R. Höllwieser; M. Faber; U. M. Heller
2012-06-19
We analyze topological charge contributions from classical SU(2) center vortices with shapes of planes and spheres using different topological charge definitions, namely the center vortex picture of topological charge, a discrete version of F\\~{F} in the plaquette and hypercube definitions and the lattice index theorem. For the latter the zeromodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations are investigated. We find several problems for the individual definitions and discuss the discrepancies between the different topological charge definitions. Our results show that the interpretation of topological charge in the background of center vortices is rather subtle.
The definitions of charge and the invariance of charge
NASA Astrophysics Data System (ADS)
Ivezi?, T.
1992-02-01
The invariance of different collections of charges is examined for different definitions of charge. The complete equivalence of the covariant definition and the standard definition of charge is proved. Purcell's definition of the invariance of charge in terms of equality of fluxes of E is shown to be generally incorrect. Different experiments performed to verify the invariance of charge are discussed.
Topological charge density around static color sources
Manfried Faber; Harald Markum; Stefan Olejnik; Wolfgang Sakuler
1993-11-29
We analyze the topological structure of quenched QCD in the presence of static color sources. Distributions of the topological charge density around static quarks and mesons are computed in both phases of QCD. We observe a suppression of topological fluctuations in the vicinity of external sources. In the confinement phase, the suppression occurs in the whole flux tube between the static quark and antiquark.
Topology density correlator on dynamical domain-wall ensembles with nearly frozen topological charge
JLQCD collaboration; H. Fukaya; S. Aoki; G. Cossu; S. Hashimoto; T. Kaneko; J. Noaki
2014-11-13
Global topological charge decorrelates very slowly or even freezes in fine lattice simulations. On the other hand, its local fluctuations are expected to survive and lead to the correct physical results as long as the volume is large enough. We investigate this issue on recently generated configurations including dynamical domain-wall fermions at lattice spacings a = 0.08 fm and finer. We utilize the Yang-Mills gradient flow to define the topological charge density operator and calculate its long-distance correlation, through which we propose a new method for extracting the topological susceptibility in a sub-volume. This method takes care of the finite volume correction, which reduces the bias caused by the global topological charge. Our lattice data clearly show a shorter auto-correlation time than that of the naive definition using the whole lattice, and are less sensitive to the global topological history. Numerical results show a clear sea-quark mass dependence, which agrees well with the prediction of chiral perturbation theory.
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.
Supersymmetry algebras that include topological charges
E. Witten; D. I. Olive
1978-01-01
We show that in supersymmetric theories with solitons, the usual supersymmetry algebra is not valid; the algebra is modified to include the topological quantum numbers as central charges. Using the corrected algebra, we are able to show that in certain four dimensional gauge theories, there are no quantum corrections to the classical mass spectrum. These are theories for which Bogomolny
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.
Topological charge selection rule for phase singularities
Zacares, M.; Vijande, J.; Ferrando, A.; Merino, E.
2009-10-15
We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.
Detached topological charge on capillary bridges
Verena Schmid; Axel Voigt
2014-01-30
We numerically investigate crystalline order on negative Gaussian curvature capillary bridges. In agreement with the experimental results in [W. Irvine et al., Nature, "Pleats in crystals on curved surfaces", 2010, (468), 947]} we observe for decreasing integrated Gaussian curvature a sequence of transitions, from no defects to isolated dislocations, pleats, scars and isolated sevenfold disclinations. We especially focus on the dependency of the detached topological charge on the integrated Gaussian curvature, for which we observe, again in agreement with the experimental results, no net disclination for an integrated curvature down to -10, and a linear behaviour from there on until the disclinations match the integrated curvature of -12. The results are obtained using a phase field crystal approach on catenoid-like surfaces and are highly sensitive to the initialization.
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.
Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
Marco Cé; Cristian Consonni; Georg P. Engel; Leonardo Giusti
2015-06-19
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
NASA Astrophysics Data System (ADS)
Park, Daniel S.
