Finite volume QCD at fixed topological charge
Aoki, Sinya; Fukaya, Hidenori; Hashimoto, Shoji; Onogi, Tetsuya
2007-09-01
In finite volume the partition function of QCD with a given {theta} is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of a 1/V expansion. Applying this formula, we propose a class of methods to determine the topological susceptibility in QCD from various correlation functions calculated in a fixed topological sector.
Thermodynamics of charged topological dilaton black holes
Sheykhi, Ahmad
2007-12-15
A class of (n+1)-dimensional (n{>=}3) topological black hole solutions in Einstein-Maxwell-dilaton theory with Liouville-type potentials for the dilaton field is presented. In these spacetimes, the black hole horizon and the cosmological horizon can be an (n-1)-dimensional positive, zero, or negative constant curvature hypersurface. Because of the presence of the dilaton field, these topological black holes are neither asymptotically flat nor (anti-)de Sitter. We calculate the charge, mass, temperature, entropy, and electric potential of these solutions. We also analyze thermodynamics of these topological black holes and disclose the effect of the dilaton field on the thermal stability of the solutions.
Thermodynamics of charged topological dilaton black holes
Ahmad Sheykhi
2007-10-15
A class of $(n+1)$-dimensional topological black hole solutions in Einstein-Maxwell-dilaton theory with Liouville-type potentials for the dilaton field is presented. In these spacetimes, black hole horizon and cosmological horizon can be an $(n-1)$-dimensional positive, zero or negative constant curvature hypersurface. Because of the presence of the dilaton field, these topological black holes are neither asymptotically flat nor (anti)-de Sitter. We calculate the charge, mass, temperature, entropy and electric potential of these solutions. We also analyze thermodynamics of these topological black holes and disclose the effect of the dilaton field on the thermal stability of the solutions.
Cumulants of the QCD topological charge distribution
NASA Astrophysics Data System (ADS)
Guo, Feng-Kun; Meißner, Ulf-G.
2015-10-01
The distribution of the QCD topological charge can be described by cumulants, with the lowest one being the topological susceptibility. The vacuum energy density in a ?-vacuum is the generating function for these cumulants. In this paper, we derive the vacuum energy density in SU(2) chiral perturbation theory up to next-to-leading order keeping different up and down quark masses, which can be used to calculate any cumulant of the topological charge distribution. We also give the expression for the case of SU(N) with degenerate quark masses. In this case, all cumulants depend on the same linear combination of low-energy constants and chiral logarithm, and thus there are sum rules between the N-flavor quark condensate and the cumulants free of next-to-leading order corrections.
Trimethylaluminum: Bonding by Charge and Current Topology.
Stammler, Hans-Georg; Blomeyer, Sebastian; Berger, Raphael J F; Mitzel, Norbert W
2015-11-01
The charge density distribution of the trimethylaluminum dimer was determined by high-angle X-ray diffraction of a single crystal and quantum-chemical methods and analyzed using the quantum theory of atoms in molecules. The data can be interpreted as Al2 Me6 being predominantly ionically bonded, with clear indications of topological asymmetry for the bridging Al?C bonds owing to delocalized multicenter bonding. This interpretation is supported by the calculated magnetic response currents. The data shed new light on the bonding situation in this basic organometallic molecule, which was previously described by contradicting interpretations of bonding. PMID:26390916
Topology-based Feature Definition and Analysis
Weber, Gunther H.; Bremer, Peer-Timo; Gyulassy, Attila; Pascucci, Valerio
2010-12-10
Defining high-level features, detecting them, tracking them and deriving quantities based on them is an integral aspect of modern data analysis and visualization. In combustion simulations, for example, burning regions, which are characterized by high fuel-consumption, are a possible feature of interest. Detecting these regions makes it possible to derive statistics about their size and track them over time. However, features of interest in scientific simulations are extremely varied, making it challenging to develop cross-domain feature definitions. Topology-based techniques offer an extremely flexible means for general feature definitions and have proven useful in a variety of scientific domains. This paper will provide a brief introduction into topological structures like the contour tree and Morse-Smale complex and show how to apply them to define features in different science domains such as combustion. The overall goal is to provide an overview of these powerful techniques and start a discussion how these techniques can aid in the analysis of astrophysical simulations.
Non-Gaussianities in the topological charge distribution of the SU(3) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Cè, Marco; Consonni, Cristian; Engel, Georg P.; Giusti, Leonardo
2015-10-01
We study the topological charge distribution of the SU(3) Yang-Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang-Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t02? =6.67 (7 )×1 0-4 , where t0 is a standard reference scale, while for the ratio of the fourth cumulant over the second, we obtain R =0.233 (45 ). The latter is compatible with the expectations from the large Nc expansion, while it rules out the ? behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum nonperturbative nature.
Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
Marco Cè; Cristian Consonni; Georg P. Engel; Leonardo Giusti
2015-09-13
We study the topological charge distribution of the SU(3) Yang--Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang--Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t_0^2*chi=6.67(7)*10^-4, where t_0 is a standard reference scale, while for the ratio of the forth cumulant over the second we obtain R=0.233(45). The latter is compatible with the expectations from the large Nc expansion, while it rules out the theta-behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum non-perturbative nature.
Topological charges in 2d N=(2,2) theories and massive BPS states
Daniel S. Park
2015-07-27
We study how charges of global symmetries that are manifest in the ultra-violet definition of a theory are realized as topological charges in its infra-red effective theory for two-dimensional theories with $\\mathcal{N}=(2,2)$ supersymmetry. We focus on the charges that the states living on $S^1$ carry. The central charge---or BPS masses---of the supersymmetry algebra play a crucial role in making this correspondence precise. We study two examples: $U(1)$ gauge theories with chiral matter, and world-volume theories of "dynamical surface operators" of 4d $\\mathcal{N}=2$ gauge theories. In the former example, we show that the flavor charges of the theory are realized as topological winding numbers in the effective theory on the Coulomb branch. In the latter, we show that there is a one-to-one correspondence between topological charges of the effective theory of the dynamical surface operator and the electric, magnetic, and flavor charges of the 4d gauge theory. We also examine the topologically charged massive BPS states on $S^1$ and discover that the massive BPS spectrum is sensitive to the radius of the circle in the simplest theory---the free theory of a periodic twisted chiral field. We clarify this behavior by showing that the massive BPS spectrum on $S^1$, unlike the BPS ground states, cannot be identified as elements of a cohomology.
Topological charges in 2d N=(2,2) theories and massive BPS states
Park, Daniel S
2015-01-01
We study how charges of global symmetries that are manifest in the ultra-violet definition of a theory are realized as topological charges in its infra-red effective theory for two-dimensional theories with $\\mathcal{N}=(2,2)$ supersymmetry. We focus on the charges that the states living on $S^1$ carry. The central charge---or BPS masses---of the supersymmetry algebra play a crucial role in making this correspondence precise. We study two examples: $U(1)$ gauge theories with chiral matter, and world-volume theories of "dynamical surface operators" of 4d $\\mathcal{N}=2$ gauge theories. In the former example, we show that the flavor charges of the theory are realized as topological winding numbers in the effective theory on the Coulomb branch. In the latter, we show that there is a one-to-one correspondence between topological charges of the effective theory of the dynamical surface operator and the electric, magnetic, and flavor charges of the 4d gauge theory. We also examine the topologically charged massive ...
Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
Cé, Marco; Engel, Georg P; Giusti, Leonardo
2015-01-01
We study the topological charge distribution of the SU(3) Yang--Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang--Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t_0^2*chi=6.67(7)*10^-4, where t_0 is a standard reference scale, while for the...
Charge d-wave topological insulator
Kopaev, Yu. V.; Kapaev, V. V.; Belyavskii, V. I.
2013-10-15
Formation of a condensate of singlet electron-hole pairs in a two-dimensional metal lattice with the nesting of the Fermi contour is investigated. A numerical solution is obtained for the self-consistency equation for the insulating order parameter depending on the ratio of the coupling constants in the s- and d-wave channels of electron-hole pairing. Solutions with the pure orbital symmetry of s- and d-type are found, as well as solutions with the mixed s + d-symmetry. It is shown that in a wide range of values of the s- and d-wave coupling constants, the two-dimensional insulating order with the orbital symmetry d{sub x{sup 2}-y{sup 2}} can compete with pure ordered s- and d{sub xy}-states and mixed s + d-states. Time reversal symmetry breaking under an established real order with d{sub x{sup 2}-y{sup 2}} -wave symmetry may generate the imaginary component of the order parameter with symmetry d{sub xy} and cause a rise in topologically nontrivial d + id-wave ordering similar to the quantum Hall state in the absence of external magnetic field.
Fractional charge and spin states in topological insulator constrictions
NASA Astrophysics Data System (ADS)
Klinovaja, Jelena; Loss, Daniel
2015-09-01
We theoretically investigate the properties of two-dimensional topological insulator constrictions both in the integer and fractional regimes. In the presence of a perpendicular magnetic field, the constriction functions as a spin filter with near-perfect efficiency and can be switched by electric fields only. Domain walls between different topological phases can be created in the constriction as an interface between tunneling, magnetic fields, charge density wave, or electron-electron interaction dominated regions. These domain walls host non-Abelian bound states with fractional charge and spin and result in degenerate ground states with parafermions. If a proximity gap is induced bound states give rise to an exotic Josephson current with 8 ? periodicity.
Simultaneous Magnetic and Charge Doping of Topological Insulators with Carbon
NASA Astrophysics Data System (ADS)
Shen, Lei; Zeng, Minggang; Lu, Yunhao; Yang, Ming; Feng, Yuan Ping
2013-12-01
A two-step doping process, magnetic followed by charge or vice versa, is required to produce massive topological surface states (TSS) in topological insulators for many physics and device applications. Here, we demonstrate simultaneous magnetic and hole doping achieved with a single dopant, carbon, in Bi2Se3 by first-principles calculations. Carbon substitution for Se (CSe) results in an opening of a sizable surface Dirac gap (up to 82 meV), while the Fermi level remains inside the bulk gap and close to the Dirac point at moderate doping concentrations. The strong localization of 2p states of CSe favors spontaneous spin polarization via a p-p interaction and formation of ordered magnetic moments mediated by surface states. Meanwhile, holes are introduced into the system by CSe. This dual function of carbon doping suggests a simple way to realize insulating massive TSS.
C library for topological study of the electronic charge density.
Vega, David; Aray, Yosslen; Rodríguez, Jesús
2012-12-01
The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid-based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton-Raphson method (to find the critical points, where the gradient is null) and the Cash-Karp Runge-Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three-dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions. PMID:22865338
Optical phased array radiating optical vortex with manipulated topological charges.
Ma, Xiaoliang; Pu, Mingbo; Li, Xiong; Huang, Cheng; Pan, Wenbo; Zhao, Bo; Cui, Jianhua; Luo, Xiangang
2015-02-23
Optical antennas are key elements in quantum optics emitting and sensing, and behave wide range applications in optical domain. However, integration of optical antenna radiating orbital angular momentum is still a challenge in nano-scale. We theoretically demonstrate a sub-wavelength phased optical antenna array, which manipulates the distribution of the orbital angular momentum in the near field. Orbital angular momentum with topological charge of 4 can be obtained by controlling the phase distribution of the fundamental mode orbital angular momentum in each antenna element. Our results indicate this phased array may be utilized in high integrated optical communication systems. PMID:25836522
Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics
P. V. Buividovich; T. Kalaydzhyan; M. I. Polikarpov
2012-10-21
We study the effect of cooling on the spatial distribution of the topological charge density in quenched SU(2) lattice gauge theory with overlap fermions. We show that as the gauge field configurations are cooled, the Hausdorff dimension of regions where the topological charge is localized gradually changes from d = 2..3 towards the total space dimension. Therefore, the cooling procedure destroys some of the essential properties of the topological charge distribution.
Maximum-Likelihood Approach to Topological Charge Fluctuations in Lattice Gauge Theory
R. C. Brower; M. Cheng; G. T. Fleming; M. F. Lin; E. T. Neil; J. C. Osborn; C. Rebbi; E. Rinaldi; D. Schaich; C. Schroeder; G. Voronov; P. Vranas; E. Weinberg; O. Witzel
2014-07-24
We present a novel technique for the determination of the topological susceptibility (related to the variance of the distribution of global topological charge) from lattice gauge theory simulations, based on maximum-likelihood analysis of the Markov-chain Monte Carlo time series. This technique is expected to be particularly useful in situations where relatively few tunneling events are observed. Restriction to a lattice subvolume on which topological charge is not quantized is explored, and may lead to further improvement when the global topology is poorly sampled. We test our proposed method on a set of lattice data, and compare it to traditional methods.
Non-Gaussianity of the topological charge distribution in $\\mathrm{SU}(3)$ Yang-Mills theory
Cè, Marco
2015-01-01
In Yang-Mills theory, the cumulants of the na\\"ive lattice discretization of the topological charge evolved with the Yang-Mills gradient flow coincide, in the continuum limit, with those of the universal definition. We sketch in these proceedings the main points of the proof. By implementing the gradient-flow definition in numerical simulations, we report the results of a precise computation of the second and the fourth cumulant of the $\\mathrm{SU}(3)$ Yang-Mills theory topological charge distribution, in order to measure the deviation from Gaussianity. A range of high-statistics Monte Carlo simulations with different lattice volumes and spacings is used to extrapolate the results to the continuum limit with confidence by keeping finite-volume effects negligible with respect to the statistical errors. Our best result for the topological susceptibility is $t_0^2\\chi=6.67(7)\\times 10^{-4}$, while for the ratio between the fourth and the second cumulant we obtain $R=0.233(45)$.
Analysis of the topological charge of vortex beams using a hole wheel
NASA Astrophysics Data System (ADS)
Emile, Olivier; Emile, Janine; Viaris de Lesegno, Bruno; Pruvost, Laurence; Brousseau, Christian
2015-08-01
The measurement of the topological charge of a vortex beam is demonstrated using the diffraction pattern produced by hole wheel. The resulting mandala-like interference pattern depends on the number of holes relatively to the topological charge. The interference at the centre of the pattern —bright or dark—enables us to determine the topological charge in a procedure when hole wheels with different number of holes are applied. This method is direct and wavelength independent. It does not require any image analysis and could find applications in classical telecommunications or quantum optics using twisted light.
Charge Topology of the Coherent Dissociation of Relativistic C-11 and N-12 Nuclei
D. A. Artemenkov; V. Bradnova; A. A. Zaitsev; P. I. Zarubin; I. G. Zarubina; R. R. Kattabekov; N. K. Kornegrutsa; K. Z. Mamatkulov; P. A. Rukoyatkin; V. V. Rusakova; R. Z. Stanoeva
2015-09-02
The charge topology of coherent-dissociation events is presented for $^{11}$C and $^{12}$N nuclei of energy 1.2~\\textit{A}~GeV per nucleon bombarding nuclear track emulsions. This topology is compared with respective data for $^{7}$Be, $^{8,10}$B, $^{9,10}$C and $^{14}$N nuclei.
Charge topology of the coherent dissociation of relativistic 11C and 12N nuclei
NASA Astrophysics Data System (ADS)
Artemenkov, D. A.; Bradnova, V.; Zaitsev, A. A.; Zarubin, P. I.; Zarubina, I. G.; Kattabekov, R. R.; Kornegrutsa, N. K.; Mamatkulov, K. Z.; Rukoyatkin, P. A.; Rusakova, V. V.; Stanoeva, R.
2015-09-01
The charge topology of coherent-dissociation events is presented for 11? and 12N nuclei of energy 1.2 GeV per nucleon bombarding nuclear track emulsions. This topology is compared with respective data for 7Be, 8,10B, 9,10C, and 14N nuclei.
Decorrelation of the topological charge in tempered Hybrid Monte Carlo simulations of QCD
E. -M. Ilgenfritz; Werner Kerler; H. Stüben
1999-08-18
We study the improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering. As an indicator for decorrelation we use the topological charge.
Dilute Liquid of Instanton and Its Topological Charge Dominate the QCD Vacuum
Wang, Z. Q.; Lu, X. F.; Wang, F.
2006-11-02
APE smearing and overlap-Dirac operator are combined to filter QCD vacuum configurations. The results obtained from overlap fermions and improved 5Li cooling are compared, both of them exhibit structures of dilute liquid of instanton. Finally the overlap fermions, improved 5Li cooling and APE smearing are combined to calculate the topological charge and identify the structure of QCD vacuum. The results suggest dilute liquid of instanton dominance of topological charge fluctuations in quenched lattice QCD.
NASA Astrophysics Data System (ADS)
Wang, Xin; Liang, Shi-Dong
2013-02-01
We explore the charge transfer in the telomere G-Quadruplex (TG4) DNA theoretically by the nonequilibrium Green's function method, and reveal the topological effect of the charge transport in TG4 DNA. The consecutive TG4 (CTG4) is semiconducting with 0.2 0.3 eV energy gap. Charges transfer favorably in the CTG4, but are trapped in the nonconsecutive TG4 (NCTG4). The global conductance is inversely proportional to the local conductance for NCTG4. The topological structure transition from NCTG4 to CTG4 induces abruptly 3nA charge current, which provide a microscopic clue to understand the telomerase activated or inhibited by TG4. Our findings reveal the fundamental property of charge transfer in TG4 and its relationship with the topological structure of TG4.
Wang, Xin
2015-01-01
We explore charge transfer in the telomere G-Quadruplex (TG4) DNA theoretically by the nonequilibrium Green's function method, and reveal the topological effect of charge transport in TG4 DNA. The consecutive TG4(CTG4) is semiconducting with 0.2 ~ 0.3eV energy gap. Charges transfers favorably in the consecutive TG4, but are trapped in the non-consecutive TG4 (NCTG4). The global conductance is inversely proportional to the local conductance for NCTG4. The topological structure transition from NCTG4 to CTG4 induces abruptly ~ 3nA charge current, which provide a microscopic clue to understand the telomerase activated or inhibited by TG4. Our findings reveal the fundamental property of charge transfer in TG4 and its relationship with the topological structure of TG4.
Towards A More Physically Adequate Definition of Randomness: A Topological Approach
Kreinovich, Vladik
Towards A More Physically Adequate Definition of Randomness: A Topological Approach Vladik definition is too general: e.g., it includes some clearly nonÂphysical situations when the set of all random Kreinovich Department of Computer Science, University of Texas at El Paso El Paso, TX 79968, USA, vladik
Towards A More Physically Adequate Definition of Randomness: A Topological Approach
Kreinovich, Vladik
Towards A More Physically Adequate Definition of Randomness: A Topological Approach Vladik definition is too general: e.g., it includes some clearly non-physical situations when the set of all random Kreinovich Department of Computer Science, University of Texas at El Paso El Paso, TX 79968, USA, vladik
P-V criticality of higher dimensional charged topological dilaton de Sitter black holes
NASA Astrophysics Data System (ADS)
Zhao, Hui-Hua; Zhang, Li-Chun; Ma, Meng-Sen; Zhao, Ren
2014-09-01
There are both the black hole horizon and the cosmological horizon for the charged topological dilaton de Sitter spacetime. The thermodynamic quantities on both horizons satisfy the first law of black hole thermodynamics. Because all of these thermodynamic quantities depend on the mass M, the electric charge Q, and the cosmological constant l, the two horizons are not independent. Considering the connection between the black hole horizon and the cosmological horizon, we derive the effective thermodynamic quantities of the (n +1)-dimensional charged topological dilaton de Sitter spacetime. We find that the charged topological dilaton black hole in de Sitter spacetime has a similar phase transition and critical behavior to that in anti-de Sitter spacetime.
Momentum polarization: An entanglement measure of topological spin and chiral central charge
NASA Astrophysics Data System (ADS)
Tu, Hong-Hao; Zhang, Yi; Qi, Xiao-Liang
2013-11-01
Topologically ordered states are quantum states of matter with topological ground-state degeneracy and quasiparticles carrying fractional quantum numbers and fractional statistics. The topological spin ?a=2?ha is an important property of a topological quasiparticle, which is the Berry phase obtained in the adiabatic self-rotation of the quasiparticle by 2?. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge c. In this paper we propose an approach to compute the topological spin and chiral central charge in lattice models by defining a quantity that we call the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a “partial translation operator.” We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination ha-(c)/(24) of topological spin and central charge. Results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model and the ?=1/2 Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wave function, which verify the analytic formula with high accuracy and further suggest that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides an efficient approach to extract characteristic quantities of topological states of matter from finite size numerics.
Xing Huang; Soo-Jong Rey; Yang Zhou
2014-01-21
We construct three-dimensional N=2 supersymmetric conformal field theories on conic spaces. Built upon the fact that the partition function depends solely on the Reeb vector of the Killing vector, we propose that holographic dual of these theories are four-dimensional, supersymmetric charged topological black holes. With the supersymmetry localization technique, we study conserved supercharges, free energy, and Renyi entropy. At planar large N limit, we demonstrate perfect agreement between the superconformal field theories and the supersymmetric charged topological black holes.
Huang, Xing; Zhou, Yang
2014-01-01
We construct three-dimensional N=2 supersymmetric conformal field theories on conic spaces. Built upon the fact that the partition function depends solely on the Reeb vector of the Killing vector, we propose that holographic dual of these theories are four-dimensional, supersymmetric charged topological black holes. With the supersymmetry localization technique, we study conserved supercharges, free energy, and Renyi entropy. At planar large N limit, we demonstrate perfect agreement between the superconformal field theories and the supersymmetric charged topological black holes.
NASA Astrophysics Data System (ADS)
Barnes, G.; Longcope, D. W.; Leka, K. D.
2004-05-01
Magnetic Charge Topology (MCT) models represent the field in the solar corona as being due to collection of point magnetic charges located at or below the photosphere. These models have the advantage of providing a simple quantitative description of the field topology. We apply MCT to time series of magnetograms from the U. Hawai`i/Mees Solar Observatory Imaging Vector Magnetograph (IVM). We first describe the evolution of the magnetic topology of the region, by calculating such quantities as the magnetic flux connecting each pair of point sources, and the number and locations of magnetic separators, which are likely to be the location of reconnection in the solar corona. Using the changes in the magnitudes of the point sources, and in the connectivity matrix, we estimate the rate at which flux is emerging and submerging through the photosphere, and the rate at which reconnection is happening in the corona. By tracking the changes in the locations of the sources, we are also able to estimate the horizontal velocities. This work was performed under Air Force Office of Scientific Research contracts F49620-03-C-0019 and F49620-02-C-0191.
S1×S2 wormholes and topological charge
NASA Astrophysics Data System (ADS)
Ridgway, S. Alexander
1994-07-01
I investigate solutions to the Euclidean Einstein-matter field equations with the topology S1×S2×R in a theory with a massless periodic scalar field and electromagnetism. These solutions carry the winding number of the periodic scalar as well as magnetic flux. They induce violations of a quasitopological conservation law which conserves the product of the magnetic flux and winding number on the background spacetime. I extend these solutions to a model with stable loops of superconducting cosmic string and interpret them as contributing to the decay of such loops.
Dumping topological charges on neighbors: ice manifolds for colloids and vortices
NASA Astrophysics Data System (ADS)
Nisoli, Cristiano
2014-11-01
We investigate the recently reported analogies between pinned vortices in nano-structured superconductors or colloids in optical traps, and spin ice materials. It has been found experimentally and numerically that both colloids and vortices exhibit ice or quasi-ice manifolds. However, the frustration of colloids and vortices differs essentially from spin ice at the vertex level. We show that the effective vertex energetics of the colloidal/vortex systems is made identical to that of spin ice materials by the contribution of an emergent field associated to the topological charge of the vertex. The similarity extends to the local low-energy dynamics of the ice manifold, where the effect of geometric hard constraints can be subsumed into the spatial modulation of the emergent field, which mediates an entropic interaction between topological charges. There, as in spin ice materials, genuine ice manifolds enter a Coulomb phase, whereas quasi-ice manifolds posses a well defined screening length, provided by a plasma of embedded topological charges. We also show that such similarities break down in lattices of mixed coordination because of topological charge transfer between sub-latices. This opens interesting perspective for extensions beyond physics, to social and economical networks.
Charge quantisation without magnetic poles: a topological approach to electromagnetism
Romero Solha
2015-09-28
The present work provides a theoretical explanation for the quantisation of electric charges, an open problem since Millikan's oil drop experiment in 1909. This explanation is based solely on Maxwell's theory, it recasts Electromagnetic theory under the language of complex line bundles; therefore, neither magnetic poles nor quantum mechanics are invoked. The existence of magnetic poles was essentially the only theoretical explanation for charge quantisation (e.g. Dirac's magnetic pole), and there is no experimental data supporting their existence ---on the contrary, they have never been observed.
Disorder Effects in Charge Transport and Spin Response of Topological Insulators
NASA Astrophysics Data System (ADS)
Zhao, Lukas Zhonghua
Topological insulators are a class of solids in which the non-trivial inverted bulk band structure gives rise to metallic surface states that are robust against impurity backscattering. First principle calculations predicted Bi2Te3, Sb2Te3 and Bi2Se3 to be three-dimensional (3D) topological insulators with a single Dirac cone on the surface. The topological surface states were subsequently observed by angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM). The investigations of charge transport through topological surfaces of 3D topological insulators, however, have faced a major challenge due to large charge carrier densities in the bulk donated by randomly distributed defects such as vacancies and antisites. This bulk disorder intermixes surface and bulk conduction channels, thereby complicating access to the low-energy (Dirac point) charge transport or magnetic response and resulting in the relatively low measured carrier mobilities. Moreover, charge inhomogeneity arising from bulk disorder can result in pronounced nanoscale spatial fluctuations of energy on the surface, leading to the formation of surface `puddles' of different carrier types. Great efforts have been made to combat the undesirable effects of disorder in 3D topological insulators and to reduce bulk carriers through chemical doping, nanostructure fabrication, and electric gating. In this work we have developed a new way to reduce bulk carrier densities using high-energy electron irradiation, thereby allowing us access to the topological surface quantum channels. We also found that disorder in 3D topological insulators can be beneficial. It can play an important part in enabling detection of unusual magnetic response from Dirac fermions and in uncovering new excitations, namely surface superconductivity in Dirac `puddles'. In Chapter 3 we show how by using differential magnetometry we could probe spin rotation in the 3D topological material family (Bi2Se 3, Bi2Te3 and Sb2Te3), and describe our detection of paramagnetic singularity in the magnetic susceptibility at low magnetic fields that persists up to room temperature, and which we have demonstrated to arise from the surfaces of the samples. The singularity is universal to the entire family, largely independent of the bulk carrier density, and consistent with the existence of electronic states near the spin-degenerate Dirac point of the 2D helical metal. The exceptional thermal stability of the signal points to an intrinsic surface cooling process, probably of thermoelectric organ, and establishes a sustainable platform for the singular field-tunable Dirac spin response. In Chapter 4 we describe our discovery of surface superconductivity in a hole-conducting topological insulator Sb2Te3 with transition to zero resistance induced through a minor tuning of growth chemistry that depletes bulk conduction channels. The depletion shifts Fermi energy towards the Dirac point as witnessed by over two orders of magnitude reduced bulk hole density and by the largest carrier mobility (~ 25,000 cm 2 V-1 s-1) found in any topological material. Direct evidence from transport, the unprecedentedly large diamagnetic screening, and the presence of up to ~ 25 meV gaps in differential conductance detected by scanning tunneling spectroscopy (STM) reveal the superconducting condensate to emerge first in surface puddles at unexpectedly high temperature, near 50 K. Percolative Josephson paths mediated by diffusing quasiparticles establish global phase coherence around 9 K. Rich structure of this state lends itself to manipulation and tuning via growth conditions and the topological material's parameters such as Fermi velocity and mean free path. In Chapter 5 we describe a new approach we have developed to reaching stable charge neutrality in 3D topological materials. The technique uses swift (~ 2.5 MeV energy) electron beams to compensate charged bulk defects and bring the Fermi level back into the bulk gap. By controlling the beam fluence we could tune bulk conductivity from p- (hole-like) to n-type (ele
Topological charges of three-dimensional Dirac semimetals with rotation symmetry
NASA Astrophysics Data System (ADS)
Yang, Bohm-Jung; Morimoto, Takahiro; Furusaki, Akira
2015-10-01
In general, the stability of a band crossing point indicates the presence of a quantized topological number associated with it. In particular, the recent discovery of three-dimensional Dirac semimetals in Na3Bi and Cd3As2 demonstrates that a Dirac point with fourfold degeneracy can be stable as long as certain crystalline symmetries are supplemented in addition to the time-reversal and inversion symmetries. However, the topological charges associated with Na3Bi and Cd3As2 are not clarified yet. In this work, we identify the topological charge of three-dimensional Dirac points. It is found that although the simultaneous presence of the time-reversal and inversion symmetries forces the net chiral charge to vanish, a Dirac point can carry another quantized topological charge when an additional rotation symmetry is considered. Two different classes of Dirac semimetals are identified depending on the nature of the rotation symmetries. First, the conventional symmorphic rotational symmetry which commutes with the inversion gives rise to the class I Dirac semimetals having a pair of Dirac points on the rotation axes. Since the topological charges of each pair of Dirac points have the opposite sign, a pair creation or a pair annihilation is required to change the number of Dirac points in the momentum space. On the other hand, the class II Dirac semimetals possess a single isolated Dirac point at a time-reversal invariant momentum, which is protected by a screw rotation. The nonsymmorphic nature of screw rotations allows the anticommutation relation between the rotation and inversion symmetries, which enables to circumvent the doubling of the number of Dirac points and create a single Dirac point at the Brillouin zone boundary.
Charge quantisation without magnetic poles: A topological approach to electromagnetism
NASA Astrophysics Data System (ADS)
Solha, Romero
2016-01-01
The present work provides a theoretical explanation for the quantisation of electric charges, an open problem since Millikan's oil drop experiment in 1909. This explanation is based solely on Maxwell's theory, it recasts Electromagnetic theory under the language of complex line bundles; therefore, neither magnetic poles nor quantum mechanics are invoked.
Direct Observation of Chiral Topological Solitons in 1D Charge-Density Waves
NASA Astrophysics Data System (ADS)
Kim, Tae-Hwan; Cheon, Sangmo; Lee, Sung-Hoon; Yeom, Han Woong
2015-03-01
Macroscopic and classical solitons are easily and ubiquitously found, from tsunami to blood pressure pulses, but those in microscopic scale are hard to observe. While the existence of such topological solitons were predicted theoretically and evidenced indirectly by the transport and infrared spectroscopy measurements, the direct observation has been hampered by their high mobility and small dimension. In this talk, we show direct observation of topological solitons in the quasi-1D charge-density wave (CDW) ground state of indium atomic wires, which are consisting of interacting double Peierls chains. Such solitons exhibit a characteristic spatial variation of the CDW amplitudes as expected from the electronic structure. Furthermore, these solitons have an exotic hidden topology originated by topologically different 4-fold degenerate CDW ground states. Their exotic topology leads to the chirality of 1D topological solitons through interaction between two solitons in the double Peierls chains. Detailed scanning tunneling microscopy and spectroscopy reveal their chiral nature at the atomic scale. This work paves the avenue toward the microscopic exploitation of the peculiar properties of nanoscale chiral solitons.
Low dimensional long range topological charge structure in the QCD vacuum
I. Horvath; S.J. Dong; T. Draper; F.X. Lee; K.F. Liu; N. Mathur; H.B. Thacker; J.B. Zhang
2003-12-01
While sign-coherent 4-dimensional structures cannot dominate topological charge fluctuations in the QCD vacuum at all scales due to reflection positivity, it is possible that enhanced coherence exists over extended space-time regions of lower dimension. Using the overlap Dirac operator to calculate topological charge density, we present evidence for such structure in pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium configuration is dominated by two oppositely-charged sign-coherent connected structures (``sheets'') covering about 80% of space-time. Each sheet is built from elementary 3-d cubes connected through 2-d faces, and approximates a low-dimensional curved manifold (or possibly a fractal structure) embedded in the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18% of the most intense space-time points organized into a global long-range structure, involving connected parts spreading over maximal possible distances. We find that the skeleton is locally 1-dimensional and propose that its geometrical properties might be relevant for understanding the possible role of topological charge fluctuations in the physics of chiral symmetry breaking.
An acoustic charge transport imager for high definition television applications
NASA Technical Reports Server (NTRS)
Hunt, W. D.; Brennan, Kevin F.
1994-01-01
The primary goal of this research is to develop a solid-state high definition television (HDTV) imager chip operating at a frame rate of about 170 frames/sec at 2 Megapixels per frame. This imager offers an order of magnitude improvement in speed over CCD designs and will allow for monolithic imagers operating from the IR to the UV. The technical approach of the project focuses on the development of the three basic components of the imager and their integration. The imager chip can be divided into three distinct components: (1) image capture via an array of avalanche photodiodes (APD's), (2) charge collection, storage and overflow control via a charge transfer transistor device (CTD), and (3) charge readout via an array of acoustic charge transport (ACT) channels. The use of APD's allows for front end gain at low noise and low operating voltages while the ACT readout enables concomitant high speed and high charge transfer efficiency. Currently work is progressing towards the development of manufacturable designs for each of these component devices. In addition to the development of each of the three distinct components, work towards their integration is also progressing. The component designs are considered not only to meet individual specifications but to provide overall system level performance suitable for HDTV operation upon integration. The ultimate manufacturability and reliability of the chip constrains the design as well. The progress made during this period is described in detail in Sections 2-4.
NASA Astrophysics Data System (ADS)
Durganandini, P.
2015-03-01
We consider thin planar charged quantum rings on the surface of a three dimensional topological insulator coated with a thin ferromagnetic layer. We show theoretically, that when the ring is threaded by a magnetic field, then, due to the Aharanov-Bohm effect, there are not only the well known circulating persistent currents in the ring but also oscillating persistent Hall voltages across the thin ring. Such oscillating persistent Hall voltages arise due to the topological magneto-electric effect associated with the axion electrodynamics exhibited by the surface electronic states of the three dimensional topological insulator when time reversal symmetry is broken. We further generalize to the case of dipole currents and show that analogous Hall dipole voltages arise. We also discuss the robustness of the effect and suggest possible experimental realizations in quantum rings made of semiconductor heterostructures. Such experiments could also provide new ways of observing the predicted topological magneto-electric effect in three dimensional topological insulators with time reversal symmetry breaking. I thank BCUD, Pune University, Pune for financial support through research grant.
On the critical phenomena and thermodynamics of charged topological dilaton AdS black holes
NASA Astrophysics Data System (ADS)
Zhao, Ren; Zhao, Hui-Hua; Ma, Meng-Sen; Zhang, Li-Chun
2013-12-01
In this paper, we study the phase structure and equilibrium state space geometry of charged topological dilaton black holes in ( n+1)-dimensional anti-de Sitter spacetime. By considering the pairs of parameters ( P˜ V) and ( Q˜ U) as variables, we analyze the phase structure and critical phenomena of black holes and discuss the relation between the two kinds of critical phenomena. We find that the phase structures and critical phenomena drastically depend on the cosmological constant l (or the static electric charge Q of the black holes), dimensionality n and dilaton field ?.
Surface states of charge carriers in epitaxial films of the topological insulator Bi2Te3
NASA Astrophysics Data System (ADS)
Luk'yanova, L. N.; Boikov, Yu. A.; Danilov, V. A.; Usov, O. A.; Volkov, M. P.; Kutasov, V. A.
2014-05-01
The galvanomagnetic properties of p-type bismuth telluride heteroepitaxial films grown by the hot wall epitaxy method on oriented muscovite mica substrates have been investigated. Quantum oscillations of the magnetoresistance associated with surface electronic states in three-dimensional topological insulators have been studied in strong magnetic fields ranging from 6 to 14 T at low temperatures. The cyclotron effective mass, charge carrier mobility, and parameters of the Fermi surface have been determined based on the results of analyzing the magnetoresistance oscillations. The dependences of the cross-sectional area of the Fermi surface S( k F), the wave vector k F, and the surface concentration of charge carriers n s on the frequency of magnetoresistance oscillations in p-type Bi2Te3 heteroepitaxial films have been obtained. The experimentally observed shift of the Landau level index is consistent with the value of the Berry phase, which is characteristic of topological surface states of Dirac fermions in the films. The properties of topological surface states of charge carriers in p-type Bi2Te3 films obtained by analyzing the magnetoresistance oscillations significantly expand fields of practical application and stimulate the investigation of transport properties of chalcogenide films.
Charged Particle Environment Definition for NGST: Model Development
NASA Technical Reports Server (NTRS)
Blackwell, William C.; Minow, Joseph I.; Evans, Steven W.; Hardage, Donna M.; Suggs, Robert M.
2000-01-01
NGST will operate in a halo orbit about the L2 point, 1.5 million km from the Earth, where the spacecraft will periodically travel through the magnetotail region. There are a number of tools available to calculate the high energy, ionizing radiation particle environment from galactic cosmic rays and from solar disturbances. However, space environment tools are not generally available to provide assessments of charged particle environment and its variations in the solar wind, magnetosheath, and magnetotail at L2 distances. An engineering-level phenomenology code (LRAD) was therefore developed to facilitate the definition of charged particle environments in the vicinity of the L2 point in support of the NGST program. LRAD contains models tied to satellite measurement data of the solar wind and magnetotail regions. The model provides particle flux and fluence calculations necessary to predict spacecraft charging conditions and the degradation of materials used in the construction of NGST. This paper describes the LRAD environment models for the deep magnetotail (XGSE < -100 Re) and solar wind, and presents predictions of the charged particle environment for NGST.
Miyamoto, K.; Suizu, K.; Akiba, T.; Omatsu, T.
2014-06-30
A terahertz (THz) spiral phase plate with high transmission (>90% after Fresnel correction) and low dispersion has been developed based on the Tsurupica olefin polymer. Direct observations of the topological charge (both magnitude and sign) of a THz vortex beam are performed by using a THz camera with tilted lens focusing and radial defect introduction. The vortex outputs with a topological charge of ±1 (or ±2) are obtained at a frequency of 2 (or 4) THz.
Quasi-Local Conserved Charges of Spin-3 Topologically Massive Gravity
Setare, M R
2016-01-01
In this paper we obtain conserved charges of spin-3 topologically massive gravity by using a quasi-local formalism. We find a general formula to calculate conserved charge of the spin-3 topologically massive gravity corresponds to a Killing vector field $\\xi$. We show that this general formula reduces to the previous one for the ordinary spin-3 gravity presented in \\cite{31} when we take into account only transformation under diffeomorphism, without considering generalized Lorentz gauge transformation (i.e. $\\lambda _{\\xi} =0$), and by taking $\\frac{1}{\\mu}\\rightarrow 0$. Then we obtain a general formula for the entropy of black hole solutions of the spin-3 topologically massive gravity. Finally we apply our formalism to calculate energy, angular momentum and entropy of a special black hole solution and we find that obtained results are consistent with previous results in the limiting cases. Moreover our result for energy, angular momentum and entropy are consistent with the first law of black hole mechanics.
