Symmetry-based Approach Research Articles

Interorbital antisymmetric hopping generated flat bands on kagome and pyrochlore Lattices

Flat bands are intriguing platforms for correlated and topological physics. Various methods have been developed to create flat bands utilizing lattice geometry, but the investigation of orbital symmetry in multiorbital materials is a new area of focus. Here, we introduce a site symmetry-based approach to emerging multiorbital 2D and 3D flat bands on the kagome and pyrochlore lattices. As a conceptual advance, the one-orbital flat bands are shown to originate as mutual eigenstates of isolated molecular motifs. Further developing the mutual eigenstate method for multiple orbitals transforming differently under the site symmetries, we derive interorbital hopping generated flat bands from the antisymmetric interorbital Hamiltonian and introduce group-theoretic descriptions of the flat band wavefunctions. Realizations of multiorbital flat bands in realistic materials are shown to be possible in the Slater-Koster formalism. Our findings provide new directions for exploring flat-band electronic structures for novel correlated and topological quantum states.

Nondestructive global corrosion measurement using guided wavefield data

Metallic structures often face degradation, and corrosion ranks among the most prevalent forms of deterioration. Accurate quantification of corrosion is crucial, especially for structures exposed to harsh environmental conditions, such as marine vessels and offshore installations. Because the traditional measurement methods based on scanning by ultrasonic gauge are time-consuming and provide only rough information on the thickness variability, there is a need to develop new robust and accurate diagnostics methods. This paper aims to investigate the corrosion monitoring of metal plates using guided wave propagation. Guided waves propagate within the entire volume of the specimen. If it is undamaged and isotropic, the velocity in all directions is the same, and the spreading wavefront takes a circular shape. The primary assumption presented in this paper is that the potential damage caused by corrosion leads to disturbance of this symmetry. The study shows Bilateral and Rotational Corrosion Symmetry Degree (BCSD and RCSD) functions, demonstrating a consistent decrease in symmetry values with increasing degree of degradation (DoD) caused by the corrosion process. The main aim of the study was to test the possibility of corrosion monitoring by using variable number of sensors comprising the transducer network. Also, the influence of the distance between the sensors affecting the size of the monitored area on the corrosion monitoring procedure was investigated. The paper contains the results of numerical and experimental campaigns conducted for corroded plates characterized by variable DoD and monitored using nine different transducers configurations. It is the first step in developing a novel measurement procedure specially designed for the ship and offshore industry. Therefore, because of the initial stage of the study, the last part of the paper discusses the limitations and drawbacks of the presented wave symmetry-based approach.

Symmetry-based study and dynamics of casual bulk viscous matter-dominated universe

The dynamics of cosmological expansion is studied for a spatially flat matter-dominated universe filled with barotropic casual bulk viscous fluid. The evolution equation for the Hubble parameter is derived using Friedmann equations and conservation law for the viscous fluid, in which the viscous pressure is modeled by truncated version of the full Israel-Stewart theory of bulk viscosity. We use a Lie symmetry-based approach to study the evolution of the expansion rate of the Universe. The model equation possesses eight-parameter Lie symmetry generators and gives two different analytic group invariant solutions for the Hubble parameter. Expressions for various important cosmological parameters are obtained and values are estimated analytically for the explanation of the evolution dynamics of the Universe. The interesting features of the obtained symmetry-based solutions are that, one satisfies the present acceleration of the Universe, while the other could not support present accelerating phase, rather represents a universe dominated by non-viscous stiff fluid. We make useful checks on the observational constraints on the model parameters from the latest released observational data. The accelerating phase of the current universe is investigated using observational bounds and compared the model under investigation with the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model. The evolutionary cosmic phases obtained from the analysis of the Lie symmetry-based solutions correspond to the association with the critical points in the equivalent phase space. These interesting features are investigated and analyzed using dynamical systems approach.