2015-07-01
We study how charges of global symmetries that are manifest in the ultraviolet definition of a theory are realized as topological charges in its infrared effective theory for two-dimensional theories with N =(2 ,2 ) supersymmetry. We focus on the charges that the states living on S1 carry. The central charge—or Bogomol'nyi-Prasad-Sommerfield (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 four-dimensional 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 four-dimensional gauge theory. We also examine the topologically charged massive BPS states on S1 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 S1, 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 ...
The Topological Charges of the an(1) Affine Toda Solitons
NASA Astrophysics Data System (ADS)
McGhee, William A.
The topological charges of the an(1) affine Toda solitons are considered. A general formula is presented for the number of charges associated with each soliton, as well as an expression for the charges themselves. For each soliton the charges are found to lie in the corresponding fundamental representation, though in general these representations are not filled. Bach soliton’s topological charges are invariant under cyclic permutations of the simple roots plus the extended root or, equivalently, under the action of the Coxeter element (with a particular ordering). Multisolitons are considered and are found to have topological charges filling the remainder of the fundamental representations as well as the entire weight lattice. The article concludes with a discussion of some of the other affine Toda theories.
Effect of topology on the critical charge in graphene
Chakraborty, Baishali; Gupta, Kumar S. [Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700064 (India); Sen, Siddhartha [CRANN School of Physics, Trinity College, Dublin 2 (Ireland)
2011-03-15
We show that the critical charge for the Dirac excitations in gapless graphene depends on the spatial topology of the sample. In particular, for graphene cones, the effective value of the critical charge can tend toward zero for a suitable angle of the conical sample. We discuss the nature of the scattering phase shifts, quasibound state energies, and local density of states for a gapless graphene cone and determine the dependence of these physical quantities on the sample topology.
Stable structures with high topological charge in nonlinear photonic quasicrystals
Law, K J H; Kevrekidis, P G; Bishop, A R
2010-01-01
Stable vortices with topological charge of 3 and 4 are examined numerically and analytically in photonic quasicrystals created by interference of 5 as well as 8 beams, in the cases of cubic as well as saturable nonlinearities. These structures are experimentally realizable, including a prototypical example of a stable charge 4 vortex. Direct numerical simulations corroborate the analytical and numerical linear stability analysis predictions.
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...
The anomalous transport of axial charge: topological vs non-topological fluctuations
Iatrakis, Ioannis; Yin, Yi
2015-01-01
Axial charge imbalance is an essential ingredient in novel effects associated with chiral anomaly such as chiral magnetic effects (CME). In a non-Abelian plasma with chiral fermions, local axial charge can be generated a) by topological fluctuations which would create domains with non-zero winding number b) by conventional non-topological thermal fluctuations. We provide a holographic evaluations of medium's response to dynamically generated axial charge density in hydrodynamic limit and examine if medium's response depends on the microscopic origins of axial charge imbalance. We show a local domain with non-zero winding number would induce a non-dissipative axial current due to chiral anomaly. We illustrate holographically that a local axial charge imbalance would be damped out with the damping rate related to Chern-Simon diffusive constant. By computing chiral magnetic current in the presence of dynamically generated axial charge density, we found that the ratio of CME current over the axial charge density ...
Bradlyn, Barry
2015-01-01
We show that the topological central charge of a topological phase can be directly accessed from the ground-state wavefunctions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at least up to addition of another topological invariant that arises in some cases. For trial wavefunctions that are given by conformal blocks (chiral correlation functions) in a conformal field theory (CFT), we carry out this calculation analytically, using the hypothesis of generalized screening. The topological central charge is found to be that of the underlying CFT used in the construction, as expected. The calculation makes use of the gravitational anomaly in the chiral CFT. It is also shown that the Hall conductivity can be obtained in an analogous way from the U($1$) gauge anomaly.
NASA Astrophysics Data System (ADS)
Bradlyn, Barry; Read, N.
