Number Of Topologies Research Articles

Topological amplitudes of charmed baryon decays in the SU(3)F limit

Charmed baryon decay plays an important role in studying the weak and strong interactions. Topological diagram is an intuitive tool for analyzing the dynamics of heavy hadron decays. In this work, we investigate the topological diagrams of charmed baryon antitriplet (Bc3¯) decays into a light baryon octet (B8) and a light meson (M). A one-to-one mapping between the topological diagram and the invariant tensor is established. The topological diagrams of the Bc3¯→B8SM modes (where B8S and B8A are the q1↔q2 symmetric and antisymmetric octets) and the diagrams with a quark loop are presented for the first time. The completeness of topologies is confirmed by permutation. The linear relations of topologies are obtained by deriving the relation between the topological amplitudes constructed by the third- and second-rank octet tensors. It is found the topologies contributing to the Bc3¯→B8SM modes can be determined by the topologies contributing to the Bc3¯→B8AM modes, and vice versa. The equations of SU(3) irreducible amplitudes decomposed by topologies are derived through two different intermediate amplitudes. However, the inverse solution does not exist since the number of topologies exceeds number of SU(3) irreducible amplitudes. Applying this framework to the Standard Model, it is found there are thirteen independent SU(3) irreducible amplitudes contributing to the Bc3¯→B8M decays. Among these, four amplitudes associated with three-dimensional operators are significant for CP asymmetries. Considering the suppressions due to small Cabibbo-Kobayashi-Maskawa matrix elements and the Körner-Pati-Woo theorem, the branching fractions of charmed baryon decays are dominated by five SU(3) irreducible amplitudes in the SU(3)F limit. Quark-loop diagrams could enhance the U-spin breaking effects and increase the branching fraction difference of two decay channels. Systematic measurements of branching fractions of the singly Cabibbo-suppressed modes could help identify promising channels for searching for CP asymmetries in the charmed baryon sector. Published by the American Physical Society 2024

Estimation of the Chances to Find New Phenomena at the LHC in a Model-Agnostic Combinatorial Analysis

In this paper, we estimate the number of event topologies that have the potential to be produced in pp collisions at the Large Hadron Collider (LHC) without violating kinematic and other constraints. We use numerical calculations and combinatorics, guided by large-scale Monte Carlo simulations of Standard Model (SM) processes. Then, we set the upper limit on the probability that new physics may escape detection, assuming a model-agnostic approach. The calculated probability is unexpectedly large, and the fact that LHC has not found new physics until now is not entirely surprising. Theoretical limitations and experimental challenges in observing new physics within the studied exclusive event classes are examined.

Topological properties of black holes in five-dimensional gauged supergravity

In this paper, we study the topological properties of five-dimensional rotating charged black holes in different ensembles.The topological numbers for the black holes are gotten in the grand canonical and canonical ensembles, which are 1. When the charge and cosmological constant disappear, their topological numbers are 0. When the pressure is lower than the critical pressure, the phase transition exists in the canonical ensemble. However, the phase transition also exists in the grand canonical ensemble when the pressure is higher than the critical pressure and two independent rotational parameters are a=1 and b=−1. This may be due to the fact that the values of the rotational parameters change the supersymmetry of the black hole and lead to the phase transition.

Proof of bulk-edge correspondence for band topology by Toeplitz algebra

Abstract We rigorously yet concisely prove the bulk-edge correspondence for general d-dimensional (dD) topological insulators in complex Altland-Zirnbauer classes, which states that the bulk topological number equals to the edge-mode index. Specifically, an essential formula is discovered that links the quantity expressed by Toeplitz algebra, i.e., hopping terms on the lattice with an edge, to the Fourier series on the bulk Brillouin zone. We then apply it to chiral models and utilize exterior differential calculations, instead of the sophisticated K -theory, to show that the winding number of bulk system equals to the Fredholm index of 1D edge Hamiltonian, or to the sum of edge winding numbers for higher odd dimensions. Moreover, this result is inherited to the even dimensional Chern insulators as each of them can be mapped to an odd dimensional chiral model. It is revealed that the Chern number of bulk system is identical to the spectral flow of 2D edge Hamiltonian, or to the negative sum of edge Chern numbers for higher even dimensions. Our methods and conclusions are friendly to physicists and could be easily extended to other physical scenarios.

Coherent high-power terahertz vortex generation with tunable orbital angular momentum based on transverse phase mask shaping

Abstract Terahertz (THz) radiation has become a significant tool in cutting-edge research due to its superior properties. THz vortices with tunable orbital angular momentum are particularly attractive to the scientific community due to their well-defined discrete azimuthal phase around the propagation axis. However, the generation of high-power THz radiation with orbital angular momentum remains a challenge for most existing technologies. In this paper, a new method for generating coherent high-power THz vortices with tunable orbital angular momentum and frequency is proposed by combining frequency beating and transverse phase mask shaping techniques. Theoretical analyses and numerical simulations indicate that this method can generate coherent THz vortices with peak powers in the tens of megawatts and tunable topological charge numbers.