Quantum Charges and Spacetime Topology: The Emergence of New Superselection Sectors
NASA Astrophysics Data System (ADS)
Brunetti, Romeo; Ruzzi, Giuseppe
2009-04-01
A new form of superselection sectors of topological origin is developed. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize the notion of representations of nets of C*-algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts’ cohomological analysis to the case where 1-cocycles bear non-trivial unitary representations of the fundamental group of the spacetime, equivalently of its Cauchy surface in the case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras generated by the 1-cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove that any 1-cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored. This second part much resembles what in literature is known as geometric phases. Indeed, by the very geometrical origin of the 1-cocycles that we discuss in the paper, they are essential tools in the theory of net bundles, and the topological part is related to their holonomy content. At the end we prove the existence of net representations.
NASA Astrophysics Data System (ADS)
Mao, Ting; Wang, Z. D.
2015-01-01
Majorana bound states have been a focus of condensed matter research for their potential applications in topological quantum computation. Here we utilize two charge-qubit arrays to explicitly simulate a DIII class one-dimensional superconductor model where Majorana end states can appear. Combined with one braiding operation, universal single-qubit operations on a Majorana-based qubit can be implemented by a controllable inductive coupling between two charge qubits at the ends of the arrays. We further show that in a similar way, a controlled-not gate for two topological qubits can be simulated in four charge-qubit arrays. Although the current scheme may not truly realize topological quantum operations, we elaborate that the operations in charge-qubit arrays are indeed robust against certain local perturbations.
Chen, Zhiyi; Zhao, Lukas; Park, Kyungwha; Garcia, Thor Axtmann; Tamargo, Maria C.; Krusin-Elbaum, Lia
2015-01-01
Access to charge transport through Dirac surface states in topological insulators (TIs) can be challenging due to their intermixing with bulk states or nontopological two-dimensional electron gas (2DEG) quantum well states caused by bending of electronic bands near the surface. The band bending arises via charge transfer from surface adatoms or interfaces and, therefore, the choice of layers abutting topological surfaces is critical. Here we report molecular beam epitaxial growth of Bi2Se3/ZnxCd1–xSe superlattices that hold only one topological surface channel per TI layer. The topological nature of conducting channels is supported by ?-Berry phase evident from observed Shubnikov de Haas quantum oscillations and by the associated two-dimensional (2D) weak antilocalization quantum interference correction to magnetoresistance. Both density functional theory (DFT) calculations and transport measurements suggest that a single topological Dirac cone per TI layer can be realized by asymmetric interfaces: Se-terminated ZnxCd1–xSe interface with the TI remains “electronically intact”, while charge transfer occurs at the Zn-terminated interface. Our findings indicate that topological transport could be controlled by adjusting charge transfer from nontopological spacers in hybrid structures. PMID:26348593
Topological charges in SL(2,R) covariant massive 11-dimensional and type IIB supergravity
NASA Astrophysics Data System (ADS)
Callister, Andrew K.; Smith, Douglas J.
2009-12-01
In this paper we construct closed expressions that correspond to the topological charges of the various 1/2-BPS states of the maximal 10- and 11-dimensional supergravity theories. These expressions are related to the structure of the supersymmetry algebras in curved spacetimes. We mainly focus on IIB supergravity and 11-dimensional supergravity in a double M9-brane background, with an emphasis on the SL(2,R) multiplet structure of the charges and how these map between theories. This includes the charges corresponding to the multiplets of 7- and 9-branes in IIB. We find that examining the possible multiplet structures of the charges provides another tool for exploring the spectrum of BPS states that appear in these theories. As a prerequisite to constructing the charges we determine the field equations and multiplet structure of the 11-dimensional gauge potentials, extending previous results on the subject. The massive gauge transformations of the fields are also discussed. We also demonstrate how these massive gauge transformations are compatible with the construction of an SL(2,R) covariant kinetic term in the 11-dimensional Kaluza-Klein monopole worldvolume action.
Development of a subwavelength grating vortex coronagraph of topological charge 4 (SGVC4)
NASA Astrophysics Data System (ADS)
Delacroix, Christian; Absil, Olivier; Carlomagno, Brunella; Piron, Pierre; Forsberg, Pontus; Karlsson, Mikael; Mawet, Dimitri; Habraken, Serge; Surdej, Jean
2014-08-01
One possible solution to achieve high contrast direct imaging at a small inner working angle (IWA) is to use a vector vortex coronagraph (VVC), which provides a continuous helical phase ramp in the focal plane of the telescope with a phase singularity in its center. Such an optical vortex is characterized by its topological charge, i.e., the number of times the phase accumulates 2? radians along a closed path surrounding the singularity. Over the past few years, we have been developing a charge-2 VVC induced by rotationally symmetric subwavelength gratings (SGVC2), also known as the Annular Groove Phase Mask (AGPM). Since 2013, several SGVC2s (or AGPMs) were manufactured using synthetic diamond substrate, then validated on dedicated optical benches, and installed on 10-m class telescopes. Increasing the topological charge seems however mandatory for cancelling the light of bright stars which will be partially resolved by future Extremely Large Telescopes in the near-infrared. In this paper, we first detail our motivations for developing an SGVC4 (charge 4) dedicated to the near-infrared domain. The challenge lies in the design of the pattern which is unrealistic in the theoretically perfect case, due to state-of-the-art manufacturing limitations. Hence, we propose a new realistic design of SGVC4 with minimized discontinuities and optimized phase ramp, showing conclusive improvements over previous works in this field. A preliminary validation of our concept is given based on RCWA simulations, while full 3D finite-difference time-domain simulations (and eventually laboratory tests) will be required for a final validation.
Topological Extensions of Noether Charge Algebras carried by D-p-branes
Hanno Hammer
1997-11-17
We derive the fully extended supersymmetry algebra carried by D-branes in a massless type IIA superspace vacuum. We find that the extended algebra contains not only topological charges that probe the presence of compact spacetime dimensions but also pieces that measure non-trivial configurations of the gauge field on the worldvolume of the brane. Furthermore there are terms that measure the coupling of the non-triviality of the worldvolume regarded as a U(1)-bundle of the gauge field to possible compact spacetime dimensions. In particular, the extended algebra carried by the D-2-brane can contain the charge of a Dirac monopole of the gauge field. In the course of this work we derive a set of generalized Gamma-matrix identities that include the ones presently known for the IIA case. In the first part of the paper we give an introduction to the basic notions of Noether current algebras and charge algebras; furthermore we find a Theorem that describes in a general context how the presence of a gauge field on the worldvolume of an embedded object transforming under the symmetry group on the target space alters the algebra of the Noether charges, which otherwise would be the same as the algebra of the symmetry group. This is a phenomenon recently found by Sorokin and Townsend in the case of the M-5-brane, but here we show that it holds quite generally, and in particular also in the case of D-branes.
Topological hydrogen-bond definition to characterize the structure and dynamics of liquid water.
Henchman, Richard H; Irudayam, Sheeba Jem
2010-12-23
A definition that equates a hydrogen bond topologically with a local energy well in the potential energy surface is used to study the structure and dynamics of liquid water. We demonstrate the robustness of this hydrogen-bond definition versus the many other definitions which use fixed, arbitrary parameters, do not account for variable molecular environments, and cannot effectively resolve transition states. Our topology definition unambiguously shows that most water molecules are double acceptors but sizable proportions are single or triple acceptors. Almost all hydrogens are found to take part in hydrogen bonds. Broken hydrogen bonds only form when two molecules try to form two hydrogen bonds between them. The double acceptors have tetrahedral geometry, lower potential energy, entropy, and density, and slower dynamics. The single and triple acceptors have trigonal and trigonal bipyramidal geometry and when considered together have higher density, potential energy, and entropy, faster dynamics, and a tendency to cluster. These calculations use an extended theory for the entropy of liquid water that takes into account the variable number of hydrogen bonds. Hydrogen-bond switching is shown to depend explicitly on the variable number of hydrogen bonds accepted and the presence of interstitial water molecules. Transition state theory indicates that the switching of hydrogen bonds is a mildly activated process, requiring only a moderate distortion of hydrogen bonds. Three main types of switching events are observed depending on whether the donor and acceptor are already sharing a hydrogen bond. The switch may proceed with no intermediate or via a bifurcated-oxygen or cyclic dimer, both of which have a broken hydrogen bond and symmetric and asymmetric forms. Switching is found to be strongly coupled to whole-molecule vibration, particularly for the more mobile single and triple acceptors. Our analysis suggests that even though water is heterogeneous in terms of the number of hydrogen bonds, the coupling between neighbors on various length and time scales brings about greater continuity in its properties. PMID:21114302
Phase fluctuations and the absence of topological defects in photo-excited charge ordered nickelate
Lee, W.S.; Chuang, Y.D.; Moore, R.G.; Zhu, Y.; Patthey, L.; Trigo, M.; Lu, D.H.; Kirchmann, P.S.; Krupin, O.; Yi, M.; Langner, M.; Huse, N.; Robinson, J.S.; Chen, Y.; Zhou, S.Y.; Coslovich, G.; Huber, B.; Reis, D.A.; Kaindl, R.A.; Schoenlein, R.W.; Doering, D.; Denes, P.; Schlotter, W.F.; Turner, J.J.; Johnson, S.L.; Fö rst, M.; Sasagawa, T.; Kung, Y.F.; Sorini, A.P.; Kemper, A.F.; Moritz, B.; Devereaux, T.P.; Lee, D.-H.; Shen, Z.X.; Hussain, Z.
2012-01-01
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La1.75Sr0.25NiO4 to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.
Phase Fluctuations and the Absence of Topological Defects in Photo-excited Charge Ordered Nickelate
Lee, W.S.; Chuang, Y.D.; Moore, R.G.; Zhu, Y.; Patthey, L.; Trigo, M.; Lu, D.H.; Kirchmann, P.S.; Krupin, O.; Yi, M.; Langner, M.; Huse, N.; Robinson, J.S.; Chen, Y.; Zhou, S.Y.; Coslovich, G.; Huber, B.; Reis, D.A.; Kaindl, R.A.; Schoenlein, R.W.; Doering, D.
2012-05-15
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La{sub 1.75}Sr{sub 0.25}NiO{sub 4} to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.
An Acoustic Charge Transport Imager for High Definition Television
NASA Technical Reports Server (NTRS)
Hunt, William D.; Brennan, Kevin; May, Gary; Glenn, William E.; Richardson, Mike; Solomon, Richard
1999-01-01
This project, over its term, included funding to a variety of companies and organizations. In addition to Georgia Tech these included Florida Atlantic University with Dr. William E. Glenn as the P.I., Kodak with Mr. Mike Richardson as the P.I. and M.I.T./Polaroid with Dr. Richard Solomon as the P.I. The focus of the work conducted by these organizations was the development of camera hardware for High Definition Television (HDTV). The focus of the research at Georgia Tech was the development of new semiconductor technology to achieve a next generation solid state imager chip that would operate at a high frame rate (I 70 frames per second), operate at low light levels (via the use of avalanche photodiodes as the detector element) and contain 2 million pixels. The actual cost required to create this new semiconductor technology was probably at least 5 or 6 times the investment made under this program and hence we fell short of achieving this rather grand goal. We did, however, produce a number of spin-off technologies as a result of our efforts. These include, among others, improved avalanche photodiode structures, significant advancement of the state of understanding of ZnO/GaAs structures and significant contributions to the analysis of general GaAs semiconductor devices and the design of Surface Acoustic Wave resonator filters for wireless communication. More of these will be described in the report. The work conducted at the partner sites resulted in the development of 4 prototype HDTV cameras. The HDTV camera developed by Kodak uses the Kodak KAI-2091M high- definition monochrome image sensor. This progressively-scanned charge-coupled device (CCD) can operate at video frame rates and has 9 gm square pixels. The photosensitive area has a 16:9 aspect ratio and is consistent with the "Common Image Format" (CIF). It features an active image area of 1928 horizontal by 1084 vertical pixels and has a 55% fill factor. The camera is designed to operate in continuous mode with an output data rate of 5MHz, which gives a maximum frame rate of 4 frames per second. The MIT/Polaroid group developed two cameras under this program. The cameras have effectively four times the current video spatial resolution and at 60 frames per second are double the normal video frame rate.
Chen, Yue; Fang, Zhao-Xiang; Ren, Yu-Xuan; Gong, Lei; Lu, Rong-De
2015-09-20
Optical vortices are associated with a spatial phase singularity. Such a beam with a vortex is valuable in optical microscopy, hyper-entanglement, and optical levitation. In these applications, vortex beams with a perfect circle shape and a large topological charge are highly desirable. But the generation of perfect vortices with high topological charges is challenging. We present a novel method to create perfect vortex beams with large topological charges using a digital micromirror device (DMD) through binary amplitude modulation and a narrow Gaussian approximation. The DMD with binary holograms encoding both the spatial amplitude and the phase could generate fast switchable, reconfigurable optical vortex beams with significantly high quality and fidelity. With either the binary Lee hologram or the superpixel binary encoding technique, we were able to generate the corresponding hologram with high fidelity and create a perfect vortex with topological charge as large as 90. The physical properties of the perfect vortex beam produced were characterized through measurements of propagation dynamics and the focusing fields. The measurements show good consistency with the theoretical simulation. The perfect vortex beam produced satisfies high-demand utilization in optical manipulation and control, momentum transfer, quantum computing, and biophotonics. PMID:26406501
Hurtubise, David E.
148 Basic Differential Topology Definition 5.46 Assume that M, N, and Z are oriented smooth manifolds, Z is a closed submanifold of N, M is compact, and dim(M) + dim(Z) = dim(N). For any smooth map f : M N, the Homotopy Transversality Theorem (Theorem 5.17) implies that there is a smooth map f1
The Ehrenfest force field: Topology and consequences for the definition of an atom in a molecule
NASA Astrophysics Data System (ADS)
Pendás, A. Martín; Hernández-Trujillo, J.
2012-10-01
The Ehrenfest force is the force acting on the electrons in a molecule due to the presence of the other electrons and the nuclei. There is an associated force field in three-dimensional space that is obtained by the integration of the corresponding Hermitian quantum force operator over the spin coordinates of all of the electrons and the space coordinates of all of the electrons but one. This paper analyzes the topology induced by this vector field and its consequences for the definition of molecular structure and of an atom in a molecule. Its phase portrait reveals: that the nuclei are attractors of the Ehrenfest force, the existence of separatrices yielding a dense partitioning of three-dimensional space into disjoint regions, and field lines connecting the attractors through these separatrices. From the numerical point of view, when the Ehrenfest force field is obtained as minus the divergence of the kinetic stress tensor, the induced topology was found to be highly sensitive to choice of Gaussian basis sets at long range. Even the use of large split valence and highly uncontracted basis sets can yield spurious critical points that may alter the number of attraction basins. Nevertheless, at short distances from the nuclei, in general, the partitioning of three-dimensional space with the Ehrenfest force field coincides with that induced by the gradient field of the electron density. However, exceptions are found in molecules where the electron density yields results in conflict with chemical intuition. In these cases, the molecular graphs of the Ehrenfest force field reveal the expected atomic connectivities. This discrepancy between the definition of an atom in a molecule between the two vector fields casts some doubts on the physical meaning of the integration of Ehrenfest forces over the basins of the electron density.
Membranes with topological charge and AdS{sub 4}/CFT{sub 3} correspondence
Klebanov, Igor R.; Pufu, Silviu S.; Tesileanu, Tiberiu
2010-06-15
If the second Betti number b{sub 2} of a Sasaki-Einstein manifold Y{sup 7} does not vanish, then M-theory on AdS{sub 4}xY{sup 7} possesses 'topological' U(1){sup b}{sub 2} gauge symmetry. The corresponding Abelian gauge fields come from three-form fluctuations with one index in AdS{sub 4} and the other two in Y{sup 7}. We find black membrane solutions carrying one of these U(1) charges. In the zero-temperature limit, our solutions interpolate between AdS{sub 4}xY{sup 7} in the UV and AdS{sub 2}xR{sup 2}xsquashed Y{sup 7} in the IR. In fact, the AdS{sub 2}xR{sup 2}xsquashed Y{sup 7} background is by itself a solution of the supergravity equations of motion. These solutions do not appear to preserve any supersymmetry. We search for their possible instabilities and do not find any. We also discuss the meaning of our charged membrane backgrounds in a dual quiver Chern-Simons gauge theory with a global U(1) charge density. Finally, we present a simple analytic solution which has the same IR but different UV behavior. We reduce this solution to type IIA string theory, and perform T-duality to type IIB. The type IIB metric turns out to be a product of the squashed Y{sup 7} and the extremal Banados-Teitelboim-Zanelli black hole. We discuss an interpretation of this type IIB background in terms of the (1+1)-dimensional conformal field theory on D3-branes partially wrapped over the squashed Y{sup 7}.
NASA Astrophysics Data System (ADS)
Beck, Horst P.
2015-10-01
The notion of a "size" of the ions plays an important role in crystal chemistry. In this paper we demonstrate how "size" varies with the combination of elements and also with varying stoichiometric composition of a compound taking the A-Ti-O series (A = Li, Na, K, Mg, Ca, Sr, Ba) as an example. We analyse the correlation between the topology of a structure, i.e. the coordination geometry and the distances observed, and the charges of the atoms as derived from a Bader analysis of the electron distribution which has been calculated in DFT relaxations of the structures. We demonstrate how charge relations of the atoms in specific stoichiometric relations are strictly fixed within small ranges which are constraint by electronegativity differences of the constituting atoms and how atomic charges are "delicately" balanced by minute movements of the atoms and changes in coordination. The balance of charges proves to be a decisive structure determining parameter.
An acoustic charge transport imager for high definition television applications
NASA Technical Reports Server (NTRS)
Hunt, William D.; Brennan, Kevin F.; Summers, Chris J.
1992-01-01
In this report we present the progress during the second six month period of the project. This includes both experimental and theoretical work on the acoustic charge transport (ACT) portion of the chip, the theoretical program modelling of both the avalanche photodiode (APD) and the charge transfer and overflow transistor and the materials growth and fabrication part of the program.
Topology of charge density and elastic properties of Ti3SiC2 polymorphs
Yu, Rong; Zhang, Xiao Feng; He, Lian Long; Ye, Heng Qiang
2004-06-24
Using an all-electron, full potential first-principles method, we have investigated the topology of charge density and elastic properties of the two polymorphs, alpha and beta, of Ti3SiC2. The bonding effect was analyzed based on Bader's quantum theory of ''atoms in molecules'' (AIM). It was found that the Ti-Si bonding effect is significantly weaker in beta than in alpha, giving less stabilizing effect for beta. The Si-C bonds, which are absent in alpha, are formed in beta and provide additional stabilizing effect for beta. In contrast to conventional thinking, there is no direction interaction between Ti atoms in both alpha and beta. The calculated elastic properties are in good agreement with the experimental results, giving the bulk modulus of about 180 GPa and the Poisson's ratio of 0.2. The beta phase is generally softer than the alpha phase. As revealed by the direction dependent Young's modulus, there is only slight elastic anisotropy in Ti3SiC2. For alpha, Young's modulus is minimum in the c direction and maximum in the directions 42o from c. For beta, the maximum lies in the c direction, in part due to the formation of Si-C bonds in this direction.
Phase transitions in charged topological black holes dressed with a scalar hair
Cristian Martinez; Alejandra Montecinos
2010-09-28
Phase transitions in charged topological black holes dressed with a scalar field are studied. These black holes are solutions of the Einstein-Maxwell theory with a negative cosmological constant and a conformally coupled real self-interacting scalar field. Comparing, in the grand canonical ensemble, the free energies of the hairy and undressed black holes two different phase transitions are found. The first of them is one of second-order type and it occurs at a temperature defined by the value of the cosmological constant. Below this temperature an undressed black hole spontaneously acquires a scalar hair. The other phase transition is one of first-order type. The corresponding critical temperature, which is bounded from above by the one of the previous case, strongly depends on the coupling constant of the quartic self-interaction potential, and this transition only appears when the coupling constant is less than a certain value. In this case, below the critical temperature the undressed black is thermodynamically favored. However, when the temperature exceeds the critical value a hairy black hole is likely to be occur.
NASA Astrophysics Data System (ADS)
Malzard, Simon; Poli, Charles; Schomerus, Henning
2015-11-01
We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in the absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-Hermitian versions of time-reversal symmetry, chirality, and charge conjugation) emerge dynamically.
Ye, Peng
A large class of symmetry-protected topological phases (SPT) in boson/spin systems have been recently predicted by the group cohomology theory. In this work, we consider bosonic SPT states at least with charge symmetry ...
An acoustic charge transport imager for high definition television applications
NASA Technical Reports Server (NTRS)
Hunt, W. D.; Brennan, K. F.; Summers, C. J.
1994-01-01
The primary goal of this research is to develop a solid-state television (HDTV) imager chip operating at a frame rate of about 170 frames/sec at 2 Megapixels/frame. This imager will offer an order of magnitude improvements in speed over CCD designs and will allow for monolithic imagers operating from the IR to UV. The technical approach of the project focuses on the development of the three basic components of the imager and their subsequent integration. The camera chip can be divided into three distinct functions: (1) image capture via an array of avalanche photodiodes (APD's); (2) charge collection, storage, and overflow control via a charge transfer transistor device (CTD); and (3) charge readout via an array of acoustic charge transport (ACT) channels. The use of APD's allows for front end gain at low noise and low operating voltages while the ACT readout enables concomitant high speed and high charge transfer efficiency. Currently work is progressing towards the optimization of each of these component devices. In addition to the development of each of the three distinct components, work towards their integration and manufacturability is also progressing. The component designs are considered not only to meet individual specifications but to provide overall system level performance suitable for HDTV operation upon integration. The ultimate manufacturability and reliability of the chip constrains the design as well. The progress made during this period is described in detail.
Skouroupathis, A.; Panagopoulos, H.
2005-11-01
We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power-divergent additive renormalization of the topological susceptibility is calculated to 3 loops. Our work serves also as a test case of the techniques and limitations of lattice perturbation theory, it being the first 3-loop computation in the literature involving overlap fermions.
NASA Astrophysics Data System (ADS)
Kee, Hae-Young; Chen, Yige
2015-03-01
Designing materials is one of intense topics in modern condensed matter physics. Recently, how to achieve a topological insulator in transition metal oxides with strong spin-orbit coupling became an interesting subject. We have investigated possible topological phases in orthorhombic perovskite Iridium (Ir) oxide superlattices grown along the [001] crystallographic axis. We found that bilayer Ir oxide superlattices exhibit quantized anomalous Hall effects in magnetic topological insulating phases. We also found, depending on the stacking of two layers, a valley Hall insulator with nontrivial valley dependent surface modes and a topological crystalline insulator with the crystal symmetry protected edge states can be realized. Experimental tools to detect such topological phases are also discussed.
NASA Astrophysics Data System (ADS)
Avishai, Y.; Luck, J. M.
2008-06-01
This is the first of two papers devoted to tight-binding electronic spectra on graphs with the topology of the sphere. In this work the one-electron spectrum is investigated as a function of the radial magnetic field produced by a magnetic charge sitting at the centre of the sphere. The latter is an integer multiple of the quantized magnetic charge of the Dirac monopole, that integer defining the gauge sector. An analysis of the spectrum is carried out for the five platonic solids (tetrahedron, cube, octahedron, dodecahedron and icosahedron), the C60 fullerene and two families of polyhedra, the diamonds and the prisms. Except for the fullerene, all the spectra are obtained in closed form. They exhibit a rich pattern of degeneracies. The total energy at half-filling is also evaluated in all the examples as a function of the magnetic charge.
Kerman, Andrew J.
It has long been thought that macroscopic phase coherence breaks down in effectively lower-dimensional superconducting systems even at zero temperature due to enhanced topological quantum phase fluctuations. In ...
An acoustic charge transport imager for high definition television applications
NASA Technical Reports Server (NTRS)
Hunt, William D.; Brennan, Kevin F.; Summers, Christopher J.
1993-01-01
This report covers: (1) invention of a new, ultra-low noise, low operating voltage APD which is expected to offer far better performance than the existing volume doped APD device; (2) performance of a comprehensive series of experiments on the acoustic and piezoelectric properties of ZnO films sputtered on GaAs which can possibly lead to a decrease in the required rf drive power for ACT devices by 15dB; (3) development of an advanced, hydrodynamic, macroscopic simulator used for evaluating the performance of ACT and CTD devices and aiding in the development of the next generation of devices; (4) experimental development of CTD devices which utilize a p-doped top barrier demonstrating charge storage capacity and low leakage currents; (5) refinements in materials growth techniques and in situ controls to lower surface defect densities to record levels as well as increase material uniformity and quality.
NASA Astrophysics Data System (ADS)
Mahfouzi, Farzad; Nagaosa, Naoto; Nikoli?, Branislav K.
2014-09-01
Using the charge-conserving Floquet-Green function approach to open quantum systems driven by an external time-periodic potential, we analyze how spin current pumped by the precessing magnetization of a ferromagnetic (F) layer is injected laterally into the interface with strong spin-orbit coupling (SOC) and converted into charge current flowing in the same direction. In the case of a metallic interface with the Rashba SOC used in recent experiments [J. C. R. Sánchez, L. Vila, G. Desfonds, S. Gambarelli, J. P. Attané, J. M. De Teresa, C. Magén, and A. Fert, Nat. Commun. 4, 2944 (2013), 10.1038/ncomms3944], both spin IS? and charge I current flow within the interface where I /IS?? 2-8% (depending on the precession cone angle), while for a F/topological-insulator (F/TI) interface employed in related experiments [Y. Shiomi, K. Nomura, Y. Kajiwara, K. Eto, M. Novak, K. Segawa, Y. Ando, and E. Saitoh, arXiv:1312.7091] the conversion efficiency is greatly enhanced (I /IS?? 40-60%) due to perfect spin-momentum locking on the surface of a TI. The spin-to-charge conversion occurs also when spin current is pumped vertically through the F/TI interface with smaller efficiency (I /IS?˜0.001%), but with the charge current signal being sensitive to whether the Dirac fermions at the interface are massive or massless.
Definition of the topological structure of the automatic control system of spacecrafts
NASA Astrophysics Data System (ADS)
Zelenkov, P. V.; Karaseva, M. V.; Tsareva, E. A.; Tsarev, R. Y.
2015-01-01
The paper considers the problem of selection the topological structure of the automated control system of spacecrafts. The integer linear model of mathematical programming designed to define the optimal topological structure for spacecraft control is proposed. To solve the determination problem of topological structure of the control system of spacecrafts developed the procedure of the directed search of some structure variants according to the scheme "Branch and bound". The example of the automated control system of spacecraft development included the combination of ground control stations, managing the spacecraft of three classes with a geosynchronous orbit with constant orbital periods is presented.
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
Garcia-March, Miguel-Angel; Zacares, Mario; Sahu, Sarira; Ceballos-Herrera, Daniel E.
2009-05-15
We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schroedinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.
Topology and shape optimization of induced-charge electro-osmotic micropumps
Gregersen, M. M.
For a dielectric solid surrounded by an electrolyte and positioned inside an externally biased parallel-plate capacitor, we study numerically how the resulting induced-charge electro-osmotic (ICEO) flow depends on the ...
NASA Astrophysics Data System (ADS)
de Vries, E. K.; Kamerbeek, A. M.; Koirala, N.; Brahlek, M.; Salehi, M.; Oh, S.; van Wees, B. J.; Banerjee, T.
2015-11-01
Topological insulators provide a new platform for spintronics due to the spin texture of the surface states that are topologically robust against elastic backscattering. Here we report on an investigation of the measured voltage obtained from efforts to electrically probe spin-momentum locking in the topological insulator Bi2Se3 using ferromagnetic contacts. Upon inverting the magnetization of the ferromagnetic contacts, we find a reversal of the measured voltage. Extensive analysis of the bias and temperature dependence of this voltage was done, considering the orientation of the magnetization relative to the current. Our findings indicate that the measured voltage can arise due to fringe-field-induced Hall voltages, different from current-induced spin polarization of the surface state charge carriers, as reported recently. Understanding the nontrivial origin of the measured voltage is important for realizing spintronic devices with topological insulators.
Charged Particle Environment Definition for NGST: L2 Plasma Environment Statistics
NASA Technical Reports Server (NTRS)
Minow, Joseph I.; Blackwell, William C.; Neergaard, Linda F.; Evans, Steven W.; Hardage, Donna M.; Owens, Jerry K.
2000-01-01
The plasma environment encountered by the Next Generation Space Telescope satellite in a halo orbit about L2 can include the Earth's magnetotail and magnetosheath in addition to the solar wind depending on the orbital radius chosen for the mission. Analysis of plasma environment impacts on the satellite requires knowledge of the average and extreme plasma characteristics to assess the magnitude of spacecraft charging and materials degradation expected for the mission lifetime. This report describes the analysis of plasma data from instruments onboard the IMP 8 and Geotail spacecraft used to produce the plasma database for the LRAD engineering-level phenomenology code developed to provide the NGST L2 environment definition.
The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's
P. Collet; J. -P. Eckmann
1998-05-20
We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a constructive implementation of a bound on the inertial range of such equations. Using this bound, we are able to propose a finite sampling algorithm which allows (in principle) to measure this entropy from experimental data.
Topological black holes dressed with a conformally coupled scalar field and electric charge
Martinez, Cristian; Troncoso, Ricardo; Staforelli, Juan Pablo
2006-08-15
Electrically charged solutions for gravity with a conformally coupled scalar field are found in four dimensions in the presence of a cosmological constant. If a quartic self-interaction term for the scalar field is considered, there is a solution describing an asymptotically locally AdS charged black hole dressed with a scalar field that is regular on and outside the event horizon, which is a surface of negative constant curvature. This black hole can have negative mass, which is bounded from below for the extremal case, and its causal structure shows that the solution describes a ''black hole inside a black hole''. The thermodynamics of the nonextremal black hole is analyzed in the grand canonical ensemble. The entropy does not follow the area law, and there is an effective Newton constant which depends on the value of the scalar field at the horizon. If the base manifold is locally flat, the solution has no electric charge, and the scalar field has a vanishing stress-energy tensor so that it dresses a locally AdS spacetime with a nut at the origin. In the case of vanishing self interaction, the solutions also dress locally AdS spacetimes, and if the base manifold is of negative constant curvature a massless electrically charged hairy black hole is obtained. The thermodynamics of this black hole is also analyzed. It is found that the bounds for the black holes parameters in the conformal frame obtained from requiring the entropy to be positive are mapped into the ones that guarantee cosmic censorship in the Einstein frame.
Anomalies, gauge field topology, and the lattice
Michael Creutz
2010-11-02
Motivated by the connection between gauge field topology and the axial anomaly in fermion currents, I use the fourth power of the naive Dirac operator to define a local lattice measure of topological charge. For smooth gauge fields this reduces to the usual topological density. For typical gauge field configurations in a numerical simulation, however, quantum fluctuations dominate, and the sum of this density over the system does not generally give an integer winding. On cooling with respect to the Wilson gauge action, instanton like structures do emerge. As cooling proceeds, these objects tend shrink and finally "fall through the lattice." Modifying the action can block the shrinking at the expense of a loss of reflection positivity. The cooling procedure is highly sensitive to the details of the initial steps, suggesting that quantum fluctuations induce a small but fundamental ambiguity in the definition of topological susceptibility.
Netzel, Jeanette; van Smaalen, Sander
2009-01-01
Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T ? 20?K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (l max = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C—C, C—N and C—O bonds, and for hydrogen bonds together with covalent C—H and N—H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H?O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997) ?. An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds. PMID:19767685
Bouchard, Frédéric; De Leon, Israel; Schulz, Sebastian A.; Upham, Jeremy; Karimi, Ebrahim; Boyd, Robert W.
2014-09-08
Orbital angular momentum associated with the helical phase-front of optical beams provides an unbounded “space” for both classical and quantum communications. Among the different approaches to generate and manipulate orbital angular momentum states of light, coupling between spin and orbital angular momentum allows a faster manipulation of orbital angular momentum states because it depends on manipulating the polarisation state of light, which is simpler and generally faster than manipulating conventional orbital angular momentum generators. In this work, we design and fabricate an ultra-thin spin-to-orbital angular momentum converter, based on plasmonic nano-antennas and operating in the visible wavelength range that is capable of converting spin to an arbitrary value of orbital angular momentum ?. The nano-antennas are arranged in an array with a well-defined geometry in the transverse plane of the beam, possessing a specific integer or half-integer topological charge q. When a circularly polarised light beam traverses this metasurface, the output beam polarisation switches handedness and the orbital angular momentum changes in value by ?=±2q? per photon. We experimentally demonstrate ? values ranging from ±1 to ±25 with conversion efficiencies of 8.6%?±?0.4%. Our ultra-thin devices are integratable and thus suitable for applications in quantum communications, quantum computations, and nano-scale sensing.
Dordevic, S V; Wolf, M S; Stojilovic, N; Lei, Hechang; Petrovic, C
2013-02-20
We present the results of an infrared spectroscopy study of topological insulators Bi(2)Se(3), Bi(2)Te(3) and Sb(2)Te(3). Reflectance spectra of all three materials look similar, with a well defined plasma edge. However, there are some important differences. Most notably, as temperature decreases the plasma edge shifts to lower frequencies in Bi(2)Se(3), whereas in Bi(2)Te(3) and Sb(2)Te(3) it shifts to higher frequencies. In the loss function spectra we identify asymmetric broadening of the plasmon, and assign it to the presence of charge inhomogeneities. It remains to be seen if charge inhomogeneities are characteristic of all topological insulators, and whether they are of intrinsic or extrinsic nature. PMID:23328626
Seidler, Tomasz; Champagne, Benoît
2015-07-15
The impact of atomic charge definition for describing the crystal polarizing electric field has been assessed in view of predicting the linear and nonlinear optical susceptibilities of molecular crystals. In this approach, the chromophores are embedded in the electric field of its own point charges, which are evaluated through a self-consistent procedure including charge scaling to account for the screening of the dielectric. Once the crystal field is determined, dressed molecular polarizabilities and hyperpolarizabilities are calculated and used as input of an electrostatic interaction scheme to evaluate the crystal linear and nonlinear optical responses. It is observed that many charge definitions (i) based on partitioning the electron density (QTAIM), (ii) obtained by analyzing the quantum-chemical wavefunction (Mulliken, MBS, and NBO), and (iii) derived by fitting to the electrostatic potential (MK, CHelpG, and HLYGAt) give very consistent results and are equally valid whereas Hirshfeld partitioning and CM5 charge parametrizations underestimate the refractive indices and second-order nonlinear optical susceptibilities. An alternative approach omitting charge scaling is demonstrated to overestimate the different crystal optical properties. On the other hand, the molecule embedding approach provides results in close agreement with those calculated with a charge field obtained from periodic boundary condition calculations. PMID:26144533
Skinner, B.; Chen, T.; Shklovskii, B. I.
2013-09-15
In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review, we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to variable-range hopping at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential in passing from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of time-reversal symmetry breaking, affects the disorder potential at the surface and the mid-gap density of states.
A topological theory of the Physical Vacuum
R. M. Kiehn
2006-03-01
This article examines how the physical presence of field energy and particulate matter could influence the topological properties of space time. The theory is developed in terms of vector and matrix equations of exterior differential forms. The topological features and the dynamics of such exterior differential systems are studied with respect to processes of continuous topological evolution. The theory starts from the sole postulate that field properties of a Physical Vacuum (a continuum) can be defined in terms of a vector space domain, of maximal rank, infinitesimal neighborhoods, that supports a Basis Frame as a 4 x 4 matrix of C2 functions with non-zero determinant. The basis vectors of such Basis Frames exhibit differential closure. The particle properties of the Physical Vacuum are defined in terms of topological defects (or compliments) of the field vector space defined by those points where the maximal rank, or non-zero determinant, condition fails. The topological universality of a Basis Frame over infinitesimal neighborhoods can be refined by particular choices of a subgroup structure of the Basis Frame, [B]. It is remarkable that from such a universal definition of a Physical Vacuum, specializations permit the deduction of the field structures of all four forces, from gravity fields to Yang Mills fields, and associate the origin of topological charge and topological spin to the Affine torsion coefficients of the induced Cartan Connection matrix [C] of 1-forms.
Topological Solitons in Physics.
ERIC Educational Resources Information Center
Parsa, Zohreh
1979-01-01
A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)
Abhishek Chowdhury; A. Harindranath; Jyotirmoy Maiti
2015-04-14
Towards the goal of extracting the continuum properties, we have studied the Topological Charge Density Correlator (TCDC) and the Inverse Participation Ratio (IPR) for the topological charge density ($q(x)$) in SU(3) Lattice Yang-Mills theory for relatively small lattice spacings including some smaller than those explored before. With the help of recently proposed open boundary condition, it is possible to compute observables at a smaller lattice spacing since {\\em trapping problem} is absent. On the other hand, the reference energy scale provided by Wilson flow allows us to study their scaling behavior in contrast to previously proposed smearing techniques. The behavior of TCDC for different lattice spacings at a fixed HYP smearing level shows apparent scaling violations. In contrast, at a particular Wilson flow time $t$ for all the lattice spacings investigated (except the largest one), the TCDC data show universal behavior within our statistical uncertainties. The continuum properties of TCDC are studied by investigating the small flow time behavior. We have also extracted the pseudoscalar glueball mass from TCDC, which appears to be insensitive to the lattice spacings (0.0345 fm $\\leq a\\leq$ 0.0667 fm) and agrees with the value extracted using anisotropic lattices, within statistical errors. Further, we have studied the localization property of $q(x)$ through IPR whose continuum behavior can be probed through the small values of Wilson flow time and observed the decrease of IPR with decreasing Wilson flow time. A detailed study of $q(x)$ under Wilson flow time revealed that as Wilson flow time decreases, the proximity of the regions of positive and negative charge densities of large magnitudes increases, and the charge density appears to be more delocalized resulting in the observed behavior of IPR.
H. Bombin; M. A. Martin-Delgado
2008-03-30
We introduce the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a gauge symmetry reduction mechanism. When symmetry is reduced in several islands only, this imposes boundary conditions to the rest of the system giving rise to topological ground state degeneracy. This degeneracy is related to the existence of topological fluxes in between islands or, alternatively, hidden charges at islands. Additionally, island deformations give rise to an extension of topological quantum computation beyond quasiparticles.
