Monopole Loops Research Articles

Three-dimensional Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}$$\\end{document} topological insulators without reflection symmetry

In recent decades, the Altland-Zirnabuer (AZ) table has proven incredibly powerful in delineating constraints for topological classification of a given band-insulator based on dimension and (nonspatial) symmetry class, and has also been expanded by considering additional crystalline symmetries. Nevertheless, realizing a three-dimensional (3D), time-reversal symmetric (class AII) topological insulator (TI) in the absence of reflection symmetries, with a classification beyond the Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}_{2}$$\\end{document} paradigm remains an open problem. In this work we present a general procedure for constructing such systems within the framework of projected topological branes (PTBs). In particular, a 3D projected brane from a “parent” four-dimensional topological insulator exhibits a Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}$$\\end{document} topological classification, corroborated through its response to the inserted bulk monopole loop. More generally, PTBs have been demonstrated to be an effective route to performing dimensional reduction and embedding the topology of a (d+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(d+1)$$\\end{document}-dimensional “parent” Hamiltonian in d dimensions, yielding lower-dimensional topological phases beyond the AZ classification without additional symmetries. Our findings should be relevant for the metamaterial platforms, such as photonic and phononic crystals, topolectric circuits, and designer systems.

Photonic Spin Hopfions and Monopole Loops.

Spin textures with various topological orders are of great theoretical and practical interest. Hopfion, a spin texture characterized by a three-dimensional topological order was recently realized in electronic spin systems. Here, we show that monochromatic light can be structured such that its photonic spin exhibits a hopfion texture in the three-dimensional real space. We also provide ways to construct spin textures of arbitrary Hopf charges. When extending the system to four dimensions by introducing a parameter dimension, a new type of topological defect in the form of a monopole loop in photonic spin is encountered. Each point on the loop is a topological spin defect in three dimensions, and the loop itself carries quantized Hopf charges. Such photonic spin texture and defect may find application in control and sensing of nanoparticles, and optical generation of topological texture in motions of particles or fluids.

Microwave Grooved SRR Sensor for Detecting Low Concentration Ethanol-Blended Petrol

The rise in global energy demand due to economic development and an increase in population, have posed major concerns regarding energy security and environmental impact. Ethanol-blended petrol is an emerging alternative fuel that is considered cost-effective and environmentally friendly. However, the detection of low concentrations of ethanol in petrol is a significant challenge, especially as most nations mandate the blending of petrol with 5%-25% ethanol. This paper proposes a microwave sensor operating at 2.4GHz ISM band frequency to detect low concentrations of ethanol in petrol. The change in the magnitude of the reflection coefficient is adopted as the main sensing parameter. A single-frequency sensor composed of a square-shaped monopole loop antenna embedded with an SRR is proposed, which avoids the need for a wideband interrogation signal. The proposed design utilizes a filter paper wetted with the ethanol-petrol solution, placed along the split edge of the SRR, thus the use of complex and costly fluidic channels and space-consuming sample holders is avoided, bringing down the cost and complexity. The device dimensions are small, 4.2cm x 4.5cm. The sensitivity achieved in terms of amplitude change of the reflection coefficient is 2.83dB/5 % change of ethanol concentration in petrol, at a fixed frequency. In terms of the received power at 2.4GHz, the sensitivity is 2dBm/5 % change of ethanol concentration. Overall, this proposed sensor offers a simple, cost-effective, and efficient solution for detecting low concentrations of ethanol in petrol, which can aid in the adoption of ethanol-blended petrol as a viable alternative fuel.

In situ nonlinear Rayleigh wave technique to characterize the tensile plastic deformation of stainless steel 316L