Geometry, Topology and p-Adic Numbers in Geospatial Data Modelling, Management and Processing: Review and Future Approaches

Abstract. Geometry and topology are both central concepts in geospatial data modelling and management. While geometry is the central concept for computational geometry applications, e.g. to intersect surfaces and solids in 3D space, topology is helpful for many application classes starting from city modelling to subsurface modelling and indoor navigation. Furthermore, p-adic numbers are useful for describing hierarchical processes on topological models. In this paper we first shortly review geometry- and topology-based approaches used for geospatial applications. We then describe our approach on turning geometry “upside down” focusing on topology during the whole process of distributed geospatial computing, data modelling, data management, and simulation. Furthermore, the way to use p-adic numbers for the description of hierarchical processes on topological models is shown for the example of simulation and the idea of p-adic analysis in distributed simulations is presented in the context of topological city and building models. The approach opens new insights such as topological relationships, components, and efficiently studying of the approximate behaviour of processes in the built environment using distributed computational systems. Finally, exemplary applications are presented to underline the importance of this new approach.

On the topological number in Kelvin’s circulation of inviscid fluids

Kelvin’s circulation, as a loop integral of the velocity field, is first shown to be equal to ΓC=2πΔnΓ1+constant in an inviscid fluid, with Γ1 a unit circulation. The integer Δn is interpreted as the number of net 2π-rotations of the velocity vector in one cyclicality along the circulation loop and hence it is a topological number. Different from the linkage number in the helicity invariant, which only exists in 3D space, the topological number in the circulation invariant is independent of the spatial dimension. A further study reveals that this new topological phase 2πΔn is rooted at the gauge invariance of the circulation and it is a counterpart of the Berry’s phase in the quantum system.

Switchable phase modulation and multifunctional metasurface with vanadium dioxide layer

Abstract Metasurface, comprising subwavelength unit cells, offers a flexible modulation of the optical phase. However, traditional metasurfaces are typically engineered to function solely in one mode, limiting their efficiency and adaptability. In this study, we proposed a switchable metasurface consisting of gold bars deposited on polyimide and vanadium dioxide (VO2) layer. Upon the phase transition of VO2, this switchable metasurface exhibits functionality in both transmissive and reflective modes. Specifically, it efficiently converts left circularly polarized (LCP) light into right circularly polarized (RCP) light. For the dielectric (metallic) phases of VO2, the design behaves as metalens with a focal length of 1000 (906) μm at working frequency of 1.2 THz, respectively. Furthermore, the vortex phase can be effectively manipulated with topological number from 1 to 4 through the analysis of the electric field distribution. A directional emission from 12.9° to 42.2° is obtained in the reflective mode and Airy beam paths way can also be well regulated at 1.49 THz. The phase modulation is further achieved by varying the inter-mediums and its thickness. Finally, the sensing ability is explored with different covered solution. Consequently, this multifunctional and adaptable metasurface offers valuable insights for the development of reflectors, modulators, lenses and sensors.

Quantifying the topology of magnetic skyrmions in three dimensions.

Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number. However, in real systems with the finite thickness of the device material being larger than the magnetic exchange length, the skyrmion spin texture extends into the third dimension and cannot be assumed as homogeneous. Using soft x-ray laminography, we reconstruct with about 20-nanometer spatial (voxel) size the full three-dimensional spin texture of a skyrmion in an 800-nanometer-diameter and 95-nanometer-thin disk patterned into a 30× [iridium/cobalt/platinum] multilayered film. A quantitative analysis finds that the evolution of the radial profile of the topological skyrmion number is nonuniform across the thickness of the disk. Estimates of the micromagnetic energy densities suggest that the changes in topological profile are related to nonuniform competing energetic interactions. Our results provide a foundation for nanoscale metrology for spintronics devices using topology as a design parameter.

Analytic approach for computation of topological number of integrable vortex on torus

Detailed structures of vortices on a torus are discovered by performing an analytic method to calculate the vortex number. We focus on analytic vortex solutions to the Chern-Simons-Higgs theory, whose governing equation is the so-called Jackiw-Pi equation. The equation is one of the integrable vortex equations and is reduced to Liouville’s equation. The requirement of continuity of the Higgs field strongly restricts the characteristics and the fundamental domain of the vortices. Also considered are the decompactification limits of the vortices on a torus, in which “flux loss” phenomena occasionally occur.