Generating symmetry-protected long-range entanglement

Entanglement between spatially distant qubits is perhaps the most counterintuitive and vital resource for distributed quantum computing. However, despite a few special cases, there is no known general procedure to maximally entangle two distant parts of an interacting many-body system. Here we present a symmetry-based approach, whereby one applies several timed pulses to drive a system to a particular symmetry sector with maximal bipartite long-range entanglement. As a concrete example, we demonstrate how a simple sequence of on-site pulses on a qubit array can efficiently produce multiple stable nonlocal Bell pairs, realizable in present-day atomic and photonic experimental platforms. More generally, our approach paves a route for exotic state preparation by harnessing symmetry. For instance, we show how it allows the creation of long-sought-after superconducting η pairs in a repulsive Hubbard model. Published by the American Physical Society 2024

A Simple Microwave Imaging System for Food Product Inspection through a Symmetry-Based Microwave Imaging Approach.

In the food industry, there is a growing demand for cost-effective methods for the inline inspection of food items able to non-invasively detect small foreign bodies that may have contaminated the product during the production process. Microwave imaging may be a valid alternative to the existing technologies, thanks to its inherently low-cost and its capability of sensing low-density contaminants. In this paper, a simple microwave imaging system specifically designed to enable the inspection of a large variety of food products is presented. The system consists of two circularly loaded antipodal Vivaldi antennas with a very large operative band, from 1 to 15 GHz, thus allowing a suitable spatial resolution for different food products, from mostly fatty to high water-content foods. The antennas are arranged in such a way as to collect a signal that can be used to exploit a recently proposed real-time microwave imaging strategy, leveraging the inherent symmetries that usually characterize food items. The system is experimentally characterized, and the achieved results compare favorably with the design specifications and numerical simulations. Relying on these positive results, the first experimental proof of the effectiveness of the entire system is presented confirming its efficacy.

Studies of Density Contrast of Cold Dark Matter in Cosmological Radiation and Dark Energy Background: A Symmetry-Based Approach

Studies of Density Contrast of Cold Dark Matter in Cosmological Radiation and Dark Energy Background: A Symmetry-Based Approach

Neutrino Mixing Sum Rules and the Littlest Seesaw

In this work, we study the neutrino mixing sum rules arising from discrete symmetries and the class of Littlest Seesaw (LS) neutrino models. These symmetry-based approaches all offer predictions for the cosine of the leptonic CP phase cosδ in terms of the mixing angles, θ13, θ12, θ23, while the LS models also predict the sine of the leptonic CP phase sinδ, as well as making other predictions. In particular, we study the solar neutrino mixing sum rules, arising from charged lepton corrections to tri-bimaximal (TB), bimaximal (BM), golden ratio (GR) and hexagonal (HEX) neutrino mixing, and the atmospheric neutrino mixing sum rules, arising from preserving one of the columns of these types of mixing—for example, the first or second column of the TB mixing matrix (TM1 or TM2)—and we confront them with an up-to-date global fit of the neutrino oscillation data. We show that some mixing sum rules, such as an atmospheric neutrino mixing sum rule arising from a version of neutrino golden ratio mixing (GRa1), are already excluded at 3σ, and we determine the remaining models allowed by the data. We also consider the more predictive LS models (which obey the TM1 sum rules and offer further predictions) based on constrained sequential dominance CSD(n) with n≈3. We compare for the first time the three cases n=2.5, n=3 and n=1+6≈3.45, which are favored by theoretical models, using a new type of analysis to accurately predict the observables θ12, θ23 and δ. We study all the above approaches, solar and atmospheric mixing sum rules and LS models, together so that they may be compared and to give an up-to-date analysis of the predictions of all of these possibilities, when confronted with the most recent global fits.

Symmetry in the Bit-Stream Converter Design

The paper presents the results of the study of the influence of symmetry in the design of bit-stream digital converters. We have shown realizations of the symmetry-based approach at different levels: at the level of basic elements, functional converters, and at the level of processes occurring in bit-streaming devices. Using symmetry in design, we have developed basic bit-stream elements that realize frequently used transformations with good technical performance. As a research result, we present descriptions and implementation results of the designed symmetric bit-stream devices in FPGA chips. Using the proposed elements and the concept of symmetric bit-stream device design, we designed and presented a specialized computing module for a temperature sensor controller.