NASA Astrophysics Data System (ADS)
Tanda, Satoshi; Matsuyama, Toyoki; Oda, Migaku; Asano, Yasuhiro; Yakubo, Kousuke
2006-08-01
I. Topology as universal concept. Optical vorticulture / M. V. Berry. On universality of mathematical structure in nature: topology / T. Matsuyama. Topology in physics / R. Jackiw. Isoholonomic problem and holonomic quantum computation / S. Tanimura -- II. Topological crystals. Topological crystals of NbSe[symbol] / S. Tanda ... [et al.]. Superconducting states on a Möbius strip / M. Hayashi ... [et al.]. Structure analyses of topological crystals using synchrotron radiation / Y. Nogami ... [et al.]. Transport measurement for topological charge density waves / T. Matsuura ... [et al.]. Theoretical study on Little-Parks oscillation in nanoscale superconducting ring / T. Suzuki, M. Hayashi and H. Ebisawa. Frustrated CDW states in topological crystals / K. Kuboki ... [et al.]. Law of growth in topological crystal / M. Tsubota ... [et al.]. Synthesis and electric properties of NbS[symbol]: possibility of room temperature charge density wave devices / H. Nobukane ... [et al.]. How does a single crystal become a Möbius strip? / T. Matsuura ... [et al.]. Development of X-ray analysis method for topological crystals / K. Yamamoto ... [et al.] -- III. Topological materials. Femtosecond-timescale structure dynamics in complex materials: the case of (NbSe[symbol])[symbol]I / D. Dvorsek and D. Mihailovic. Ultrafast dynamics of charge-density-wave in topological crystals / K. Shimatake ... [et al.]. Topology in morphologies of a folded single-chain polymer / Y. Takenaka, D. Baigl and K. Yoshikawa. One to two-dimensional conversion in topological crystals / T. Toshima, K. Inagaki and S. Tanda. Topological change of Fermi surface in Bismuth under high pressure / M. Kasami ... [et al.]. Topological change of 4, 4'-bis[9-dicarbazolyl]-2, 2'-biphenyl (CBP) by international rearrangement / K. S. Son ... [et al.]. Spin dynamics in Heisenberg triangular system VI5 cluster studied by [symbol]H-NMR / Y. Furukawa ... [et al.]. STM/STS on NbSe[symbol] nanotubes / K. Ichimura ...[et al.]. Nanofibers of hydrogen storage alloy / I. Saita ... [et al.]. Synthesis of stable icosahedral quasicrystals in Zn-Sc based alloys and their magnetic properties / S. Kashimoto and T. Ishimasa. One-armed spiral wave excited by eam pressure in accretion disks in Be/X-Ray binaries / K. Hayasaki and A. T. Okazaki -- IV. Topological defects and excitations. Topological excitations in the ground state of charge density wave systems / P. Monceau. Soliton transport in nanoscale charge-density-wave systems / K. Inagaki, T. Toshima and S. Tanda. Topological defects in triplet superconductors UPt3, Sr[symbol]RuO[symbol], etc. / K. Maki ... [et al.]. Microscopic structure of vortices in type II superconductors / K. Machida ... [et al.]. Microscopic neutron investigation of the Abrikosov state of high-temperature superconductors / J. Mesot. Energy dissipation at nano-scale topological defects of high-Tc superconductors: microwave study / A. Maeda. Pressure induced topological phase transition in the heavy Fermion compound CeAl[symbol] / H. Miyagawa ... [et al.]. Explanation for the unusual orientation of LSCO square vortex lattice in terms of nodal superconductivity / M. Oda. Local electronic states in Bi[symbol]Sr[symbol]CaCu[symbol]O[symbol] / A. Hashimoto ... [et al.] -- V. Topology in quantum phenomena. Topological vortex formation in a Bose-Einstein condensate of alkali-metal atoms / M. Nakahara. Quantum phase transition of [symbol]He confined in nano-porous media / K. Shirahama, K. Yamamoto and Y. Shibayama. A new mean-field theory for Bose-Einstein condensates / T. Kita. Spin current in topological cristals / Y. Asano. Antiferromagnetic defects in non-magnetic hidden order of the heavy-electron system URu[symbol]Si[symbol] / H. Amitsuka, K. Tenya and M. Yokoyama. Magnetic-field dependences of thermodynamic quantities in the vortex state of Type-II superconductors / K. Watanabe, T. Kita and M. Arai. Three-magnon-mediated nuclear spin relaxation in quantum ferrimagnets of topological origin / H. Hori and S, Yamamoto. Topological aspects of wave function statistics at t
Ando, Yuichiro; Hamasaki, Takahiro; Kurokawa, Takayuki; Ichiba, Kouki; Yang, Fan; Novak, Mario; Sasaki, Satoshi; Segawa, Kouji; Ando, Yoichi; Shiraishi, Masashi
2014-11-12
We detected the spin polarization due to charge flow in the spin nondegenerate surface state of a three-dimensional topological insulator by means of an all-electrical method. The charge current in the bulk-insulating topological insulator Bi1.5Sb0.5Te1.7Se1.3 (BSTS) was injected/extracted through a ferromagnetic electrode made of Ni80Fe20, and an unusual current-direction-dependent magnetoresistance gave evidence for the appearance of spin polarization, which leads to a spin-dependent resistance at the BSTS/Ni80Fe20 interface. In contrast, our control experiment on Bi2Se3 gave null result. These observations demonstrate the importance of the Fermi-level control for the electrical detection of the spin polarization in topological insulators. PMID:25330016
NASA Astrophysics Data System (ADS)
Amonett, John
In the beginning, there was quark gluon plasma (QGP). QGP persisted for only on the order of microseconds after the Big Bang. This exotic state of matter consists of deconfined quarks and gluons under extreme conditions. It is believed that the QGP state can be recreated in the laboratory through heavy-ion collisions at ultra-high energies. The Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory appears to produce sufficiently high energy to exceed the threshold for creating the QGP phase. There are four experiments at RHIC, and one of the largest is the Solenoidal Tracker at RHIC (STAR). The STAR detector utilizes a Time Projection Chamber with full azimuthal acceptance to track as many as thousands of produced particles from a single nucleus-nucleus collision. The QGP state of matter has many proposed signatures. This project explores the anisotropic elliptic flow properties of gold (Au) on gold collisions. Elliptic flow corresponds to the second harmonic coefficient (v 2) of a Fourier decomposition of the transverse momentum distribution of emitted particles. Elliptic flow is the dominant term in the quantitative description of the collective motion among the particles produced in this type of heavy-ion collision. The focus of this dissertation is on a single type of particle, the charged kaon (K+/-). Charged kaons are the least massive particles that contain strange quarks. Using conventional techniques based on rate of energy loss, identification of charged kaons becomes difficult above a momentum of ˜600 MeV/c. This project uses a topological method to identify decaying charged kaons up to transverse momenta ˜4 GeV/c. Our topological method has the drawback of relatively low efficiency, which decreases with increasing momentum. The data set studied in this dissertation corresponds to gold on gold interactions at the maximum energy of the RHIC machine, and collisions across the full range of impact parameters are analyzed. Possible charged kaons are tagged from a list of candidates. The viable charged kaons are chosen using a series of stringent identification criteria. The reaction plane is determined for each event, and elliptic flow is calculated, correcting for the systematic effects caused by the finite reaction plane resolution. The dependence of elliptic flow on transverse momentum is highly significant when different particle types can be compared. The data for charged kaons falls into a pattern where there is a universal curve for the amount of flow per constituent quark as a function of the quark's transverse momentum. This universal curve can account for the flow observed for all known particle types. It suggests that the collective motion must have been imparted during the early phase of the collision when a QGP state existed. A different pattern would be expected if the collective motion had been imparted after the quarks had coalesced into hadrons, or if the QGP state had not been formed at all. The dissertation discusses the significance of the new evidence, and the caveats and possible alternative explanations.
NASA Astrophysics Data System (ADS)
Barnes, G.; Leka, K. D.; Longcope, D. W.
2003-05-01
The complexity of the coronal magnetic field extrapolated from a Magnetic Charge Topology (MCT) model, is examined for pre-event signatures unique to solar energetic phenomena. Although extensive use has been made of quantities measured at the photosphere, it is important to consider the magnetic field in the corona, where (for example) the hard X-ray signatures of energy release in solar flares are observed. By quantifying the inferred coronal magnetic topology we are no longer limited to considering solely the magnetic state of the photosphere. MCT is applied to temporally sampled photospheric magnetic data from the U. Hawai`i Imaging Vector Magnetograph, for 24 flare-event and flare-quiet epochs from seven active regions. We outline the methodology employed for automating the application of MCT to large data sets of complex active regions: partitioning the observed Bz at the photosphere, assigning a charge to each partition, and using this charge distribution to extrapolate the field in the corona. From the resulting field we compute the connectivity matrix ? ij, the location of null points and the intersection of separatrix surfaces, i.e. separator field lines. Parameters are constructed to describe, for example, the magnetic connectivities, the magnetic flux in those connections, and the number of separators. Examining particular events results in no obvious trends in the magnitude and temporal evolution of the parameters just prior to flare events. Thus, we employ the same quantitative statistical approach outlined in Leka and Barnes [this session], i.e. applying discriminant analysis and Hotelling's T2-test, and ranking all four-variable discriminant functions as a proxy for a single all-variable discriminant function. We present those parameters which consistently appear in the best combinations, indicating that they may play an important role in defining a pre-event coronal state. This work was performed under Air Force Office of Scientific Research contracts F49620-00-C-0004, F49620-03-C-0019 and F49620-02-C-0191.
Patel, Ankur; Nagesh, K V; Kolge, Tanmay; Chakravarthy, D P
2011-04-01
LCL resonant converter based repetitive capacitor charging power supply (CCPS) is designed and developed in the division. The LCL converter acts as a constant current source when switching frequency is equal to the resonant frequency. When both resonant inductors' values of LCL converter are same, it results in inherent zero current switching (ZCS) in switches. In this paper, ac analysis with fundamental frequency approximation of LCL resonant tank circuit, frequency dependent of current gain converter followed by design, development, simulation, and practical result is described. Effect of change in switching frequency and resonant frequency and change in resonant inductors ratio on CCPS will be discussed. An efficient CCPS of average output power of 1.2 kJ/s, output voltage 3 kV, and 300 Hz repetition rate is developed in the division. The performance of this CCPS has been evaluated in the laboratory by charging several values of load capacitance at various repetition rates. These results indicate that this design is very feasible for use in capacitor-charging applications. PMID:21529043
NASA Astrophysics Data System (ADS)
Patel, Ankur; Nagesh, K. V.; Kolge, Tanmay; Chakravarthy, D. P.
2011-04-01
LCL resonant converter based repetitive capacitor charging power supply (CCPS) is designed and developed in the division. The LCL converter acts as a constant current source when switching frequency is equal to the resonant frequency. When both resonant inductors' values of LCL converter are same, it results in inherent zero current switching (ZCS) in switches. In this paper, ac analysis with fundamental frequency approximation of LCL resonant tank circuit, frequency dependent of current gain converter followed by design, development, simulation, and practical result is described. Effect of change in switching frequency and resonant frequency and change in resonant inductors ratio on CCPS will be discussed. An efficient CCPS of average output power of 1.2 kJ/s, output voltage 3 kV, and 300 Hz repetition rate is developed in the division. The performance of this CCPS has been evaluated in the laboratory by charging several values of load capacitance at various repetition rates. These results indicate that this design is very feasible for use in capacitor-charging applications.
Topological pumping over a photonic Fibonacci quasicrystal
Verbin, Mor
Quasiperiodic lattices have recently been shown to be a nontrivial topological phase of matter. Charge pumping—one of the hallmarks of topological states of matter—was recently realized for photons in a one-dimensional ...
ERIC Educational Resources Information Center
Lynch, Mark
2012-01-01
We continue our study of topological X-rays begun in Lynch ["Topological X-rays and MRI's," iJMEST 33(3) (2002), pp. 389-392]. We modify our definition of a topological magnetic resonance imaging and give an affirmative answer to the question posed there: Can we identify a closed set in a box by defining X-rays to probe the interior and without…
NASA Astrophysics Data System (ADS)
Ebrahimi, A.; Habibi Khorassani, S. M.; Delarami, H.
2009-11-01
Individual hydrogen bond (HB) energies have been estimated in several systems involving multiple HBs such as adenine-thymine and guanine-cytosine using electron charge densities calculated at X⋯H hydrogen bond critical points (HBCPs) by atoms in molecules (AIM) method at B3LYP/6-311++G ?? and MP2/6-311++G ?? levels. A symmetrical system with two identical H bonds has been selected to search for simple relations between ?HBCP and individual EHB. Correlation coefficient between EHB and ?HBCP in the base of linear, quadratic, and exponential equations are acceptable and equal to 0.95. The estimated individual binding energies EHB are in good agreement with the results of atom-replacement approach and natural bond orbital analysis (NBO). The EHB values estimated from ? values at H⋯X BCP are in satisfactory agreement with the main geometrical parameter H⋯X. With respect to the obtained individual binding energies, the strength of a HB depends on the substituent and the cooperative effects of other HBs.
Thermodynamic and topological phase diagrams of correlated topological insulators
NASA Astrophysics Data System (ADS)
Zdulski, Damian; Byczuk, Krzysztof
2015-09-01
A definition of topological phases of density matrices is presented. The topological invariants in case of both noninteracting and interacting systems are extended to nonzero temperatures. The influence of electron interactions on topological insulators at finite temperatures is investigated. A correlated topological insulator is described by the Kane-Mele model, which is extended by the interaction term of the Falicov-Kimball type. Within the Hartree-Fock and the Hubbard I approximations, thermodynamic and topological phase diagrams are determined where the long-range order is included. The results show that correlation effects lead to a strong suppression of the existence of the nontrivial topological phase. In the homogeneous phase, we find a purely correlation driven phase transition into the topologically trivial Mott insulator.
Lu, Ling
The application of topology, the mathematics of conserved properties under continuous deformations, is creating a range of new opportunities throughout photonics. This field was inspired by the discovery of topological ...
NASA Astrophysics Data System (ADS)
Mahfouzi, Farzad
Current and future technological needs increasingly motivate the intensive scientific research of the properties of materials at the nano-scale. One of the most important domains in this respect at present concerns nano-electronics and its diverse applications. The great interest in this domain arises from the potential reduction of the size of the circuit components, maintaining their quality and functionality, and aiming at greater efficiency, economy, and storage characteristics for the corresponding physical devices. The aim of this thesis is to present a contribution to the analysis of the electronic charge and spin transport phenomena that occur at the quantum level in nano-structures. This thesis spans the areas of quantum transport theory through time-dependent systems, electron-boson interacting systems and systems of interest to spintronics. A common thread in the thesis is to develop the theoretical foundations and computational algorithms to numerically simulate such systems. In order to optimize the numerical calculations I resort to different techniques (such as graph theory in finding inverse of a sparse matrix, adaptive grids for integrations and programming languages (e.g., MATLAB and C++) and distributed computing tools (MPI, CUDA). Outline of the Thesis: After giving an introduction to the topics covered in this thesis in Chapter 1, I present the theoretical foundations to the field of non-equilibrium quantum statistics in Chapter 2. The applications of this formalism and the results are covered in the subsequent chapters as follows: Spin and charge quantum pumping in time-dependent systems: Covered in Chapters 3, 4 and 5, this topics was initially motivated by experiments on measuring voltage signal from a magnetic tunnel junction (MTJ) exposed to a microwave radiation in ferromagnetic resonance (FMR) condition. In Chapter 3 we found a possible explanation for the finite voltage signal measured from a tunnel junction consisting of only a single ferromagnet (FM). I show that this could be due to the existence of Rashba spin-orbit coupling (SOC) at the interface of the FM and insulator. Assuming that the measured signals are quantum mechanical effect where a solution to the time dependent Schrodinger equation is required, I use Keldysh Green function formalism to introduce a "multi-photon" approach which takes into account the effects of time-dependent term exactly up to scatterings from a finite number of photons. We then proceed to find the corresponding Green function numerically using a recursive method which allows us to increase the size of the system significantly. We also implement other approximations such as adiabatic and rotating frame approaches and compared them with our approach. In Chapter 4, I investigate the spin and charge pumping from a precessing magnetization attached to the edge of a 2-dimensional topological insulator (2DTI). We show that, in this system a huge spin current (or voltage signal if the FM covers only one edge) can be pumped for very small cone angles of the precessing FM (proportional to the intensity of the applied microwave). In Chapter 5 I present the third project in this field of research, where, I investigated the pumping from FM attached to a 3-dimensional TI. Spin-transfer torque: Presented in Chapter 6, in this work I investigate the torque induced by a flow of spin-polarized current into a FM and check the condition in which it can cause the magnetization to flip. Motivated by recent experimental developments in the field, here I consider systems with strong SOC such as TIs within a magnetic tunnel junction (MTJ) heterostructure. In the theoretical part I show the correct way (as opposed to the conventional approach used in some theoretical works which suffers from violation of the gauge invariance) to calculate linear-response torque to the external applied voltage and for the numerical calculation I adopted a parallelized adaptive integration algorithm in order to take care of very sharp changes that appear in momentum and energy dependence of t
NASA Astrophysics Data System (ADS)
Karzig, Torsten; Bardyn, Charles-Edouard; Lindner, Netanel H.; Refael, Gil
2015-07-01
The interaction between light and matter can give rise to novel topological states. This principle was recently exemplified in Floquet topological insulators, where classical light was used to induce a topological electronic band structure. Here, in contrast, we show that mixing single photons with excitons can result in new topological polaritonic states—or "topolaritons." Taken separately, the underlying photons and excitons are topologically trivial. Combined appropriately, however, they give rise to nontrivial polaritonic bands with chiral edge modes allowing for unidirectional polariton propagation. The main ingredient in our construction is an exciton-photon coupling with a phase that winds in momentum space. We demonstrate how this winding emerges from the finite-momentum mixing between s -type and p -type bands in the electronic system and an applied Zeeman field. We discuss the requirements for obtaining a sizable topological gap in the polariton spectrum and propose practical ways to realize topolaritons in semiconductor quantum wells and monolayer transition metal dichalcogenides.
Topology Explains Why Automobile Sunshades Fold Oddly
ERIC Educational Resources Information Center
Feist, Curtis; Naimi, Ramin
2009-01-01
Automobile sunshades always fold into an "odd" number of loops. The explanation why involves elementary topology (braid theory and linking number, both explained in detail here with definitions and examples), and an elementary fact from algebra about symmetric group.
Quantum gates with topological phases
Ionicioiu, Radu
2003-09-01
We investigate two models for performing topological quantum gates with the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and two-qubit Abelian phases can be enacted with the AB effect using charge qubits, whereas the AC effect can be used to perform all single-qubit gates (Abelian and non-Abelian) for spin qubits. Possible experimental setups suitable for a solid-state implementation are briefly discussed.
Fermions as topological objects
V. N. Yershov
2005-10-30
A preon-based composite model of the fundamental fermions is discussed, in which the fermions are bound states of smaller entities -- primitive charges (preons). The preon is regarded as a dislocation in a dual 3-dimensional manifold -- a topological object with no properties, save its unit mass and unit charge. It is shown that the dualism of this manifold gives rise to a hierarchy of complex structures resembling by their properties three families of the fundamental fermions. Although just a scheme for building a model of elementary particles, this description yields a quantitative explanation of many observable particle properties, including their masses.
Topological structures in the Husimi flow
Matheus Veronez; Marcus A. M. de Aguiar
2015-07-28
We study the topological properties of the quantum phase space current in the Husimi representation, focusing on the dynamical differences, induced by these properties, between the quantum and the classical flows. We show that the zeros of the Husimi function are stagnation points of the current and have a nonzero topological charge. Due to overall charge conservation, new stagnation points with opposite charge appear in pairs in the Husimi current and they have important roles in dynamical processes. As an example we show the topological effect of the zeros in the transmission rate of particle through a potential barrier.
A Design of Topological Predicates for Complex Crisp and Fuzzy Regions
GÃ¼ting, Ralf Hartmut
A Design of Topological Predicates for Complex Crisp and Fuzzy Regions Markus Schneider Fern and definition of their topological relationships. This paper gives a formal definition of complex crisp regionsÂ ical predicates can be defined on them. Second, topological predicates so far only operate on crisp
John L. Friedman; Kristin Schleich; Donald M. Witt
1995-06-09
All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove here the conjecture that general relativity does not allow an observer to probe the topology of spacetime: any topological structure collapses too quickly to allow light to traverse it. More precisely, in a globally hyperbolic, asymptotically flat spacetime satisfying the null energy condition, every causal curve from $\\scri^-$ to ${\\scri}^+$ is homotopic to a topologically trivial curve from $\\scri^-$ to ${\\scri}^+$. (If the Poincar\\'e conjecture is false, the theorem does not prevent one from probing fake 3-spheres).
Topological pumping over a photonic Fibonacci quasicrystal
NASA Astrophysics Data System (ADS)
Verbin, Mor; Zilberberg, Oded; Lahini, Yoav; Kraus, Yaacov E.; Silberberg, Yaron
2015-02-01
Quasiperiodic lattices have recently been shown to be a nontrivial topological phase of matter. Charge pumping—one of the hallmarks of topological states of matter—was recently realized for photons in a one-dimensional off-diagonal Harper model implemented in a photonic waveguide array. However, if the relationship between topological pumps and quasiperiodic systems is generic, one might wonder how to observe it in the canonical and most studied quasicrystalline system in one dimension—the Fibonacci chain. This chain is expected to facilitate a similar phenomenon, yet its discrete nature hinders the experimental study of such topological effects. Here, we overcome this obstacle by utilizing the topological equivalence of a family of quasiperiodic models which ranges from the Fibonacci chain to the Harper model. Implemented in photonic waveguide arrays, we observe the topological properties of this family, and perform a topological pumping of photons across a Fibonacci chain.
Yang, Zhaoju; Gao, Fei; Shi, Xihang; Lin, Xiao; Gao, Zhen; Chong, Yidong; Zhang, Baile
2015-03-20
The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers. PMID:25839273
The U(1) Topological Gauge Field Theory for Topological Defects in Liquid Crystals
Yi-shi Duan; Li Zhao; Xin-hui Zhang; Tie-yan Si
2005-12-27
A novel U(1) topological gauge field theory for topological defects in liquid crystals is constructed by considering the U(1) gauge field is invariant under the director inversion. Via the U(1) gauge potential decomposition theory and the $\\phi$-mapping topological current theory, the decomposition expression of U(1) gauge field and the unified topological current for monopoles and strings in liquid crystals are obtained. It is revealed that monopoles and strings are located in different spatial dimensions and their topological charges are just the winding numbers of $\\phi$-mapping.
Topological forms of information
Baudot, Pierre; Bennequin, Daniel
2015-01-13
We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: 1) classical probabilities and random variables; 2) quantum probabilities and observable operators; 3) dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes. We discuss briefly its application to complex data, in particular to the structures of information flows in biological systems. This short note summarizes results obtained during the last years by the authors. The proofs are not included, but the definitions and theorems are stated with precision.
Topological forms of information
NASA Astrophysics Data System (ADS)
Baudot, Pierre; Bennequin, Daniel
2015-01-01
We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: 1) classical probabilities and random variables; 2) quantum probabilities and observable operators; 3) dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes. We discuss briefly its application to complex data, in particular to the structures of information flows in biological systems. This short note summarizes results obtained during the last years by the authors. The proofs are not included, but the definitions and theorems are stated with precision.
Topology of the Standard Model, I: Fermions
Steve Gersten
2015-12-26
The Harari-Shupe model for fermions is extended to a topological model which contains an explanation for the observed fact that there are only three generations of fermions. Topological explanations are given for $\\beta$-decay and for proton decay predicted in supersymmetry and string theories. An explanation is given for the observed fact that the three generations of fermions have such similar properties. The concept of "color" is incorporated into the model in a topologically meaningful way. Conservation laws are defined and discussed in the context of the algebraic topology of the model, and preon number is proved to be linearly determined by charge, weak isospin, and color.
NASA Astrophysics Data System (ADS)
Luminet, Jean-Pierre
2015-08-01
Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.
NASA Astrophysics Data System (ADS)
Pavanello, Michele; Neugebauer, Johannes
2011-10-01
Marcus theory of electron transfer (ET) and Förster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys. 130, 234102 (2009), 10.1063/1.3148777], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ET reactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston-Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensed-phase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.
D’Avanzo, Antonella
2010-01-01
Monopoles are solutions of an SU(2) gauge theory in R3 satisfying a lower bound for energy and certain asymptotic conditions, which translate as topological properties encoded in their charge. Using methods from integrable ...
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 12 Banks and Banking 3 2011-01-01 2011-01-01 false Finance charge. 226.4 Section 226.4 Banks and... LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is the cost of...) Charges by third parties. The finance charge includes fees and amounts charged by someone other than...
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 12 Banks and Banking 3 2010-01-01 2010-01-01 false Finance charge. 226.4 Section 226.4 Banks and... LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is the cost of...) Charges by third parties. The finance charge includes fees and amounts charged by someone other than...
Sheng Li; Yishi Duan
1998-10-09
The topological structure of the electric topological current of the locally gauge invariant Maxwell-Chern-Simons Model and its bifurcation is studied. The electric topological charge is quantized in term of winding number. The Hopf indices and Brouwer degree labeled the local topological structure of the electric topological current. Using $\\Phi $-mapping method and implicity theory, the electric topological current is found generating or annihilating at the limit points and splitting or merging at the bifurcate points. The total electric charge holds invariant during the evolution.
Topological Aspects of Information Retrieval.
ERIC Educational Resources Information Center
Egghe, Leo; Rousseau, Ronald
1998-01-01
Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
Ando, Yoichi
In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The ...
Helene Porchon
2012-01-25
In this paper, we introduce the foundation of a fractal topological space constructed via a family of nested topological spaces endowed with subspace topologies, where the number of topological spaces involved in this family is related to the appearance of new structures on it. The greater the number of topological spaces we use, the stronger the subspace topologies we obtain. The fractal manifold model is brought up as an illustration of space that is locally homeomorphic to the fractal topological space.
Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
Aganagic, Mina; Ooguri, Hirosi; Saulina, Natalia; Vafa, Cumrun
2005-01-28
We count the number of bound states of BPS black holes on local Calabi-Yau three-folds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a q-deformed Yang-Mills theory on the Riemann surface. Following the recent connection between the black hole entropy and the topological string partition function, we find that for a large black hole charge N, up to corrections of O(e^-N), Z_BH is given as a sum of a square of chiral blocks, each of which corresponds to a specific D-brane amplitude. The leading chiral block, the vacuum block, corresponds to the closed topological string amplitudes. The sub-leading chiral blocks involve topological string amplitudes with D-brane insertions at 2g-2 points on the Riemann surface analogous to the Omega points in the large N 2d Yang-Mills theory. The finite N amplitude provides a non-perturbative definition of topological strings in these backgrounds. This also leads to a novel non-perturbative formulation of c=1 non-critical string at the self-dual radius.
Topological BF field theory description of topological insulators
Cho, Gil Young; Moore, Joel E.
2011-06-15
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Da Silva, David; Han, Liqi; Faivre, Robert; Costes, Evelyne
2014-01-01
Background and Aims The impact of a fruit tree's architecture on its performance is still under debate, especially with regard to the definition of varietal ideotypes and the selection of architectural traits in breeding programmes. This study aimed at providing proof that a modelling approach can contribute to this debate, by using in silico exploration of different combinations of traits and their consequences on light interception, here considered as one of the key parameters to optimize fruit tree production. Methods The variability of organ geometrical traits, previously described in a bi-parental population, was used to simulate 1- to 5-year-old apple trees (Malus × domestica). Branching sequences along trunks observed during the first year of growth of the same hybrid trees were used to initiate the simulations, and hidden semi-Markov chains previously parameterized were used in subsequent years. Tree total leaf area (TLA) and silhouette to total area ratio (STAR) values were estimated, and a sensitivity analysis was performed, based on a metamodelling approach and a generalized additive model (GAM), to analyse the relative impact of organ geometry and lateral shoot types on STAR. Key Results A larger increase over years in TLA mean and variance was generated by varying branching along trunks than by varying organ geometry, whereas the inverse was observed for STAR, where mean values stabilized from year 3 to year 5. The internode length and leaf area had the highest impact on STAR, whereas long sylleptic shoots had a more significant effect than proleptic shoots. Although the GAM did not account for interactions, the additive effects of the geometrical factors explained >90% of STAR variation, but much less in the case of branching factors. Conclusions This study demonstrates that the proposed modelling approach could contribute to screening architectural traits and their relative impact on tree performance, here viewed through light interception. Even though trait combinations and antagonism will need further investigation, the approach opens up new perspectives for breeding and genetic selection to be assisted by varietal ideotype definition. PMID:24723446
M. R. Setare
2002-10-20
In this paper we discuss the question of whether the entropy of cosmological horizon in Topological Reissner-Nordstr\\"om- de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. Furthermore, we find that the entropy of black hole horizon can also be rewritten in terms of the Cardy-Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. Our result is in favour of the dS/CFT correspondence.
T-Duality of Topological Insulators
Varghese Mathai; Guo Chuan Thiang
2015-09-03
Topological insulators and D-brane charges in string theory can both be classified by the same family of groups. In this paper, we extend this connection via a geometric transform, giving a novel duality of topological insulators which can be viewed as a condensed matter analog of T-duality in string theory. For 2D Chern insulators, this duality exchanges the rank and Chern number of the valence bands.
Topological susceptibility with the improved Asqtad action
C. Bernard et al.
2004-01-06
As a test of the chiral properties of the improved Asqtad (staggered fermion) action, we have been measuring the topological susceptibility as a function of quark masses for 2 + 1 dynamical flavors. We report preliminary results, which show reasonable agreement with leading order chiral perturbation theory for lattice spacing less than 0.1 fm. The total topological charge, however, shows strong persistence over Monte Carlo time.
T-duality of topological insulators
NASA Astrophysics Data System (ADS)
Mathai, Varghese; Thiang, Guo Chuan
2015-10-01
Topological insulators and D-brane charges in string theory can both be classified by the same family of groups. In this paper, we extend this connection via a geometric transform, giving a novel duality of topological insulators which can be viewed as a condensed matter analog of T-duality in string theory. For 2D Chern insulators, this duality exchanges the rank and Chern number of the valence bands.
Topological Mott insulator by block spin phenomenology
NASA Astrophysics Data System (ADS)
Kim, Yun Ki; Son, Kwang Chul; Koo, Je Huan
2015-11-01
We investigate the relationship between topological Mott insulators and spin glasses. By first explaining the phase of spin glass on the basis of finite sized block spin concepts, we then introduce the three-dimensional insulating phase of a topological insulator with a finite bulk bandgap as the pairing of block spins comprised of many random spins with respective majority spin directions. However, the two-dimensional edge state of the topological insulator may be thought of as the pairing of triplet spins with a zero bandgap. Topological insulators can be transformed into ordinary insulators below a certain temperature. Electric field-induced transitions between normal and topological insulators are possible as explained by means of composite charges.
Topological Black Holes -- Outside Looking In
R. B. Mann
1997-09-15
I describe the general mathematical construction and physical picture of topological black holes, which are black holes whose event horizons are surfaces of non-trivial topology. The construction is carried out in an arbitrary number of dimensions, and includes all known special cases which have appeared before in the literature. I describe the basic features of massive charged topological black holes in $(3+1)$ dimensions, from both an exterior and interior point of view. To investigate their interiors, it is necessary to understand the radiative falloff behaviour of a given massless field at late times in the background of a topological black hole. I describe the results of a numerical investigation of such behaviour for a conformally coupled scalar field. Significant differences emerge between spherical and higher genus topologies.
Hasselblatt, Boris
TOPOLOGICAL ENTROPY FOR NONUNIFORMLY CONTINUOUS MAPS BORIS HASSELBLATT, ZBIGNIEW NITECKI, AND JAMES of the standard defini- tions of topological entropy for a continuous self-map f : X X from the case when X There are two standard definitions of topological entropy for a continuous self-map of a compact metric space
Observation of unconventional quantum spin textures in topological insulators.
Hsieh, D; Xia, Y; Wray, L; Qian, D; Pal, A; Dil, J H; Osterwalder, J; Meier, F; Bihlmayer, G; Kane, C L; Hor, Y S; Cava, R J; Hasan, M Z
2009-02-13
A topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetry-based classification of condensed matter. Exotic spin-transport phenomena, such as the dissipationless quantum spin Hall effect, have been speculated to originate from a topological order whose identification requires a spin-sensitive measurement, which does not exist to this date in any system. Using Mott polarimetry, we probed the spin degrees of freedom and demonstrated that topological quantum numbers are completely determined from spin texture-imaging measurements. Applying this method to Sb and Bi(1-x)Sb(x), we identified the origin of its topological order and unusual chiral properties. These results taken together constitute the first observation of surface electrons collectively carrying a topological quantum Berry's phase and definite spin chirality, which are the key electronic properties component for realizing topological quantum computing bits with intrinsic spin Hall-like topological phenomena. PMID:19213915
Induced topological pressure for topological dynamical systems
Xing, Zhitao; Chen, Ercai
2015-02-15
In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure.
Topological insulators and superconductors from string theory
Ryu, Shinsei; Takayanagi, Tadashi
2010-10-15
Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and superconductors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the {theta} term in various dimensions. This sheds light on topological insulators and superconductors beyond noninteracting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).
Topological Aspects of Differential Chains
Jenny Harrison; Harrison Pugh
2011-01-02
In this paper we investigate the topological properties of the space of differential chains 'B(U) defined on an open subset U of a Riemannian manifold M. We show that 'B(U) is not generally reflexive, identifying a fundamental difference between currents and differential chains. We also give several new brief (though non-constructive) definitions of the space 'B(U), and prove that it is a separable ultrabornological (DF)-space. Differential chains are closed under dual versions of fundamental operators of the Cartan calculus on differential forms. The space has good properties some of which are not exhibited by currents B'(U) or D'(U). For example, chains supported in finitely many points are dense in 'B(U) for all open U in M, but not generally in the strong dual topology of B'(U).
Deficient topological measures and functionals generated by them
Svistula, Marina G
2013-05-31
This paper looks at the properties of deficient topological measures, which are a generalization of topological measures. Integration of a real function that is continuous on a compact set with respect to a deficient topological measure is also investigated. The notions of r- and l-functionals are introduced and an analogue of the Riesz representation theorem is obtained for them. As corollaries, both well-known and new results for quasi-integrals and topological measures are presented (for example, a new version of the definition of a quasi-integral). Bibliography: 16 titles.
Topological phases and topological entropy of two-dimensional systems with finite correlation length
Papanikolaou, Stefanos; Fradkin, Eduardo; Raman, Kumar S.
2007-12-01
We elucidate the topological features of the entanglement entropy of a region in two-dimensional quantum systems in a topological phase with a finite correlation length {xi}. First, we suggest that simpler reduced quantities, related to the von Neumann entropy, could be defined to compute the topological entropy. We use our methods to compute the entanglement entropy for the ground-state wave function of a quantum eight-vertex model in its topological phase and show that a finite correlation length adds corrections of the same order as the topological entropy which come from sharp features of the boundary of the region under study. We also calculate the topological entropy for the ground state of the quantum dimer model on a triangular lattice by using a mapping to a loop model. The topological entropy of the state is determined by loop configurations with a nontrivial winding number around the region under study. Finally, we consider extensions of the Kitaev wave function, which incorporate the effects of electric and magnetic charge fluctuations, and use it to investigate the stability of the topological phase by calculating the topological entropy.
Topological binding and elastic interactions of microspheres and fibres in a nematic liquid crystal.
Nikkhou, M; Škarabot, M; Muševi?, I
2015-03-01
We present a detailed analysis of topological binding and elastic interactions between a long, and micrometer-diameter fiber, and a microsphere in a homogeneously aligned nematic liquid crystal. Both objects are surface treated to produce strong perpendicular anchoring of the nematic liquid crystal. We use the opto-thermal micro-quench of the laser tweezers to produce topological defects with prescribed topological charge, such as pairs of a Saturn ring and an anti-ring, hyperbolic and radial hedgehogs on a fiber, as well as zero-charge loops. We study the entanglement and topological charge interaction between the topological defects of the fiber and sphere and we observe a huge variety of different entanglement topologies and defect-mediated elastic bindings. We explain all observed phenomena with simple topological rule: like topological charges repel each other and opposite topological charges attract. These binding mechanisms not only demonstrate the fascinating topology of nematic colloids, but also open a novel route to the assembly of very complex topological networks of fibers, spheres and other objects for applications in liquid crystal photonics. PMID:25813607
Study of charges transferability for use in force fields
NASA Astrophysics Data System (ADS)
Maciel, Glauciete S.; Garcia, Edgardo
2006-03-01
This Letter examines the topological neighborhood effects on atomic partial charges and their transferability. To determine neighborhood effects, we used Breneman and Wiberg's CHELPG charges calculated at B3LYP/6-31G* theory level and AM1 geometries for a test set of 324 molecules of insecticides, ferroelectric liquid crystals (FLC) and antiinflammatories. The Qcode atomic descriptor was applied to represent topological neighborhood. Calculated molecular dipole moments using averaged charges with various neighbor numbers indicate that partial charges have a strong dependence with the molecular topology. Five or more neighbors are demonstrated to be typically needed for accurate partial charges transferability.
Topological Expansion, Study and Applications
Helene Porchon
2012-11-13
In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to any fractal family of topological spaces is expanding. In particular, we prove that the more a topological space expands, the finer the topology of its indexed states is. Using multi-homeomorphisms over associated coproduct topological spaces, we define a locally expandable topological space and we prove that a locally expandable topological space has a topological expansion. Specifically, we prove that the expanding fractal manifold is locally expandable and has a natural topological expansion.
Electrically Tunable Magnetism in Magnetic Topological Insulators
NASA Astrophysics Data System (ADS)
Wang, Jing; Lian, Biao; Zhang, Shou-Cheng
2015-07-01
The external controllability of the magnetic properties in topological insulators would be important both for fundamental and practical interests. Here we predict the electric-field control of ferromagnetism in a thin film of insulating magnetic topological insulators. The decrease of band inversion by the application of electric fields results in a reduction of magnetic susceptibility, and hence in the modification of magnetism. Remarkably, the electric field could even induce the magnetic quantum phase transition from ferromagnetism to paramagnetism. We further propose a transistor device in which the dissipationless charge transport of chiral edge states is controlled by an electric field. In particular, the field-controlled ferromagnetism in a magnetic topological insulator can be used for voltage based writing of magnetic random access memories in magnetic tunnel junctions. The simultaneous electrical control of magnetic order and chiral edge transport in such devices may lead to electronic and spintronic applications for topological insulators.
A hierarchy of topological tensor network states
Buerschaper, Oliver; Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching ; Mombelli, Juan Martin; Aguado, Miguel
2013-01-15
We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independent framework of tensor networks based on the algebraic setting of finite-dimensional Hopf C*-algebras. At the top of the hierarchy we identify ground states of new topological lattice models extending Kitaev's quantum double models [Ann. Phys. 303, 2 (2003)]. For these states we exhibit the mechanism responsible for their non-zero topological entanglement entropy by constructing an entanglement renormalization flow. Furthermore, we argue that the hierarchy states are related to each other by the condensation of topological charges.