Impact of Barrow’s entropy on topological classification of higher-dimensional black holes

In this paper, we explore the impact of Barrow’s entropy on the topological classification of d-dimensional black holes (BHs). Specifically, we examine the Gauss–Bonnet (GB) and singly rotating Kerr black holes (KBHs) as well as their AdS counterparts. We notice that Barrow’s entropy significantly influences the topological numbers of these BHs. To understand these effects, we use the thermodynamic domain — the space defined by thermodynamic variables like temperature and pressure — to study topologically inspired defects in the BHs. These defects are points in the thermodynamic domain where singular or discontinuous behavior occurs. By computing the winding numbers of these defects, which are integers that count how many times a loop around the defect encircles the origin, we can understand the local and global topology of the BHs. Our analysis suggest that the topological number [Formula: see text] derived from Barrow’s statistics differs from the one obtained using Gibbs–Boltzmann statistics. Furthermore, we observe that BHs can undergo topological phase transitions that characterize them in different thermodynamic topological classes. Overall, these findings demonstrate the importance of Barrow’s entropy in understanding the topological classification of BHs, and highlight the potential for further research in this area.

Topology of charged AdS black hole in restricted phase space* *Supported by the National Natural Science Foundation of China (12075143, 12375050), and the Natural Science Foundation of Shanxi Province, China (202203021221209, 202303021211180)

The local topological properties of black hole systems can be expressed through winding numbers as defects. To date, AdS black hole thermodynamics are often depicted by the dual parameters of in the extended phase space, while there have been several studies on the black hole thermodynamics in the restricted phase space. In this paper, we analyze the topological properties of charged AdS black holes in the restricted phase space under the higher-dimension and higher-order curvature gravity frame. The results show that the topological number of the charged black hole in the same canonical ensembles is a constant and is independent of the concrete dual thermodynamical parameters. However, the topological number in the grand canonical ensemble is different from that in the canonical ensemble for the same black hole system. Furthermore, these results are independent of dimension d and highest order k of the Lanczos-Lovelock densities.

Variational MonteCarlo Study of the 1/9-Magnetization Plateau in Kagome Antiferromagnets.

Motivated by very recent experimental observations of the 1/9-magnetization plateaus in YCu_{3}(OH)_{6+x}Br_{3-x} and YCu_{3}(OD)_{6+x}Br_{3-x}, our study delves into the magnetic-field-induced phase transitions in the nearest-neighbor antiferromagnetic Heisenberg model on the kagome lattice using the variational MonteCarlo technique. We uncover a phase transition from a zero-field Dirac spin liquid to a field-induced magnetically disordered phase that exhibits the 1/9-magnetization plateau. Through a comprehensive analysis encompassing the magnetization distribution, spin correlations, chiral order parameter, topological entanglement entropy, ground-state degeneracy, Chern number, and excitation spectrum, we pinpoint the phase associated with this magnetization plateau as a chiral Z_{3} topological quantum spin liquid and elucidate its diverse physical properties.

Eliminating Skyrmion Hall Effect in Ferromagnetic Skyrmions.

Skyrmion Hall effect (SkHE) remains an obstacle for the application of magnetic skyrmions. While methods have been established to cancel or compensate SkHE in artificial antiferromagnets and ferrimagnets, eliminating intrinsic SkHE in ferromagnets is still a big challenge. Here, we propose a strategy to eliminate SkHE by intercalating nonmagnetic elements into van der Waals bilayer ferromagnets featuring in-plane ferromagnetism. The in-plane magnetism, along with a delicate balance among exchange interactions, Dzyaloshinskii-Moriya interactions (DMI), and magnetocrystalline anisotropy, creates interlayer bimerons/quadmerons, whose polarity can be controlled by DMI. Opposite DMI in the upper and lower layers results in opposite polarity and topological charge number Q-locking of topological spin texture, therefore, eliminating the SkHE. By intercalating Sr (Ba) in bilayer VSe2, we identify ten topological magnetic structures with zero topological charge number. Furthermore, we present a phase diagram illustrating diverse magnetic configurations achievable within the bimagnetic atomic layer, offering valuable guidance for future investigations.

Topology of black hole thermodynamics via Rényi statistics

In this paper, we investigate the topological numbers of the four-dimensional Schwarzschild black hole, d-dimensional Reissner–Nordström (RN) black hole, d-dimensional singly rotating Kerr black hole and five-dimensional Gauss–Bonnet black hole via the Rényi statistics. We find that the topological number calculated via the Rényi statistics is different from that obtained from the Gibbs–Boltzmann (GB) statistics. However, what is interesting is that the topological classifications of different black holes are consistent in both the Rényi and GB statistics: the four-dimensional RN black hole, four-dimensional and five-dimensional singly rotating Kerr black holes, five-dimensional charged and uncharged Gauss–Bonnet black holes belong to the same kind of topological class, and the four-dimensional Schwarzschild black hole and d(>5)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d(>5)$$\\end{document}-dimensional singly rotating Kerr black holes belong to another kind of topological class. In addition, our results suggest that the topological numbers calculated via the Rényi statistics in asymptotically flat spacetime background are equal to those calculated from the standard GB statistics in asymptotically AdS spacetime background, which provides more evidence for the connection between the nonextensivity of the Rényi parameter 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} and the cosmological constant 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}.