2015-04-01
We show that the topological central charge of a topological phase can be directly accessed from the ground-state wave functions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at least up to addition of another topological invariant that arises in some cases. For trial wave functions that are given by conformal blocks (chiral correlation functions) in a conformal field theory (CFT), we carry out this calculation analytically, using the hypothesis of generalized screening. The topological central charge is found to be that of the underlying CFT used in the construction, as expected. The calculation makes use of the gravitational anomaly in the chiral CFT. It is also shown that the Hall conductivity can be obtained in an analogous way from the U(1) gauge anomaly.
Wilson mass dependence of the overlap topological charge density
Peter J. Moran; Derek B. Leinweber; Jianbo Zhang
2010-11-04
The dependence of the overlap Dirac operator on the Wilson-mass regulator parameter is studied through calculations of the overlap topological charge densities at a variety of Wilson-mass values. In this formulation, the Wilson-mass is used in the negative mass region and acts as a regulator governing the scale at which the Dirac operator is sensitive to topological aspects of the gauge field. We observe a clear dependence on the value of the Wilson-mass and demonstrate how these values can be calibrated against a finite number of stout-link smearing sweeps. The overlap topological charge density is also computed using a pre-smeared gauge field for the input kernel. We show how applying the overlap operator leads to further filtering of the gauge field. The results suggest that the freedom typically associated with smearing algorithms, through the variable number of sweeps, also exists in the overlap operator, through the variable Wilson-mass parameter.
Rotating One-Half Topological Charge Dyon
Teh, Rosy; Wong, Khai-Ming
2012-01-01
Recently, we have shown the existence of a finite energy one-half monopole. In this paper, we would like to introduce electric charge into the one-half monopole configuration, thus creating a one-half dyon. This one-half dyon possesses finite energy, magnetic dipole moment and angular momentum. Hence it is able to rotate in the presence of an external magnetic field. Similar to the single pole dyons and the MAP dyons, this one-half dyon possesses critical (maximum) electric charge, total energy, and magnetic dipole moment when the Higgs self-coupling constant is nonvanishing, and the electric charge parameter approaches one. This one-half dyon solution does not satisfy the first order Bogomol'nyi equations and is a non-BPS solution in the limit of vanishing Higgs self-coupling constant.
The anomalous transport of axial charge: topological vs non-topological fluctuations
Ioannis Iatrakis; Shu Lin; Yi Yin
2015-06-03
Axial charge imbalance is an essential ingredient in novel effects associated with chiral anomaly such as chiral magnetic effects (CME). In a non-Abelian plasma with chiral fermions, local axial charge can be generated a) by topological fluctuations which would create domains with non-zero winding number b) by conventional non-topological thermal fluctuations. We provide a holographic evaluations of medium's response to dynamically generated axial charge density in hydrodynamic limit and examine if medium's response depends on the microscopic origins of axial charge imbalance. We show a local domain with non-zero winding number would induce a non-dissipative axial current due to chiral anomaly. We illustrate holographically that a local axial charge imbalance would be damped out with the damping rate related to Chern-Simon diffusive constant. By computing chiral magnetic current in the presence of dynamically generated axial charge density, we found that the ratio of CME current over the axial charge density is independent of the origin of axial charge imbalance in low frequency and momentum limit. Finally, a stochastic hydrodynamic equation of the axial charge is formulated by including both types of fluctuations.
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.
Characterization of topological charge and orbital angular momentum of shaped optical vortices.