Open string amplitudes of closed topological vertex
Kanehisa Takasaki; Toshio Nakatsu
2015-11-20
The closed topological vertex is the simplest ``off-strip'' case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein can be obtained by gluing a single topological vertex to an ``on-strip'' subdiagram of the tree-like web diagram. If non-trivial partitions are assigned to just two parallel external lines of the web diagram, the amplitudes can be calculated with the aid of techniques borrowed from the melting crystal models. These amplitudes are thereby expressed as matrix elements, modified by simple prefactors, of an operator product on the Fock space of 2D charged free fermions. This fermionic expression can be used to derive $q$-difference equations for generating functions of special subsets of the amplitudes. These $q$-difference equations may be interpreted as the defining equation of a quantum mirror curve.
Electrically Tunable Magnetism in Magnetic Topological Insulators.
Wang, Jing; Lian, Biao; Zhang, Shou-Cheng
2015-07-17
The external controllability of the magnetic properties in topological insulators would be important both for fundamental and practical interests. Here we predict the electric-field control of ferromagnetism in a thin film of insulating magnetic topological insulators. The decrease of band inversion by the application of electric fields results in a reduction of magnetic susceptibility, and hence in the modification of magnetism. Remarkably, the electric field could even induce the magnetic quantum phase transition from ferromagnetism to paramagnetism. We further propose a transistor device in which the dissipationless charge transport of chiral edge states is controlled by an electric field. In particular, the field-controlled ferromagnetism in a magnetic topological insulator can be used for voltage based writing of magnetic random access memories in magnetic tunnel junctions. The simultaneous electrical control of magnetic order and chiral edge transport in such devices may lead to electronic and spintronic applications for topological insulators. PMID:26230818
Open string amplitudes of closed topological vertex
Takasaki, Kanehisa
2015-01-01
The closed topological vertex is the simplest "off-strip" case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein can be obtained by gluing a single topological vertex to an "on-strip" subdiagram of the tree-like web diagram. If non-trivial partitions are assigned to just two parallel external lines of the web diagram, the amplitudes can be calculated with the aid of techniques borrowed from the melting crystal models. These amplitudes are thereby expressed as matrix elements, modified by simple prefactors, of an operator product on the Fock space of 2D charged free fermions. This fermionic expression can be used to derive $q$-difference equations for generating functions of special subsets of the amplitudes. These $q$-difference equations may be interpreted as the defining equation of a quantum mirror curve.
Electrically Tunable Magnetism in Magnetic Topological Insulators
NASA Astrophysics Data System (ADS)
Zhang, Shou-Cheng; Wang, Jing; Lian, Biao
2015-03-01
The external controllability of the magnetic properties in topological insulators would be important both for fundamental and practical interests. Here we predict the electric-field control of ferromagnetism in a thin film of insulating magnetic topological insulators. The decrease of band inversion by the application of electric fields results in a reduction of magnetic susceptibility, and hence in the modication of magnetism. Remarkably, the electric field could even induce the magnetic quantum phase transition from ferromagnetism to paramagnetism. We further propose a topological transistor device in which the dissipationless charge transport of chiral edge states is controlled by an electric field. The simultaneous electrical control of magnetic order and chiral edge transport in such a device may lead to electronic and spintronic applications for topological insulators. This work is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. DE-AC02-76SF00515.
- criticality of topological black holes in Lovelock-Born-Infeld gravity
NASA Astrophysics Data System (ADS)
Mo, Jie-Xiong; Liu, Wen-Biao
2014-04-01
To understand the effect of third order Lovelock gravity, - criticality of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and in some more detail than the previous literature. A detailed analysis of the limit case is performed for the seven-dimensional black holes. It is shown that, for the spherical topology, - criticality exists for both the uncharged and the charged cases. Our results demonstrate again that the charge is not the indispensable condition of - criticality. It may be attributed to the effect of higher derivative terms of the curvature because similar phenomenon was also found for Gauss-Bonnet black holes. For , there would be no - criticality. Interesting findings occur in the case , in which positive solutions of critical points are found for both the uncharged and the charged cases. However, the - diagram is quite strange. To check whether these findings are physical, we give the analysis on the non-negative definiteness condition of the entropy. It is shown that, for any nontrivial value of , the entropy is always positive for any specific volume . Since no - criticality exists for in Einstein gravity and Gauss-Bonnet gravity, we can relate our findings with the peculiar property of third order Lovelock gravity. The entropy in third order Lovelock gravity consists of extra terms which are absent in the Gauss-Bonnet black holes, which makes the critical points satisfy the constraint of non-negative definiteness condition of the entropy. We also check the Gibbs free energy graph and "swallow tail" behavior can be observed. Moreover, the effect of nonlinear electrodynamics is also included in our research.
Sufficient symmetry conditions for Topological Quantum Order
Nussinov, Zohar; Ortiz, Gerardo
2009-01-01
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn–Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order. PMID:19805113
Topological orders with global gauge anomalies
NASA Astrophysics Data System (ADS)
You, Yi-Zhuang; Xu, Cenke
2015-08-01
By definition, the physics of the d -dimensional (dim) boundary of a (d +1 ) -dim symmetry protected topological (SPT) state cannot be realized as itself on a d -dim lattice. If the symmetry of the system is unitary, then a formal way to determine whether a d -dim theory must be a boundary or not, is to couple this theory to a gauge field (or to "gauge" its symmetry), and check if there is a gauge anomaly. In this paper we discuss the following question: Can the boundary of a SPT state be driven into a fully gapped topological order which preserves all the symmetries? We argue (conjecture) that if the gauge anomaly of the boundary is "perturbative," then the boundary must remain gapless; while if the boundary only has global gauge anomaly but no perturbative anomaly, then it is possible to gap out the boundary by driving it into a topological state, when d ?2 . We will demonstrate this conjecture with two examples: (1) the 3 d spin-1/2 chiral fermion with the well-known Witten's global anomaly [Phys. Lett. 117, 324 (1982), 10.1016/0370-2693(82)90728-6], which can be realized on the boundary of a 4 d topological superconductor with SU(2) or U (1 ) ?Z2 symmetry; and (2) the 4 d boundary of a 5 d topological superconductor with the same symmetry. We show that these boundary systems can be driven into a fully gapped Z2 N topological order with topological degeneracy, but this Z2 N topological order cannot be future driven into a trivial confined phase that preserves all the symmetries due to some special properties of its topological defects. Our study also leads to exotic states of matter in pure 3 d space.
Coulomb screening in graphene with topological defects
Baishali Chakraborty; Kumar S. Gupta; Siddhartha Sen
2015-02-20
We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green's function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green's function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.
Vortex Motion In Charged Fluids
G. N. Stratopoulos; T. N. Tomaras
1994-05-18
A non-relativistic scalar field coupled minimally to electromagnetism supports in the presence of a homogeneous background electric charge density the existence of smooth, finite-energy topologically stable flux vortices. The static properties of such vortices are studied numerically in the context of a two parameter model describing this system as a special case. It is shown that the electrostatic and the mexican hat potential terms of the energy are each enough to ensure the existence of vortex solutions. The interaction potential of two minimal vortices is obtained for various values of the parameters. It is proven analytically that a free isolated vortex with topological charge $N\
Boundaries and Topological Algorithms
Fleck, Margaret Morrison
1988-09-01
This thesis develops a model for the topological structure of situations. In this model, the topological structure of space is altered by the presence or absence of boundaries, such as those at the edges of objects. ...
Topological susceptibility near Tc in SU(3) gauge theory
NASA Astrophysics Data System (ADS)
Xiong, Guang-Yi; Zhang, Jian-Bo; Chen, Ying; Liu, Chuan; Liu, Yu-Bin; Ma, Jian-Ping
2016-01-01
Topological charge susceptibility ?t for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for ?t with values decreasing from (188 (1) MeV) 4 to (67 (3) MeV) 4 as the temperature increased from zero temperature to 1.9Tc which demonstrates the existence of topological excitations far above Tc. The 4th order cumulant c4 of topological charge, as well as the ratio c4 /?t is also investigated. Results of c4 show step-like behavior near Tc while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.
Topological confinement in bilayer graphene.
Martin, Ivar; Blanter, Ya M; Morpurgo, A F
2008-01-25
We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally and emphasize their relevance for valleytronics. PMID:18233021
Topological wave functions and the 4D-5D lift
NASA Astrophysics Data System (ADS)
Gao, Peng; Pioline, Boris
2008-07-01
We revisit the holomorphic anomaly equations satisfied by the topological string amplitude from the perspective of the 4D-5D lift, in the context of ``magic'' Script N = 2 supergravity theories. In particular, we interpret the Gopakumar-Vafa relation between 5D black hole degeneracies and the topological string amplitude as the result of a canonical transformation from 4D to 5D charges. Moreover we use the known Bekenstein-Hawking entropy of 5D black holes to constrain the asymptotic behavior of the topological wave function at finite topological coupling but large Kähler classes. In the process, some subtleties in the relation between 5D black hole degeneracies and the topological string amplitude are uncovered, but not resolved. Finally we extend these considerations to the putative one-parameter generalization of the topological string amplitude, and identify the canonical transformation as a Weyl reflection inside the 3D duality group.
A new class of non-topological solitons
NASA Technical Reports Server (NTRS)
Frieman, Joshua A.; Lynn, Bryan W.
1989-01-01
A class of non-topological solitons was constructed in renormalizable scalar field theories with nonlinear self-interactions. For large charge Q, the soliton mass increases linearly with Q, i.e., the soliton mass density is approximately independent of charge. Such objects could be naturally produced in a phase transition in the early universe or in the decay of superconducting cosmic strings.
Battenfeld, Ingo
2008-01-01
This thesis presents Topological Domain Theory as a powerful and flexible framework for denotational semantics. Topological Domain Theory models a wide range of type constructions and can interpret many computational features. Furthermore, it has close connections to established frameworks for denotational semantics, as well as to well-studied mathematical theories, such as topology and computable analysis....We begin by describing the categories of Topological Domain Theory, and their categorical structure. In particular, we recover the basic constructions of domain theory, such as products, function spaces, fixed points and recursive types, in the context of Topological Domain Theory....As a central contribution, we give a detailed account of how computational effects can be modelled in Topological Domain Theory. Following recent work of Plotkin and Power, who proposed to construct effect monads via free algebra functors, this is done by showing that free algebras for a large class of parametrised equational theories exist in Topological Domain Theory. These parametrised equational theories are expressive enough to generate most of the standard examples of effect monads. Moreover, the free algebras in Topological Domain Theory are obtained by an explicit inductive construction, using only basic topological and set-theoretical principles....We also give a comparison of Topological and Classical Domain Theory. The category of omega-continuous dcpos embeds into Topological Domain Theory, and we prove that this embedding preserves the basic domain-theoretic constructions in most cases. We show that the classical powerdomain constructions on omega-continuous dcpos, including the probabilistic powerdomain, can be recovered in Topological Domain Theory.... of the categories of Topological Domain Theory in this realizability topos, and prove the corresponding categories to be internally complete and weakly small. This enables us to show that Topological Domain Theory can model the polymorphic lambda...In summary, this thesis shows that Topological Domain Theory supports a wide range of semantic constructions, including the standard domain-theoretic constructions, computational effects and polymorphism, all within a single setting....
Kalb, Jeffrey L.; Lee, David S.
2008-01-01
Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.
Photonic Floquet topological insulators.
Rechtsman, Mikael C; Zeuner, Julia M; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2013-04-11
Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on their surfaces. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism-one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport-a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate (z) acts as 'time'. Thus the helicity of the waveguides breaks z-reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering. PMID:23579677
Game Theory and Topological Phase Transition
Tieyan Si
2008-03-29
Phase transition is a war game. It widely exists in different kinds of complex system beyond physics. Where there is revolution, there is phase transition. The renormalization group transformation, which was proved to be a powerful tool to study the critical phenomena, is actually a game process. The phase boundary between the old phase and new phase is the outcome of many rounds of negotiation between the old force and new force. The order of phase transition is determined by the cutoff of renormalization group transformation. This definition unified Ehrenfest's definition of phase transition in thermodynamic physics. If the strategy manifold has nontrivial topology, the topological relation would put a constrain on the surviving strategies, the transition occurred under this constrain may be called a topological one. If the strategy manifold is open and noncompact, phase transition is simply a game process, there is no table for topology. An universal phase coexistence equation is found, it sits at the Nash equilibrium point. Inspired by the fractal space structure demonstrated by renormalization group theory, a conjecture is proposed that the universal scaling law of a general phase transition in a complex system comes from the coexistence equation around Nash equilibrium point. Game theory also provide us new understanding to pairing mechanism and entanglement in many body physics.
NASA Astrophysics Data System (ADS)
Metlitski, Max A.; Kane, C. L.; Fisher, Matthew P. A.
2015-09-01
A three-dimensional electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface termination of an ETI supports an odd number of Dirac cones. In this paper, we deduce a symmetry-respecting, gapped surface termination of an ETI, which carries an intrinsic two-dimensional (2d) topological order, Moore-Read×U (1) -2 . The Moore-Read sector supports non-Abelian charge 1 /4 anyons, while the Abelian, U (1) -2 , (antisemion) sector is electrically neutral. Time-reversal symmetry is implemented in this surface phase in a highly nontrivial way. Moreover, it is impossible to realize this phase strictly in 2d, simultaneously preserving its implementation of both the particle-number and time-reversal symmetries. A one-dimensional (1d) edge on the ETI surface between the topologically ordered phase and the topologically trivial time-reversal-broken phase with a Hall conductivity ?x y=1 /2 carries a right-moving neutral Majorana mode, a right-moving bosonic charge mode, and a left-moving bosonic neutral mode. The topologically ordered phase is separated from the surface superconductor by a direct second-order phase transition in the X Y* universality class, which is driven by the condensation of a charge 1 /2 boson, when approached from the topologically ordered side, and proliferation of a flux 4 ? (2 h c /e ) vortex, when approached from the superconducting side. In addition, we prove that time-reversal invariant (interacting) electron insulators with no intrinsic topological order and electromagnetic response characterized by a ? angle, ? =? , do not exist if the electrons transform as Kramers singlets under time reversal.
Diagnosing Deconfinement and Topological Order
K. Gregor; David A. Huse; R. Moessner; S. L. Sondhi
2010-11-18
Topological or deconfined phases are characterized by emergent, weakly fluctuating, gauge fields. In condensed matter settings they inevitably come coupled to excitations that carry the corresponding gauge charges which invalidate the standard diagnostic of deconfinement---the Wilson loop. Inspired by a mapping between symmetric sponges and the deconfined phase of the $Z_2$ gauge theory, we construct a diagnostic for deconfinement that has the interpretation of a line tension. One operator version of this diagnostic turns out to be the Fredenhagen-Marcu order parameter known to lattice gauge theorists and we show that a different version is best suited to condensed matter systems. We discuss generalizations of the diagnostic, use it to establish the existence of finite temperature topological phases in $d \\ge 3$ dimensions and show that multiplets of the diagnostic are useful in settings with multiple phases such as $U(1)$ gauge theories with charge $q$ matter. [Additionally we present an exact reduction of the partition function of the toric code in general dimensions to a well studied problem.
Circuital characterisation of space-charge motion with a time-varying applied bias
NASA Astrophysics Data System (ADS)
Kim, Chul; Moon, Eun-Yi; Hwang, Jungho; Hong, Hiki
2015-07-01
Understanding the behaviour of space-charge between two electrodes is important for a number of applications. The Shockley-Ramo theorem and equivalent circuit models are useful for this; however, fundamental questions of the microscopic nature of the space-charge remain, including the meaning of capacitance and its evolution into a bulk property. Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit. We describe two approaches to this problem, both of which are based on energy conservation: the energy-to-current transformation rule, and an energy-equivalence-based definition of capacitance. We identify a significant capacitive current due to the rate of change of the capacitance. Further analysis shows that Shockley-Ramo theorem does not apply with a time-varying applied bias, and an additional electric-field-based current is identified to describe the resulting motion of the space-charge. Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes.
Circuital characterisation of space-charge motion with a time-varying applied bias.
Kim, Chul; Moon, Eun-Yi; Hwang, Jungho; Hong, Hiki
2015-01-01
Understanding the behaviour of space-charge between two electrodes is important for a number of applications. The Shockley-Ramo theorem and equivalent circuit models are useful for this; however, fundamental questions of the microscopic nature of the space-charge remain, including the meaning of capacitance and its evolution into a bulk property. Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit. We describe two approaches to this problem, both of which are based on energy conservation: the energy-to-current transformation rule, and an energy-equivalence-based definition of capacitance. We identify a significant capacitive current due to the rate of change of the capacitance. Further analysis shows that Shockley-Ramo theorem does not apply with a time-varying applied bias, and an additional electric-field-based current is identified to describe the resulting motion of the space-charge. Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes. PMID:26133999
Circuital characterisation of space-charge motion with a time-varying applied bias
Kim, Chul; Moon, Eun-Yi; Hwang, Jungho; Hong, Hiki
2015-01-01
Understanding the behaviour of space-charge between two electrodes is important for a number of applications. The Shockley-Ramo theorem and equivalent circuit models are useful for this; however, fundamental questions of the microscopic nature of the space-charge remain, including the meaning of capacitance and its evolution into a bulk property. Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit. We describe two approaches to this problem, both of which are based on energy conservation: the energy-to-current transformation rule, and an energy-equivalence-based definition of capacitance. We identify a significant capacitive current due to the rate of change of the capacitance. Further analysis shows that Shockley-Ramo theorem does not apply with a time-varying applied bias, and an additional electric-field-based current is identified to describe the resulting motion of the space-charge. Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes. PMID:26133999
An overview of charging environments
NASA Technical Reports Server (NTRS)
Gabriel, S. B.; Garrett, H. B.
1989-01-01
A brief synopsis of the natural environments that play a role in spacecraft charging is presented. Environments that cause both surface and internal charging are discussed along with the mechanisms involved. The geosynchronous and low altitude regions of the Earth's magnetosphere/ionosphere are considered and simple descriptions of each environment presented. As material properties are critical to the charging process, definition of material properties important to charging, which can be affected by the environment, are also described. Several space experiments are proposed that would help fill the gaps in the knowledge of the performance of materials in a charging environment.
Tunable Dirac Fermion Dynamics in Topological Insulators
Chen, Chaoyu; Xie, Zhuojin; Feng, Ya; Yi, Hemian; Liang, Aiji; He, Shaolong; Mou, Daixiang; He, Junfeng; Peng, Yingying; Liu, Xu; Liu, Yan; Zhao, Lin; Liu, Guodong; Dong, Xiaoli; Zhang, Jun; Yu, Li; Wang, Xiaoyang; Peng, Qinjun; Wang, Zhimin; Zhang, Shenjin; Yang, Feng; Chen, Chuangtian; Xu, Zuyan; Zhou, X. J.
2013-01-01
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving relativistic Dirac fermions which are responsible for exotic quantum phenomena and potential applications in spintronics and quantum computations. It is essential to understand how the Dirac fermions interact with other electrons, phonons and disorders. Here we report super-high resolution angle-resolved photoemission studies on the Dirac fermion dynamics in the prototypical Bi2(Te,Se)3 topological insulators. We have directly revealed signatures of the electron-phonon coupling and found that the electron-disorder interaction dominates the scattering process. The Dirac fermion dynamics in Bi2(Te3?xSex) topological insulators can be tuned by varying the composition, x, or by controlling the charge carriers. Our findings provide crucial information in understanding and engineering the electron dynamics of the Dirac fermions for fundamental studies and potential applications. PMID:23934507
Periodic table for topological insulators and superconductors
Alexei Kitaev
2009-01-20
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z_2. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.
Higgsless superconductivity from topological defects in compact BF terms
NASA Astrophysics Data System (ADS)
Diamantini, M. Cristina; Trugenberger, Carlo A.
2015-02-01
We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalisable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D - 1)-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. In the average field approximation, the corresponding uniform emergent charge creates a gap for the (D - 2)-dimensional branes via the Magnus force, the dual of the Lorentz force. One particular combination of intrinsic and emergent charge fluctuations that leaves the total charge distribution invariant constitutes an isolated gapless mode leading to superfluidity. The remaining massive modes organise themselves into a D-dimensional charged, massive vector. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2) and the topological order (4) are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realised as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors.
V.1Semi-topological K-Theory Eric M. Friedlander and Mark E. Walker *
(Xan ),oftheanalyticspaceXan associatedtoX.(Thesuperscript"sst"standsfor "singular semi-topological".) In a similar vein filtration on singular coho- mology H (Xan , Q). To give the reader some sense of the definition of semi
1 Semi-topological K-theory Eric M. Friedlander1
. (The su- perscript "sst" stands for "singular semi-topological".) In a similar vein, the real semi filtration on singular cohomology H (Xan , Q). To give the reader some sense of the definition of semi
Considerations for Multiprocessor Topologies
NASA Technical Reports Server (NTRS)
Byrd, Gregory T.; Delagi, Bruce A.
1987-01-01
Choosing a multiprocessor interconnection topology may depend on high-level considerations, such as the intended application domain and the expected number of processors. It certainly depends on low-level implementation details, such as packaging and communications protocols. The authors first use rough measures of cost and performance to characterize several topologies. They then examine how implementation details can affect the realizable performance of a topology.
Manipulating topological states by imprinting non-collinear spin textures
Streubel, Robert; Han, Luyang; Im, Mi -Young; Kronast, Florian; Rößler, Ulrich K.; Radu, Florin; Abrudan, Radu; Lin, Gungun; Schmidt, Oliver G.; Fischer, Peter; et al
2015-03-05
Topological magnetic states, such as chiral skyrmions, are of great scientific interest and show huge potential for novel spintronics applications, provided their topological charges can be fully controlled. So far skyrmionic textures have been observed in noncentrosymmetric crystalline materials with low symmetry and at low temperatures. We propose theoretically and demonstrate experimentally the design of spin textures with topological charge densities that can be tailored at ambient temperatures. Tuning the interlayer coupling in vertically stacked nanopatterned magnetic heterostructures, such as a model system of a Co/Pd multilayer coupled to Permalloy, the in-plane non-collinear spin texture of one layer can bemore »imprinted into the out-of-plane magnetised material. We observe distinct spin textures, e.g. vortices, magnetic swirls with tunable opening angle, donut states and skyrmion core configurations. We show that applying a small magnetic field, a reliable switching between topologically distinct textures can be achieved at remanence« less
Manipulating topological states by imprinting non-collinear spin textures.
Streubel, Robert; Han, Luyang; Im, Mi-Young; Kronast, Florian; Rößler, Ulrich K; Radu, Florin; Abrudan, Radu; Lin, Gungun; Schmidt, Oliver G; Fischer, Peter; Makarov, Denys
2015-01-01
Topological magnetic states, such as chiral skyrmions, are of great scientific interest and show huge potential for novel spintronics applications, provided their topological charges can be fully controlled. So far skyrmionic textures have been observed in noncentrosymmetric crystalline materials with low symmetry and at low temperatures. We propose theoretically and demonstrate experimentally the design of spin textures with topological charge densities that can be tailored at ambient temperatures. Tuning the interlayer coupling in vertically stacked nanopatterned magnetic heterostructures, such as a model system of a Co/Pd multilayer coupled to Permalloy, the in-plane non-collinear spin texture of one layer can be imprinted into the out-of-plane magnetised material. We observe distinct spin textures, e.g. vortices, magnetic swirls with tunable opening angle, donut states and skyrmion core configurations. We show that applying a small magnetic field, a reliable switching between topologically distinct textures can be achieved at remanence. PMID:25739643
Manipulating Topological States by Imprinting Non-Collinear Spin Textures
Streubel, Robert; Han, Luyang; Im, Mi-Young; Kronast, Florian; Rößler, Ulrich K.; Radu, Florin; Abrudan, Radu; Lin, Gungun; Schmidt, Oliver G.; Fischer, Peter; Makarov, Denys
2015-01-01
Topological magnetic states, such as chiral skyrmions, are of great scientific interest and show huge potential for novel spintronics applications, provided their topological charges can be fully controlled. So far skyrmionic textures have been observed in noncentrosymmetric crystalline materials with low symmetry and at low temperatures. We propose theoretically and demonstrate experimentally the design of spin textures with topological charge densities that can be tailored at ambient temperatures. Tuning the interlayer coupling in vertically stacked nanopatterned magnetic heterostructures, such as a model system of a Co/Pd multilayer coupled to Permalloy, the in-plane non-collinear spin texture of one layer can be imprinted into the out-of-plane magnetised material. We observe distinct spin textures, e.g. vortices, magnetic swirls with tunable opening angle, donut states and skyrmion core configurations. We show that applying a small magnetic field, a reliable switching between topologically distinct textures can be achieved at remanence. PMID:25739643
Manipulating topological states by imprinting non-collinear spin textures
Streubel, Robert; Han, Luyang; Im, Mi -Young; Kronast, Florian; Rößler, Ulrich K.; Radu, Florin; Abrudan, Radu; Schmidt, Oliver G.; Fischer, Peter; Makarov, Denys
2015-03-05
Topological magnetic states, such as chiral skyrmions, are of great scientific interest and show huge potential for novel spintronics applications, provided their topological charges can be fully controlled. So far skyrmionic textures have been observed in noncentrosymmetric crystalline materials with low symmetry and at low temperatures. We propose theoretically and demonstrate experimentally the design of spin textures with topological charge densities that can be tailored at ambient temperatures. Tuning the interlayer coupling in vertically stacked nanopatterned magnetic heterostructures, such as a model system of a Co/Pd multilayer coupled to Permalloy, the in-plane non-collinear spin texture of one layer can be imprinted into the out-of-plane magnetised material. We observe distinct spin textures, e.g. vortices, magnetic swirls with tunable opening angle, donut states and skyrmion core configurations. We show that applying a small magnetic field, a reliable switching between topologically distinct textures can be achieved at remanence
Notes on topological insulators
Dan Li; Ralph M. Kaufmann; Birgit Wehefritz-Kaufmann
2015-06-15
This paper is a survey of the $\\mathbb{Z}/\\mathbb{Z}_2$-valued invariants of topological insulators in condensed matter physics. The $\\mathbb{Z}$-valued topological invariant was originally called the TKNN invariant in physics, which has been fully understood as the first Chern number. The $\\mathbb{Z}_2$ invariant is more mysterious, we will devote our efforts to reviewing its equivalent descriptions from different points of view. We emphasize that both invariants are realizations of some index theorems in condensed matter physics. Topological K-theory also plays an important role in the classification of topological insulators with different symmetries.
Noncommutative localization in topology
Ranicki, Andrew
2003-08-14
The topological applications of the Cohn noncommutative localization considered in this paper deal with spaces (especially manifolds) with infinite fundamental group, and involve localizations of infinite group rings ...
Topological Quantum Computation with the universal R matrix for Ising anyons
Lachezar S. Georgiev
2008-12-12
We show that the braid-group extension of the monodromy-based topological quantum computation scheme of Das Sarma et al. can be understood in terms of the universal R matrix for the Ising model giving similar results to those obtained by direct analytic continuation of multi-anyon Pfaffian wave functions. It is necessary, however, to take into account the projection on spinor states with definite total parity which is responsible for the topological entanglement in the Pfaffian topological quantum computer.
Topology and its Applications 154 (2007) 894907 www.elsevier.com/locate/topol
Mouron, Chris
2007-01-01
Topology and its Applications 154 (2007) 894907 www.elsevier.com/locate/topol Positive entropy on the interval, not much is known about the topology of the inverse limit space. In this paper, entropy such that V U. The original definition of entropy is due to Adler et al. [1]. Let X be a compact metric space
Topological Dynamics of 2D Cellular CiE 2008, Athens
Theyssier, Guillaume
The Onion Skin Trick 5 Research Directions #12;Overview of the talk 1 Cellular Automata 2 Topological Dynamics 3 The Core Construction 4 The Onion Skin Trick 5 Research Directions #12;Definition Syntactical Cellular Automata 2 Topological Dynamics 3 The Core Construction 4 The Onion Skin Trick 5 Research
Supersymmetric black holes with lens-space topology.
Kunduri, Hari K; Lucietti, James
2014-11-21
We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional supergravity. It is regular on and outside an event horizon of lens-space topology L(2,1). It is the first example of an asymptotically flat black hole with lens-space topology. The solution is characterized by a charge, two angular momenta, and a magnetic flux through a noncontractible disk region ending on the horizon, with one constraint relating these. PMID:25479484
Topological aspect of black hole with Skyrme hair
Yi-Shi Duan; Xin-Hui Zhang; Li Zhao
2007-03-19
Based on the $\\phi$-mapping topological current theory, we show that the presence of the black hole leaves fractional baryon charge outside the horizon in the Einstein-Skyrme theory. A topological current is derived from the Einstein-Skyrme system, which corresponds to the monopoles around the black hole. The branch process (splitting, merging and intersection) is simply discussed during the evolution of the monopoles.
Topological black holes in Horava-Lifshitz gravity
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi
2009-07-15
We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature 2k in Horava-Lifshitz theory. Without loss of generality, one may take k=1, 0, and -1. The black hole solution is asymptotically anti-de Sitter with a nonstandard asymptotic behavior. Using the Hamiltonian approach, we define a finite mass associated with the solution. We discuss the thermodynamics of the topological black holes and find that the black hole entropy has a logarithmic term in addition to an area term. We find a duality in Hawking temperature between topological black holes in Horava-Lifshitz theory and Einstein's general relativity: the temperature behaviors of black holes with k=1, 0, and -1 in Horava-Lifshitz theory are, respectively, dual to those of topological black holes with k=-1, 0, and 1 in Einstein's general relativity. The topological black holes in Horava-Lifshitz theory are thermodynamically stable.
Experimental Discovery of Topological Insulators and Related Superconductors
Hasan, M. Zahid
2010-09-15
Most quantum states of condensed matter are categorized by the symmetries they break. The remarkable discovery of charge Quantum Hall effects (1980s) revealed that there exists an organizational principle of matter based only on the topological distinctions, but in the presence of time-reversal symmetry breaking. In the past few years, theoretical developments suggest that new classes of topological states of matter might exist that are purely topological in nature in the sense that they do not break time-reversal symmetry, and hence can be realized without any applied magnetic field: "Quantum Hall-like effects without Magnetic Fields." This talk describes our discovery of new topologically ordered states of matter (topological insulators) and discusses the unusual electro-magnetic, spin, and superconducting properties this novel phase of quantum matter might exhibit and their potential applications.
Twisted gauge theory model of topological phases in three dimensions
NASA Astrophysics Data System (ADS)
Wan, Yidun; Wang, Juven C.; He, Huan
2015-07-01
We propose an exactly solvable lattice Hamiltonian model of topological phases in 3 +1 dimensions, based on a generic finite group G and a 4-cocycle ? over G . We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the 3-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasiexcitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the S L (3 ,Z ) generators as the modular S and T matrices of the ground states, which yield a set of topological quantum numbers classified by ? and quantities derived from ? . Our model fulfills a Hamiltonian extension of the (3 +1 )-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group G . This work is presented to be accessible for a wide range of physicists and mathematicians.
Topological solitons in 8-spinor mie electrodynamics
Rybakov, Yu. P.
2013-10-15
We investigate the effective 8-spinor field model suggested earlier as the generalization of nonlinear Mie electrodynamics. We first study in pure spinorial model the existence of topological solitons endowed with the nontrivial Hopf invariant Q{sub H}, which can be interpreted as the lepton number. Electromagnetic field being included as the perturbation, we estimate the energy and the spin of the localized charged configuration.
Topological Phase Transition without Gap Closing
Ezawa, Motohiko; Tanaka, Yukio; Nagaosa, Naoto
2013-01-01
Topological phase transition is accompanied with a change of topological numbers. According to the bulk-edge correspondence, the gap closing and the breakdown of the adiabaticity are necessary at the phase transition point to make the topological number ill-defined. However, the gap closing is not always needed. In this paper, we show that two topological distinct phases can be continuously connected without gap closing, provided the symmetry of the system changes during the process. Here we propose the generic principles how this is possible by demonstrating various examples such as 1D polyacetylene with the charge-density-wave order, 2D silicene with the antiferromagnetic order, 2D silicene or quantum well made of HgTe with superconducting proximity effects and 3D superconductor Cu doped Bi2Se3. It is argued that such an unusual phenomenon can occur when we detour around the gap closing point provided the connection of the topological numbers is lost along the detour path. PMID:24071900
Comprehensible Presentation of Topological Information
Weber, Gunther H.
2013-01-01
applications in other topological data analysis settings.based on topological analysis over a data set. Contours, theTopological information has proven very valuable in the analysis of scientific data.
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2013 CFR
2013-01-01
... by law on a time deposit used as security for an extension of credit. (7) Real-estate related fees... 12 Banks and Banking 3 2013-01-01 2013-01-01 false Finance charge. 226.4 Section 226.4 Banks and...) TRUTH IN LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge...
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2012 CFR
2012-01-01
... deposit used as security for an extension of credit. (7) Real-estate related fees. The following fees in a... 12 Banks and Banking 3 2012-01-01 2012-01-01 false Finance charge. 226.4 Section 226.4 Banks and... LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is the cost...
12 CFR 1026.4 - Finance charge.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 12 Banks and Banking 9 2014-01-01 2014-01-01 false Finance charge. 1026.4 Section 1026.4 Banks and Banking BUREAU OF CONSUMER FINANCIAL PROTECTION TRUTH IN LENDING (REGULATION Z) § 1026.4 Finance charge. (a) Definition. The finance charge is the cost of consumer credit as a dollar amount. It includes...
A Battery Charger and State of Charge Indicator
NASA Technical Reports Server (NTRS)
Latos, T. S.
1984-01-01
A battery charger which has a full wave rectifier in series with a transformer isolated 20 kHz dc-dc converter with high frequency switches, which are programmed to actively shape the input dc line current to be a mirror image of the ac line voltage is discussed. The power circuit operates at 2 kW peak and 1 kW average power. The BC/SCI has two major subsystems: (1) the battery charger power electronics with its controls; and (2) a microcomputer subsystem which is used to acquire battery terminal data and exercise the state of charge software programs. The state of charge definition employed is the energy remaining in the battery when extracted at a 10 kW rate divided by the energy capacity of a fully charged new battery. The battery charger circuit is an isolated boost converter operating at an internal frequency of 20 kHz. The switches selected for the battery charger are the single most important item in determining its efficiency. The combination of voltage and current requirements dictate the use of high power NPN Darlington switching transistors. The power circuit topology is a three switch design which utilizes a power FET on the center tap of the isolation transformer and the power Darlingtons on each of the two ends. An analog control system is employed to accomplish active input current waveshaping as well as the necessary regulation.
Battery charger and state of charge indicator. Final report
Latos, T.S.
1984-04-15
The battery charger has a full-wave rectifier in series with a transformer isolated 20 kHz dc-dc converter with high frequency switches which are programmed to actively shape the input ac line current to be a mirror image of the ac line voltage. The power circuit is capable of operating at 2 kW peak and 1 kW average power. The BC/SCI has two major subsystems: (1) the battery charger power electronics with its controls; and (2) a microcomputer subsystem which is used to acquire battery terminal data and exercise the state-of-charge software programs. The state-of-charge definition employed is the energy remaining in the battery when extracted at a 10 kW rate divided by the energy capacity of a fully charged new battery. The battery charger circuit is an isolated boost converter operating at an internal frequency of 20 kHz. The switches selected for the battery charger are the single most important item in determining its efficiency. The combination of voltage and current requirements dictated the use of high power NPN Darlington switching transistors. The power circuit topology developed is a three switch design utilizing a power FET on the center tap of the isolation transformer and the power Darlingtons on each of the two ends. An analog control system is employed to accomplish active input current waveshaping as well as the necessary regulation.
Topological currents in black phosphorus with broken inversion symmetry
Low, Tony; Guinea, Francisco
2015-01-01
We examine the nature of topological currents in black phosphorus when its inversion symmetry is deliberately broken. Here, the conduction and valence band edges are located at the $\\Gamma$ point of the rectangular Brillouin zone, and they exhibit strong anisotropy along its two crystal axes. We will show below that these salient features lead to a linear transverse neutral topological currents, accompanied also by a non-linear transverse charge current at the Fermi surface. These topological currents are maximal when the in-plane electric field is applied along the zigzag crystal axes, but zero along the armchair direction.
1996-07-01
The time dependence of B{sub d}{sup 0}-B{sub d}{sup 0} mixing has been measured using a sample of 150,000 hadronic Z{sup 0} decays collected by the SLD experiment at the SLC between 1993 and 1995. The analysis identifies the semileptonic decays of B mesons with high (p, p{sub t}) leptons and reconstructs the B meson decay length and charge by vertexing the lepton with a partially reconstructed D meson. Vertex charge is used to enrich the selection of neutral over charged B mesons. This method results in a sample of 581 neutral decays with high charge purity. The B candidate is tagged at production with a combined tag that exploits the large polarized b forward-backward asymmetry in conjunction with the opposite hemisphere b jet charge. The final state is tagged by the sign of the high (p, p{sub t}) lepton. From their preliminary analysis the authors find a mass difference between the two B{sub d}{sup 0} mass eigenstates of, {Delta}m{sub d} = 0.452 {+-} 0.074(stat) {+-} 0.049(syst) ps{sup {minus}1}.
Petkova, V. B.
2013-10-15
Areview of the notion, properties and the use of topological defects in 2d conformal field theories is presented. An emphasis is made on the recent interpretation of such operators in non-rational theories, as describing Wilson-'t Hooft loop operators of N = 2 supersymmetric 4d topological theories.
Mirkin, Sergei
DNA Topology: Fundamentals Sergei M Mirkin, University of Illinois at Chicago, Illinois, USA Topological characteristics of DNA and specifically DNA supercoiling influence all major DNA transactions in living cells. DNA supercoiling induces the formation of unusual secondary structure by specific DNA
Topological Quantum Distillation
H. Bombin; M. A. Martin-Delgado
2007-03-29
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits. This allows us to extend their application also to quantum teleportation, dense coding and computation with magic states.
Topological color code and symmetry-protected topological phases
NASA Astrophysics Data System (ADS)
Yoshida, Beni
2015-06-01
We study (d -1 ) -dimensional excitations in the d -dimensional color code that are created by transversal application of the Rd phase operators on connected subregions of qubits. We find that such excitations are the superpositions of electric charges and can be characterized by the fixed-point wave functions of (d -1 ) -dimensional bosonic symmetry-protected topological (SPT) phases with (Z2) ?d symmetry. While these SPT excitations are localized on (d -1 ) -dimensional boundaries, their creation requires operations acting on all qubits inside the boundaries, reflecting the nontriviality of emerging SPT wave functions. Moreover, these SPT excitations can be physically realized as transparent gapped domain walls which exchange excitations in the color code. Namely, in the three-dimensional color code, the domain wall, associated with the transversal R3 operator, exchanges a magnetic flux and a composite of a magnetic flux and the looplike SPT excitation, revealing rich possibilities of boundaries in higher-dimensional TQFTs. We also find that magnetic fluxes and the looplike SPT excitations exhibit nontrivial three-loop braiding statistics in three dimensions as a result of the fact that the R3 phase operator belongs to the third level of the Clifford hierarchy. We believe that the connection between SPT excitations, fault-tolerant logical gates and gapped domain walls, established in this paper, can be generalized to a large class of topological quantum codes and TQFTs.