A Novel Algorithm for Merging Bayesian Networks

The article presents a novel algorithm for merging Bayesian networks generated by different methods, such as expert knowledge and data-driven approaches, while leveraging a symmetry-based approach. The algorithm combines the strengths of each input network to create a more comprehensive and accurate network. Evaluations on traffic accident data from Prague in the Czech Republic and accidents on railway crossings demonstrate superior predictive performance, as measured by prediction error metric. The algorithm identifies and incorporates symmetric nodes into the final network, ensuring consistent representations across different methods. The merged network, incorporating nodes selected from both the expert and algorithm networks, provides a more comprehensive and accurate representation of the relationships among variables in the dataset. Future research could focus on extending the algorithm to deal with cycles and improving the handling of conditional probability tables. Overall, the proposed algorithm demonstrates the effectiveness of combining different sources of knowledge in Bayesian network modeling.

Symmetry-based computational search for novel binary and ternary 2D materials

We present a symmetry-based systematic approach to explore the structural and compositional richness of two-dimensional materials. We use a ‘combinatorial engine’ that constructs candidate compounds by occupying all possible Wyckoff positions for a certain space group with combinations of chemical elements. These combinations are restricted by imposing charge neutrality and the Pauling test for electronegativities. The structures are then pre-optimized with a specially crafted universal neural-network force-field, before a final step of geometry optimization using density-functional theory is performed. In this way we unveil an unprecedented variety of two-dimensional materials, covering the whole periodic table in more than 30 different stoichiometries of form A n B m or A n B m C k . Among the discovered structures, we find examples that can be built by decorating nearly all Platonic and Archimedean tessellations as well as their dual Laves or Catalan tilings. We also obtain a rich, and unexpected, polymorphism for some specific compounds. We further accelerate the exploration of the chemical space of two-dimensional materials by employing machine-learning-accelerated prototype search, based on the structural types discovered in the systematic search. In total, we obtain around 6500 compounds, not present in previous available databases of 2D materials, with a distance to the convex hull of thermodynamic stability smaller than 250 meV/atom.

An efficient material search for room-temperature topological magnons.

Topologically protected magnon surface states are highly desirable as an ideal platform to engineer low-dissipation spintronics devices. However, theoretical prediction of topological magnons in strongly correlated materials proves to be challenging because the ab initio density functional theory calculations fail to reliably predict magnetic interactions in correlated materials. Here, we present a symmetry-based approach, which predicts topological magnons in magnetically ordered crystals, upon applying external perturbations such as magnetic/electric fields and/or mechanical strains. We apply this approach to carry out an efficient search for magnetic materials in the Bilbao Crystallographic Server, where, among 198 compounds with an over 300-K transition temperature, we identify 12 magnetic insulators that support room-temperature topological magnons. They feature Weyl magnons with surface magnon arcs and magnon axion insulators with either chiral surface or hinge magnon modes, offering a route to realize energy-efficient devices based on protected surface magnons.

Symmetry-based identification and enumeration of independent tensor properties in nonlinear and chiral optics.

For many laser-based methods of material characterization and analysis, a tensor formulation of theory is necessary, especially in techniques that exploit nonlinear or chiral optics. The fundamental interactions that underpin such methods offer various levels of approach to theory, but the most rigorous often lead to equations of considerable complexity. To compute the values for individual material parameters frequently demands making assumptions of extreme simplicity, overly dependent on calculational method, yet still providing unsatisfactory results. A pragmatic and entirely rigorous symmetry-based approach to the irreducible tensorial structures circumvents many of these problems, securing reliable results and guiding the pathway to applications. Instead of focusing on individual tensor components, such an approach can rapidly determine the number of linearly independent quantities-and hence the number of operationally different setups necessary for full characterization. By such means, one can directly ascertain how variations of optical polarization and beam geometry can reliably capture the response of any material system. The use of an irreducible tensor method operates independently of any means that might be chosen to calculate material properties. It removes the need for common simplifying assumptions, such as the approximation of tensorial structure by a scalar representation, adoption of a two-state model, or disregarding near-resonance damping. It also obviates any dependence on a choice of simulation package or quantum-calculational software. In this paper, the principles are set down and illustrated by application to experiments of varying degrees of complexity, including interactions of growing significance in the realm of chiral nonlinear optics. Limitations of this approach are also critically assessed.