Amaral, Anderson M; Falcão-Filho, Edilson L; de Araújo, Cid B
2014-12-01
Optical vortices (OV) are usually associated to cylindrically symmetric light beams. However, they can have more general geometries that extends their applicability. Since the typical experimental characterization methods are not appropriate for OV with arbitrary shapes, we discuss in this work how the definitions of the classical orbital angular momentum and the topological charge can be used to retrieve these informations in the general case. The concepts discussed are experimentally demonstrated and may be specially useful in areas such as optical tweezers and plasmonics. PMID:25606960
$?^\\prime$ meson mass from topological charge density correlator in QCD
JLQCD collaboration; H. Fukaya; S. Aoki; G. Cossu; S. Hashimoto; T. Kaneko; J. Noaki
2015-09-03
The flavor-singlet component of the eta prime meson is related to the topological structure of the SU(3) gauge field through the chiral anomaly. We perform a 2+1-flavor lattice QCD calculation and demonstrate that the two-point function of a gluonically defined topological charge density after a short Yang-Mills gradient flow contains the propagation of the eta prime meson, by showing that its mass in the chiral and continuum limit is consistent with the experimental value. The gluonic correlator does not suffer from the contamination of the pion contribution, and the clean signal is obtained at significantly lower numerical cost compared to the conventional method with the quark bilinear operators.
Hui, Xiaonan; Zhang, Weite; Jin, Xiaofeng; Chi, Hao; Zhang, Xianmin
2015-01-01
The topological charge of an electromagnetic vortex beam depends on its wavefront helicity. For mixed vortex beams composed of several different coaxial vortices, the topological charge spectrum can be obtained by Fourier transform. However, the vortex beam is generally divergent and imperfect. It makes it significant to investigate the local topological charges, especially in radio frequency regime. Fourier transform based methods are restrained by the uncertainty principle and cannot achieve high angular resolution and mode resolution simultaneously. In this letter, an analysis method for local topological charges of vortex beams is presented based on the empirical mode decomposition (EMD). From EMD, the intrinsic mode functions (IMFs) can be obtained to construct the bases of the electromagnetic wave, and each local topological charge can be respectively defined. With this method the local value achieves both high resolution of azimuth angle and topological charge, meanwhile the amplitudes of each OAM mode...
Sub-nanometer free electrons with topological charge.
Schattschneider, P; Stöger-Pollach, M; Löffler, S; Steiger-Thirsfeld, A; Hell, J; Verbeeck, J
2012-04-01
The holographic mask technique is used to create freely moving electrons with quantized angular momentum. With electron optical elements they can be focused to vortices with diameters below the nanometer range. The understanding of these vortex beams is important for many applications. Here, we produce electron vortex beams and compare them to a theory of electrons with topological charge. The experimental results show excellent agreement with simulations. As an immediate application, fundamental experimental parameters like spherical aberration and partial coherence are determined. PMID:22459114
Spanning of Topological sectors, charge and susceptibility with naive Wilson fermions
Abhishek Chowdhury; Asit K. De; Sangita De Sarkar; A. Harindranath; Santanu Mondal; Anwesa Sarkar; Jyotirmoy Maiti
2011-11-08
We study the topological charge and the topological susceptibility in lattice QCD with two degenerate flavors of naive Wilson fermions at two values of lattice spacings and different volumes, for a range of quark masses. Configurations are generated with DDHMC/HMC algorithms and smoothened with HYP smearing. We present integrated autocorrelation time for both topological charge and topological susceptibility at the two lattice spacing values studied. The spanning of different topological sectors as a function of the hopping parameter kappa is presented. The expected chiral behaviour of the topological susceptibility (including finite volume dependence) is observed.
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.
Thermodynamics of topological nonlinear charged Lifshitz black holes
Zangeneh, M Kord; Dehghani, M H
2015-01-01
In this paper, we construct a new class of analytic topological Lifshitz black holes with constant curvature horizon in the presence of power-law Maxwell field in four and higher dimensions. We find that in order to obtain these exact Lifshitz solutions, we need a dilaton and at least three electromagnetic fields. Interestingly enough, we find that the reality of the charge of the electromagnetic field which is needed for having solutions with curved horizon rules out black holes with hyperbolic horizon. Next, we study the thermodynamics of these nonlinear charged Lifshitz black holes with spherical and flat horizons by calculating all the conserved and thermodynamic quantities of the solutions. Furthermore, we obtain a generalized Smarr formula and show that the first law of thermodynamics is satisfied. Finally, we perform a stability analysis in both canonical and grand-canonical ensembles. We find that the solutions are thermally stable in a proper ranges of the metric parameters.