The acoustic nonlinearity parameter β is sensitive to dislocation parameters, which continuously change during plastic deformation. Dislocation-based damage in structures/components is the source of the failure; thus, β has been studied as a metric for non-destructive evaluation. This work consists of two parts: the development of an in situ experimental setup for nonlinear Rayleigh wave measurements, and characterization of the dependence of β on applied stress at different levels of initial plastic strain. First, we introduce an experimental setup and methods for repeatable in situ nonlinear ultrasonic measurements. Details on design considerations and measurement schemes are provided. In the second part, β was measured in situ during an incremental monotonic tensile test. The measured β monotonically decreases with plastic strain, but it is relatively insensitive to the applied stress during elastic deformation. This result highlights three aspects of the evolution of β, which have not been sufficiently emphasized in prior work: the apparent insensitivity of β to the applied stress during elastic deformation, decreasing β with plastic deformation, and the saturation of β. We attribute the trend of decreasing β to a scaling of β with monopole loop length during plastic deformation, which depends on initial microstructure. The saturation of β at 1.8% coincides with a planar-to-wavy transition of dislocation structures. The in situ nonlinear ultrasonic experimental method presented in this work is significant as the in situ results can provide broader insights on β and dislocation-based damage evolution than ex situ measurements alone.

Axion Mass from Magnetic Monopole Loops.

We show that axions interacting with Abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their energy spectrum. The axion potential can also be understood as a type of instanton effect due to a Euclidean monopole worldline winding around its dyon collective coordinate. We calculate this effect, which has features in common with both non-Abelian instantons and Euclidean brane instantons. To provide consistency checks, we argue that this axion potential vanishes in the presence of a massless charged fermion and that it is robust against the presence of higher-derivative corrections in the effective Lagrangian. Finally, as a first step toward connecting with particle phenomenology and cosmology, we discuss the regime in which this potential is important in determining the dark matter relic abundance in a hidden sector containing an Abelian gauge group, monopoles, and axions.

Simple Reconfigurable Circularly Polarized Antenna at Three Bands.

In this paper, a simple design for a triple-band circularly polarized (CP) antenna with the capability of switching its polarization between dual-sense CPs is presented. The proposed antenna is comprised of a monopole loop antenna as a primary radiator. By placing a parasitic loop around the primary radiator, an additional CP band is achieved. Reconfigurability of the polarization between right-hand CP (RHCP) and left-hand CP (LHCP) at three different frequencies of 2.5, 3.3, and 3.8 GHz was realized by controlling the ON/OFF states of two PIN diodes. For validation, the fabricated antenna yielded an impedance bandwidth of 52.6% (2.34–4.01 GHz), while the axial ratio bandwidths for both the RHCP and LHCP states were 3.5% (2.47–2.56 GHz), 6.6% (3.20–3.42 GHz), and 2.4% (3.74–3.83 GHz). The measured broadside gains within the axial ratio bandwidth were 1.2, 2.7, and 1.4 dBi, respectively. Compared to other reconfigurable multi-band CP antennas, the proposed design is the first work to achieve a reconfigurable polarization at three distinct bands at a low fabrication cost by using only two diodes. The proposed antenna is suitable for WLAN and WiMAX applications.

Design of Circularly Polarized Conical RFID Reader Antenna Based on Natural Boundary Conditions

A novel design approach to circularly polarized (CP) conical RFID reader antenna is presented in this paper. First, operational principle of the proposed antenna is revealed by exploring the distribution of natural boundary conditions. It is demonstrated that due to the introduction of a shorting pin, the proposed antenna is dominated by two resonate modes, i.e., the monopole mode and loop mode, as the symmetrical property of conventional planar conical antenna is disturbed. As a result, the respective natural boundary conditions from these two modes will be sequentially excited with an interval of one-quarter of temporal period, thus the surface current becomes rotated and a CP wave is radiated. Prototypes with CP bidirectional and unidirectional radiation centered at 2.4 GHz are then fabricated and tested. It is shown that they can achieve a 3-dB axial ratio bandwidth about 5.38% and 2.84% in + y direction, respectively, which is further demonstrated that the design approach can be employed to effectively generate CP radiation without the use of orthogonal structures, modified ground plane as well as extra polarizer.

Instantons and monopoles

This study is part of a research program aimed to investigate the relations between instantons, monopoles, and chiral symmetry breaking. Monopoles are important 3-dimensional topological configurations existing in QCD, which are believed to produce colour confinement. Instantons are 4-dimensional topological configurations and are known to be related to chiral symmetry breaking. To study the relation between monopoles and instantons we generate configurations adding to the vacuum state static monopole-antimonopole pairs of opposite charges by use of a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops to the configurations. We then count the number of fermion zero modes using Overlap fermions as a tool. As a result we find that each monopole-antimonopole pair of magnetic charge one adds one zero mode of chirality $\pm1$, i.e. one instanton of topological charge $\pm1$.