Thermodynamic topology of D = 4,5 Horava Lifshitz black hole in two ensembles

In this paper, we investigate the thermodynamic topology of four and five-dimensional Hořava-Lifshitz (HL) black holes within Hořava gravity. To analyze their thermodynamic topology, we treat these HL black holes as topological defects in their thermodynamic spaces and compute the winding numbers at these defects. Our study is conducted in two different ensembles: the fixed ϵ ensemble and the fixed ζ ensemble, where ϵ is a parameter of the HL black holes, and ζ is its conjugate parameter. In the fixed ϵ ensemble, we consider three different horizon types: spherical (k=+1), flat (k=0), and hyperbolic (k=−1), while in the fixed ζ ensemble, we examine two horizon types: spherical (k=+1) and hyperbolic (k=−1). For all the aforementioned cases, we study the local and global topology of these black holes and classify them into topological classes based on their topological charges. We calculate the topological number for each case. This process uncovers some novel phase diagrams that reveal a number of multiple defect curve phenomenon. Additionally, we explore how the topological charge of these black holes depends on the values of the thermodynamic parameters. Our findings indicate that the thermodynamic topology of Hořava-Lifshitz black holes in D=4,5 is significantly influenced by the type of horizon, the choice of ensemble, the values of pressure, and the parameters ϵ or ζ.

Topological classes of thermodynamics of the rotating charged AdS black holes in gauged supergravities

In this paper, we investigate the topological numbers of rotating charged AdS black holes in both four- and five-dimensional gauged supergravity theories. Our analysis is conducted within the framework of the thermodynamical topological approach to black holes, utilizing the generalized off-shell Helmholtz free energy. We demonstrate that the number of rotation parameters plays a significant role in determining the topological numbers of five-dimensional rotating AdS black holes. Moreover, our findings indicate that the topological numbers of both four- and five-dimensional rotating AdS black holes are not influenced by the number of electric charge parameters. This highlights a distinct difference in how rotation and electric charge parameters impact the thermodynamic topological properties of these black holes.

Topology and phase transition for EPYM AdS black hole in thermal potential

As we all know the local topological properties of thermodynamical systems can be expressed by the winding numbers as the defects. The topological number that is the sum of all winding numbers can be used to classify the global topological nature of thermodynamical systems. In this paper, we construct a kind of thermal potential and then put the Einstein-power-Yang-Mills AdS black hole in it. Through the analysis of the geometric characteristics of the thermal potential based on the complex analysis we find the topological number is an invariant that is same as shown in the way of the Duan's ϕ-mapping topological current [Sci. Sin. 9, 1072 (1979)]. Furthermore, we adopt the Kramer's escape rate method to investigate the intensity of the first-order phase transition.

Thermodynamic topology of Kerr-Sen black holes via Rényi statistics

In the present study, we investigate the topological properties of black holes in terms of Rényi statistics as an extension of the Gibbs-Boltzmann (GB) statistics, aiming to characterize the non-Boltzmannian thermodynamic topology of Kerr-Sen and dyonic Kerr-Sen black holes. Through this research, we discover that the topological number derived via Rényi statistics differs from that obtained through GB statistics. Interestingly, although the nonextensive parameter λ changes the topological number, the topological classification of the Kerr-Sen and dyonic Kerr-Sen black holes remains consistent under both GB and Rényi statistics. In addition, the topological numbers associated with these two types of black holes without cosmological constant using Rényi entropy processes are the same as the AdS cases of them by considering the GB entropy, as further evidenced by such a study found here. This indicates the cosmological constant has some potential connections with the nonextensive parameter from the perspective of thermodynamic topology.

Beyond large complex structure: quantized periods and boundary data for one-modulus singularities

We study periods in an integral basis near all possible singularities in one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near large complex structure points these asymptotic periods are well understood in terms of the topological data of the mirror Calabi-Yau manifold. The aim of this work is to characterize the period data near other boundaries in moduli space such as conifold and K-points. Using results from Hodge theory, we provide the general form of these periods in a quantized three-cycle basis. Based on these periods we compute the prepotential and related physical couplings of the underlying supergravity theory. Moreover, we elucidate the meaning of the model-dependent coefficients that appear in these expressions: these can be identified with certain topological and arithmetic numbers associated to the singular geometry at the moduli space boundary. We illustrate our findings by studying a wide set of examples.