Tunable topological phononic crystals
Chen, Ze-Guo
2015-01-01
Topological insulators, first observed in electronic systems, have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial bandgaps. Such bandgaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that is verified by the Chern number calculation and edge mode analysis. The topology of the bandgap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.
NASA Technical Reports Server (NTRS)
Hunt, W. D.; Brennan, K. F.; Summers, C. J.; Cameron, Thomas P.
1996-01-01
This thesis addresses the acoustoelectric issues concerning the amplification of surface acoustic waves (SAWs) and the reflection of SAWs from slanted reflector gratings on GaAs, with application to a novel acoustic charge transport (ACT) device architecture. First a simple model of the SAWAMP was developed, which was subsequently used to define the epitaxially grown material structure necessary to provide simultaneously high resistance and high electron mobility. In addition, a segmented SAWAMP structure was explored with line widths on the order of an acoustic wavelength. This resulted in the demonstration of SAWAMPS with an order of magnitude less voltage and power requirements than previously reported devices. A two-dimensional model was developed to explain the performance of devices with charge confinement layers less then 0.5 mm, which was experimentally verified. This model was extended to predict a greatly increased gain from the addition of a ZnO overlay. These overlays were experimentally attempted, but no working devices were reported due to process incompatibilities. In addition to the SAWAMP research, the reflection of SAWs from slanted gratings on GaAs was also studied and experimentally determined reflection coefficients for both 45 deg grooves and Al stripes on GaAs have been reported for the first time. The SAWAMp and reflector gratings were combined to investigate the integrated ring oscillator for application to the proposed ACT device and design parameters for this device have been provided.
Algebraic Ktheory of rings from a topological viewpoint Dominique Arlettaz
the basic definitions of the algebraic KÂtheory of rings and an overview of the main classical theorems developments p. 53 References p. 54 0. Introduction Algebraic KÂtheory is a relatively new mathematical domain is familiar with the basic notions and results in algebraic topology, homotopy theory and homological algebra
Topological solitons in helical strings.
Nisoli, Cristiano; Balatsky, Alexander V
2015-06-01
The low-energy physics of (quasi)degenerate one-dimensional systems is typically understood as the particle-like dynamics of kinks between stable, ordered structures. Such dynamics, we show, becomes highly nontrivial when the ground states are topologically constrained: a dynamics of the domains rather than on the domains which the kinks separate. Motivated by recently reported observations of charged polymers physio-adsorbed on nanotubes, we study kinks between helical structures of a string wrapping around a cylinder. While their motion cannot be disentangled from domain dynamics, and energy and momentum is not concentrated in the solitons, the dynamics of the domains can be folded back into a particle-like description of the local excitations. PMID:26172728
Polydispersity-driven topological defects as order-restoring excitations
Yao, Zhenwei; Olvera de la Cruz, Monica
2014-01-01
The engineering of defects in crystalline matter has been extensively exploited to modify the mechanical and electrical properties of many materials. Recent experiments on manipulating extended defects in graphene, for example, show that defects direct the flow of electric charges. The fascinating possibilities offered by defects in two dimensions, known as topological defects, to control material properties provide great motivation to perform fundamental investigations to uncover their role in various systems. Previous studies mostly focus on topological defects in 2D crystals on curved surfaces. On flat geometries, topological defects can be introduced via density inhomogeneities. We investigate here topological defects due to size polydispersity on flat surfaces. Size polydispersity is usually an inevitable feature of a large variety of systems. In this work, simulations show well-organized induced topological defects around an impurity particle of a wrong size. These patterns are not found in systems of identical particles. Our work demonstrates that in polydispersed systems topological defects play the role of restoring order. The simulations show a perfect hexagonal lattice beyond a small defective region around the impurity particle. Elasticity theory has demonstrated an analogy between the elementary topological defects named disclinations to electric charges by associating a charge to a disclination, whose sign depends on the number of its nearest neighbors. Size polydispersity is shown numerically here to be an essential ingredient to understand short-range attractions between like-charge disclinations. Our study suggests that size polydispersity has a promising potential to engineer defects in various systems including nanoparticles and colloidal crystals. PMID:24706918
48 CFR 252.239-7005 - Rates, charges, and services.
Code of Federal Regulations, 2011 CFR
2011-10-01
...Rates, charges, and services. As prescribed...Rates, Charges, and Services (NOV 2005) (a) Definition —Governmental...shall furnish the services and facilities under...offered to any other customer. (e)...
48 CFR 252.239-7005 - Rates, charges, and services.
Code of Federal Regulations, 2010 CFR
2010-10-01
...Rates, charges, and services. As prescribed...Rates, Charges, and Services (NOV 2005) (a) Definition —Governmental...shall furnish the services and facilities under...offered to any other customer. (e)...
Topological Inflation in Supergravity
Kawasaki, M; Yamaguchi, M; Yanagida, T; Sakai, Nobuyuki; Yamaguchi, Masahide
2000-01-01
We investigate a topological inflation model in supergravity. By means of numerical simulations, it is confirmed that topological inflation really takes place in supergravity. We also show that the condition for successful inflation depends not only on the vacuum-expectation value (VEV) of inflaton field but also on the form of its K\\"ahler potential. In fact, it is found that the required VEV of the inflaton $\\phi$ can be as small as $ \\simeq 1 \\times M_G$, where $M_{G}$ is the gravitational scale. This observation makes the topological inflation model more attractive.
The Cardy-Verlinde formula and entropy of Topological Kerr-Newman black holes in de Sitter spaces
M. R. Setare; M. B. Altaie
2003-07-19
In this paper we show that the entropy of cosmological horizon in 4-dimensional Topological Kerr-Newman-de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. Furthermore, we find that the entropy of black hole horizon can also be rewritten in terms of the Cardy-Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. Such result presume a well-defined dS/CFT correspondence, which has not yet attained the credibility of its AdS analogue.
Quantum Circuit Model Topological Model
Rowell, Eric C.
Quantum Circuit Model Topological Model Comparison of Models Topological Quantum Computation Eric Rowell Texas A&M University October 2010 Eric Rowell Topological Quantum Computation #12;Quantum Circuit Model Topological Model Comparison of Models Outline 1 Quantum Circuit Model Gates, Circuits
Topology of three-dimensional separated flows
NASA Technical Reports Server (NTRS)
Tobak, M.; Peake, D. J.
1981-01-01
Based on the hypothesis that patterns of skin-friction lines and external streamlines reflect the properties of continuous vector fields, topology rules define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane). The restricted number of singular points and the rules that they obey are considered as an organizing principle whose finite number of elements can be combined in various ways to connect together the properties common to all steady three dimensional viscous flows. Introduction of a distinction between local and global properties of the flow resolves an ambiguity in the proper definition of a three dimensional separated flow. Adoption of the notions of topological structure, structural stability, and bifurcation provides a framework to describe how three dimensional separated flows originate and succeed each other as the relevant parameters of the problem are varied.
Axion field theory approach and the classification of interacting topological superconductors
Yingfei Gu; Xiao-Liang Qi
2015-12-15
In this paper, we discuss the topological classification of time-reversal invariant topological superconductors. Based on the axion field theory developed in a previous work (Phys. Rev. B ${\\bf 87}$ 134519 (2013)), we show how a simple quantum anomaly in vortex-crossing process predicts a $\\mathbb{Z}_{16}$ classification of interacting topological superconductors, in consistency with other approaches. We also provide a general definition of the quantum anomaly and a general geometric argument that explains the $\\mathbb{Z}_{16}$ on more general grounds. Furthermore, we generalize our approach to all $4n$ dimensions (with $n$ an integer), and compare our results with other approaches to the topological classification.
Winding numbers of phase transition points for one-dimensional topological systems
NASA Astrophysics Data System (ADS)
Li, Linhu; Yang, Chao; Chen, Shu
2015-10-01
We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter, which overcomes the problem of ill definition of winding numbers on the transition points. By applying our scheme to the extended Kitaev model and to the extended Su-Schrieffer-Heeger model, we demonstrate that the topological phase transition can be well characterized by winding numbers of transition points, which reflect the change of the winding number of topologically different phases across the phase transition points.
Axion field theory approach and the classification of interacting topological superconductors
Gu, Yingfei
2015-01-01
In this paper, we discuss the topological classification of time-reversal invariant topological superconductors. Based on the axion field theory developed in a previous work (Phys. Rev. B ${\\bf 87}$ 134519 (2013)), we show how a simple quantum anomaly in vortex-crossing process predicts a $\\mathbb{Z}_{16}$ classification of interacting topological superconductors, in consistency with other approaches. We also provide a general definition of the quantum anomaly and a general geometric argument that explains the $\\mathbb{Z}_{16}$ on more general grounds. Furthermore, we generalize our approach to all $4n$ dimensions (with $n$ an integer), and compare our results with other approaches to the topological classification.
Electrically tunable surface-to-bulk coherent coupling in topological insulator thin films
Steinberg, Hadar
We study coherent electronic transport in charge-density-tunable microdevices patterned from thin films of the topological insulator (TI) Bi[subscript 2]Se[subscript 3]. The devices exhibit pronounced electric field effect, ...
NASA Astrophysics Data System (ADS)
Xu, B.; Jiang, W. S.; Zhu, Q. S.
2015-05-01
In this work, we concentrate on the hierarchy and completeness of roof topology, and the aim is to avoid or correct the errors in roof topology. The hierarchy of topology is expressed by the hierarchical roof topology graph (HRTG) in accord with the definition of CityGML LOD (level of details). We decompose the roof topology graph (RTG) with a progressive approach while maintain the integrality and consistency of the data set simultaneously. Common feathers like collinear ridges or boundaries are calculated integrally to maintain their completeness. The roof items will only detected locally to decrease the error caused by data spare or mutual interference. Finally, a topology completeness test is adopted to detect and correct errors in roof topology, which results in a complete and hierarchical building model. Experiments shows that our methods have obvious improvements to the RTG based reconstruction method, especially for sparse data or roof topology with ambiguous.
Electro-Magnetic Waves within a Model for Charged Solitons
Dmitry Borisyuk; Manfried Faber; Alexander Kobushkin
2007-08-23
We analyze the model of topological fermions (MTF), where charged fermions are treated as soliton solutions of the field equations. In the region far from the sources we find plane waves solutions with the properties of electro-magnetic waves.
42 CFR 405.509 - Determining the inflation-indexed charge.
Code of Federal Regulations, 2010 CFR
2010-10-01
...2010-10-01 false Determining the inflation-indexed charge. 405.509... § 405.509 Determining the inflation-indexed charge. (a) Definition. For purposes of this section, inflation-indexed charge means...
Layered Topological Crystalline Insulators.
Kim, Youngkuk; Kane, C L; Mele, E J; Rappe, Andrew M
2015-08-21
Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the interlayer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) (?1,?2) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) monolayer/h-BN heterostructure and can be tuned by mechanical strain. Our results shed light on the role of the MCNs on inequivalent mirror-symmetric planes in reciprocal space and open new possibilities for finding new topological materials. PMID:26340198
Layered Topological Crystalline Insulators
NASA Astrophysics Data System (ADS)
Kim, Youngkuk; Kane, C. L.; Mele, E. J.; Rappe, Andrew M.
2015-08-01
Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the interlayer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) (?1,?2 ) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) monolayer/h -BN heterostructure and can be tuned by mechanical strain. Our results shed light on the role of the MCNs on inequivalent mirror-symmetric planes in reciprocal space and open new possibilities for finding new topological materials.
50 CFR 1.5 - Officer in Charge.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 50 Wildlife and Fisheries 1 2010-10-01 2010-10-01 false Officer in Charge. 1.5 Section 1.5 Wildlife and Fisheries UNITED STATES FISH AND WILDLIFE SERVICE, DEPARTMENT OF THE INTERIOR GENERAL PROVISIONS DEFINITIONS § 1.5 Officer in Charge. Officer in Charge means any person in charge of a national fish hatchery, national wildlife refuge,...
A Proposed Definition of Functional Integrals
J. LaChapelle
2015-01-07
Functional integrals are defined in terms of families of locally compact topological groups and their associated Banach-valued Haar integrals. The definition abandons the hope of defining a genuine measure on the integral domain, and instead gives a topological realization of localization in the integral domain leading to measurable subspaces that characterize meaningful functional integrals. The proposed definition is natural in the sense that it includes other successful approaches to functional integrals within a broader framework. In turn, the framework suggests new and potentially useful functional integrals.
NASA Astrophysics Data System (ADS)
Budich, Jan Carl; Diehl, Sebastian
2015-04-01
We investigate the topological properties of density matrices, motivated by the question to what extent phenomena such as topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The notion of geometric phases has been extended from pure to mixed states by Uhlmann [Rep. Math. Phys. 24, 229 (1986), 10.1016/0034-4877(86)90055-8], who discovered an emergent gauge theory over the density matrices based on their pure state representation in a larger Hilbert space. However, since the uniquely defined square root ?{? } of a density matrix ? provides a global gauge, this construction is always topologically trivial. Here, we study a more restrictive gauge structure which can be topologically nontrivial and is capable of resolving homotopically distinct mappings of density matrices subject to various spectral constraints. Remarkably, in this framework, topological invariants can be directly defined and calculated for mixed states. In the limit of pure states, the well-known system of topological invariants for gapped band structures at zero temperature is reproduced. We compare our construction with recent approaches to Chern insulators at finite temperature.
Topological solitons in the noncommutative plane and quantum Hall Skyrmions
Ezawa, Z.F.; Tsitsishvili, G.
2005-10-15
We analyze topological solitons in the noncommutative plane by taking a concrete instance of the quantum Hall system with the SU(N) symmetry, where a soliton is identified with a Skyrmion. It is shown that a topological soliton induces an excitation of the electron number density from the ground-state value around it. When a judicious choice of the topological charge density J{sub 0}(x) is made, it acquires a physical reality as the electron density excitation {delta}{rho}{sup cl}(x) around a topological soliton, {delta}{rho}{sup cl}(x)=-J{sub 0}(x). Hence a noncommutative soliton carries necessarily the electric charge proportional to its topological charge. A field-theoretical state is constructed for a soliton state irrespectively of the Hamiltonian. In general, it involves an infinitely many parameters. They are fixed by minimizing its energy once the Hamiltonian is chosen. We study explicitly the cases where the system is governed by the hard-core interaction and by the noncommutative CP{sup N-1} model, where all these parameters are determined analytically and the soliton excitation energy is obtained.
Seeing the magnetic monopole through the mirror of topological surface states
Qi, Xiao-Liang; Li, Rundong; Zang, Jiadong; Zhang, Shou-Cheng; /Stanford U., Phys. Dept. /Fudan U.
2010-03-25
Existence of the magnetic monopole is compatible with the fundamental laws of nature, however, this illusive particle has yet to be detected experimentally. In this work, we show that an electric charge near the topological surface state induces an image magnetic monopole charge due to the topological magneto-electric effect. The magnetic field generated by the image magnetic monopole can be experimentally measured, and the inverse square law of the field dependence can be determined quantitatively. We propose that this effect can be used to experimentally realize a gas of quantum particles carrying fractional statistics, consisting of the bound states of the electric charge and the image magnetic monopole charge.
Combinational Reasoning of Quantitative Fuzzy Topological Relations for Simple Fuzzy Regions
Liu, Bo; Li, Dajun; Xia, Yuanping; Ruan, Jian; Xu, Lili; Wu, Huanyi
2015-01-01
In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models. PMID:25775452
A short overview of the "Topological recursion"
B. Eynard
2014-12-12
This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall how computing large size asymptotics in random matrices, has allowed to discover some fascinating and ubiquitous geometric invariants. Specializations of this method recover many classical invariants, like Gromov--Witten invariants, or knot polynomials (Jones, HOMFLY,...). In this short review, we give some examples, give definitions, and review some properties and applications of the formalism.
Evidence for Tadpole Cancellation in the Topological String
Johannes Walcher
2009-02-04
We study the topological string on compact Calabi-Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a BPS expansion only if the topological charge of the D-brane is equal to that of the orientifold plane. We interpret this as a manifestation of a general tadpole cancellation condition in the topological string that is necessary for decoupling of A- and B-model in loop amplitudes. Our calculations in the A-model involve an adapted version of existing localization techniques, and give predictions for the real enumerative geometry of higher genus curves in Calabi-Yau manifolds. In the B-model, we introduce an extension of the holomorphic anomaly equation to unoriented strings.
Positive topological entropy for multi-bump magnetic fields
Andreas Knauf; Frank Schulz; Karl Friedrich Siburg
2012-08-27
We study the dynamics of a charged particle in a planar magnetic field which consists of $n\\geq 2$ disjoint localized peaks. We show that, under mild geometric conditions, this system is semi-conjugated to the full shift on $n$ symbols and, hence, carries positive topological entropy.
Pair Production of Topological anti de Sitter Black Holes
R. B. Mann
1996-07-28
The pair creation of black holes with event horizons of non-trivial topology is described. The spacetimes are all limiting cases of the cosmological $C$ metric. They are generalizations of the $(2+1)$ dimensional black hole and have asymptotically anti de Sitter behaviour. Domain walls instantons can mediate their pair creation for a wide range of mass and charge.
Unusual spin dynamics in topological insulators.
Dóra, Balázs; Simon, Ferenc
2015-01-01
The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form around the Zeeman energy in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC, and the anisotropy of the DSS reveals the orientation of the underlying spin texture of topological states. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as ?(d-1) with d?=?2 and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as d?=?2K?-?1 with K the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems. PMID:26439629
Unusual spin dynamics in topological insulators
Dóra, Balázs; Simon, Ferenc
2015-01-01
The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form around the Zeeman energy in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC, and the anisotropy of the DSS reveals the orientation of the underlying spin texture of topological states. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as ?d?1 with d?=?2 and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as d?=?2K???1 with K the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems. PMID:26439629
Topological Insulators Avoid the Parity Anomaly
Michael Mulligan; F. J. Burnell
2013-01-17
The surface of a 3+1d topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2+1d system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field. Here we explain why such a state can exist on the boundary of a 3+1d system without breaking these symmetries, even if the number of boundary components is odd. This is accomplished from two complementary perspectives: topological quantization conditions and regularization. We first discuss the conditions under which (continuous) large gauge transformations may exist when the theory lives on a boundary of a higher-dimensional spacetime. Next, we show how the higher-dimensional bulk theory is essential in providing a parity-invariant regularization of the theory living on the lower-dimensional boundary or defect.
Unusual spin dynamics in topological insulators
NASA Astrophysics Data System (ADS)
Dóra, Balázs; Simon, Ferenc
2015-10-01
The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form around the Zeeman energy in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC, and the anisotropy of the DSS reveals the orientation of the underlying spin texture of topological states. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as ?d-1 with d?=?2 and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as d?=?2K?-?1 with K the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems.
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2013-10-01
The valley Chern and spin-valley Chern numbers are the key concepts in valleytronics. They are topological numbers in the Dirac theory but not in the tight-binding model. We analyze the bulk-edge correspondence between the two phases which have the same Chern and spin-Chern numbers but different valley Chern and spin-valley Chern numbers. Though the edge state between them is topologically trivial in the tight-binding model, it is shown to be as robust as the topological one both for zigzag and armchair edges. We construct Y-junctions made of topological edges. They satisfy the topological Kirchhoff law, where the topological charges are conserved at the junction. We may interpret a Y-junction as a scattering process of particles which have four topological numbers. It would be a milestone of future topological electronics.
Topology Matters: Network topology affects outcomes from community ecology neutral models
Jenny, Bernhard
Topology Matters: Network topology affects outcomes from community ecology neutral models Denis topology for neutral ecology community models, following the simulation approach of Graham Bell of these topologies on model outcomes. Key Words: neutral model, community ecology, topology, simulation model
Monopole content of topological clusters: Have Kraan-van Baal calorons been found?
NASA Astrophysics Data System (ADS)
Ilgenfritz, E.-M.; Martemyanov, B. V.; Müller-Preussker, M.; Veselov, A. I.
2005-02-01
Using smearing of equilibrium lattice fields generated at finite temperature in the confined phase of SU(2) lattice gauge theory, we have investigated the emerging topological objects (clusters of topological charge). Analyzing their monopole content according to the Polyakov gauge and the maximally Abelian gauge, we characterize part of them to correspond to nonstatic calorons or static dyons in the context of Kraan-van Baal caloron solutions with nontrivial holonomy. The behavior of the Polyakov loop inside these clusters and the (model-dependent) topological charges of these objects support this interpretation.
Detectability of Torus Topology
NASA Astrophysics Data System (ADS)
Fabre, Ophélia; Prunet, Simon; Uzan, Jean-Philippe
2014-05-01
The global shape, or topology, of the universe is not constrained by the equations of General Relativity, which only describe the local universe. As a consequence, the boundaries of space are not fixed and topologies different from the trivial infinite Euclidean space are possible. The cosmic microwave background (CMB) is the most efficient tool to study topology and test alternative models. Multi-connected topologies, such as the 3-torus, are of great interest because they are anisotropic and allow us to test a possible violation of isotropy in CMB data. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature. This signature can be used to distinguish an infinite space from a multi-connected space on sizes larger than the diameter of the last scattering surface (D LSS ). With the help of the Kullback-Leibler divergence, we set the size of the edge of the biggest distinguishable torus with CMB temperature fluctuations and E-modes of polarization to 1.15 D LSS . CMB temperature fluctuations allow us to detect universes bigger than the observable universe, whereas E-modes are efficient to detect universes smaller than the observable universe.
LHCb Topological Trigger Reoptimization
Tatiana Likhomanenko; Philip Ilten; Egor Khairullin; Alex Rogozhnikov; Andrey Ustyuzhanin; Michael Williams
2015-10-02
The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. Methods studied include cascading, ensembling and blending techniques. Furthermore, novel boosting techniques have been implemented that will help reduce systematic uncertainties in Run 2 measurements. We demonstrate that the reoptimized topological trigger is expected to significantly improve on the Run 1 performance for a wide range of b-hadron decays.
1. Theory of CW-Complexes 1. Definitions.
Johannson, Klaus
1. Theory of CW-Complexes 1. Definitions. A CW-complex is a topological space which is the disjoint unions of open cells * *(= spaces homeomorphic to the n-ball { x 2 Rn+1 | |x| 1 }). This definition is intuiti* *ve. However, it is not good enough. For instance, it does not describe a unique
Topological Defects in Cosmology
Alejandro Gangui
2001-10-11
Topological defects are ubiquitous in condensed-matter physics but only hypothetical in the early universe. In spite of this, even an indirect evidence for one of these cosmic objects would revolutionize our vision of the cosmos. We give here an introduction to the subject of cosmic topological defects and their possible observable signatures. Beginning with a review of the basics of general defect formation and evolution, we then focus on mainly two topics in some detail: conducting strings and vorton formation, and some specific imprints in the cosmic microwave background radiation from simulated cosmic strings.
Charged Cylindrical Black Holes in Conformal Gravity
Jackson Levi Said; Joseph Sultana; Kristian Zarb Adami
2013-01-04
Considering cylindrical topology we present the static solution for a charged black hole in conformal gravity. We show that unlike the general relativistic case there are two different solutions, both including a factor that when set to zero recovers the familiar static charged black string solution in Einstein's theory. This factor gives rise to a linear term in the potential that also features in the neutral case and may have significant ramifications for particle trajectories.
Topological Structure in Visual Perception.
ERIC Educational Resources Information Center
Chen, L.
1982-01-01
Three experiments on tachistoscopic perception of visual stimuli demonstrate that the visual system is sensitive to global topological properties. The results indicate that extraction of global topological properties is a basic factor in perceptual organization. (Author)
Adiabatic Preparation of Topological Order
NASA Astrophysics Data System (ADS)
Hamma, Alioscia; Lidar, Daniel
2007-03-01
Topological order characterizes those phases of matter that defy the standard description in terms of symmetry breaking and local order parameters. Topological order is found in nature in the fractional quantum Hall effect. Topologically ordered systems have ground state degeneracy that is robust against perturbations, which has given the root to topological quantum information processing. We discusss the second order quantum phase transition between a spin-polarized phase and a topologically ordered string-net condensed phase. Next we show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by O(?n). This provides a physically plausible method for constructing a topological quantum memory. We discuss applications to topological and adiabatic quantum computing.
Geometry-Preserving Topological Landscapes
Beketayev, Kenes
2014-01-01
topological landscape. We demonstrate the use of our technique in case of performance data analysis.topological landscapes; the capability to com- pare several functions via their landscapes; and an example appli- cation in performance data analysis.
Topological Quantum Computing Jacob Colbert
Rosner, Jonathan L.
Topological Quantum Computing Jacob Colbert 3/5/2011 Contents 1 Introduction 1 2 Typical Quantum Computing 2 2.1 What is Quantum Computing? . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Quantum Error Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4 Topological Quantum Computing
Topological insulators with SU(2) Landau levels
Yi Li; Shou-Cheng Zhang; Congjun Wu
2013-10-23
We construct continuum models of 3D and 4D topological insulators by coupling spin-1/2 fermions to an SU(2) background gauge field, which is equivalent to a spatially dependent spin-orbit coupling. Higher dimensional generalizations of flat Landau levels are obtained in the Landau-like gauge. The 2D helical Dirac modes with opposite helicities and 3D Weyl modes with opposite chiralities are spatially separated along the third and fourth dimensions, respectively. Stable 2D helical Fermi surfaces and 3D chiral Fermi surfaces appear on open boundaries, respectively. The charge pumping in 4D Landau level systems shows quantized 4D quantum Hall effect.
Topological Catastrophe and Isostructural Phase Transition in Calcium
NASA Astrophysics Data System (ADS)
Jones, Travis E.; Eberhart, Mark E.; Clougherty, Dennis P.
2010-12-01
We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find, at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C' elastic modulus of fcc Ca, while C44 remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure.
Topology of Document Retrieval Systems.
ERIC Educational Resources Information Center
Everett, Daniel M.; Cater, Steven C.
1992-01-01
Explains the use of a topological structure to examine the closeness between documents in retrieval systems and analyzes the topological structure of a vector-space model, a fuzzy-set model, an extended Boolean model, a probabilistic model, and a TIRS (Topological Information Retrieval System) model. Proofs for the results are appended. (17…
Topological censorship and chronology protection
John L. Friedman; Atsushi Higuchi
2008-06-03
Over the past two decades, substantial efforts have been made to understand the way in which physics enforces the ordinary topology and causal structure that we observe, from subnuclear to cosmological scales. We review the status of topological censorship and the topology of event horizons; chronology protection in classical and semiclassical gravity; and related progress in establishing quantum energy inequalities.
Multiple Dirac fermions from a topological insulator and graphene superlattice
NASA Astrophysics Data System (ADS)
Jin, Hosub; Im, Jino; Song, Jung-Hwan; Freeman, Arthur J.
2012-01-01
Graphene and three-dimensional topological insulators are well-known Dirac materials whose bulk and surface states are governed by Dirac equations. They not only show good transport properties but also carry various quanta related to the geometrical phase such as charge, spin, and valley Hall conductances. Therefore, it is a great challenge to combine the two Dirac materials together, realizing multiple Dirac fermions. By using first-principles density-functional-theory calculations, we demonstrate such a system built from topological insulator-band insulator-graphene superlattice structures. Hexagonal boron nitride is proposed as an ideal band-insulating material in gluing graphene and topological insulators, providing a good substrate for graphene and a sharp interface with a topological insulator. The power factors for p-type doping are largely enhanced due to the charge-conducting channels through multiple Dirac cones. The systems characterized by the coexistence of the topologically protected interfacial and graphene Dirac cones can pave the way for developing integrated devices for electronics, spintronics and valleytronics applications.
Topological order in interacting one-dimensional Bose Systems
NASA Astrophysics Data System (ADS)
Grusdt, Fabian; Höning, Michael; Fleischhauer, Michael
2015-05-01
We discuss topological aspects of one-dimensional inversion-symmetric systems of interacting bosons, which can be implemented in current experiments with ultra cold atoms. We consider both integer and fractional fillings of a topologically non-trivial Bloch band. Our starting point is the chiral-symmetric Su-Schrieffer-Heeger (SSH) model of non-interacting fermions, which can be realized by hard-core bosons. When the hard-core constraint is removed, we obtain a bosonic system with inversion-symmetry protected topological order. Because the chiral symmetry is broken by finite interactions, the bulk-boundary correspondence of the SSH model is no longer valid. Nevertheless we show that the fractional part of the charge which is localized at the edge can distinguish topologically trivial- from non-trivial states. We generalize our analysis by including nearest neighbor interactions and present a topological classification of the resulting quarter-filling Mott insulating phase. In this case fractionally charged bulk excitations exist, which we identify in the grand-canonical phase diagram. F.G. acknowledges support from the Graduate School of Material Science MAINZ.
Clarke, John
1980-09-01
The purpose of this article is to review the theory of charge imbalance, and to discuss its relevance to a number of experimental situations. We introduce the concepts of quasiparticle charge and charge imbalance, and discuss the generation and detection of charge imbalance by tunneling. We describe the relaxation of the injected charge imbalance by inelastic scattering processes, and show how the Boltzmann equation can be solved to obtain the steady state quasiparticle distribution and the charge relaxation rate. Details are given of experiments to measure charge imbalance and the charge relaxation rate when inelastic scattering is the predominant relaxation mechanism. Experiments on and theories of other charge relaxation mechanisms are discussed, namely relaxation via elastic scattering in the presence of energy gap anisotropy, or in the presence of a pair breaking mechanism such as magnetic impurities or an applied supercurrent or magnetic field. We describe three other situations in which charge imbalance occurs, namely the resistance of the NS interface, phase slip centers, and the flow of a supercurrent in the presence of a temperature gradient.
Fractional charge in a nut-shell
NASA Astrophysics Data System (ADS)
Boyanovsky, D.; Blankenbecler, R.
1985-04-01
We study the physics of charge fractionalization using simple methods. The strategy is to count the number of states of the theory with solitons relative to the same theory with trivial background fields. The interplay between high and low energy contributions is exposed and the topological properties clarified.
Internet Topology Benoit Donnet
Bonaventure, Olivier
- Projects 7 · Mapping projects are based on traceroute - skitter/Archipelago ([claffy et al.]) 7 #12;INL - skitter/Archipelago ([claffy et al.]) - DIMES ([Shavitt & Shir]) 7 #12;INL Seminar - Internet Topology Discovery IP Level - Projects 7 · Mapping projects are based on traceroute - skitter/Archipelago ([claffy et
Topological Crystalline Insulators
NASA Astrophysics Data System (ADS)
Hsieh, Timothy
2015-03-01
Topological crystalline insulators (TCI) are new phases of matter in which nontrivial band topology and crystal symmetry unite to protect metallic states on the boundary. Remarkably, TCIs have been predicted and observed in the conveniently simple rocksalt SnTe class of IV-VI semiconductors. Despite the simple crystal structure, the interplay between topology and crystal symmetry in these materials have led to a rich variety of new phenomena, including the coexistence of massless and massive Dirac fermions arising from ferroelectric distortion and strain-induced flat band superconductivity. These new physical mechanisms are not only of intrinsic interest but may also find application in new transistor devices. After discussing the topological nature and potential uses of IV-VI family TCIs, I will present recent predictions of TCIs in several anti-perovskite materials. The origin of TCI in this new class of materials is strikingly different and involves the band inversion of two J = 3/2 quartets of Dirac fermions, which together form a ``Dirac octet.'' As interactions play a significant role in many anti-perovskites, this prediction serves as first step toward realizing TCIs in strongly correlated systems. This work is supported by NSF Graduate Research Fellowship No. 0645960 and DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010526.
Submitted to Topology Proceedings
Pottmann, Helmut
Submitted to Topology Proceedings A NEW CRITERION FOR DISK-LIKE CRYSTALLOGRAPHIC REPTILES BENO(T) = 1(T) . . . n(T) a crystallographic reptile if the collection {(T) : } tiles the plane to closed disk; reptile. This work is supported in part by National Natural Science Foundation of China
Rendering the Topological Spines
Nieves-Rivera, D.
2015-05-05
Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (?ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ?ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.
LHCb Topological Trigger Reoptimization
Likhomanenko, T; Khairullin, E; Rogozhnikov, A; Ustyuzhanin, A; Williams, M
2015-01-01
The main b-physics trigger algorithm used by the LHCb experiment is the so- called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training....
LHCb Topological Trigger Reoptimization
Likhomanenko, Tatiana; Khairullin, Egor; Rogozhnikov, Alex; Ustyuzhanin, Andrey; Williams, Michael
2015-01-01
The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. ...
Topological phases with generalized global symmetries
Beni Yoshida
2015-08-14
We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported on a $(d+1)$-colorable graph by using a family of unitary phase gates, known as multi-qubit control-$Z$ gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Non-triviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Topological phases with generalized global symmetries
Yoshida, Beni
2015-01-01
We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported on a $(d+1)$-colorable graph by using a family of unitary phase gates, known as multi-qubit control-$Z$ gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Non-triviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Real Arnold complexity versus real topological entropy for birational transformations
N. Abarenkova; J. -Ch. Anglès d'Auriac; S. Boukraa; S. Hassani; J. -M. Maillard
1999-06-04
We consider a family of birational transformations of two variables, depending on one parameter, for which simple rational expressions with integer coefficients, for the exact expression of the dynamical zeta function, have been conjectured. together with an equality between the asymptotic of the Arnold complexity and the exponential of the topological entropy. This identification takes place for the birational mapping seen as a mapping bearing on two complex variables. We revisit this identification between these two quite `universal complexities' by considering now the mapping as a mapping bearing on two real variables. The definitions of the two previous `topological' complexities (Arnold complexity and topological entropy) are modified according to this real-variables point of view. Most of the `universality' is lost, but the identification survives.
NASA Technical Reports Server (NTRS)
Minow, Joseph I.
2014-01-01
(1) High energy (>100keV) electrons penetrate spacecraft walls and accumulate in dielectrics or isolated conductors; (2) Threat environment is energetic electrons with sufficient flux to charge circuit boards, cable insulation, and ungrounded metal faster than charge can dissipate; (3) Accumulating charge density generates electric fields in excess of material breakdown strenght resulting in electrostatic discharge; and (4) System impact is material damage, discharge currents inside of spacecraft Faraday cage on or near critical circuitry, and RF noise.
Helical Spin Order from Topological Dirac and Weyl Semimetals
NASA Astrophysics Data System (ADS)
Sun, Xiao-Qi; Zhang, Shou-Cheng; Wang, Zhong
2015-08-01
We study dynamical mass generation and the resultant helical spin orders in topological Dirac and Weyl semimetals, including the edge states of quantum spin Hall insulators, the surface states of weak topological insulators, and the bulk materials of Weyl semimetals. In particular, the helical spin textures of Weyl semimetals manifest the spin-momentum locking of Weyl fermions in a visible manner. The spin-wave fluctuations of the helical order carry electric charge density; therefore, the spin textures can be electrically controlled in a simple and predictable manner.
Topological magnetization jumps in a confined chiral soliton lattice
NASA Astrophysics Data System (ADS)
Kishine, Jun-ichiro; Bostrem, I. G.; Ovchinnikov, A. S.; Sinitsyn, Vl. E.
2014-01-01
We demonstrate that a finite-size chiral soliton lattice formed in a chiral helimagnet with fixed boundary conditions exhibits magnetization jumps in a response to the magnetic field applied perpendicular to the chiral axis. The imposed boundary conditions lead to confinement of topological charges and quantized spatial periods of the soliton lattice. Building an envelope of the ground-state energies belonging to different topological sectors, we find the magnetization jumps related with the level crossing. After numerically establishing the quantization condition, we also develop a field-theoretical model to support the numerical results.
Topological nature of optical bound states in the continuum.
Zhen, Bo; Hsu, Chia Wei; Lu, Ling; Stone, A Douglas; Solja?i?, Marin
2014-12-19
Optical bound states in the continuum (BICs) have recently been realized in photonic crystal slabs, where the disappearance of out-of-plane radiation turns leaky resonances into guided modes with infinite lifetimes. We show that such BICs are vortex centers in the polarization directions of far-field radiation. They carry conserved and quantized topological charges, defined by the winding number of the polarization vectors, which ensure their robust existence and govern their generation, evolution, and annihilation. Our findings connect robust BICs in photonics to a wide range of topological physical phenomena. PMID:25554906
Flat bands in topological media
T. T. Heikkila; N. B. Kopnin; G. E. Volovik
2011-07-26
Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. Here we show that in gapless topological media, the bulk-surface and bulk-vortex correspondence is more effective: it produces topologically protected gapless fermions without dispersion -- the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Fermi points (Weyl points). Flat band has an extremely singular density of states, and we show that this property may give rise in particular to surface superconductivity which could exist even at room temperature.
40 CFR 98.430 - Definition of the source category.
Code of Federal Regulations, 2014 CFR
2014-07-01
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40 CFR 98.430 - Definition of the source category.
Code of Federal Regulations, 2013 CFR
2013-07-01
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Robust Topology-Based Analysis of Large Scale Data
Pascucci, Valerio
regular point Classical definitions Simulation of Differentiability 2D 3D1D )( ixf)(xF 1 )( - = n Bx n n f x f x x x x f x f x x x x L M O M L )()( ji vFvF = 2D Multi-Saddle 3D Multi of Rayleigh-Taylor instability. Multi-scale time tracking of combustion particles. Topological analysis
EDITORIAL: Topological data analysis Topological data analysis
NASA Astrophysics Data System (ADS)
Epstein, Charles; Carlsson, Gunnar; Edelsbrunner, Herbert
2011-12-01
Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide methods for discretizing and compressing the information present in a geometric object so as to provide a useful, small representation of the object. The articles in this special issue are concerned with the applications of topology to the analysis of data sets. The adaptation of topological techniques from pure mathematics to the study of data from real systems is a project which has been undertaken during the past two decades, and the present volume contains various contributions to that project. At the current state of development, homology and persistence are two of the most popular topological techniques used in this context. Homology goes back to the beginnings of topology in Poincaré's influential papers. It is the idea that the connectivity of a space is determined by its cycles of different dimensions, and that these cycles organize themselves into abelian groups, called homology groups. Better known than these groups are their ranks, the Betti numbers of the space, which are non-negative integers that count the number of independent cycles in each dimension. To give an example, the zeroth Betti number counts the components, and the first counts the loops. A crucial feature of homology groups is that, given a reasonably explicit description of a space, their computation is an exercise in linear algebra. Even better known than the Betti numbers is the Euler characteristic, which we know from Poincaré's work, is equal to the alternating sum of the Betti numbers, which can be computed without computing the homology groups themselves. To give evidence that these numbers have relevant practical applications, we mention that integrating the Euler characteristic over a domain with sensor information can be used to count objects in the domain. This alone would not explain the popularity of homology groups, which we see rooted in the fact that they hit a sweet-spot that offers relatively strong discriminative power, and a clear intuitive meaning, all at a surprisingly low computational cost. Even these desirable qualities would not be sufficient if it were not pos
Topological phases reviewed: The Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases
McKellar, B. H. J.; He, X-G.; Klein, A. G.