Determination of Antenna Q from the Reflection-Coefficient Data [Antenna Designer's Notebook

Equivalent circuits containing frequency-variable radiation resistances are postulated for small monopole and small loop antennas above a ground plane. The equivalent circuits are valid below the first natural resonance frequency. By adding an external series inductance or a parallel capacitance, the antenna's Q is evaluated with the use of an invariant form for the reflection coefficient. The antenna's Q obtained this way accurately predicts the maximum obtainable bandwidth for either a single- or double-tuned matched antenna. At frequencies above the first resonance, the Q is evaluated by approximating the impedance or the reflection coefficient with polynomials within a narrow frequency range.

Magnetic monopole loops generated from two-instanton solutions: Jackiw-Nohl-Rebbi versus ’t Hooft instanton

In our previous paper [N. Fukui, K.-I. Kondo, A. Shibata, and T. Shinohara, Phys. Rev. D 82, 045015 (2010)], we have shown that the Jackiw-Nohl-Rebbi (JNR) two-instanton generates a circular loop of magnetic monopole in the four-dimensional Euclidean SU(2) Yang-Mills theory. On the other hand, it is claimed in Brower et al. [Phys. Rev. D 55, 6313 (1997); Nucl. Phys. B, Proc. Suppl. 53, 488 (1997)] that the 't Hooft two-instanton does not generate magnetic monopole loop. It seems that the two results are inconsistent with each other, since the JNR two-instanton converges to the 't Hooft two-instanton in a certain limit. In this paper, we clarify that the two results are compatible with each other by demonstrating how the magnetic monopole loop generated from the JNR two-instanton deforms in the process of taking the 't Hooft two-instanton limit.

Low-Profile Leaky Wave Electric Monopole Loop Antenna Using the $\beta=0$ Regime of a Ferrite-Loaded Open Waveguide

A novel low-profile leaky-wave electric monopole loop antenna in the regime of a composite right/left-handed (CRLH) ferrite-loaded open waveguide is presented. Despite its closed configuration, this structure supports a traveling-wave mode due to its non-reciprocity. Moreover, this mode exhibits an infinite wavelength in the regime, achieved at the transition frequency between the backward and forward CRLH bands, which leads to an electric monopole antenna field distribution when the loop is electrically small. The structure is analyzed theoretically and shown to admit, for a given loop width, different groups of discrete modes. The modes within each group converge to the unique mode of the straight waveguide when the radius of the loop becomes very large, as a consequence of the decreased curvature of the structure. A complete antenna, with a wire feed and a stub matching section, is demonstrated by both full-wave and experimental results. The omnidirectional azimuthal gain of the antenna is of -5 dBi with a co-to-cross polarization discrimination in excess of 20 dB. Removal of the ground plane would lead to a unique electric dipole loop antenna.

Jackiw-Nohl-Rebbi two-instanton as a source of magnetic monopole loop

We demonstrate that a Jackiw-Nohl-Rebbi solution, as the most general two-instanton, generates a circular loop of magnetic monopole in four-dimensional Euclidean $SU(2)$ Yang-Mills theory, in contrast to the one-instanton solution in the regular gauge for which no such magnetic monopole loops exist. These results together with our previous result indicate that a two-instanton solution and a two-meron solution with the same asymptotic behavior in the long distance are responsible for quark confinement based on the dual superconductivity picture.

Gauge-invariant magnetic monopole dominance in quark confinement

We show that a gauge-invariant magnetic monopole can be defined in Yang-Mills theory without matter fields, using a non-Abelian Stokes theorem and change of field variables a la Cho-Faddeev-Niemi, instead of using the Abelian projection. In fact, we give a first exact solution representing a magnetic monopole loop due to a meron pair with the non-trivial Pontryagin index. In addition, we summarize remarkable results of numerical simulations based on a new formulation of Yang-Mills theory: “Abelian” dominance and magnetic monopole dominance in the string tension. Finally, we discuss a novel feature in the case of SU ( 3 ) gauge group.

