charged line and a diminution of the pressure between two parallel lines in comparison with the uniformly charged ones (with the same mean charge densities).

On Finslerian extension of special relativity

In this paper, we demonstrate that Robb-Geroch’s definition of a relativistic interval admits a simple and fairly natural generalization leading to a Finsler extension of special relativity. Another justification for such an extension goes back to the works of Lalan and Alway and, finally, was put on a solid basis and systematically investigated by Bogoslovsky under the name “Special-relativistic theory of locally anisotropic spacetime”. The isometry group of this spacetime, DISIM[Formula: see text], is a deformation of the Cohen and Glashow’s very special relativity symmetry group ISIM(2). Thus, the deformation parameter [Formula: see text] can be regarded as an analog of the cosmological constant characterizing the deformation of the Poincaré group into the de Sitter (anti-de Sitter) group. The simplicity and naturalness of Finslerian extension in the context of this paper adds weight to the argument that the possibility of a nonzero value of [Formula: see text] should be carefully considered.

Non-Markovian dynamics of a single excitation within many-body dissipative systems

We explore the dynamics of $N$ coupled atoms to a generic bosonic reservoir under specific system symmetries. In the regime of multiple atoms coupled to a single reservoir with identical couplings, we identify remarkable effects, notably that the initial configuration of the atomic excited state amplitudes strongly impacts the dynamics of the system and can even fully sever the system from its environment. Additionally, we find that steady state amplitudes of the excited states become independent of the choice of the reservoir. The framework introduced is applied to a structured photonic reservoir associated with a photonic crystal, where we show it reproduces previous theoretical and experimental results and it predicts superradiant behaviour within the single-excitation regime.

Anomalous and topological Hall effects of ferromagnetic Fe3Sn2 epitaxial films with kagome lattice

Fe3Sn2, a ferromagnetic alloy with a kagome lattice, has attracted much attention from research communities owing to its special crystal structure and symmetry, which gives rise to numerous intriguing magneto-electronic properties, including the topological Hall effect, skyrmionic bubbles, Dirac cones, and Weyl points. To study such physical properties, Fe3Sn2 epitaxial films without buffer layers are in urgent need. In this work, we fabricated the Fe3Sn2 epitaxial films without buffer layers using the facing-target magnetron sputtering method, and their magneto-electronic transport properties were investigated systematically. It is found that the sign of the Hall resistivity slope in a high-field region is reversed when the temperature decreases below 100 K, suggesting a temperature-induced transition of charge carriers from electrons to holes. Moreover, a non-negligible topological Hall resistivity subtracted from the anomalous Hall resistivity is depicted, and its value is comparable to that of the Fe3Sn2 single crystals. These results not only offer a clear understanding of ferromagnetic Fe3Sn2 films with the kagome lattice but also provide guidance for fabrication and application of epitaxial Fe3Sn2 films.

Emergence of paraelectric, improper antiferroelectric, and proper ferroelectric nematic phases in a liquid crystal composed of polar molecules.

We have elaborated a theoretical approach for the description of polar nematic phases observed by Nishikawa etal. [Adv. Mater. 29, 1702354 (2017)0935-964810.1002/adma.201702354], their structures, and transitions between them. Specific symmetry contributions to the pair molecular potentials provide the molecular mechanisms responsible for the formation of proper and improper polarity on the macroscopic level. An improper antiferroelectric nematic M2 phase can arise between paraelectric nematic M1 and proper ferroelectric nematic MP in the temperature scale. The local polarization in M2 arises mostly due to the local splay deformation. The director distribution in M2 represents the conjugation of cylindrical waves with opposite splay and polarization signs. The director and polarization are parallel to the cylindrical domain axes in the middle of each cylinder but exhibit considerable (mostly radial) deformation on the periphery of each cylinder. Polarization vectors are mostly stacked antiparallel on the borders between the domains without the director disruption. The domain size decreases with the decreasing temperature, the percentage of the antiferroelectric decouplings increases, and M2 exhibits the first-order phase transition into proper ferroelectric MP. With the increasing temperature the domain size in the M2 phase increases, the domination of particular polar orientation of molecules reduces, and finally, the domain size diverges at particular temperature corresponding to the second-order phase transition from M2 to paraelectric M1. Variations of the polar and nonpolar orientational order parameters are estimated within each phase and between the phases. Our experimental and computer simulation results (also presented in the paper) fully support our theoretical findings.

Fingerprints of hot-phonon physics in time-resolved correlated quantum lattice dynamics

The time dynamics of the energy flow from electronic to lattice degrees of freedom in pump-probe setups could be strongly affected by the presence of a hot-phonon bottleneck, which can sustain longer coherence of the optically excited electronic states. Recently, hot-phonon physics has been experimentally observed and theoretically described in MgB_22, the electron-phonon based superconductor with T_{c}\approx 39Tc≈39 K. By employing a combined ab-initio and a semiclassical approach and by taking MgB_22 as an example, here we propose a novel path for revealing the presence and characterizing the properties of hot phonons through a direct analysis of the information encoded in the lattice inter-atomic correlations. Such method exploits the underlying symmetry of the E_{2g}E2g hot modes characterized by a out-of-phase in-plane motion of the two boron atoms. Since hot phonons occur typically at high-symmetry points of the Brillouin zone, with specific symmetries of the lattice displacements, the present analysis is quite general and it could aid in revealing the hot-phonon physics in other promising materials, such as graphene, boron nitride, black phosphorus, or even underdoped cuprates.

Solving a System of Sylvester-like Quaternion Matrix Equations

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable. As an application of the system, we consider a special symmetry solution, named the η-Hermitian solution, for a system of quaternion matrix equations. Moreover, we present an algorithm and a numerical example to verify the main results of this paper.

Platonic Solids and Symmetric Solutions of the N-vortex Problem on the Sphere

We consider the N-vortex problem on the sphere assuming that all vortices have equal strength. We develop a theoretical framework to analyse solutions of the equations of motion with prescribed symmetries. Our construction relies on the discrete reduction of the system by twisted subgroups of the full symmetry group that rotates and permutes the vortices. Our approach formalises and extends ideas outlined previously by Tokieda (C R Acad Sci, Paris I 333:943–946, 2001) and Soulière and Tokieda (J Fluid Mech 460:83–92, 2002) and allows us to prove the existence of several 1-parameter families of periodic orbits. These families either emanate from equilibria or converge to collisions possessing a specific symmetry. Our results are applied to show existence of families of small nonlinear oscillations emanating from the Platonic solid equilibria.