Design of observers with gain adaptation for systems with disturbances: An orbital symmetry-based approach

We propose a framework for designing global observers for nonlinear systems with disturbances under geometric conditions based on orbital symmetries. Under some additional restrictions these orbital symmetry-based conditions boil down to geometric homogeneity (at infinity) conditions. Our observers are the result of the combination of a first filter, a state norm estimator, with a second filter adaptively tuned by the first and when compared with the existing literature have a completely novel structure, inherited by the orbital symmetry-based conditions. The observers exploit the geometric properties of orbital symmetries which are one-parameter groups of transformations capable of mapping the system state into neighbourhoods with parametrized width.

Integration of Cypoviruses into polyhedrin matrix.

Unlike in other viruses, in Cypoviruses the genome is doubly protected since their icosahedral capsids are embedded into a perfect polyhedrin crystal. Current experimental methods cannot resolve the resulting interface structure and we propose a symmetry-based approach to predict it. We reveal a remarkable match between the surfaces of Cypovirus and the outer polyhedrin matrix. The match arises due to the preservation of the common tetragonal symmetry, allowing perfect contacts of polyhedrin trimers with VP1 and VP5 capsid proteins. We highlight a crucial role of the VP5 proteins in embedding the Cypovirus into the polyhedrin matrix and discuss the relationship between the nucleoside triphosphatase activity of the proteins and their role in the superstructure formation. Additionally, we propose an electrostatic mechanism that drives the viral superstructure disassembly occurring in the alkaline environment of the insect intestines. Our study may underpin novel strategies for engineering proteinaceous nanocontainers in diverse biotechnological and chemical applications.

Percolative, Multifractal, and Symmetry Properties of the Surface at Nanoscale of Cu-Ni Bimetallic Thin Films Deposited by RF-PECVD

We explored the morphological and 3D spatial properties of Cu/Ni thin films obtained by a co-deposition process. The 3D AFM topographic maps analysis indicated that the films displayed different morphologies and rough profiles dictated by their singular directional inhomogeneities. Moreover, Minkowski’s volume showed that the Cu/Ni films deposited after 15 and 20 min had a similar relative distribution of matter as a function of height, which is different from the individual Cu films. The Minkowski boundary and connectivity point out that the percolative properties of the Cu/Ni samples were similar to each other. However, they were distinct from the percolative features of the Cu sample. It was also observed that the surface microtexture of the films showed similar spatial complexity, dominant spatial frequencies, and topographical uniformity. For the Cu/Ni thin films, the Minkowski functionals morphological analysis showed that the type of film dictated the surface percolation. In contrast, clear fingerprints of multifractal behavior in all the samples were also observed, indicating that the multifractality degree increased with the sputtering time, supporting the significant vertical growth of the Cu/Ni thin film deposited after 20 min. Aside from that, the results from a symmetry-based approach indicated that the vertical growth dynamics of individual Cu and Cu/Ni thin films were different in terms of scaling symmetry, where we observed that the sputtering induced the formation of less asymmetric topographies regarding their multiscaling behavior. Finally, our findings suggested that the sputtering process can be employed to tune the percolative properties, multifractality, and scaling symmetry of the films, inducing different vertical growth dynamics, which can be useful in the optimization of the fabrication of bimetallic surfaces for technological purposes.

Unitary limit in heavy nuclei

The unitary limit refers to a scattering problem at infinite scattering length where a scattering state becomes bound. Such a limit is experimentally accessible in systems of cold atoms at the vicinity of Feshbach resonances. In nuclear physics, a physical manifestation of the unitary limit is of interest both from the experimental challenge to measure such a limit in nuclei and from the theoretical aspects that accompany that limit such as conformal symmetry, a quantum critical point and the BCS-BEC crossover. In this talk the application of a symmetry-based approach to the unitary limit in collective states of heavy, even-even nuclei is presented that is performed by means of the Interacting Boson Model of nuclear structure in conjunction with the Feshbach formalism of nuclear reactions. The results of this application start from the determination of what is to be measured in the experiment for the examination of the unitary limit in collective nuclear states. That is the fluctuations of the cross-section of the A+2n compound nucleus. The primary theoretical result concerns the representations of conformal symmetry in A+2n compound nuclei via the fluctuations of cross sections.