Topological charge using cooling and the gradient flow
Alexandrou, Constantia; Jansen, Karl
2015-01-01
The equivalence of cooling to the gradient flow when the cooling step $n_c$ and the continuous flow step of gradient flow $\\tau$ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate $n_c$ and $\\tau$ and show that the results for the topological charge become equivalent when rescaling $\\tau \\simeq n_c/({3-15 c_1})$ where $c_1$ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with $N_f=2+1+1$ twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling $\\tau \\simeq n_c/({3-15 c_1})$ leads to equivalent results.
Topological charge using cooling and the gradient flow
Constantia Alexandrou; Andreas Athenodorou; Karl Jansen
2015-09-14
The equivalence of cooling to the gradient flow when the cooling step $n_c$ and the continuous flow step of gradient flow $\\tau$ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate $n_c$ and $\\tau$ and show that the results for the topological charge become equivalent when rescaling $\\tau \\simeq n_c/({3-15 c_1})$ where $c_1$ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with $N_f=2+1+1$ twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling $\\tau \\simeq n_c/({3-15 c_1})$ leads to equivalent results.
(2+1)-dimensional charged black hole in topologically massive electrodynamics.
Andrade, Tomás; Bañados, Máximo; Benguria, Rafael D; Gomberoff, Andrés
2005-07-01
The 2+1 black hole coupled to a Maxwell field can be charged in two different ways. Besides a Coulomb field, whose potential grows logarithmically in the radial coordinate, there also exists a topological charge due to the existence of a noncontractible cycle. The topological charge does not gravitate and is somehow decoupled from the black hole. This situation changes if one turns on the Chern-Simons term for the Maxwell field. First, the flux integral at infinity becomes equal to the topological charge. Second, demanding regularity of the black hole horizon, the Coulomb charge must vanish identically. Hence, in 2+1 topologically massive electrodynamics coupled to gravity, the black hole can support holonomies only for the Maxwell field. This means that the charged black hole is constructed from the vacuum by means of spacetime identifications. PMID:16090671
Thermodynamics of topological nonlinear charged Lifshitz black holes
M. Kord Zangeneh; A. Sheykhi; M. H. Dehghani
2015-08-12
In this paper, we construct a new class of analytic topological Lifshitz black holes with constant curvature horizon in the presence of power-law Maxwell field in four and higher dimensions. We find that in order to obtain these exact Lifshitz solutions, we need a dilaton and at least three electromagnetic fields. Interestingly enough, we find that the reality of the charge of the electromagnetic field which is needed for having solutions with curved horizon rules out black holes with hyperbolic horizon. Next, we study the thermodynamics of these nonlinear charged Lifshitz black holes with spherical and flat horizons by calculating all the conserved and thermodynamic quantities of the solutions. Furthermore, we obtain a generalized Smarr formula and show that the first law of thermodynamics is satisfied. We also perform a stability analysis in both canonical and grand-canonical ensemble. We find that the solutions are thermally stable in a proper ranges of the metric parameters. Finally, we comment on the dynamical stability of the obtained solutions under perturbations in four dimensions.
Thermodynamics of topological nonlinear charged Lifshitz black holes
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Sheykhi, A.; Dehghani, M. H.
2015-07-01
In this paper, we construct a new class of analytic topological Lifshitz black holes with constant curvature horizon in the presence of a power-law Maxwell field in four or more dimensions. We find that in order to obtain these exact Lifshitz solutions, we need a dilaton and at least three electromagnetic fields. Interestingly enough, we find that the reality of the charge of the electromagnetic field which is needed for having solutions with a curved horizon rules out black holes with a hyperbolic horizon. Next, we study the thermodynamics of these nonlinear charged Lifshitz black holes with spherical and flat horizons by calculating all of the conserved and thermodynamic quantities of the solutions. Furthermore, we obtain a generalized Smarr formula and show that the first law of thermodynamics is satisfied. We also perform a stability analysis in both canonical and grand-canonical ensembles. We find that the solutions are thermally stable in proper ranges of the metric parameters. Finally, we comment on the dynamical stability of the obtained solutions under perturbations in four dimensions.