2014-03-05
There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of 'an electric dipole encircles magnetic charges' was realised experimentally, and discuss possible future experimental realisations.
Quist, Daniel A. (Los Alamos, NM); Gavrilov, Eugene M. (Los Alamos, NM); Fisk, Michael E. (Jemez, NM)
2008-01-15
A method enables the topology of an acyclic fully propagated network to be discovered. A list of switches that comprise the network is formed and the MAC address cache for each one of the switches is determined. For each pair of switches, from the MAC address caches the remaining switches that see the pair of switches are located. For each pair of switches the remaining switches are determined that see one of the pair of switches on a first port and the second one of the pair of switches on a second port. A list of insiders is formed for every pair of switches. It is determined whether the insider for each pair of switches is a graph edge and adjacent ones of the graph edges are determined. A symmetric adjacency matrix is formed from the graph edges to represent the topology of the data link network.
Cosmology from Topological Defects
Alejandro Gangui
2003-03-21
The potential role of cosmic topological defects has raised interest in the astrophysical community for many years now. In this set of notes, we give an introduction to the subject of cosmic topological defects and some of their possible observable signatures. We begin with a review of the basics of general defect formation and evolution, we briefly comment on some general features of conducting cosmic strings and vorton formation, as well as on the possible role of defects as dark energy, to end up with cosmic structure formation from defects and some specific imprints in the cosmic microwave background radiation from simulated cosmic strings. A detailed, pedagogical explanation of the mechanism underlying the tiny level of polarization discovered in the cosmic microwave background by the DASI collaboration (and recently confirmed by WMAP) is also given, and a first rough comparison with some predictions from defects is provided.
Gods as Topological Invariants
Daniel Schoch
2012-04-01
We show that the number of gods in a universe must equal the Euler characteristics of its underlying manifold. By incorporating the classical cosmological argument for creation, this result builds a bridge between theology and physics and makes theism a testable hypothesis. Theological implications are profound since the theorem gives us new insights in the topological structure of heavens and hells. Recent astronomical observations can not reject theism, but data are slightly in favor of atheism.
Topological confinement and superconductivity
Al-hassanieh, Dhaled A; Batista, Cristian D
2008-01-01
We derive a Kondo Lattice model with a correlated conduction band from a two-band Hubbard Hamiltonian. This mapping allows us to describe the emergence of a robust pairing mechanism in a model that only contains repulsive interactions. The mechanism is due to topological confinement and results from the interplay between antiferromagnetism and delocalization. By using Density-Matrix-Renormalization-Group (DMRG) we demonstrate that this mechanism leads to dominant superconducting correlations in aID-system.
Algebraic versus Topologic Anomalies
V. Aldaya; M. Calixto; J. Guerrero
1997-02-08
Within the frame of a Group Approach to Quantization anomalies arise in a quite natural way. We present in this talk an analysis of the basic obstructions that can be found when we try to translate symmetries of the Newton equations to the Quantum Theory. They fall into two classes: algebraic and topologic according to the local or global character of the obstruction. We present here one explicit example of each.
Estrada, Rolando; Tomasi, Carlo; Schmidler, Scott C.; Farsiu, Sina
2015-01-01
Tree-like structures are fundamental in nature, and it is often useful to reconstruct the topology of a tree—what connects to what—from a two-dimensional image of it. However, the projected branches often cross in the image: the tree projects to a planar graph, and the inverse problem of reconstructing the topology of the tree from that of the graph is ill-posed. We regularize this problem with a generative, parametric tree-growth model. Under this model, reconstruction is possible in linear time if one knows the direction of each edge in the graph—which edge endpoint is closer to the root of the tree—but becomes NP-hard if the directions are not known. For the latter case, we present a heuristic search algorithm to estimate the most likely topology of a rooted, three-dimensional tree from a single two-dimensional image. Experimental results on retinal vessel, plant root, and synthetic tree datasets show that our methodology is both accurate and efficient. PMID:26353004
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Quantum algorithm for topological and geometric analysis of data
NASA Astrophysics Data System (ADS)
Lloyd, Seth; Zanardi, Paolo; Garnerone, Silvano
2015-03-01
Topological methods for analyzing data sets provide a powerful technique for extracting useful information from data. Data that represents geometric features of the world typically gives a distorted picture of those features, if only because the devices and systems that sense the world and that generate the data by their very nature induce distortions. By definition, topological features are those that persist under continuous distortions of the data. Topological methods can therefore identify features of the real system from which the data was collected, but that have been distorted by the data collection process. Persistent homology is a sophisticated tool for identifying such topological features -connected components, holes, or voids - and for determining how such features persist as the data is viewed at different scales. This talk presents quantum machine learning algorithms for calculating Betti numbers in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian (the quantities that famously allow one to ``hear the shape of a drum''). The algorithms provide an exponential speedup over classical algorithms for topological and geometrical data analysis.
Transportation Network Topologies
NASA Technical Reports Server (NTRS)
Holmes, Bruce J.; Scott, John M.
2004-01-01
A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation's 21st century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21st century. Clearly, new thinking is required for transportation that can scale to meet to the realities of a networked, knowledge-based economy in which the value of time is a new coin of the realm. This paper proposes a framework, or topology, for thinking about the problem of scalability of the system of networks that comprise the aviation system. This framework highlights the role of integrated communication-navigation-surveillance systems in enabling scalability of future air transportation networks. Scalability, in this vein, is a goal of the recently formed Joint Planning and Development Office for the Next Generation Air Transportation System. New foundations for 21PstP thinking about air transportation are underpinned by several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems. Complexity science and modern network theory give rise to one of the technological developments of importance. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of scalability, efficiency, robustness, resilience, and other metrics. The paper offers an air transportation system topology as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system architectures, and airspace architectures and procedural concepts. The topology proposed considers air transportation as a system of networks, within which strategies for scalability of the topology may be enabled by technologies and policies. In particular, the effects of scalable ICNS concepts are evaluated within this proposed topology. Alternative business models are appearing on the scene as the old centralized hub-and-spoke model reaches the limits of its scalability. These models include growth of point-to-point scheduled air transportation service (e.g., the RJ phenomenon and the 'Southwest Effect'). Another is a new business model for on-demand, widely distributed, air mobility in jet taxi services. The new businesses forming around this vision are targeting personal air mobility to virtually any of the thousands of origins and destinations throughout suburban, rural, and remote communities and regions. Such advancement in air mobility has many implications for requirements for airports, airspace, and consumers. These new paradigms could support scalable alternatives for the expansion of future air mobility to more consumers in more places.
Transportation Network Topologies
NASA Technical Reports Server (NTRS)
Holmes, Bruce J.; Scott, John
2004-01-01
A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation's 21st century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21st century. Clearly, new thinking is required for transportation that can scale to meet to the realities of a networked, knowledge-based economy in which the value of time is a new coin of the realm. This paper proposes a framework, or topology, for thinking about the problem of scalability of the system of networks that comprise the aviation system. This framework highlights the role of integrated communication-navigation-surveillance systems in enabling scalability of future air transportation networks. Scalability, in this vein, is a goal of the recently formed Joint Planning and Development Office for the Next Generation Air Transportation System. New foundations for 21st thinking about air transportation are underpinned by several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems. Complexity science and modern network theory give rise to one of the technological developments of importance. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of scalability, efficiency, robustness, resilience, and other metrics. The paper offers an air transportation system topology as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system architectures, and airspace architectures and procedural concepts. The topology proposed considers air transportation as a system of networks, within which strategies for scalability of the topology may be enabled by technologies and policies. In particular, the effects of scalable ICNS concepts are evaluated within this proposed topology. Alternative business models are appearing on the scene as the old centralized hub-and-spoke model reaches the limits of its scalability. These models include growth of point-to-point scheduled air transportation service (e.g., the RJ phenomenon and the Southwest Effect). Another is a new business model for on-demand, widely distributed, air mobility in jet taxi services. The new businesses forming around this vision are targeting personal air mobility to virtually any of the thousands of origins and destinations throughout suburban, rural, and remote communities and regions. Such advancement in air mobility has many implications for requirements for airports, airspace, and consumers. These new paradigms could support scalable alternatives for the expansion of future air mobility to more consumers in more places.
Charge Independence and Charge Symmetry
Gerald A. Miller; Willem T. H. van Oers
1994-09-14
Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed.
On topological terms in the O(3) nonlinear sigma model
NASA Astrophysics Data System (ADS)
Tsurumaru, Toyohiro; Tsutsui, Izumi
1999-08-01
Topological terms in the O(3) nonlinear sigma model in (1+1) and (2+1) dimensions are re-examined based on the description of the SU(2)-valued field g. We first show that the topological soliton term in (1+1) dimensions arises from the unitary representations of the group characterizing the global structure of the symmetry inherent in the description, in a manner analogous to the appearance of the ?-term in Yang-Mills theory in (3+1) dimensions. We then present a detailed argument as to why the conventional Hopf term, which is the topological counterpart in (2+1) dimensions and has been widely used to realize fractional spin and statistics, is ill-defined unless the soliton charge vanishes. We show how this restriction can be lifted by means of a procedure proposed recently, and provide its physical interpretation as well.
Momentum dependence of the topological susceptibility with overlap fermions
Yoshiaki Koma; Ernst-Michael Ilgenfritz; Karl Koller; Miho Koma; Gerrit Schierholz; Thomas Streuer; Volker Weinberg
2010-12-07
Knowledge of the derivative of the topological susceptibility at zero momentum is important for assessing the validity of the Witten-Veneziano formula for the eta' mass, and likewise for the resolution of the EMC proton spin problem. We investigate the momentum dependence of the topological susceptibility and its derivative at zero momentum using overlap fermions in quenched lattice QCD simulations. We expose the role of the low-lying Dirac eigenmodes for the topological charge density, and find a negative value for the derivative. While the sign of the derivative is consistent with the QCD sum rule for pure Yang-Mills theory, the absolute value is overestimated if the contribution from higher eigenmodes is ignored.
Topological gap states of semiconducting armchair graphene ribbons
Y. H. Jeong; S. C. Kim; S. -R. Eric Yang
2015-05-31
In semiconducting armchair graphene ribbons a chiral lattice deformation can induce pairs of topological gap states with opposite energies. Near the critical value of the deformation potential these kink and antikink states become almost degenerate with zero energy and have a fractional charge one-half. Such a semiconducting armchair ribbon represents a one-dimensional topological insulator with nearly zero energy end states. Using data collapse of numerical results we find that the shape of the kink displays an anomalous power-law dependence on the width of the local lattice deformation. We suggest that these gap states may be probed in optical measurements. However, "metallic" armchair graphene ribbons with a gap induced by many-electron interactions have no gap states and are not topological insulators.
Energy Harvesting by Sweeping Voltage-Escalated Charging of a Reconfigurable Supercapacitor Array
Shinozuka, Masanobu
Energy Harvesting by Sweeping Voltage-Escalated Charging of a Reconfigurable Supercapacitor Array charge pump to perform maximum power-transfer track- ing (MPTT) while charging a reservoir supercapacitor. The supercapacitors in the RSA can be dynamically configured for series or parallel topologies by means of a switch
ON TOPOLOGICAL TITS BUILDINGS AND THEIR CLASSIFICATION
Spatzier, Ralf
ON TOPOLOGICAL TITS BUILDINGS AND THEIR CLASSIFICATION by KEITH BURNS (1) and RA*F SPATZIER (2) Abstract We define topological Tits buildings. If a topological building A satisfies some technical the notion of a topological Tits building. Roughly speaking, this is a Tits building A with a topology which
Bundle gerbes for topological insulators
Krzysztof Gawedzki
2015-12-03
Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter systems via equivariant bundle gerbes. The construction covers static and periodically driven systems with time reversal invariance in 2 and 3 space dimensions. It involves refinements of geometry of gerbes that are discussed in the first lecture, the second one being devoted to the applications to topological insulators.
Noncommuting momenta of topological solitons.
Watanabe, Haruki; Murayama, Hitoshi
2014-05-16
We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force. PMID:24877932
Liu, Qihang; Zhang, Xiuwen; Abdalla, L B; Fazzio, Adalberto; Zunger, Alex
2015-02-11
The study of topological insulators has generally involved search of materials that have this property as an innate quality, distinct from normal insulators. Here we focus on the possibility of converting a normal insulator into a topological one by application of an external electric field that shifts different bands by different energies and induces a specific band inversion, which leads to a topological state. Phosphorene is a two-dimensional (2D) material that can be isolated through mechanical exfoliation from layered black phosphorus, but unlike graphene and silicene, single-layer phosphorene has a large band gap (1.5-2.2 eV). Thus, it was unsuspected to exhibit band inversion and the ensuing topological insulator behavior. Using first-principles calculations with applied perpendicular electric field F? on few-layer phosphorene we predict a continuous transition from the normal insulator to a topological insulator and eventually to a metal as a function of F?. The tuning of topological behavior with electric field would lead to spin-separated, gapless edge states, that is, quantum spin Hall effect. This finding opens the possibility of converting normal insulating materials into topological ones via electric field and making a multifunctional "field effect topological transistor" that could manipulate simultaneously both spin and charge carrier. We use our results to formulate some design principles for looking for other 2D materials that could have such an electrical-induced topological transition. PMID:25607525
NASA Astrophysics Data System (ADS)
Li, Tianhe; Guo, Huaiming; Chen, Shu; Shen, Shun-Qing
2015-04-01
The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises three kinds of phases: superfluid, persisted charge-density-wave and Mott insulators, and emergent insulators in the presence of nearest-neighbor hoppings. We find that all emergent insulators are topological, which are characterized by the Berry phase ? and a pair of degenerate in-gap boundary states. The mechanism of the topological bosonic insulators is qualitatively discussed and the ones with higher fillings can be understood as a 1/3 -filling topological phase on a background of trivial charge-density-wave or Mott insulators.
United States. Bonneville Power Administration.
1993-12-01
The Bonneville Power Administration`s definition of terms are documented here. The terms primarily focus on transmission, generation and distribution, but also cover BPA services and responsibilities.
NASA Astrophysics Data System (ADS)
Gu, Genda
2014-03-01
The discovery of 3D topological insulator materials and topological superconductor open up a new research field in the condensed matter physics. In order to search for the ideal topological insulator, topological crystalline insulator and topological superconductor, we have grown a large number of the single crystals of Bi-system (Bi-Sb-Te-Se) topological insulator Pb-system (Pb-Sn-In-Te-Se) topological crystalline insulator and their topological superconductor. We have measured the physical properties on these single crystals by various techniques. We have studied the effect of crystal growth condition, impurity and composition on the bulk electrical conductivity of these single crystals. We try to find out which composition and crystal growth condition is the best for the ideal topological insulator, topological crystalline insulator and topological superconductor. We have got the bulk topological superconductor with Tc = 5K. This work is supported by DOE under contract No. DE-AC02-98CH10886.
Costeira, M J; Ruivo, I; Miguel, C; Ferreira, P; Almeida, A; Azevedo, I; Silva, G; Aguiar, A
1998-11-01
Posterior choanal atresia is a congenital malformation which can occur isolated or in combination to additional malformations. In CHARGE association the other anomalies are: coloboma, heart disease, retarded development/growth or central nervous system abnormalities, genital hypoplasia or hypogonadism and ear abnormalities or deafness. The authors present three cases of CHARGE association and they also review the clinical findings required for the diagnosis. PMID:10021803
Topological States in Partially-PT -Symmetric Azimuthal Potentials
NASA Astrophysics Data System (ADS)
Kartashov, Yaroslav V.; Konotop, Vladimir V.; Torner, Lluis
2015-11-01
We introduce partially-parity-time (p PT ) -symmetric azimuthal potentials composed from individual PT -symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potential excitations carrying topological dislocations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such nonconservative ratchetlike structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully-P T -symmetric potentials. The vortex solitons in the p P T - and P T -symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles.
Controlled Spin Transport in Planar Systems Through Topological Exciton
Abhinav, Kumar
2015-01-01
It is shown that a charge-neutral spin-1 exciton, possibly realizable only in planar systems like graphene and topological insulators, can be effectively used for controlled spin transport in such media. The effect of quantum and thermal fluctuations yield a parametric excitation threshold for its realization. This planar exciton differs from the conventional ones, as it owes its existence to the topological Chern-Simons (CS) term. The parity and time-reversal violating CS term can arise from quantum effects in systems with parity-breaking mass-gap. The spinning exciton naturally couples to magnetic field, leading to the possibility of controlled spin transport. Being neutral, it is immune to a host of effect, which afflicts spin transport through charged fermions.
Dirac Quantization and Fractional Magnetoelectric Effect on Interacting Topological Insulators
K. -S. Park; H. Han
2010-10-10
We use Dirac quantization of flux to study fractional charges and axion angles \\theta in interacting topological insulators with gapless surface modes protected by time-reversal symmetry. In interacting topological insulators, there are two types of fractional axion angle due to conventional odd and nontrivial even flux quantization at the boundary. On even flux quantization in a gapped time reversal invariant system, we show that there is a halved quarter fractional quantum Hall effect on the surface with Hall conductance of p/4q e2/2h with p and q odd integers. The gapless surface modes can be characterized by a nontrivial Z2 anomaly emerged from the even flux quantization. It is suggested that the electron can be regarded as a bound state of fractionally charged quarks confined by a nonabelian color gauge field on the Dirac quantization of complex spinor fields.
Topological characterization and dynamics of a fermionic fractional Chern insulator
NASA Astrophysics Data System (ADS)
Pollmann, Frank; Grushin, Adolfo; Motruk, Johannes; Zaletel, Michael
2015-03-01
Using the density matrix renormalization group (DMRG) method on a cylinder geometry, we characterize the fractional Chern insulator (FCI) state in the Haldane honeycomb lattice model at ? = 1 / 3 filling of the lowest band and check its stability. We investigate the chiral and topological properties of this state through (i) its Hall conductivity, (ii) the topological entanglement entropy, (iii) the U(1) charge spectral flow of the many body entanglement spectrum, and (iv) the charge of the anyons. As the interaction strength is lowered, we observe a direct transition from the FCI into a metallic phase and find indications for the transition to be of first order. Since our approach does not rely on any band or subspace projection, we are able to prove the stability of the fractional state in the presence of interactions exceeding the band gap, as has been suggested in the literature. Additionally, we investigate the characteristic dynamics of the FCI phase using time dependent DMRG.
Topological States in Partially-PT-Symmetric Azimuthal Potentials.
Kartashov, Yaroslav V; Konotop, Vladimir V; Torner, Lluis
2015-11-01
We introduce partially-parity-time (pPT)-symmetric azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potential excitations carrying topological dislocations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such nonconservative ratchetlike structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully-PT-symmetric potentials. The vortex solitons in the pPT- and PT-symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles. PMID:26588383
7 CFR 62.301 - Payment of fees and other charges.
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2010-01-01
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Entangled networks, synchronization, and optimal network topology.
Donetti, Luca; Hurtado, Pablo I; Muñoz, Miguel A
2005-10-28
A new family of graphs, entangled networks, with optimal properties in many respects, is introduced. By definition, their topology is such that it optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost optimal in many senses, and with plenty of potential applications in computer science or neuroscience. PMID:16383953
Hagedorn transition and topological entanglement entropy
Fen Zuo; Yi-Hong Gao
2015-11-06
We extend our previous study of free large-$N$ gauge theories on a sphere to the geometric entropy, or the double Wick-rotated entanglement entropy. Same as the thermal entropy, the high-temperature expansion of the geometric entropy in the ``deconfined'' phase contains a universal constant term, $-N^2/4$. We identify this as the topological entanglement entropy of the dimensional reduced 3D theory. In the confining phase, the recently proposed 2D modular description is employed to study the high-temperature expansion/continuation. It is shown that there is always a logarithmic divergence, and no constant term can be isolated definitely. For ${\\mathcal N}=4$ super Yang-Mills theory, the results obtained here are compared with that at strong coupling from the holographic derivation.
Hagedorn transition and topological entanglement entropy
Zuo, Fen
2015-01-01
We extend our previous study of free large-$N$ gauge theories on a sphere to the geometric entropy, or the double Wick-rotated entanglement entropy. Same as the thermal entropy, the high-temperature expansion of the geometric entropy in the ``deconfined'' phase contains a universal constant term, $-N^2/4$. We identify this as the topological entanglement entropy of the dimensional reduced 3D theory. In the confining phase, the recently proposed 2D modular description is employed to study the high-temperature expansion/continuation. It is shown that there is always a logarithmic divergence, and no constant term can be isolated definitely. For ${\\mathcal N}=4$ super Yang-Mills theory, the results obtained here are compared with that at strong coupling from the holographic derivation.
Long Range Topological Order, the Chiral Condensate, and the Berry Connection in QCD
Thacker, H B
2014-01-01
Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a Berry connection, which is a gauge connection obtained from the phase of the electron wave function transported over momentum space rather than coordinate space. The phase of a closed Wilson loop of the Berry connection around the Brillouin zone defines a topological order parameter which labels discrete flux vacua. The conducting states are surface modes on the domain walls between discrete vacua. Evidence from large-$N_c$ chiral dynamics, holographic QCD, and Monte Carlo observations has pointed to a picture of the QCD vacuum that is very similar to that of a topological insulator, with discrete quasivacua labelled by $\\theta$ angles that differ by mod $2\\pi$. In this picture, the domain walls are membranes of Chern-Simons charge, and the quark condensate consists of surface ...
Non-topological solitons in field theories with kinetic self-coupling
NASA Astrophysics Data System (ADS)
Diaz-Alonso, Joaquin; Rubiera-Garcia, Diego
2007-09-01
We investigate some fundamental features of a class of non-linear relativistic Lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which are finite-energy and stable. We determine general conditions for the existence and stability of these non-topological soliton solutions. In particular, we perform a linear stability analysis that goes beyond the usual Derrick-like criteria. On the basis of these considerations we obtain a complete characterization of the soliton-supporting members of the aforementioned class of non-linear field theories. We then classify the family of soliton-supporting theories according to the central and asymptotic behaviors of the soliton field, and provide illustrative explicit examples of models belonging to each of the corresponding sub-families. In the present work we restrict most of our considerations to one and many-components scalar models. We show that in these cases the finite-energy static spherically symmetric solutions are stable against charge-preserving perturbations, provided that the vacuum energy of the model vanishes and the energy density is positive definite. We also discuss briefly the extension of the present approach to models involving other types of fields, but a detailed study of this more general scenario will be addressed in a separate publication.
Experimental Evidence for Topological Doping in the Cuprates
Tranquada, J. M.
1999-04-06
Some recent experiments that provide support for the concept of topological doping in cuprate superconductors are discussed. Consistent with the idea of charge segregation, it is argued that the scattering associated with the ''resonance'' peak found in YBa{sub 2}Cu{sub 3}O{sub 6+x} and Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} comes from the Cu spins and not from the doped holes.
Part I. The Cosmological Vacuum from a Topological Perspective
R. M. Kiehn
2007-12-07
This article examines how the physical presence of field energy and particulate matter can be interpreted in terms of the topological properties of space-time. The theory is developed in terms of vector and matrix equations of exterior differential systems, which are not constrained by tensor diffeomorphic equivalences. The first postulate defines the field properties (a vector space continuum) of the Cosmological Vacuum in terms of matrices of basis functions that map exact differentials into neighborhoods of exterior differential 1-forms (potentials). The second postulate requires that the field equations must satisfy the First Law of Thermodynamics dynamically created in terms of the Lie differential with respect to a process direction field acting on the exterior differential forms that encode the thermodynamic system. The vector space of infinitesimals need not be global and its compliment is used to define particle properties as topological defects embedded in the field vector space. The potentials, as exterior differential 1-forms, are not (necessarily) uniquely integrable: the fibers can be twisted, leading to possible Chiral matrix arrays of certain 3-forms defined as Topological Torsion and Topological Spin. A significant result demonstrates how the coefficients of Affine Torsion are related to the concept of Field excitations (mass and charge); another demonstrates how thermodynamic evolution can describe the emergence of topological defects in the physical vacuum.
Charge without charge in quarks
Harry Schiff
2013-08-06
With appropriate gauge transformations, field can replace electric charge in quarks. Classical quarks, in a necessary non-gauge invariant formulation, are used for illustration, bringing to the fore the limitations of the usual electric charge densities for single particles in Coulomb equations. The results are encouraging; the solutions for the Coulomb potentials apply individually to each quark in a shell structure. A remarkably simple relation emerges between the Coulomb and weak potentials.
NASA Astrophysics Data System (ADS)
Qu, Dong-Xia; Kou, Xufeng; Lang, Murong; Crowhurst, Jonathan; Armstrong, Michael; Zaug, Joseph; Wang, Kang L.; Chapline, George
2015-03-01
The remarkable nature of surface states in topological insulators is expected to have a unique photocurrent response to electromagnetic radiation. However, the surface and bulk photo-excited charge transport mechanisms, in relation to the band bending at the electrode-topological insulator interface, have not been well understood. Here, we present scanning photocurrent microscopy measurements on a gated topological insulator microdevice and show that the spin-polarized photocurrent displays direction reversal near the electrical contact interfaces. We discuss two possible mechanisms, which alternatively play dominant roles in the helicity-dependent photocurrent map. Our analysis determines the magnitude of each contribution, and reveals the governing process under different gate conditions.
NASA Astrophysics Data System (ADS)
Xu, Yang; Miotkowski, Ireneusz; Liu, Chang; Tian, Jifa; Nam, Hyoungdo; Alidoust, Nasser; Hu, Jiuning; Shih, Chih-Kang; Hasan, M. Zahid; Chen, Yong P.
2014-12-01
A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically protected gapless surface states. One of the most distinct electronic transport signatures predicted for such topological surface states (TSS) is a well-defined half-integer quantum Hall effect (QHE) in a magnetic field, where the surface Hall conductivities become quantized in units of (1/2)e2/h (e being the electron charge, h the Planck constant) concomitant with vanishing resistance. Here, we observe a well-developed QHE arising from TSS in an intrinsic TI of BiSbTeSe2. Our samples exhibit surface-dominated conduction even close to room temperature, whereas the bulk conduction is negligible. At low temperatures and high magnetic fields perpendicular to the top and bottom surfaces, we observe well-developed integer quantized Hall plateaux, where the two parallel surfaces each contribute a half-integer e2/h quantized Hall conductance, accompanied by vanishing longitudinal resistance. When the bottom surface is gated to match the top surface in carrier density, only odd integer QH plateaux are observed, representing a half-integer QHE of two degenerate Dirac gases. This system provides an excellent platform to pursue a plethora of exotic physics and novel device applications predicted for TIs, ranging from magnetic monopoles and Majorana particles to dissipationless electronics and fault-tolerant quantum computers.
NASA Astrophysics Data System (ADS)
Maas, Axel
2015-03-01
Two popular perspectives on the non-perturbative domain of Yang-Mills theories are either in terms of the gluons themselves or in terms of collective gluonic excitations, i.e. topological excitations. If both views are correct, then they are only two different representations of the same underlying physics. One possibility to investigate this connection is by the determination of gluon correlation functions in topological background fields, as created by the smearing of lattice configurations. This is performed here for the minimal Landau gauge gluon propagator, ghost propagator, and running coupling, both in momentum and position space for SU(2) Yang-Mills theory. The results show that the salient low-momentum features of the propagators are qualitatively retained under smearing at sufficiently small momenta, in agreement with an equivalence of both perspectives. However, the mid-momentum behavior is significantly affected. These results are also relevant for the construction of truncations in functional methods, as they provide hints on necessary properties to be retained in truncations.
A natural topological insulator.
Gehring, P; Benia, H M; Weng, Y; Dinnebier, R; Ast, C R; Burghard, M; Kern, K
2013-03-13
The earth's crust and outer space are rich sources of technologically relevant materials which have found application in a wide range of fields. Well-established examples are diamond, one of the hardest known materials, or graphite as a suitable precursor of graphene. The ongoing drive to discover novel materials useful for (opto)electronic applications has recently drawn strong attention to topological insulators. Here, we report that Kawazulite, a mineral with the approximate composition Bi2(Te,Se)2(Se,S), represents a naturally occurring topological insulator whose electronic properties compete well with those of its synthetic counterparts. Kawazulite flakes with a thickness of a few tens of nanometers were prepared by mechanical exfoliation. They exhibit a low intrinsic bulk doping level and correspondingly a sizable mobility of surface state carriers of more than 1000 cm(2)/(V s) at low temperature. Based on these findings, further minerals which due to their minimized defect densities display even better electronic characteristics may be identified in the future. PMID:23438015
Fractionally charged skyrmions in fractional quantum Hall effect.
Balram, Ajit C; Wurstbauer, U; Wójs, A; Pinczuk, A; Jain, J K
2015-01-01
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region. PMID:26608906
Fractionally charged skyrmions in fractional quantum Hall effect
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.
2015-01-01
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region. PMID:26608906
Topological Fermi-liquid theory
Yong-Soo Jho; Ki-Seok Kim
2015-04-06
Quantum anomalies have been playing an essential role not only in particle physics but also in modern condensed matter physics, in particular, for topological states of matter. They are responsible for quantum number fractionalization in solitonic objects (Goldstone-Wilczek currents), deconfined quantum criticality (emergent non-abelian chiral anomaly) gapless boundary states and anomalous (quantized) electrical and thermal (Hall) transport phenomena, and etc, driving one branch of condensed matter physics. Furthermore, recent advances on topological states of matter have blurring out the boundary between high energy physics and condensed matter physics besides the string-theory application of the AdS/CFT conjecture. In this study, we generalize physics of insulating topological states of matter into a metallic phase, where effects of electron correlations can be incorporated to cause exotica. We propose a novel metallic state identified with a topological Fermi-liquid fixed point and described by a topological Fermi-liquid theory, where electromagnetic properties are governed by axion electrodynamics originating from chiral anomaly, thus which should be distinguished from the Landau's Fermi-liquid fixed point described by Landau's Fermi-liquid theory. We speculate that the topological Fermi-liquid theory lays the foundation stone of a topological Landau-Ginzburg theory for phase transitions from the topological Fermi-liquid state, which generalizes the Landau-Ginzburg theory for phase transitions from the Landau's Fermi-liquid state.
Quantum entanglement and topological entanglement
Kauffman, Louis H.
Quantum entanglement and topological entanglement Louis H Kauffman1 and Samuel J Lomonaco Jr2 1 topological entangle- ment and quantum entanglement. Specifically, we propose that it is more fun- damental unitary operators that are capable of creating quantum entanglement. 1. Introduction This paper discusses
NONABELIAN ALGEBRAIC TOPOLOGY Ronald Brown
NONABELIAN ALGEBRAIC TOPOLOGY By Ronald Brown IMA Preprint Series # 1982 ( July 2004 ) INSTITUTE Algebraic Topology Ronald Brown September 7, 2004 UWB Math Preprint 04.15 Abstract This is an extended-categories: foundations and applications', June 7-18, 2004, organised by John Baez and Peter May. Introduction This talk
Azimuthal Charged-Particle Correlations and Possible Local Strong Parity Violation
Redwine, Robert P.
Parity-odd domains, corresponding to nontrivial topological solutions of the QCD vacuum, might be created during relativistic heavy-ion collisions. These domains are predicted to lead to charge separation of quarks along ...
Concept Model on Topological Learning
NASA Astrophysics Data System (ADS)
Ae, Tadashi; Kioi, Kazumasa
2010-11-01
We discuss a new model for concept based on topological learning, where the learning process on the neural network is represented by mathematical topology. The topological learning of neural networks is summarized by a quotient of input space and the hierarchical step induces a tree where each node corresponds to a quotient. In general, the concept acquisition is a difficult problem, but the emotion for a subject is represented by providing the questions to a person. Therefore, a kind of concept is captured by such data and the answer sheet can be mapped into a topology consisting of trees. In this paper, we will discuss a way of mapping the emotional concept to a topological learning model.
Green Functions for Topology Change
Jerome Martin; Nelson Pinto-Neto; Ivano Damiao Soares
2003-08-21
We explicitly calculate the Green functions describing quantum changes of topology in Friedman-Lemaitre-Robertson-Walker Universes whose spacelike sections are compact but endowed with distinct topologies. The calculations are performed using the long wavelength approximation at second order in the gradient expansion. We argue that complex metrics are necessary in order to obtain a non-vanishing Green functions and interpret this fact as demonstrating that a quantum topology change can be viewed as a quantum tunneling effect. We demonstrate that quantum topological transitions between curved hypersurfaces are allowed whereas no transition to or from a flat section is possible, establishing thus a selection rule. We also show that the quantum topology changes in the direction of negatively curved hypersurfaces are strongly enhanced as time goes on, while transitions in the opposite direction are suppressed.
Shapes of topological RNA structures.
Huang, Fenix W D; Reidys, Christian M
2015-12-01
A topological RNA structure is derived by fattening the edges of a contact structure into ribbons. The shape of a topological RNA structure is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one, as well as isolated vertices. A shape contains the key topological information of the molecular conformation and for fixed topological genus there exist only finitely many such shapes. In this paper we compute the generating polynomial of shapes of fixed topological genus g. We furthermore derive an algorithm having O(glog?g) time complexity uniformly generating shapes of genus g and discuss some applications in the context of databases of RNA pseudoknot structures. PMID:26482318
PROTECTED VETERAN DEFINITIONS TITLE DEFINITION
Capecchi, Mario R.
PROTECTED VETERAN DEFINITIONS TITLE DEFINITION Veteran of the Vietnam Era Veteran of the U because of a service connected disability. "Vietnam era veteran" also includes any veteran of the U and May 7, 1975. Special Disabled Veteran Veteran who served on active duty in the U.S. military ground
Finding topological center of a geographic space via road network
NASA Astrophysics Data System (ADS)
Gao, Liang; Miao, Yanan; Qin, Yuhao; Zhao, Xiaomei; Gao, Zi-You
2015-02-01
Previous studies show that the center of a geographic space is of great importance in urban and regional studies, including study of population distribution, urban growth modeling, and scaling properties of urban systems, etc. But how to well define and how to efficiently extract the center of a geographic space are still largely unknown. Recently, Jiang et al. have presented a definition of topological center by their block detection (BD) algorithm. Despite the fact that they first introduced the definition and discovered the 'true center', in human minds, their algorithm left several redundancies in its traversal process. Here, we propose an alternative road-cycle detection (RCD) algorithm to find the topological center, which extracts the outmost road-cycle recursively. To foster the application of the topological center in related research fields, we first reproduce the BD algorithm in Python (pyBD), then implement the RCD algorithm in two ways: the ArcPy implementation (arcRCD) and the Python implementation (pyRCD). After the experiments on twenty-four typical road networks, we find that the results of our RCD algorithm are consistent with those of Jiang's BD algorithm. We also find that the RCD algorithm is at least seven times more efficient than the BD algorithm on all the ten typical road networks.
VALUATIONS CENTERED AT A TWO-DIMENSIONAL REGULAR LOCAL RING: INFIMA AND TOPOLOGIES
VALUATIONS CENTERED AT A TWO-DIMENSIONAL REGULAR LOCAL RING: INFIMA AND TOPOLOGIES JOSNEI NOVACOSKI not guarantee the existence of infimum for a non-empty set of valuations. We give a more general definition of a rooted non-metric tree and prove that the set of all valuations has this more general property, namely we
Fuzzy Topological Predicates, Their Properties, and Their Integration into Query Languages
Güting, Ralf Hartmut
a model of fuzzy regions and focuses on the definition of topological predicates between them. Moreover with continuously changing proper ties (such as population density, soil quality, vegetation, pollution, temperature, air pressure), oceans, deserts, English speaking areas, or mountains and valleys. The transition
Majorana fermions in chiral topological ferromagnetic nanowires
NASA Astrophysics Data System (ADS)
Dumitrescu, Eugene; Roberts, Brenden; Tewari, Sumanta; Sau, Jay D.; Das Sarma, S.
2015-03-01
Motivated by a recent experiment in which zero-bias peaks have been observed in scanning tunneling microscopy (STM) experiments performed on chains of magnetic atoms on a superconductor, we show, by generalizing earlier work, that a multichannel ferromagnetic wire deposited on a spin-orbit coupled superconducting substrate can realize a nontrivial chiral topological superconducting state with Majorana bound states localized at the wire ends. The nontrivial topological state occurs for generic parameters requiring no fine tuning, at least for very large exchange spin splitting in the wire. We theoretically obtain the signatures which appear in the presence of an arbitrary number of Majorana modes in multiwire systems incorporating the role of finite temperature, finite potential barrier at the STM tip, and finite wire length. These signatures are presented in terms of spatial profiles of STM differential conductance, which clearly reveal zero-energy Majorana end modes and the prediction of a multiple Majorana based fractional Josephson effect. A substantial part of this work is devoted to a detailed critical comparison between our theory and the recent STM experiment claiming the observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. The conclusion of this detailed comparison is that although the experimental observations are not manifestly inconsistent with our theoretical findings, the very small topological superconducting gap and the very high temperature of the experiment make it impossible to decisively verify the existence of a localized Majorana zero mode, as the spectral weight of the Majorana mode is necessarily spread over a very broad energy regime exceeding the size of the gap. Such an extremely broad (and extremely weak) conductance peak could easily arise from any subgap states existing in the rather complex system studied experimentally and may or may not have anything to do with a putative Majorana zero mode as discussed in the first half of our paper. Thus, although the experimental findings are indeed consistent with a highly broadened and weakened Majorana zero-bias peak, much lower experimental temperatures (and/or much larger experimental topological superconducting gaps) are necessary for any definitive conclusion.
Topology in QCD and the axion abundance
Ryuichiro Kitano; Norikazu Yamada
2015-10-21
The temperature dependence of the topological susceptibility in QCD, chi_t, essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched approximation. Since our purpose here is to estimate the range expected in unquenched QCD through quenched simulations, hybrid Monte Carlo (HMC) algorithm is employed instead of heatbath algorithm. We obtain an indication that unquenched calculations of chi_t encounter the serious problem of autocorrelation already at T~2Tc or even below with the plain HMC. In the second part, we revisit the axion abundance. The absolute value and the temperature dependence of chi_t in real QCD can be significantly different from that in the quenched approximation, and is not well established above the critical temperature. Motivated by this fact and precedent arguments which disagree with the conventional instanton picture, we estimate the axion abundance in an extreme case where chi_t decreases much faster than the conventional power-like behavior. We find a significant enhancement of the axion abundance in such a case.