Translational Symmetry-Aware Facade Parsing for 3-D Building Reconstruction

Effectively parsing the facade is essential to 3-D building reconstruction, which is a significant computer vision problem for digital entertainment. Although having achieved the promising results in semantic parsing, deep learning methods cannot directly make use of the architectural rules that play an important role in man-made structures. This article presents a novel translational symmetry-based approach. The unified facade parsing network integrates both segmentation and detection branches as the base parser. A translational symmetry measurement-based module is proposed to refine the initial results. After converting the facades into shape grammars, we employ an off-the-shelf rendering engine like Blender to reconstruct the high-quality 3-D models using procedural modeling. We conduct experiments on three public datasets, where our proposed approach outperforms the state-of-the-art methods.

A symmetry-based approach to the characterization of complex surface morphologies: Application in CuO and NiO nanostructures

In recent years, bottom-up nanofabrication techniques and especially solution-based ones have gained significant popularity due to their relatively facile implementation, low-cost and design flexibility that allows the development of a plethora of three-dimensional nanostructures and nanoarchitectures. Nonetheless, despite the apparent simplicity of the methods, the resulting nanostructures are often morphologically and hierarchically complex with no apparent way of appropriately describing their features in a quantifiable and methodological way. In this work, we propose a symmetry-based approach for the quantitative characterization of the morphology of nanostructured surfaces. The key idea is to characterize the morphology of nanostructures by means of the fundamental spatial symmetry metrics and the deviations from the fully symmetrical counterparts. The focus of the proposed methodology is on the translational and scaling symmetry, which are investigated through the mathematical tools of Fourier and (multi)fractal analysis, respectively. The calculated metrics characterizing these symmetries are the period and the fractal dimension of surfaces while the deviations are quantified by the disorder parameter ω d related to the FWHM of Fourier peak and by the asymmetry of the multifractal spectrum for the translational and scaling symmetry respectively. As an initial study case and in order to demonstrate its suitability, the developed symmetry-based methodology was applied to nickel oxide (NiO) and copper oxide (CuO) nanostructures hydrothermally-grown on silicon substrates. The results show that even in the cases where the surfaces display similar symmetry metrics (period, fractal dimension) the symmetry-based approach reveals subtle, but quantifiable differences in the deviations from full symmetries which are not easily identified by other approaches. • A symmetry-based method for nanometrological analysis of complex nanomorphologies is developed and implemented. • It detects and quantifies the spatial symmetries in surfaces and the deviations from these (surface disorder). • Fourier, correlation and (multi) fractal analysis are used. • The method is successfully applied in CuO and NiO nanostructures hydrothermally grown on silicon substrates. • It captures subtle differences in nanosurface translational and scaling disorder and evaluates material/process origins.

Hidden symmetry of the static response of black holes: applications to Love numbers

We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schrödinger algebra mathfrak{sh} (1) = mathfrak{sl} (2, ℝ) ⋉ mathcal{H} . The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black hole in the test field approximation from a symmetry-based approach. First we show that the (horizontal) symmetry protecting the vanishing of the Love numbers recently exhibited by Hui et al., dubbed the HJPSS symmetry, coincides with one of the mathfrak{sl} (2, ℝ) generators of the Schrödinger group. Then, it is demonstrated that the HJPSS symmetry is selected thanks to the spontaneous breaking of the full Schrödinger symmetry at the horizon down to a simple abelian sub-group. The latter can be understood as the symmetry protecting the regularity of the test field at the horizon. In the 4-dimensional case, this provides a symmetry protection for the vanishing of the Schwarzschild Love numbers. Our results trivially extend to the Kerr case.

A new effective potential for deuteron

We calculate for the first time the static properties of the deuteron, within the framework of supersymmetric quantum mechanics, analytically. A new effective potential and its partner are derived from a superpotential so that all parameters are fitted by the experimental data. An analytical expression is obtained for the deuteron wave function and contributions of the orthogonal 13 S 1 and 13 D 1 states are determined, explicitly. Compared to one pion exchange, the superpotential produces an electrostatic as well as two pion exchange terms for the potential. The saddle point radius of the potential and the maximum of the wave function are linearly proportional. In comparison with other methods, the approach presented in this paper is a new and extensible symmetry-based approach that, despite its straightforward calculations and explicit analytical expressions, provides a good explanation for two-body effective interactions such as two-nucleon systems and diatomic molecules.