Topological Charge in Two Flavors QCD with Optimal Domain-Wall Fermion
Tung-Han Hsieh; Ting-Wai Chiu; Yao-Yuan Mao
2011-01-02
We measure the topological charge of the gauge configurations generated by lattice simulations of 2 flavors QCD on a $ 16^3 \\times 32 $ lattice, with Optimal Domain-Wall Fermion (ODWF) at $ N_s = 16 $ and plaquette gauge action at $ \\beta = 5.90 $. Using the Adaptive Thick-Restart Lanczos algorithm, we project the low-lying modes of the 4D effective Dirac operator of ODWF, and obtain the topological charge and topological susceptibility. Our result of topological susceptibility agrees with the sea-quark mass dependence predicted by the chiral perturbation theory, and provides a determination of the chiral condensate.
Nonlinear Charged Black Holes in AdS Quasi-Topological Gravity
NASA Astrophysics Data System (ADS)
Ghanaatian, Mohammad; Bazrafshan, Afsaneh
2013-11-01
In this paper, we present the static charged solutions of quartic quasi-topological gravity in the presence of a nonlinear electromagnetic field. Two branches of these solutions present black holes with one or two horizons or a naked singularity depending on the charge and mass of the black hole. The entropy of the charged black holes of fourth-order quasi-topological gravity through the use of Wald formula is computed and the mass, temperature and the charge of these black holes are found as well. We show that black holes with spherical, flat and hyperbolical horizon in quasi-topological gravity are stable for any allowed quasi-topological parameters. We also investigate the stability of nonlinear charged black holes.
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.
Polarization pattern of vector vortex beams generated by q-plates with different topological charges
Marrucci, Lorenzo
of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q] or mode-forming holographic and birefringent elements [6,1822]. Light polarization is usually thought
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.
Probing the topological charge of a vortex beam with dynamic angular double slits
Dongzhi Fu; Dongxu Chen; Ruifeng Liu; Yunlong Wang; Hong Gao; Fuli Li; Pei Zhang
2015-01-24
When a vortex beam with the spiral phase structure passes through a dynamic angular double slits (ADS), the interference pattern changes alternatively between destructive and constructive at the angular bisector direction of the ADS due to their phase difference. Based on this property, we experimentally demonstrate a simple method, which can precisely and efficiently determine the topological charge of vortex beams. What is more, this scheme allows determining both the modulus and sign of the topological charge of vortex beams simultaneously.
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.
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.
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.
6. Matrix Lie groups 6.1. Definition and the basic theorem. A topological group is
Varadarajan, Veeravalli S.
6. Matrix Lie groups 6.1. Definition and the basic theorem. A topological group is called a matrix Lie group if it is homeomorphic to a closed subgroup of some GL(n, R). By Von Neumann's theorem a matrix Lie group is a Lie group/We want to prove the basic theorem that the Lie structure is uniquely
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.
Importance of charge fluctuations for the topological phase in SmB(6).