Topology in QCD and the axion abundance
NASA Astrophysics Data System (ADS)
Kitano, Ryuichiro; Yamada, Norikazu
2015-10-01
The temperature dependence of the topological susceptibility in QCD, ? t , essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched approximation. Since our purpose here is to estimate the range expected in unquenched QCD through quenched simulations, hybrid Monte Carlo (HMC) algorithm is employed instead of heat-bath algorithm. We obtain an indication that unquenched calculations of ? t encounter the serious problem of autocorrelation already at T ˜ 2 T c or even below with the plain HMC. In the second part, we revisit the axion abundance. The absolute value and the temperature dependence of ? t in real QCD can be significantly different from that in the quenched approximation, and is not well established above the critical temperature. Motivated by this fact and precedent arguments which disagree with the conventional instanton picture, we estimate the axion abundance in an extreme case where ? t decreases much faster than the conventional power-like behavior. We find a significant enhancement of the axion abundance in such a case.
Persistent optical gating of a topological insulator.
Yeats, Andrew L; Pan, Yu; Richardella, Anthony; Mintun, Peter J; Samarth, Nitin; Awschalom, David D
2015-10-01
The spin-polarized surface states of topological insulators (TIs) are attractive for applications in spintronics and quantum computing. A central challenge with these materials is to reliably tune the chemical potential of their electrons with respect to the Dirac point and the bulk bands. We demonstrate persistent, bidirectional optical control of the chemical potential of (Bi,Sb)2Te3 thin films grown on SrTiO3. By optically modulating a space-charge layer in the SrTiO3 substrates, we induce a persistent field effect in the TI films comparable to electrostatic gating techniques but without additional materials or processing. This enables us to optically pattern arbitrarily shaped p- and n-type regions in a TI, which we subsequently image with scanning photocurrent microscopy. The ability to optically write and erase mesoscopic electronic structures in a TI may aid in the investigation of the unique properties of the topological insulating phase. The gating effect also generalizes to other thin-film materials, suggesting that these phenomena could provide optical control of chemical potential in a wide range of ultrathin electronic systems. PMID:26601300
Persistent optical gating of a topological insulator
Yeats, Andrew L.; Pan, Yu; Richardella, Anthony; Mintun, Peter J.; Samarth, Nitin; Awschalom, David D.
2015-01-01
The spin-polarized surface states of topological insulators (TIs) are attractive for applications in spintronics and quantum computing. A central challenge with these materials is to reliably tune the chemical potential of their electrons with respect to the Dirac point and the bulk bands. We demonstrate persistent, bidirectional optical control of the chemical potential of (Bi,Sb)2Te3 thin films grown on SrTiO3. By optically modulating a space-charge layer in the SrTiO3 substrates, we induce a persistent field effect in the TI films comparable to electrostatic gating techniques but without additional materials or processing. This enables us to optically pattern arbitrarily shaped p- and n-type regions in a TI, which we subsequently image with scanning photocurrent microscopy. The ability to optically write and erase mesoscopic electronic structures in a TI may aid in the investigation of the unique properties of the topological insulating phase. The gating effect also generalizes to other thin-film materials, suggesting that these phenomena could provide optical control of chemical potential in a wide range of ultrathin electronic systems. PMID:26601300
Topological defect dynamics in operando battery nanoparticles
NASA Astrophysics Data System (ADS)
Ulvestad, A.; Singer, A.; Clark, J. N.; Cho, H. M.; Kim, J. W.; Harder, R.; Maser, J.; Meng, Y. S.; Shpyrko, O. G.
2015-06-01
Topological defects can markedly alter nanomaterial properties. This presents opportunities for “defect engineering,” where desired functionalities are generated through defect manipulation. However, imaging defects in working devices with nanoscale resolution remains elusive. We report three-dimensional imaging of dislocation dynamics in individual battery cathode nanoparticles under operando conditions using Bragg coherent diffractive imaging. Dislocations are static at room temperature and mobile during charge transport. During the structural phase transformation, the lithium-rich phase nucleates near the dislocation and spreads inhomogeneously. The dislocation field is a local probe of elastic properties, and we find that a region of the material exhibits a negative Poisson’s ratio at high voltage. Operando dislocation imaging thus opens a powerful avenue for facilitating improvement and rational design of nanostructured materials.
Assessment and control of electrostatic charges. [hazards to space missions
NASA Technical Reports Server (NTRS)
Barrett, M.
1974-01-01
The experience is described of NASA and DOD with electrostatic problems, generation mechanisms, and type of electrostatic hazards. Guidelines for judging possible effects of electrostatic charges on space missions are presented along with mathematical formulas and definitions.
Gear tooth topological modification
NASA Technical Reports Server (NTRS)
Kish, Jules G. (Inventor); Isabelle, Charles (Inventor)
1994-01-01
The topology of parallel axis gears, such as spur and helical gears is modified to produce quieter and more smoothly operating gear sets with more uniform load distribution. A finite element analysis of the gear in its operating mode is made to produce a plot of radial and tangential deflections of the pinion and gear tooth surfaces which will occur when the gears are loaded during operation. The resultant plot is then inverted to produce a plot, or set of coordinates, which will define the path of travel of the gear tooth grinding wheel, which path is a mirror image of the plot of the finite element analysis. The resulting gears, when subjected to operating loads, will thus be deflected tangentially and radially to their optimum operating, or theoretical true involute, positions so as to produce quieter, smoother, and more evenly loaded gear trains.
Thomas Gregoire; Jay G. Wacker
2002-06-03
New theories of electroweak symmetry breaking have recently been constructed that stabilize the weak scale and do not rely upon supersymmetry. In these theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this note we study the class of theories that can be described by theory spaces and show that the fundamental group of theory space describes all the relevant classical physics in the low energy theory. The relationship between the low energy physics and the topological properties of theory space allow a systematic method for constructing theory spaces that give any desired low energy particle content and potential. This provides us with tools for analyzing and constructing new theories of electroweak symmetry breaking.
Gregoire, T; Gregoire, Thomas; Wacker, Jay G.
2002-01-01
New theories of electroweak symmetry breaking have recently been constructed that stabilize the weak scale and do not rely upon supersymmetry. In these theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this note we study the class of theories that can be described by theory spaces and show that the fundamental group of theory space describes all the relevant classical physics in the low energy theory. The relationship between the low energy physics and the topological properties of theory space allow a systematic method for constructing theory spaces that give any desired low energy particle content and potential. This provides us with tools for analyzing and constructing new theories of electroweak symmetry breaking.
Transportation Network Topologies
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia (Editor)
2004-01-01
The existing U.S. hub-and-spoke air transportation system is reaching saturation. Major aspects of the current system, such as capacity, safety, mobility, customer satisfaction, security, communications, and ecological effects, require improvements. The changing dynamics - increased presence of general aviation, unmanned autonomous vehicles, military aircraft in civil airspace as part of homeland defense - contributes to growing complexity of airspace. The system has proven remarkably resistant to change. NASA Langley Research Center and the National Institute of Aerospace conducted a workshop on Transportation Network Topologies on 9-10 December 2003 in Williamsburg, Virginia. The workshop aimed to examine the feasibility of traditional methods for complex system analysis and design as well as potential novel alternatives in application to transportation systems, identify state-of-the-art models and methods, conduct gap analysis, and thus to lay a foundation for establishing a focused research program in complex systems applied to air transportation.
Schwerdtfeger, Peter; Wirz, Lukas N; Avery, James
2015-01-01
Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:25678935
Topology optimization using polytopes
NASA Astrophysics Data System (ADS)
Gain, Arun L.; Paulino, Glaucio H.; Duarte, Leonardo S.; Menezes, Ivan F. M.
2015-08-01
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the unstructured nature and the facial connectivity between elements makes them specially attractive for topology optimization applications. Numerical anomalies in designs such as the single node connections and checkerboard pattern, which are difficult to manufacture physically, are naturally alleviated with polyhedrons. Special interpolants such as Wachspress, mean value coordinates, maximum entropy shape functions are available to handle arbitrary shaped elements. But the finite elements approaches based on these shape functions face some challenges such as accurate and efficient computation of the shape functions and their derivatives for the numerical evaluation of the weak form integrals. In the current work, we solve the governing three-dimensional elasticity state equation using a Virtual Element Method (VEM) approach. The main characteristic difference between VEM and standard finite element methods (FEM) is that in VEM the canonical basis functions are not constructed explicitly. Rather the stiffness matrix is computed directly utilizing a projection map which extracts the linear component of the deformation. Such a construction guarantees the satisfaction of the patch test (used by engineers as an indicator of optimal convergence of numerical solutions under mesh refinement). Finally, the computations reduce to the evaluation of matrices which contain purely geometric surface facet quantities. The present work focuses on the first-order VEM in which the degrees of freedom associated with the vertices. Utilizing polyhedral elements for topology optimization, we show that the mesh bias in the member orientation is alleviated.
A supersymmetric topological inflation model
Kawasaki, M; Yamaguchi, Masahide
2002-01-01
We propose a topological inflation model in supergravity. In this model, the vacuum expectation value (VEV) of the scalar field takes a value much larger than the gravitational scale $M_{G} \\simeq 2.4 \\times 10^{18}$ GeV, which is large enough to cause topological inflation. On the other hand, the expansions of the K\\"ahler potential and the superpotential beyond the gravitational scale are validated by the introduction of the Nambu-Goldstone-like shift symmetry. Thus, topological inflation inevitably takes place in our model.
Topological representations of matroid maps
Stamps, Matthew T
2011-01-01
The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we use a construction of Engstr\\"{o}m, to show that structure-preserving maps between matroids induce topological mappings between their representations; a result previously known only in the oriented case. Specifically, we show that weak maps induce continuous maps which weakly decrease Betti numbers. Among other properties, we describe how this is process is a functor from the category of matroids with weak maps to the homotopy category of topological spaces.
Green's functions for topology change
Martín, J; Soares, I D; Martin, Jerome; Pinto-Neto, Nelson; Soares, Ivano Damiao
2005-01-01
We explicitly calculate Green's functions for quantum changes of topology in Friedman-Lemaitre-Robertson-Walker Universes, whose spacelike sections are compact but with distinct topologies depending on the curvature parameter $k$. We use the long-wavelength approximation at second order, and we demonstrate that quantum topological transitions from $k=-1$ to $k=1$ (and vice-versa) are allowed whereas no transition to a flat section is possible establishing thus a selection rule. Finally, a toy model is considered where all these properties are investigated concretely.
Charged Balanced Black Rings in Five Dimensions
Burkhard Kleihaus; Jutta Kunz; Kirsten Schnülle
2010-12-22
We present balanced black ring solutions of pure Einstein-Maxwell theory in five dimensions. The solutions are asymptotically flat, and their tension and gravitational self-attraction are balanced by the repulsion due to rotation and electrical charge. Hence the solutions are free of conical singularities and possess a regular horizon which exhibits the topology S1 x S2 of a torus. We discuss the global charges and the horizon properties of the solutions and show that they satisfy a Smarr relation. We construct these black rings numerically, restricting to the case of black rings with a rotation in the direction of the S1.
Fractional electric charge and quark confinement
Sam R. Edwards; André Sternbeck; Lorenz von Smekal
2012-02-07
Owing to their fractional electric charges, quarks are blind to transformations that combine a color center phase with an appropriate electromagnetic one. Such transformations are part of a global $Z_6$-like center symmetry of the Standard Model that is lost when quantum chromodynamics (QCD) is treated as an isolated theory. This symmetry and the corresponding topological defects may be relevant to non-perturbative phenomena such as quark confinement, much like center symmetry and ordinary center vortices are in pure SU($N$) gauge theories. Here we report on our investigations of an analogous symmetry in a 2-color model with dynamical Wilson quarks carrying half-integer electric charge.
Evolution of Topological Surface States in Tunable Topological Insulators
NASA Astrophysics Data System (ADS)
Yao, Guanggeng; Luo, Ziyu; Xu, Wentao; Feng, Yuanping; Wang, Xue-Sen
2014-03-01
Bi1-xSbx (0.07< x<0.22) is the first generation of 3D topological insulators (TIs), possessing a bandgap and topological surface states (SSs) generated by spin-orbit coupling In fact, within the whole range of 0< x<1 (i.e. from pure Bi to pure Sb), a topological phase transition has to occur as the system is twisted from topologically trivial to nontrivial phases, even though it becomes a semimetal hosting a negative indirect gap Therefore, taking advantage of Fourier-transform scanning tunneling spectroscopy (FT-STS) and ab initio calculations, we investigate the progressive evolution of topological SSs in the tunable Bi1-xSbx (0< x<1) materials grown by means of molecular beam epitaxy In alloys with several representative compositions, quasiparticle interference (QPI) patterns of SSs exhibit dramatic dependence on x values, indicating that intra-surface scatterings are ultimately determined by band structures and the associated spin textures. Additionally, the corresponding simulated QPI patterns are also revealed based on ab initio calculations. Such systematic studies of the Bi1-xSbx alloy family can be further explored to tailor surface energetic and transport properties for potential applications in quantum information, spintronics and many other topological quantum phenomena.
Epithelial topology Radhika Nagpal,1
Gibson, Matt
a diverse set of animals and plants.(1) The use of such topological models to study the process of cellular structures that arise from relatively simple physical processes. These include honeycombs,(4) soap froths,(5
Topological classification of RNA structures
Michael Bon; Graziano Vernizzi; Henri Orland; A. Zee
2006-07-21
We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number, whose value quantifies the topological complexity of the folded RNA structure. In such a representation, planar diagrams correspond to pure RNA secondary structures and have zero genus, whereas non planar diagrams correspond to pseudoknotted structures and have higher genus. We analyze real RNA structures from the databases wwPDB and Pseudobase, and classify them according to their topological genus. We compare the results of our statistical survey with existing theoretical and numerical models. We also discuss possible applications of this classification and show how it can be used for identifying new RNA structural motifs.
Topological entropy and secondary folding
Sarah Tumasz; Jean-Luc Thiffeault
2012-04-30
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is exactly equal to the growth induced by the map on the fundamental group of the torus. However, in many situations the numerically-computed topological entropy is greater than the bound implied by this action. We associate this gap between the bound and the true entropy with 'secondary folding': material lines undergo folding which is not homologically forced. We examine this phenomenon both for physical rod-stirring devices and toral linked twist maps, and show rigorously that for the latter secondary folds occur.
Adiabatic preparation of topological order.
Hamma, Alioscia; Lidar, Daniel A
2008-01-25
Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms of local order parameters. Here we show that a system of n spins forming a lattice on a Riemann surface can undergo a second order quantum phase transition between a spin-polarized phase and a string-net condensed phase. This is an example of a quantum phase transition between magnetic and topological order. We furthermore show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by O(sqrt[n]). This provides a physically plausible method for constructing and initializing a topological quantum memory. PMID:18232953
Adiabatic Preparation of Topological Order
NASA Astrophysics Data System (ADS)
Hamma, Alioscia; Lidar, Daniel A.
2008-01-01
Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms of local order parameters. Here we show that a system of n spins forming a lattice on a Riemann surface can undergo a second order quantum phase transition between a spin-polarized phase and a string-net condensed phase. This is an example of a quantum phase transition between magnetic and topological order. We furthermore show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by O(n). This provides a physically plausible method for constructing and initializing a topological quantum memory.
Can topology reshape segregation patterns?
Gandica, Yerali; Carletti, Timoteo
2015-01-01
We consider a metapopulation version of the Schelling model of segregation over several complex networks and lattice. We show that the segregation process is topology independent and hence it is intrinsic to the individual tolerance. The role of the topology is to fix the places where the segregation patterns emerge. In addition we address the question of the time evolution of the segregation clusters, resulting from different dynamical regimes of a coarsening process, as a function of the tolerance parameter. We show that the underlying topology may alter the early stage of the coarsening process, once large values of the tolerance are used, while for lower ones a different mechanism is at work and it results to be topology independent.
Comprehensible Presentation of Topological Information
Weber, Gunther H.; Beketayev, Kenes; Bremer, Peer-Timo; Hamann, Bernd; Haranczyk, Maciej; Hlawitschka, Mario; Pascucci, Valerio
2012-03-05
Topological information has proven very valuable in the analysis of scientific data. An important challenge that remains is presenting this highly abstract information in a way that it is comprehensible even if one does not have an in-depth background in topology. Furthermore, it is often desirable to combine the structural insight gained by topological analysis with complementary information, such as geometric information. We present an overview over methods that use metaphors to make topological information more accessible to non-expert users, and we demonstrate their applicability to a range of scientific data sets. With the increasingly complex output of exascale simulations, the importance of having effective means of providing a comprehensible, abstract overview over data will grow. The techniques that we present will serve as an important foundation for this purpose.
Strong correlations and topological order in one-dimensional systems
NASA Astrophysics Data System (ADS)
De Gottardi, Wade Wells
This thesis presents theoretical studies of strongly correlated systems as well as topologically ordered systems in 1D. Non-Fermi liquid behavior characteristic of interacting 1D electron systems is investigated with an emphasis on experimentally relevant setups and observables. The existence of end Majorana fermions in a 1D p-wave superconductor subject to periodic, incommensurate and disordered potentials is studied. The Tomonaga-Luttinger liquid (TLL), a model of interacting electrons in one spatial dimension, is considered in the context of two systems of experimental interest. First, a study of the electronic properties of single-walled armchair carbon nanotubes in the presence of transverse electric and magnetic fields is presented. As a result of their effect on the band structure and electron wave functions, fields alter the nature of the (effective) Coulomb interaction in tubes. In particular, it is found that fields couple to nanotube bands (or valleys), a quantum degree of freedom inherited from the underlying graphene lattice. As revealed by a detailed TLL calculation, it is predicted that fields induce electrons to disperse into their spin, band, and charge components. Fields also provide a means of tuning the shell-filling behavior associated with short tubes. The phenomenon of charge fractionalization is investigated in a one-dimensional ring. TLL theory predicts that momentum-resolved electrons injected into the ring will fractionalize into clockwise- and counterclockwise-moving quasiparticles. As a complement to transport measurements in quantum wires connected to leads, non-invasive measures involving the magnetic field profiles around the ring are proposed. Topological aspects of 1D p-wave superconductors are explored. The intimate connection between non-trivial topology (fermions) and spontaneous symmetry breaking (spins) in one-dimension is investigated. Building on this connection, a spin ladder system endowed with vortex degrees of freedom is proposed in order to study the effects that inhomogeneous potentials have on the topological phase diagram. Periodic vortex patterns yield a rich parameter space for tuning into a topologically non-trivial phase. This analysis hinges on the development of a topological invariant based on the wave function of Majorana fermions which inhabit the ends of the system and are robust to disorder. The method is generalized to aperiodic and disordered potentials. The topological phase diagram of such systems is studied; numerical and analytic results are found to be in close agreement.
Spin-Charge Soldering from Tensor Higgs mechanism
Diamantini, M C
2014-01-01
Spin-charge separation, a crucial ingredient in 2D models of strongly correlated systems, in mostly considered in condensed matter applications. In this paper we present a relativistic field-theoretic model in which charged particles of spin 1/2 emerge by soldering spinless charges and magnetic vortices in a confinement quantum phase transition modelled as a tensor Higgs mechanism. The model involves two gauge fields, a vector one and a two-form gauge field interacting by the topological BF term. When this tensor gauge symmetry is spontaneously broken charges are soldered to the ends of magnetic vortices and thus confined by a linear potential. If the vector potential has a topological $\\theta $-term with value $\\theta = \\pi$, the constituents of this "meson" acquire spin 1/2 in this transition.
Spin-Charge Soldering from Tensor Higgs mechanism
M. C. Diamantini; C. A. Trugenberger
2014-03-22
Spin-charge separation, a crucial ingredient in 2D models of strongly correlated systems, in mostly considered in condensed matter applications. In this paper we present a relativistic field-theoretic model in which charged particles of spin 1/2 emerge by soldering spinless charges and magnetic vortices in a confinement quantum phase transition modelled as a tensor Higgs mechanism. The model involves two gauge fields, a vector one and a two-form gauge field interacting by the topological BF term. When this tensor gauge symmetry is spontaneously broken charges are soldered to the ends of magnetic vortices and thus confined by a linear potential. If the vector potential has a topological $\\theta $-term with value $\\theta = \\pi$, the constituents of this "meson" acquire spin 1/2 in this transition.
Fractional (Chern and topological) insulators
NASA Astrophysics Data System (ADS)
Neupert, Titus; Chamon, Claudio; Iadecola, Thomas; Santos, Luiz H.; Mudry, Christopher
2015-12-01
We review various features of interacting Abelian topological phases of matter in two spatial dimensions, placing particular emphasis on fractional Chern insulators (FCIs) and fractional topological insulators (FTIs). We highlight aspects of these systems that challenge the intuition developed from quantum Hall physics—for instance, FCIs are stable in the limit where the interaction energy scale is much larger than the band gap, and FTIs can possess fractionalized excitations in the bulk despite the absence of gapless edge modes.
Topological excitations in semiconductor heterostructures
Koushik, R.; Mukerjee, Subroto; Ghosh, Arindam; Baenninger, Matthias; Narayan, Vijay; Pepper, Michael; Farrer, Ian; Ritchie, David A.
2013-12-04
Topological defects play an important role in the melting phenomena in two-dimensions. In this work, we report experimental observation of topological defect induced melting in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. The phenomenon is characterised by measurement of conductivity which goes to zero in a Berezinskii-Kosterlitz-Thouless like transition. Further evidence is provided via low-frequency conductivity noise measurements.
Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility
Michael Engelhardt
2010-08-29
The topological susceptibility of the SU(3) random vortex world-surface ensemble, an effective model of infrared Yang-Mills dynamics, is investigated. The model is implemented by composing vortex world-surfaces of elementary squares on a hypercubic lattice, supplemented by an appropriate specification of vortex color structure on the world-surfaces. Topological charge is generated in this picture by writhe and self-intersection of the vortex world-surfaces. Systematic uncertainties in the evaluation of the topological charge, engendered by the hypercubic construction, are discussed. Results for the topological susceptibility are reported as a function of temperature and compared to corresponding measurements in SU(3) lattice Yang-Mills theory. In the confined phase, the topological susceptibility of the random vortex world-surface ensemble appears quantitatively consistent with Yang-Mills theory. As the temperature is raised into the deconfined regime, the topological susceptibility falls off rapidly, but significantly less so than in SU(3) lattice Yang-Mills theory. Possible causes of this deviation, ranging from artefacts of the hypercubic description to more physical sources, such as the adopted vortex dynamics, are discussed.
Coherent single-spin source based on topological insulators
NASA Astrophysics Data System (ADS)
Xing, Yanxia; Yang, Zhong-Liu; Sun, Qing-Feng; Wang, Jian
2015-03-01
We report on the injection of quantized pure spin current into quantum conductors. In particular, we propose an on-demand single-spin source generated by periodically varying the gate voltages of two quantum dots that are connected to a two-dimensional topological insulator via tunneling barriers. Due to the nature of the helical states of the topological insulator, one or several spin pairs can be pumped out per cycle giving rise to a pure quantized alternating spin current. Depending on the phase difference between two gate voltages, this device can serve as an on-demand single-spin emitter or single-charge emitter. Again, due to the helicity of the topological insulator, the single-spin emitter or charge emitter is dissipationless and immune to disorder. The proposed single-spin emitter can be an important building block of future spintronic devices. We gratefully acknowledge the financial support from from NSF-China under Grant (Nos. 11174032 and 11374246), NBRP of China (2012CB921303), and a RGC Grant (HKU 705212P) from the Government of HKSAR.
Haldane phase in one-dimensional topological Kondo insulators
NASA Astrophysics Data System (ADS)
Mezio, Alejandro; Lobos, Alejandro M.; Dobry, Ariel O.; Gazza, Claudio J.
2015-11-01
We investigate the ground-state properties of a recently proposed model for a topological Kondo insulator in one dimension (i.e., the p -wave Kondo-Heisenberg lattice model) by means of the density-matrix renormalization-group method. The nonstandard Kondo interaction in this model is different from the usual (i.e., local) Kondo interaction in that the localized spins couple to the "p -wave" spin density of conduction electrons, inducing a topologically nontrivial insulating ground state. Based on the analysis of the charge- and spin-excitation gaps, the string order parameter, and the spin profile in the ground state, we show that, at half filling and low energies, the system is in the Haldane phase and hosts topologically protected spin-1/2 end states. Beyond its intrinsic interest as a useful "toy model" to understand the effects of strong correlations on topological insulators, we show that the p -wave Kondo-Heisenberg model could be experimentally implemented in p -band optical lattices loaded with ultracold Fermi gases.
TRW CHARGED DROPLET SCRUBBER CORROSION STUDIES
The report gives results of corrosion studies to provide definitive data concerning the corrosive nature of coke-oven waste-heat flue gas and its effects on wet electrostatic precipitators, and specifically on TRW's Charged Droplet Scrubber (CDS). The study characterized the chem...
Spin Charge Separation in the Quantum Spin Hall State
Qi, Xiao-Liang; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
The quantum spin Hall state is a topologically non-trivial insulator state protected by the time reversal symmetry. We show that such a state always leads to spin-charge separation in the presence of a {pi} flux. Our result is generally valid for any interacting system. We present a proposal to experimentally observe the phenomenon of spin-charge separation in the recently discovered quantum spin Hall system.
Geometric aspects of charged black holes in Palatini theories
NASA Astrophysics Data System (ADS)
Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, Antonio
2015-04-01
Charged black holes in gravity theories in the Palatini formalism present a number of unique properties. Their innermost structure is topologically nontrivial, representing a wormhole supported by a sourceless electric flux. For certain values of their effective mass and charge curvature divergences may be absent, and their event horizon may also disappear yielding a remnant. We give an overview of the mathematical derivation of these solutions and discuss their geodesic structure and other geometric properties.
Definition and Objectives Consider a pedestrian navigation system which
Dalang, Robert C.
-Matching Techniques for Indoor Positioning 3D Link/Node model The map is represented by links passing through axes Navigation system Geometry Topology Position Recalibration Route Guidance Concept A dedicated motion modelDefinition and Objectives Consider a pedestrian navigation system which contains a set of inertial
46 CFR 5.11 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 1 2014-10-01 2014-10-01 false Officer in Charge, Marine Inspection. 5.11 Section 5.11 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY PROCEDURES APPLICABLE TO THE PUBLIC MARINE INVESTIGATION REGULATIONS-PERSONNEL ACTION Definitions § 5.11 Officer in Charge, Marine Inspection. Officer...
46 CFR 5.11 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 1 2011-10-01 2011-10-01 false Officer in Charge, Marine Inspection. 5.11 Section 5.11 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY PROCEDURES APPLICABLE TO THE PUBLIC MARINE INVESTIGATION REGULATIONS-PERSONNEL ACTION Definitions § 5.11 Officer in Charge, Marine Inspection. Officer...
46 CFR 5.11 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 1 2013-10-01 2013-10-01 false Officer in Charge, Marine Inspection. 5.11 Section 5.11 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY PROCEDURES APPLICABLE TO THE PUBLIC MARINE INVESTIGATION REGULATIONS-PERSONNEL ACTION Definitions § 5.11 Officer in Charge, Marine Inspection. Officer...
46 CFR 5.11 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 1 2012-10-01 2012-10-01 false Officer in Charge, Marine Inspection. 5.11 Section 5.11 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY PROCEDURES APPLICABLE TO THE PUBLIC MARINE INVESTIGATION REGULATIONS-PERSONNEL ACTION Definitions § 5.11 Officer in Charge, Marine Inspection. Officer...
46 CFR 5.11 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false Officer in Charge, Marine Inspection. 5.11 Section 5.11 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY PROCEDURES APPLICABLE TO THE PUBLIC MARINE INVESTIGATION REGULATIONS-PERSONNEL ACTION Definitions § 5.11 Officer in Charge, Marine Inspection. Officer...
ATLAS Search for the MSSM Charged Higgs Boson
Potter, Chris
2008-11-23
The discovery of a charged Higgs boson would be definitive evidence of new physics beyond the Standard Model. The discovery potential of a MSSM charged Higgs boson with the ATLAS detector at the Large Hadron Collider is presented. The study is based on the analysis of signal and background simulated in detail through the experimental apparatus.
Photoemission spectroscopy studies of new topological insulator materials
NASA Astrophysics Data System (ADS)
Weber, Andrew Patton
As the size of a solid shrinks, the ratio of surface area to bulk volume grows and surface effects become more important. In a world where technologies advance with the shrinking size of electronic devices, one phase of matter has emerged which is fit for the near future of surface-dominated performance. Moreover, it has brought a new set of ideas to solid-state physics and chemistry, especially the understanding that the discipline of topology can be applied to classify the electron band structures. The topological insulator phase yields an exotic metal surface state in which the orientation of the electron's spin is locked perpendicular to its momentum. This property suppresses backscattering (making it possible to pass spin-polarized currents through the material without loss), offers a crucial ingredient for innovative approaches to quantum computation, and provides the basis for observing unique magnetoelectric effects. However, the surface states of materials in the topological insulator phase can wildly differ, so it is of interest to systematically characterize new materials to understand how the structure in position-space is related to the spin-resolved structure of electrons in energy- and momentum-space. We will discuss this relationship as it is probed through spin- and angle-resolved photoemission spectroscopy experiments on three topological (Bi2)m(Bi2Se3)n superlattices: (a) Bi2Se3 (m = 0, n = 1), (b) Bi4Se3 (m = 1, n = 1), and (c) BiSe (m = 1, n = 2). Our studies have not only proven the topological nature of these materials, but also demonstrate how bulk band structure and polar chemical bonding control the surface metal's concentration, dispersion, and spin-orbital character. Case (a) is considered to provide an ideal model of the topological surface metal. Case (b) provides the three important findings: (1) the chemical identity of the surface-termination controls the orbital composition and energy distribution of the surface states, (2) there are two topological states in sequential bulk band gaps, (3) of these, one of topological state undergoes a hybridization effect that yields a momentum-dependent gap in the band structure as large as 85 meV. Case (c) has a practical significance in that the surface metal has a potentially record-breaking carrier density of ~1013cm?2 (estimated from the Fermi surface area), more than an order of magnitude higher than in Bi2Se3. This occurs as a result of charge transfer from the Bi2 layers to the Bi2Se3 layers.
Topological Surface States Originated Spin-Orbit Torques in Bi(2)Se(3).
Wang, Yi; Deorani, Praveen; Banerjee, Karan; Koirala, Nikesh; Brahlek, Matthew; Oh, Seongshik; Yang, Hyunsoo
2015-06-26
The three dimensional topological insulator bismuth selenide (Bi(2)Se(3)) is expected to possess strong spin-orbit coupling and spin-textured topological surface states and, thus, exhibit a high charge to spin current conversion efficiency. We evaluate spin-orbit torques in Bi(2)Se(3)/Co(40)Fe(40)B(20) devices at different temperatures by spin torque ferromagnetic resonance measurements. As the temperature decreases, the spin-orbit torque ratio increases from ?0.047 at 300 K to ?0.42 below 50 K. Moreover, we observe a significant out-of-plane torque at low temperatures. Detailed analysis indicates that the origin of the observed spin-orbit torques is topological surface states in Bi(2)Se(3). Our results suggest that topological insulators with strong spin-orbit coupling could be promising candidates as highly efficient spin current sources for exploring the next generation of spintronic applications. PMID:26197141
Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
Simon Trebst; Philipp Werner; Matthias Troyer; Kirill Shtengel; Chetan Nayak
2006-09-03
We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of `magnetic' vortices, leading to confinement of the elementary `charge' excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and discuss our results in the context of quantum computation applications.
Monolayer Topological Insulators: Silicene, Germanene, and Stanene
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2015-12-01
We report the recent progress on the theoretical aspects of monolayer topological insulators including silicene, germanene and stanene, which are monolayer honeycomb structures of silicon, germanium and tin, respectively. They show quantum spin Hall effects in nature due to the spin–orbit interaction. The band gap can be tuned by applying perpendicular electric field, which induces a topological phase transition. We also analyze the topological properties of generic honeycomb systems together with the classification of topological insulators. Phase diagrams of topological insulators and superconductors in honeycomb systems are explicitly determined. We also investigate topological electronics including a topological field-effect transistor, the topological Kirchhoff’s law and the topological spin-valleytronics.
NASA Astrophysics Data System (ADS)
Hormozi, Layla
A quantum computer must be capable of manipulating quantum information while at the same time protecting it from error and loss of quantum coherence due to interactions with the environment. Topological quantum computation (TQC) offers a particularly elegant way to achieve this. In TQC, quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum computation is carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three-dimensional space-time, and the corresponding computation depends only on the topology of the braids formed by the world-lines. Quasiparticles that can be used for TQC are expected to exist in a variety of fractional quantum Hall states, among them the so-called Fibonacci anyons. These quasiparticles are conjectured to exist in the nu = 12/5 fractional quantum Hall state which has been observed in experiments. It has been shown that qubits can be encoded using three or four Fibonacci anyons and single-qubit gates can be carried out by braiding quasiparticles within each qubit. Braids that approximate single-qubit gates can be found through brute force searching and the result can be systematically improved, to any desired accuracy, by applying the Solovay-Kitaev algorithm in SU(2). Two-qubit gates are significantly harder to implement, mostly due to the following two reasons. First, the Hilbert space of the quasiparticles forming two qubits is considerably larger than the Hilbert space of the quasiparticles of a single qubit. Therefore, performing a brute force search to find braids that approximate two-qubit gates, as well as the implementation of the Solovay-Kitaev algorithm for subsequent improvements are prohibitively more difficult. Second, to construct any entangling two-qubit gate, one needs to braid some of the quasiparticles from one qubit around quasiparticles of the other qubit. This process will inevitably lead to leakage errors, i.e. transitions from the qubit space to other available states in the Hilbert space. In this thesis, I will present several efficient methods to construct two-qubit gates using a specific class of quasiparticles. In particular, I show that the problem of finding braids that correspond to two-qubit gates can be reduced to a series of smaller problems which involve braiding only three objects at a time. The required computational power for finding these braids is equivalent to that needed to find single-qubit gates, therefore, these braids can be found with the same high degree of accuracy and efficiency. The end result of this work is an efficient procedure for translating (or "compiling") arbitrary quantum algorithms into specific braiding patterns for Fibonacci anyons, as well as quasiparticles of certain other fractional quantum Hall states that can be used for TQC.
Topological order in a correlated three-dimensional topological insulator.
Maciejko, Joseph; Chua, Victor; Fiete, Gregory A
2014-01-10
Motivated by experimental progress in the growth of heavy transition metal oxides, we theoretically study a class of lattice models of interacting fermions with strong spin-orbit coupling. Focusing on interactions of intermediate strength, we derive a low-energy effective field theory for a fully gapped, topologically ordered, fractionalized state with an eightfold ground-state degeneracy. This state is a fermionic symmetry-enriched topological phase with particle-number conservation and time-reversal symmetry. The topological terms in the effective field theory describe a quantized magnetoelectric response and nontrivial mutual braiding statistics of dynamical extended vortex loops with emergent fermions in the bulk. We explicitly compute the expected mutual statistics in a specific model on the pyrochlore lattice within a slave-particle mean-field theory. We argue that our model also provides a possible condensed-matter realization of oblique confinement. PMID:24483914
Topological magnetoelectric effects in thin films of topological insulators
NASA Astrophysics Data System (ADS)
Morimoto, Takahiro; Furusaki, Akira; Nagaosa, Naoto
2015-08-01
We propose that the topological magnetoelectric (ME) effect, a hallmark of topological insulators (TIs), can be realized in thin films of TIs in the ? =0 quantum Hall state under magnetic field or by doping two magnetic ions with opposite signs of exchange coupling. These setups have the advantage compared to previously proposed setups that a uniform configuration of magnetic field or magnetization is sufficient for the realization of the topological ME effect. To verify our proposal, we numerically calculate ME response of TI thin films in the cylinder geometry and that of effective 2D models of surface Dirac fermions. The ME response is shown to converge to the quantized value corresponding to the axion angle ? =±? in the limit of the large top and bottom surface area of TI films, where nontopological contributions from the bulk and the side surface are negligible.
Phase diagram for topological superconductivity in topological insulator nanowires
NASA Astrophysics Data System (ADS)
de Juan, Fernando; Bardarson, Jens; Ilan, Roni
2015-03-01
A topological insulator nanowire can be used as a platform to produce one dimensional topological superconductivity in the presence of magnetic fields and the proximity effect from a nearby superconductor. In this work, we discuss the conditions under which this can happen by computing the topological invariant of the system from both a continuum Dirac fermion model and a lattice realization of a TI. We demonstrate that the presence of a vortex in the order parameter winding around the wire is essential to have a non-trivial invariant. In addition, we present a full phase diagram of the model as a function of chemical potential, flux and superconducting pairing, emphasizing that not all regions present a fully gapped superconducting state. Implications for transport in normal-superconductor junctions in this system will be discussed.
Higher-dimensional Rotating Charged Black Holes
Marco M. Caldarelli; Roberto Emparan; Bert Van Pol
2011-04-06
Using the blackfold approach, we study new classes of higher-dimensional rotating black holes with electric charges and string dipoles, in theories of gravity coupled to a 2-form or 3-form field strength and to a dilaton with arbitrary coupling. The method allows to describe not only black holes with large angular momenta, but also other regimes that include charged black holes near extremality with slow rotation. We construct explicit examples of electric rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory, with horizons of spherical and non-spherical topology. We also find new families of solutions with string dipoles, including a new class of prolate black rings. Whenever there are exact solutions that we can compare to, their properties in the appropriate regime are reproduced precisely by our solutions. The analysis of blackfolds with string charges requires the formulation of the dynamics of anisotropic fluids with conserved string-number currents, which is new, and is carried out in detail for perfect fluids. Finally, our results indicate new instabilities of near-extremal, slowly rotating charged black holes, and motivate conjectures about topological constraints on dipole hair.
Electric Charge 2 Conservation of Charge 4
and attraction of particles in the atom using the same laws that apply to the leaves of an electroscope, although of Charge 4 Quantization of Charge 5 Coulomb's Law 7 Energy of a System of Charges 11 Electrical Energy in a Crystal Lattice 14 The Electric Field 15 Charge Distributions 20 Flux 21 Gauss's Law 22 Field
On the charge density and asymptotic tail of a monopole
Derek Harland; Daniel Nogradi
2015-08-13
We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose expansion in powers of 1/r agrees with that of the conventional asymptotic magnetic field to all orders. We also show that the asymptotic field can be easily calculated from the spectral curve. Explicit examples are given for known monopole solutions.