Magnetic monopole loops supported by a meron pair as the quark confiner

Magnetic monopole loops supported by a meron pair as the quark confiner

Magnetic monopole loops supported by a meron pair as the quark confiner

We give an analytical solution representing circular magnetic monopole loops joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is achieved by solving the differential equation for the adjoint color (magnetic monopole) field in the two-meron background field within the recently developed reformulation of the Yang-Mills theory. Our analytical solution corresponds to the numerical solution found by Montero and Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark confiner in the original Yang-Mills theory, as Callan, Dashen, and Gross suggested long ago.

Entropy of spatial monopole currents in pure SU(2) QCD at finite temperature

We study properties of spacelike monopole trajectories in the Maximal Abelian gauge of quenched SU(2) QCD at finite temperature. We concentrate on infrared monopole clusters which are responsible for the confinement properties of the theory. We determine numerically the effective action of the monopoles projected onto the three-dimensional time-slice. Then we derive the length distributions of the monopole loops and fix their entropy.

Instanton and Monopole in External Chromomagnetic Fields

We study properties of instanton and monopole in an external chromomagnetic field. Generally, the 't Hooft ansatz is no longer a solution of the Yang-Mills field equation in the presence of external fields. Therefore, we investigate a stabilized instanton solution with minimal total Yang-Mills action in a nontrivial topological sector. With this aim, we consider numerical minimization of the action with respect to the global color orientation, the anisotropic scale transformation and the local gauge-like transformation starting from a simple superposed gauge field of the 't Hooft ansatz and the external color field. Here, the external color field is, for simplicity, chosen to be a constant Abelian magnetic field along a certain direction. Then, the 4-dimensional rotational symmetry O(4) of the instanton solution is reduced to two 2-dimensional rotational symmetries $O(2)\times O(2)$ due to the effect of a homogeneous external field. In the space $\mib{R}^{3}$ at fixed $t$, we find a quadrupole deformation of this instanton solution. In the presence of a magnetic field $\vec{H}$, a prolate deformation occurs along the direction of $\vec{H}$. Contrastingly, in the presence of an electric field $\vec{E}$ an oblate deformation occurs along the direction of $\vec{E}$. We further discuss the local correlation between the instanton and the monopole in the external field in the maximally Abelian gauge. The external field affects the appearance of the monopole trajectory around the instanton. In fact, a monopole and anti-monopole pair appears around the instanton center, and this monopole loop seems to partially screen the external field.

Hopf defects as seeds for monopole loops

We investigate the relation between instantons and monopoles in the Laplacian Abelian Gauge using analytical methods in the continuum. Our starting point is the fact that the 't Hooft instanton with its high symmetry leads to a pointlike defect with Hopf invariant one. In order to generalise this result we partly break the symmetry by a local perturbation. We find that for generic configurations near the 't Hooft instanton the defects become loops. The analytical results show explicitly that these defects are magnetic monopoles with unit charge. In addition, the monopoles are twisted to account for the instanton number of the background.

Merons and instantons in laplacian abelian and center gauges in continuum Yang–Mills theory

Meron, instanton and instanton–antiinstanton field configurations are studied in continuum Yang–Mills theory in laplacian abelian and center gauges in order to detect their monopole and center vortex content. While a single instanton does not give rise to a center vortex, we find center vortices for merons. Furthermore we provide evidence, that merons can be interpreted as intersection points of center vortices. For the instanton–antiinstanton pair, we find a center vortex enclosing their centers, which carries two monopole loops.

Gauge independence of Abelian and monopole dominance

We formulate a stochastic gauge fixing method to study the gauge dependence of Abelian projection. In this method, one can change the gauge from the maximally Abelian one to no gauge fixing continuously. We have found that the linear part of the heavy quark potential from Abelian contribution depends little on the gauge parameter. Similar results have been obtained for the monopole contribution part. We also investigate the gauge dependence of the length of monopole loop, which is known to be important for the confinement, and monopole density. These results suggest that the picture that monopole plays an important role for the confinement of QCD dose not depend on choice of the gauge.