Topological insulators and K-theory
Dan Li; Ralph M. Kaufmann; Birgit Wehefritz-Kaufmann
2015-10-27
We try to understand the topological $\\mathbb{Z}_2$ invariant, which characterizes time reversal invariant topological insulators, in the framework of index theory and K-theory. The topological $\\mathbb{Z}_2$ invariant counts the parity of Majorana zero modes, which can be interpreted as an analytical index. So it fits perfectly into an index theorem, and the topological index provides an efficient way to compute the topological $\\mathbb{Z}_2$ invariant. Finally, the bulk-boundary correspondence gives a different perspective to view the index theorem of the topological $\\mathbb{Z}_2$ invariant.
Fractionalized topological defects in optical lattices
NASA Astrophysics Data System (ADS)
Zhang, Xing-Hai; Fan, Wen-Jun; Shi, Jin-Wei; Kou, Su-Peng
2015-10-01
Topological objects are interesting topics in various fields of physics ranging from condensed matter physics to the grand unified and superstring theories. Among those, ultracold atoms provide a playground to study the complex topological objects. In this paper we present a proposal to realize an optical lattice with stable fractionalized topological objects. In particular, we generate the fractionalized topological fluxes and fractionalized skyrmions on two-dimensional optical lattices and fractionalized monopoles on three-dimensional optical lattices. These results offer a new approach to study the quantum many-body systems on optical lattices of ultracold quantum gases with controllable topological defects, including dislocations, topological fluxes and monopoles.
Borisov, A. B.; Kishine, Jun-ichiro; Bostrem, I. G.; Ovchinnikov, A. S.
2009-04-01
We show the existence of an isolated soliton excitation over the topological ground-state configuration in chiral helimagnet with the Dzyaloshinskii-Moryia exchange and the strong easy-plane anisotropy. The magnetic field perpendicular to the helical axis stabilizes the kink crystal state which plays a role of ''topological protectorate'' for the traveling soliton with a definite handedness. To find new soliton solution, we use the Baecklund transformation technique. It is pointed out that the traveling soliton carries the magnon density and a magnetic soliton transport may be realized.
Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium.
Dreischuh, A; Paulus, G G; Zacher, F; Grasbon, F; Walther, H
1999-11-01
Multiply charged optical vortex solitons (OVS) (m=1,...,4) are generated in a thermal nonlinear medium with saturation. The respective soliton constants are found to be linearly proportional to the topological charges. Special attention is paid to the modulational instability, which is effectively suppressed by a moderate saturation but still remains an increasing function of the topological charge. For the particular experimental conditions, the recorded OVS profiles are found to be in good qualitative agreement with the numerical stationary solutions of the generalized nonlinear Schrödinger equation. PMID:11970516
Quantum Capacitance in Topological Insulators
Xiu, Faxian; Meyer, Nicholas; Kou, Xufeng; He, Liang; Lang, Murong; Wang, Yong; Yu, Xinxin; Fedorov, Alexei V.; Zou, Jin; Wang, Kang L.
2012-01-01
Topological insulators show unique properties resulting from massless, Dirac-like surface states that are protected by time-reversal symmetry. Theory predicts that the surface states exhibit a quantum spin Hall effect with counter-propagating electrons carrying opposite spins in the absence of an external magnetic field. However, to date, the revelation of these states through conventional transport measurements remains a significant challenge owing to the predominance of bulk carriers. Here, we report on an experimental observation of Shubnikov-de Haas oscillations in quantum capacitance measurements, which originate from topological helical states. Unlike the traditional transport approach, the quantum capacitance measurements are remarkably alleviated from bulk interference at high excitation frequencies, thus enabling a distinction between the surface and bulk. We also demonstrate easy access to the surface states at relatively high temperatures up to 60?K. Our approach may eventually facilitate an exciting exploration of exotic topological properties at room temperature. PMID:22993694
On topological RNA interaction structures.
Qin, Jing; Reidys, Christian M
2013-07-01
Recently a folding algorithm of topological RNA pseudoknot structures was presented in Reidys et al. (2011). This algorithm folds single-stranded ?-structures, that is, RNA structures composed by distinct motifs of bounded topological genus. In this article, we set the theoretical foundations for the folding of the two backbone analogues of ? structures: the RNA ?-interaction structures. These are RNA-RNA interaction structures that are constructed by a finite number of building blocks over two backbones having genus at most ?. Combinatorial properties of ?-interaction structures are of practical interest since they have direct implications for the folding of topological interaction structures. We compute the generating function of ?-interaction structures and show that it is algebraic, which implies that the numbers of interaction structures can be computed recursively. We obtain simple asymptotic formulas for 0- and 1-interaction structures. The simplest class of interaction structures are the 0-interaction structures, which represent the two backbone analogues of secondary structures. PMID:23829651
Topological exploration of subterranean environments
Silver, D.; Ferguson, D.; Morris, A.; Thayer, S.
2006-06-15
The need for reliable maps of subterranean spaces too hazardous for humans to occupy has motivated the development of robotic mapping tools suited to these domains. As such, this work describes a system developed for autonomous topological exploration of mine environments to facilitate the process of mapping. The exploration framework is based upon the interaction of three main components: Node detection, node matching, and edge exploration. Node detection robustly identifies mine corridor intersections from sensor data and uses these features as the building blocks of a topological map. Node matching compares newly observed intersections to those stored in the map, providing global localization during exploration. Edge exploration translates topological exploration objectives into locomotion along mine corridors. This article describes both the robotic platform and the algorithms developed for exploration, and presents results from experiments conducted at a research coal mine near Pittsburgh, PA.
Topological Mixing with Ghost Rods
Emmanuelle Gouillart; Jean-Luc Thiffeault; Matthew D. Finn
2006-05-10
Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call ghost rods, because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.
Electrically Charged Two-Dimensional Skyrmions
NASA Astrophysics Data System (ADS)
Loginov, A. Yu.
2015-04-01
The (2 + 1)-dimensional Skyrme gauge model with a Chern-Simons term is considered. The presence of the Chern-Simons term leads to the result that the Abelian gauge field of the model becomes massive. This, in turn, leads to the existence in the given model of two-dimensional skyrmions carrying magnetic flux and possessing an electric charge and, consequently, nonzero angular momentum. It is shown that the model also admits the existence of two-dimensional skyrmions, whose electrically charged fields rotate with a constant phase frequency. Due to the nontrivial topology of the configurations of the (2 + 1)-dimensional Skyrme gauge model with a Chern-Simons term, the magnetic flux, the electric charge, and the angular momentum of a rotating two-dimensional skyrmion turn out to be interrelated.
Critical Points of the Electric Field from a Collection of Point Charges
Max, N; Weinkauf, T
2007-02-16
The electric field around a molecule is generated by the charge distribution of its constituents: positively charged atomic nuclei, which are well approximated by point charges, and negatively charged electrons, whose probability density distribution can be computed from quantum mechanics. For the purposes of molecular mechanics or dynamics, the charge distribution is often approximated by a collection of point charges, with either a single partial charge at each atomic nucleus position, representing both the nucleus and the electrons near it, or as several different point charges per atom. The critical points in the electric field are useful in visualizing its geometrical and topological structure, and can help in understanding the forces and motion it induces on a charged ion or neutral dipole. Most visualization tools for vector fields use only samples of the field on the vertices of a regular grid, and some sort of interpolation, for example, trilinear, on the grid cells. There is less risk of missing or misinterpreting topological features if they can be derived directly from the analytic formula for the field, rather than from its samples. This work presents a method which is guaranteed to find all the critical points of the electric field from a finite set of point charges. To visualize the field topology, we have modified the saddle connector method to use the analytic formula for the field.
Topological Superconductivity in Dirac Semimetals
NASA Astrophysics Data System (ADS)
Kobayashi, Shingo; Sato, Masatoshi
2015-10-01
Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest the possible application of our theory to recently discovered superconducting states in Cd3As2 .
Quantum cosmology with nontrivial topologies
Vargas, T.
2008-10-10
Quantum creation of a universe with a nontrivial spatial topology is considered. Using the Euclidean functional integral prescription, we calculate the wave function of such a universe with cosmological constant and without matter. The minisuperspace path integral is calculated in the semiclassical approximation, and it is shown that in order to include the nontrivial topologies in the path integral approach to quantum cosmology, it is necessary to generalize the sum over compact and smooth 4-manifolds to sum over finite-volume compact 4-orbifolds.
Topological Superconductivity in Dirac Semimetals.
Kobayashi, Shingo; Sato, Masatoshi
2015-10-30
Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest the possible application of our theory to recently discovered superconducting states in Cd_{3}As_{2}. PMID:26565490
Topological crystallography of gas hydrates.
Gudkovskikh, Sergey V; Kirov, Mikhail V
2015-07-01
A new approach to the investigation of the proton-disordered structure of clathrate hydrates is presented. This approach is based on topological crystallography. The quotient graphs were built for the unit cells of the cubic structure I and the hexagonal structure H. This is a very convenient way to represent the topology of a hydrogen-bonding network under periodic boundary conditions. The exact proton configuration statistics for the unit cells of structure I and structure H were obtained using the quotient graphs. In addition, the statistical analysis of the proton transfer along hydrogen-bonded chains was carried out. PMID:26131899
Quark masses, the Dashen phase, and gauge field topology
Creutz, Michael
2013-12-15
The CP violating Dashen phase in QCD is predicted by chiral perturbation theory to occur when the up–down quark mass difference becomes sufficiently large at fixed down-quark mass. Before reaching this phase, all physical hadronic masses and scattering amplitudes are expected to behave smoothly with the up-quark mass, even as this mass passes through zero. In Euclidean space, the topological susceptibility of the gauge fields is positive at positive quark masses but diverges to negative infinity as the Dashen phase is approached. A zero in this susceptibility provides a tentative signal for the point where the mass of the up quark vanishes. I discuss potential ambiguities with this determination. -- Highlights: •The CP violating Dashen phase in QCD occurs when the up quark mass becomes sufficiently negative. •Before reaching this phase, all physical hadronic masses and scattering amplitudes behave smoothly with the up-quark mass. •The topological susceptibility of the gauge fields diverges to negative infinity as the Dashen phase is approached. •A zero in the topological susceptibility provides a tentative signal for the point where the mass of the up quark vanishes. •The universality of this definition remains unproven. Potential ambiguities are discussed.
Topological approach to proton spin problem: decomposition controversy and beyond
S. C. Tiwari
2015-09-10
Lorentz covariant and gauge invariant definitions of quark and gluon spin and orbital angular momenta continue to pose a great theoretical challenge. A major controversy on the fundamental concepts followed Chen et al proposal: the basic idea is to split the gauge potential into pure gauge and physical components motivated by the gauge symmetry. We term it gauge symmetry paradigm (GSP) to distinguish it from the well-known inertial frame dependent transverse-longitudinal decomposition (TLP). A thorough study adhering to the traditional meaning of Lorentz covariance and gauge invariance is reported; it leads to a new result: logically consistent development of GSP does not exist and Chen et al proposal turns out to be either trivial or metamorphosed into TLP. Going beyond the controversy and the spin sum rules the necessity for a nonperurbative QCD approach to address the proton spin problem is underlined. We suggest topological approach: generalized de Rham theorems for QCD, and spin as a topological invariant for baryons are discussed. Nonabelian Stokes theorem is applied to derive color flux for the closed loop in a variant of Burkardt's U-shaped path. Similarity between Chen et al decomposition and Kondo decomposition of the gauge potential is suggestive of a topological perspective on the Chen et al proposal with interesting physics
An improved algorithm for computing topological entropy
Block, L.; Keesling, J.; Li, S.; Peterson, K. )
1989-06-01
A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed.
Detecting topological currents in graphene superlattices
Gorbachev, R. V.
Topological materials may exhibit Hall-like currents flowing transversely to the applied electric field even in the absence of a magnetic field. In graphene superlattices, which have broken inversion symmetry, topological ...
Formation of a topological non-Fermi liquid in MnSi.
Ritz, R; Halder, M; Wagner, M; Franz, C; Bauer, A; Pfleiderer, C
2013-05-01
Fermi liquid theory provides a remarkably powerful framework for the description of the conduction electrons in metals and their ordering phenomena, such as superconductivity, ferromagnetism, and spin- and charge-density-wave order. A different class of ordering phenomena of great interest concerns spin configurations that are topologically protected, that is, their topology can be destroyed only by forcing the average magnetization locally to zero. Examples of such configurations are hedgehogs (points at which all spins are either pointing inwards or outwards) and vortices. A central question concerns the nature of the metallic state in the presence of such topologically distinct spin textures. Here we report a high-pressure study of the metallic state at the border of the skyrmion lattice in MnSi, which represents a new form of magnetic order composed of topologically non-trivial vortices. When long-range magnetic order is suppressed under pressure, the key characteristic of the skyrmion lattice--that is, the topological Hall signal due to the emergent magnetic flux associated with the topological winding--is unaffected in sign or magnitude and becomes an important characteristic of the metallic state. The regime of the topological Hall signal in temperature, pressure and magnetic field coincides thereby with the exceptionally extended regime of a pronounced non-Fermi-liquid resistivity. The observation of this topological Hall signal in the regime of the NFL resistivity suggests empirically that spin correlations with non-trivial topological character may drive a breakdown of Fermi liquid theory in pure metals. PMID:23636328
Gravitational Duality, Topologically Massive Gravity and Holographic Fluids
NASA Astrophysics Data System (ADS)
Petropoulos, P. Marios
Self-duality in Euclidean gravitational set ups is a tool for finding remarkable four-dimensional geometries. From a holographic perspective, self-duality sets a relationship between two a priori independent boundary data: the boundary energy-momentum tensor and the boundary Cotton tensor. This relationship, which can be viewed as resulting from a topological mass term for gravity boundary dynamics, survives under the Lorentzian signature and provides a tool for generating exact bulk Einstein spaces carrying, among others, nut charge. In turn, the holographic analysis exhibits perfect-fluid-like equilibrium states and the presence of non-trivial vorticity allows to show that infinite number of transport coefficients vanish.
Topological self-dual vacua of deformed gauge theories
Julio Oliva; Mauricio Valenzuela
2014-06-10
We propose a deformation principle of gauge theories in three dimensions that can describe topologically stable self-dual gauge fields, i.e., vacua configurations that in spite of their masses do not deform the background geometry and are locally undetected by charged particles. We interpret these systems as describing boundary degrees of freedom of a self-dual Yang-Mills field in $2+2$ dimensions with mixed boundary conditions. Some of these fields correspond to Abrikosov-like vortices with an exponential damping in the direction penetrating into the bulk. We also propose generalizations of these ideas to higher dimensions and arbitrary p-form gauge connections.
High voltage high repetition rate pulse using Marx topology
NASA Astrophysics Data System (ADS)
Hakki, A.; Kashapov, N.
2015-06-01
The paper describes Marx topology using MOSFET transistors. Marx circuit with 10 stages has been done, to obtain pulses about 5.5KV amplitude, and the width of the pulses was about 30?sec with a high repetition rate (PPS > 100), Vdc = 535VDC is the input voltage for supplying the Marx circuit. Two Ferrite ring core transformers were used to control the MOSFET transistors of the Marx circuit (the first transformer to control the charging MOSFET transistors, the second transformer to control the discharging MOSFET transistors).
Topological interactions in spacetimes with thick line defects
NASA Astrophysics Data System (ADS)
Moraes, Fernando; Carvalho, A. M.; Costa, Ismael V.; Oliveira, F. A.; Furtado, Claudio
2003-08-01
In this work we study the topologically induced electric self-energy and self-force on a long, straight, wire in two distinct, but similar, spacetimes: (i) the Gott-Hiscock thick cosmic string spacetime, and (ii) the spacetime of a continuous distribution of infinitely thin cosmic strings over a disk of finite radius. In each case we obtain the electric self-energy and self-force both in the internal and external regions of the defect distribution. The self-force is always repulsive, independently of the sign of the charge, and is maximum on the string’s surface, in both cases.
May, J. Peter
AN INTRODUCTION TO TOPOLOGICAL ENTROPY KAREN BUTT Abstract. We develop the basic notions necessary are then used to compute the entropy of some standard dynamical systems. Finally, we show topological entropy and Separated Sets 3 4. Topological Entropy for Some Examples 6 5. Topological Conjugacy 9 Acknowledgements 10
46 CFR 42.05-55 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 2 2012-10-01 2012-10-01 false Officer in Charge, Marine Inspection. 42.05-55 Section... FOREIGN VOYAGES BY SEA Definition of Terms Used in This Subchapter § 42.05-55 Officer in Charge, Marine... Commander, is in charge of a marine inspection zone, and may supervise or perform the duties of a...
46 CFR 42.05-55 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 2 2011-10-01 2011-10-01 false Officer in Charge, Marine Inspection. 42.05-55 Section... FOREIGN VOYAGES BY SEA Definition of Terms Used in This Subchapter § 42.05-55 Officer in Charge, Marine... Commander, is in charge of a marine inspection zone, and may supervise or perform the duties of a...
46 CFR 42.05-55 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 2 2014-10-01 2014-10-01 false Officer in Charge, Marine Inspection. 42.05-55 Section... FOREIGN VOYAGES BY SEA Definition of Terms Used in This Subchapter § 42.05-55 Officer in Charge, Marine... Commander, is in charge of a marine inspection zone, and may supervise or perform the duties of a...
46 CFR 42.05-55 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 2 2013-10-01 2013-10-01 false Officer in Charge, Marine Inspection. 42.05-55 Section... FOREIGN VOYAGES BY SEA Definition of Terms Used in This Subchapter § 42.05-55 Officer in Charge, Marine... Commander, is in charge of a marine inspection zone, and may supervise or perform the duties of a...
46 CFR 30.10-47 - Officer in Charge, Marine Inspection-TB/ALL.
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2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false Officer in Charge, Marine Inspection-TB/ALL. 30.10-47 Section 30.10-47 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY TANK VESSELS GENERAL PROVISIONS Definitions § 30.10-47 Officer in Charge, Marine Inspection—TB/ALL. The term Officer in Charge,...
46 CFR 42.05-55 - Officer in Charge, Marine Inspection.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 2 2010-10-01 2010-10-01 false Officer in Charge, Marine Inspection. 42.05-55 Section... FOREIGN VOYAGES BY SEA Definition of Terms Used in This Subchapter § 42.05-55 Officer in Charge, Marine... Commander, is in charge of a marine inspection zone, and may supervise or perform the duties of a...
Dual-topology insertion of a dual-topology membrane protein
NASA Astrophysics Data System (ADS)
Woodall, Nicholas B.; Yin, Ying; Bowie, James U.
2015-08-01
Some membrane transporters are dual-topology dimers in which the subunits have inverted transmembrane topology. How a cell manages to generate equal populations of two opposite topologies from the same polypeptide chain remains unclear. For the dual-topology transporter EmrE, the evidence to date remains consistent with two extreme models. A post-translational model posits that topology remains malleable after synthesis and becomes fixed once the dimer forms. A second, co-translational model, posits that the protein inserts in both topologies in equal proportions. Here we show that while there is at least some limited topological malleability, the co-translational model likely dominates under normal circumstances.
40 CFR 98.430 - Definition of the source category.
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2013-07-01
... Contained in Pre-Charged Equipment or Closed-Cell Foams § 98.430 Definition of the source category. (a) The...-cell foams, consists of any entity that imports or exports pre-charged equipment that contains a fluorinated GHG, and any entity that imports or exports closed-cell foams that contain a fluorinated GHG....
40 CFR 98.430 - Definition of the source category.
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2014-07-01
... Contained in Pre-Charged Equipment or Closed-Cell Foams § 98.430 Definition of the source category. (a) The...-cell foams, consists of any entity that imports or exports pre-charged equipment that contains a fluorinated GHG, and any entity that imports or exports closed-cell foams that contain a fluorinated GHG....
40 CFR 98.430 - Definition of the source category.
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2012-07-01
... Contained in Pre-Charged Equipment or Closed-Cell Foams § 98.430 Definition of the source category. (a) The...-cell foams, consists of any entity that imports or exports pre-charged equipment that contains a fluorinated GHG, and any entity that imports or exports closed-cell foams that contain a fluorinated GHG....
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40 CFR 98.430 - Definition of the source category.
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...Contained in Pre-Charged Equipment or Closed-Cell Foams § 98.430 Definition of the...contained in pre-charged equipment or closed-cell foams, consists of any entity that imports...entity that imports or exports closed-cell foams that contain a fluorinated...
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2013-07-01
... From Primary Copper Smelters § 61.171 Definitions. All terms used in this subpart shall have the... of a molten or solid material to a copper converter. Control device means the air pollution control... rate at which arsenic is charged to the copper converters in the copper converter department based...
Code of Federal Regulations, 2014 CFR
2014-07-01
... From Primary Copper Smelters § 61.171 Definitions. All terms used in this subpart shall have the... of a molten or solid material to a copper converter. Control device means the air pollution control... rate at which arsenic is charged to the copper converters in the copper converter department based...
Code of Federal Regulations, 2012 CFR
2012-07-01
... From Primary Copper Smelters § 61.171 Definitions. All terms used in this subpart shall have the... of a molten or solid material to a copper converter. Control device means the air pollution control... rate at which arsenic is charged to the copper converters in the copper converter department based...
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... GENERAL PROVISIONS Benzene § 197.505 Definitions. As used in this subpart— Action level means an airborne concentration of benzene of 0.5 parts of benzene per million parts of air calculated as an eight hour time... specifically authorized by the person in charge of the vessel to enter a regulated area. Benzene...
Code of Federal Regulations, 2010 CFR
2010-10-01
... GENERAL PROVISIONS Benzene § 197.505 Definitions. As used in this subpart— Action level means an airborne concentration of benzene of 0.5 parts of benzene per million parts of air calculated as an eight hour time... specifically authorized by the person in charge of the vessel to enter a regulated area. Benzene...
Code of Federal Regulations, 2011 CFR
2011-10-01
... GENERAL PROVISIONS Benzene § 197.505 Definitions. As used in this subpart— Action level means an airborne concentration of benzene of 0.5 parts of benzene per million parts of air calculated as an eight hour time... specifically authorized by the person in charge of the vessel to enter a regulated area. Benzene...
Code of Federal Regulations, 2012 CFR
2012-10-01
... GENERAL PROVISIONS Benzene § 197.505 Definitions. As used in this subpart— Action level means an airborne concentration of benzene of 0.5 parts of benzene per million parts of air calculated as an eight hour time... specifically authorized by the person in charge of the vessel to enter a regulated area. Benzene...
Code of Federal Regulations, 2014 CFR
2014-10-01
... GENERAL PROVISIONS Benzene § 197.505 Definitions. As used in this subpart— Action level means an airborne concentration of benzene of 0.5 parts of benzene per million parts of air calculated as an eight hour time... specifically authorized by the person in charge of the vessel to enter a regulated area. Benzene...
Code of Federal Regulations, 2012 CFR
2012-07-01
...Contained in Pre-Charged Equipment or Closed-Cell Foams § 98.438 Definitions...refrigerator, chiller, or freezer. Closed-cell foam means any foam product, excluding...foam, that is constructed with a closed-cell structure and a blowing agent...
Code of Federal Regulations, 2011 CFR
2011-07-01
...Contained in Pre-Charged Equipment or Closed-Cell Foams § 98.438 Definitions...refrigerator, chiller, or freezer. Closed-cell foam means any foam product, excluding...foam, that is constructed with a closed-cell structure and a blowing agent...
Code of Federal Regulations, 2014 CFR
2014-01-01
... electric generator may charge its customers that are based on specified performance factors, in addition to... in a nuclear power plant (i.e., loss of offsite electric power system concurrent with turbine trip... definitions. Editorial Note: For Federal Register citations affecting § 50.2, see the List of CFR...
Code of Federal Regulations, 2011 CFR
2011-01-01
... electric generator may charge its customers that are based on specified performance factors, in addition to... in a nuclear power plant (i.e., loss of offsite electric power system concurrent with turbine trip... definitions. Editorial Note: For Federal Register citations affecting § 50.2, see the List of CFR...
Code of Federal Regulations, 2012 CFR
2012-01-01
... electric generator may charge its customers that are based on specified performance factors, in addition to... in a nuclear power plant (i.e., loss of offsite electric power system concurrent with turbine trip... definitions. Editorial Note: For Federal Register citations affecting § 50.2, see the List of CFR...
Code of Federal Regulations, 2013 CFR
2013-01-01
... electric generator may charge its customers that are based on specified performance factors, in addition to... in a nuclear power plant (i.e., loss of offsite electric power system concurrent with turbine trip... definitions. Editorial Note: For Federal Register citations affecting § 50.2, see the List of CFR...
Code of Federal Regulations, 2010 CFR
2010-01-01
... electric generator may charge its customers that are based on specified performance factors, in addition to... in a nuclear power plant (i.e., loss of offsite electric power system concurrent with turbine trip... definitions. Editorial Note: For Federal Register citations affecting § 50.2, see the List of CFR...
NASA Astrophysics Data System (ADS)
Liu, Jin Hua; Wang, Hai Tao
2015-10-01
Topological quantum phase transitions are numerically investigated in a spin-1/2 dimerized and frustrated Heisenberg chain by using infinite matrix product state representation with the infinite time evolving block decimation method. Quantum fidelity approach is employed to detect the degenerate ground states and quantum phase transitions. By calculating the long-range string order parameters, we find two topological Haldane phases characterized by two long-range string orders. Also, continuous and discontinuous behaviors of von Neumann entropy show that phase transitions between two topological Haldane phases are topologically continuous and discontinuous quantum phase transitions. For the topologically continuous phase transition, the central charge at the critical point is obtained as c = 1, which means that the topologically continuous quantum phase transition belongs to the Gaussian universality class.
Continuity and Separation in Symmetric Topologies
ERIC Educational Resources Information Center
Harris, J.; Lynch, M.
2007-01-01
In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.
COSMOLOGICAL STRUCURE FORMATION WITH TOPOLOGICAL Ruth DURRER
Durrer, Ruth
if the big bang is an \\irreproducible experiment", we want to learn from it as much as possible about to a subgroup H. Depending on the topology of the vacuum manifold M, which generically is topologically equivalent to the homogeneous space G=H, topological defects may form. This is described by an order
Testing Some Black Hole/Topological String
Gustafsson, Torgny
Testing Some Black Hole/Topological String Conjectures Gregory Moore IAS, April 11, 2005 Based on, to appear #12;Introduction We will be exploring some relations between black hole en- tropy and topological of BPS black holes and topological string theory on X. We will be trying to test some
SPINES OF TOPOLOGICAL MANIFOLDS ERIK KJR PEDERSEN
Pedersen, Erik Kjær
SPINES OF TOPOLOGICAL MANIFOLDS ERIK KJÆR PEDERSEN In this paper we prove that a closed 2-connected topological manifold has a PL-spine, i. e. there is a locally tamely embedded complex such that a regular). This "spine method" together with the relative edition of regular neighborhoods of complexes in topological
Long Range Topological Order, the Chiral Condensate, and the Berry Connection in QCD
H. B. Thacker
2014-09-12
Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a Berry connection, which is a gauge connection obtained from the phase of the electron wave function transported over momentum space rather than coordinate space. The phase of a closed Wilson loop of the Berry connection around the Brillouin zone defines a topological order parameter which labels discrete flux vacua. The conducting states are surface modes on the domain walls between discrete vacua. Evidence from large-$N_c$ chiral dynamics, holographic QCD, and Monte Carlo observations has pointed to a picture of the QCD vacuum that is very similar to that of a topological insulator, with discrete quasivacua labelled by $\\theta$ angles that differ by mod $2\\pi$. In this picture, the domain walls are membranes of Chern-Simons charge, and the quark condensate consists of surface modes on these membranes, which are delocalized and thus support the long range propagation of Goldstone pions. The Berry phase in QED2 describes charge polarization of fermion-antifermion pairs, while in 4D QCD it describes the polarization of Chern-Simons membranes.
Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator
NASA Astrophysics Data System (ADS)
Lobos, Alejandro M.; Dobry, Ariel O.; Galitski, Victor
2015-04-01
Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1 /2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p -wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U =0 ). Furthermore, at low enough temperatures, the system maps onto a spin-1 /2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1 /2 end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.
ERIC Educational Resources Information Center
Bierschenk, Bernhard
Topological and algebraic scales were compared in the representation of the concept of human worth in behavioral-semantic terms. In a first experiment, seven doctoral students of Business Administration in Sweden explored the notion of worth using definitions from at least 10 dictionaries as the intentional-semantic content. Each subject served as…
Ravenel, Douglas
Life after the telescope conjecture [To appear in Algebraic K-theory and Algebraic Topology, edited, Waldhausen and McClure-Staffeldt. We offer a new definition (suggested by the failure of the telescope. The telescope conjecture (2.2 below) was first announced by the author in 1977, published in [Rav84
Crystallographic topology and its applications
Johnson, C.K.; Burnett, M.N.; Dunbar, W.D.
1996-10-01
Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.
Topological insulator nanowires and nanoribbons.
Kong, Desheng; Randel, Jason C; Peng, Hailin; Cha, Judy J; Meister, Stefan; Lai, Keji; Chen, Yulin; Shen, Zhi-Xun; Manoharan, Hari C; Cui, Yi
2010-01-01
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi(2)Se(3) material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi(2)Se(3) nanomaterials with a variety of morphologies. The synthesis of Bi(2)Se(3) nanowires and nanoribbons employs Au-catalyzed vapor-liquid-solid (VLS) mechanism. Nanowires, which exhibit rough surfaces, are formed by stacking nanoplatelets along the axial direction of the wires. Nanoribbons are grown along [1120] direction with a rectangular cross-section and have diverse morphologies, including quasi-one-dimensional, sheetlike, zigzag and sawtooth shapes. Scanning tunneling microscopy (STM) studies on nanoribbons show atomically smooth surfaces with approximately 1 nm step edges, indicating single Se-Bi-Se-Bi-Se quintuple layers. STM measurements reveal a honeycomb atomic lattice, suggesting that the STM tip couples not only to the top Se atomic layer, but also to the Bi atomic layer underneath, which opens up the possibility to investigate the contribution of different atomic orbitals to the topological surface states. Transport measurements of a single nanoribbon device (four terminal resistance and Hall resistance) show great promise for nanoribbons as candidates to study topological surface states. PMID:20030392
Phantom stars and topology change
DeBenedictis, Andrew; Garattini, Remo; Lobo, Francisco S. N.
2008-11-15
In this work, we consider time-dependent dark-energy star models, with an evolving parameter {omega} crossing the phantom divide {omega}=-1. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark-energy star into a wormhole. The criteria for this topology change are discussed and, in particular, we consider a Casimir energy approach involving quasilocal energy difference calculations that may reflect or measure the occurrence of a topology change. We denote these exotic geometries consisting of dark-energy stars (in the phantom regime) and phantom wormholes as phantom stars. The final product of this topological change, namely, phantom wormholes, have far-reaching physical and cosmological implications, as in addition to being used for interstellar shortcuts, an absurdly advanced civilization may manipulate these geometries to induce closed timelike curves, consequently violating causality.
Topological methods in combinatorial geometry
NASA Astrophysics Data System (ADS)
Karasev, Roman N.
2008-12-01
This survey is devoted to some results in the area of combinatorial and convex geometry, from classical theorems up to the latest contemporary results, mainly those results whose proofs make essential use of the methods of algebraic topology. Various generalizations of the Borsuk-Ulam theorem for a (Z_p)^k-action are explained in detail, along with applications to Knaster's problem about levels of a function on a sphere, and applications are discussed to the Lyusternik-Shnirel'man theory for estimating the number of critical points of a smooth function. An overview is given of the topological methods for estimating the chromatic number of graphs and hypergraphs, in theorems of Tverberg and van Kampen-Flores type. The author's results on the `dual' analogues of the central point theorem and Tverberg's theorem are described. Results are considered on the existence of inscribed and circumscribed polytopes of special form for convex bodies and on the existence of billiard trajectories in a convex body. Results on partition of measures by hyperplanes and other partitions of Euclidean space are presented. For theorems of Helly type a brief overview is given of topological approaches connected with the nerve of a family of convex sets in Euclidean space. Also surveyed are theorems of Helly type for common flat transversals, and results using the topology of the Grassmann manifold and of the canonical vector bundle over it are considered in detail.
Programming a Topological Quantum Computer
Simon J. Devitt; Kae Nemoto
2012-09-07
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction code, required to correct for inevitable hardware faults that will exist for a large scale quantum device. It is also a measurement based model of quantum computation, meaning that the quantum hardware is responsible only for the construction of a large, computationally universal quantum state. This quantum state is then strategically consumed, allowing for the realisation of a fully error corrected quantum algorithm. The number of physical qubits needed by the quantum hardware and the amount of time required to implement an algorithm is dictated by the manner in which this universal quantum state is consumed. In this paper we examine the problem of algorithmic optimisation in the topological lattice and introduce the required elements that will be needed when designing a classical software package to compile and implement a large scale algorithm on a topological quantum computer.
Dynamical Triangulation with Fluctuating Topology
Bas V. de Bakker
1994-11-25
We consider a dynamical triangulation model of euclidean quantum gravity where the topology is not fixed. This model is equivalent to a tensor generalization of the matrix model of two dimensional quantum gravity. A set of moves is given that allows Monte Carlo simulation of this model. Some preliminary results are presented for the case of four dimensions.
Topological Quantum Computation Zhenghan Wang
Rowell, Eric C.
Topological Quantum Computation Zhenghan Wang Microsoft Station Q & UC Sana Barbara Texas, March 26, 2015 #12;Classical Physics Turing Model Quantum Mechanics Quantum Computing Quantum Field Theory ??? String Theory ?????? Quantum field computing is the same as quantum computing. True for TQFTs (Freedman
Bei Zeng; Xiao-Gang Wen
2015-03-02
In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is not precise. We introduce the concept of \\emph{gapped quantum liquid} as a special kind of gapped quantum states that can "dissolve" any product states on additional sites. Topologically ordered states actually correspond to gapped quantum liquids with stable ground-state degeneracy. Symmetry-breaking states for on-site symmetry are also gapped quantum liquids, but with unstable ground-state degeneracy. (2) We point out that the universality classes of generalized local unitary (gLU) transformations (without any symmetry) contain both topologically ordered states and symmetry-breaking states. This allows us to use a gLU invariant -- topological entanglement entropy -- to probe the symmetry-breaking properties hidden in the exact ground state of a finite system, which does not break any symmetry. This method can probe symmetry- breaking orders even without knowing the symmetry and the associated order parameters. (3) The universality classes of topological orders and symmetry-breaking orders can be distinguished by \\emph{stochastic local (SL) transformations} (i.e.\\ \\emph{local invertible transformations}): small SL transformations can convert the symmetry-breaking classes to the trivial class of product states with finite probability of success, while the topological-order classes are stable against any small SL transformations, demonstrating a phenomenon of emergence of unitarity. This allows us to give a new definition of long-range entanglement based on SL transformations, under which only topologically ordered states are long-range entangled.
NASA Astrophysics Data System (ADS)
Zeng, Bei; Wen, Xiao-Gang
2015-03-01
In this work, we present some new understanding of topological order, including three main aspects. (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is not precise. We introduce the concept of gapped quantum liquid as a special kind of gapped quantum states that can "dissolve" any product states on additional sites. Topologically ordered states actually correspond to gapped quantum liquids with stable ground-state degeneracy. Symmetry-breaking states for on-site symmetry are also gapped quantum liquids, but with unstable ground-state degeneracy. (2) We point out that the universality classes of generalized local unitary (gLU) transformations (without any symmetry) contain both topologically ordered states and symmetry-breaking states. This allows us to use a gLU invariant—topological entanglement entropy—to probe the symmetry-breaking properties hidden in the exact ground state of a finite system, which does not break any symmetry. This method can probe symmetry- breaking orders even without knowing the symmetry and the associated order parameters. (3) The universality classes of topological orders and symmetry-breaking orders can be distinguished by stochastic local (SL) transformations (i.e., local invertible transformations): small SL transformations can convert the symmetry-breaking classes to the trivial class of product states with finite probability of success, while the topological-order classes are stable against any small SL transformations, demonstrating a phenomenon of emergence of unitarity. This allows us to give a definition of long-range entanglement based on SL transformations, under which only topologically ordered states are long-range entangled.
Ion mobility-mass spectrometry of lasso peptides: signature of a rotaxane topology.
Jeanne Dit Fouque, Kevin; Afonso, Carlos; Zirah, Séverine; Hegemann, Julian D; Zimmermann, Marcel; Marahiel, Mohamed A; Rebuffat, Sylvie; Lavanant, Hélène
2015-01-20
Ion mobility mass spectrometry data were collected on a set of five class II lasso peptides and their branched-cyclic topoisomers prepared in denaturing solvent conditions with and without sulfolane as a supercharging agent. Sulfolane was shown not to affect ion mobility results and to allow the formation of highly charged multiply protonated molecules. Drift time values of low charged multiply protonated molecules were found to be similar for the two peptide topologies, indicating the branched-cyclic peptide to be folded in the gas phase into a conformation as compact as the lasso peptide. Conversely, high charge states enabled a discrimination between lasso and branched-cyclic topoisomers, as the former remained compact in the gas phase while the branched-cyclic topoisomer unfolded. Comparison of the ion mobility mass spectrometry data of the lasso and branched-cyclic peptides for all charge states, including the higher charge states obtained with sulfolane, yielded three trends that allowed differentiation of the lasso form from the branched-cyclic topology: low intensity of highly charged protonated molecules, even with the supercharging agent, low change in collision cross sections with increasing charge state of all multiply protonated molecules, and narrow ion mobility peak widths associated with the coexistence of fewer conformations and possible conformational changes. PMID:25495527
Flórez, Juan B
2007-01-01
A detailed analysis of $Z^{'0}Z^{'0}$, $K^{+}K^{-}$ and $K^{0}\\bar{K}^{0}$ pair production in $e^{+}e^{-}$ collisions is presented by using helicity amplitudes. The trilinear bosons couplings in the $SU(3)_{C}\\otimes SU(3)_{L}\\otimes U(1)_{X}$ models without exotic electric charges are also calculated. We carry out the mentioned analysis for two models, one of them is a one family model which is an $E_6$ subgroup \\cite{b1} and the other one is a three family model with right handed neutrinos\\cite{b2,b3}. These models do not contain exotic electric charges. For them, we give explicit formulae and the corresponding numerical estimates of the cross-sections and angular distributions occurred in the processes $e^{+}e^{-}\\to Z^{'0}Z^{'0}$, $e^{+}e^{-} \\to K^{+}K^{-}$ and $e^{+}e^{-}\\to K^{0}\\bar{K}^{0}$ present in our models. We suppose these processes are invariant under $C$, $P$ and $T$ transformation.