Min, Chul-Hee; Lutz, P; Fiedler, S; Kang, B Y; Cho, B K; Kim, H-D; Bentmann, H; Reinert, F
2014-06-01
Typical Kondo insulators (KIs) can have a nontrivial Z_{2} topology because the energy gap opens at the Fermi energy (E_{F}) by a hybridization between odd- and even-parity bands. SmB_{6} deviates from such KI behavior, and it has been unclear how the insulating phase occurs. Here, we demonstrate that charge fluctuations are the origin of the topological insulating phase in SmB_{6}. Our angle-resolved photoemission spectroscopy results reveal that with decreasing temperature the bottom of the d-f hybridized band at the X[over ¯] point, which is predicted to have odd parity and is required for a topological phase, gradually shifts from below to above E_{F}. We conclude that SmB_{6} is a charge-fluctuating topological insulator. PMID:24949780
Determination of the topological charge of a twisted beam with a Fresnel bi-prism
NASA Astrophysics Data System (ADS)
Emile, Olivier; Emile, Janine; Brousseau, Christian
2014-12-01
The self-interference pattern of a Laguerre Gaussian beam using a Fresnel bi-prism is shown to be very different from what could be expected from a usual laser beam. It resembles the interference pattern that could be obtained using a double slit experiment. The interferences are shifted and the topological charge and its sign can be readily determined considering the shift order of the pattern only. However, since there is no diffraction nor absorption losses unlike in a double slit interference, such a set up could be used even for low power twisted beams or beams with high topological charge. Even fractional topological charges could be determined with an absolute precision of 0.05.
Implementing a Magnetic Charge Topology Model for Solar Active Regions
Longcope, Dana
of the solar corona is crucial to un- derstanding solar energetic events. One approach to characterizing are interlinked by coronal field lines. The level of topological activity is then quantified through the transfer of flux between regions of differing field line connectivity. We discuss in detail how to implement
Loss, Daniel
charge creation. Here we demonstrate full control over the creation, manipulation and analysis the topological charge creation and manipu- lation in a nematic liquid crystal (NLC) is achieved by using laser
Lifetime of charged and neutral B hadrons using event topology
NASA Astrophysics Data System (ADS)
Adam, W.; Adye, T.; Agasi, E.; Ajinenko, I.; Aleksan, R.; Alekseev, G. D.; Allport, P. P.; Almehed, S.; Alvsvaag, S. J.; Amaldi, U.; Amato, S.; Andreazza, A.; Andrieux, M. L.; Antilogus, P.; Anykeyev, V.; Apel, W. D.; Arnoud, Y.; Åsman, B.; Augustin, J. E.; Augustinus, A.; Baillon, P.; Bambade, P.; Barao, F.; Barate, R.; Bardin, D. Y.; Barker, G. J.; Baroncelli, A.; Barring, O.; Barrio, J. A.; Bartl, W.; Bates, M. J.; Battaglia, M.; Baubillier, M.; Baudot, J.; Becks, K.-H.; Begalli, M.; Beilliere, P.; Belokopytov, Yu.; Benvenuti, A. C.; Berggren, M.; Bertrand, D.; Bianchi, F.; Bigi, M.; Bilenky, M. S.; Billoir, P.; Bloch, D.; Blume, M.; Blyth, S.; Bocci, V.; Bolognese, T.; Bonesini, M.; Bonivento, W.; Booth, P. S. L.; Borisov, G.; Bosio, C.; Bosworth, S.; Botner, O.; Bouquet, B.; Bourdarios, C.; Bowcock, T. J. V.; Bozzo, M.; Branchini, P.; Brand, K. D.; Brenner, R. A.; Bricman, C.; Brillault, L.; Brown, R. C. A.; Bruckman, P.; Brunet, J.-M.; Bugge, L.; Buran, T.; Buys, A.; Caccia, M.; Calvi, M.; Camacho Rozas, A. J.; Camporesi, T.; Canale, V.; Canepa, M.; Cankocak, K.; Cao, F.; Carena, F.; Carrilho, P.; Carroll, L.; Caso, C.; Castillo Gimenez, M. V.; Cattai, A.; Cavallo, F. R.; Cerrito, L.; Chabaud, V.; Charpentier, Ph.; Chaussard, L.; Chauveau, J.; Checchia, P.; Chelkov, G. A.; Chierici, R.; Chliapnikov, P.; Chochula, P.; Chorowicz, V.; Cindro, V.; Collins, P.; Contreras, J. L.; Contri, R.; Cortina, E.; Cosme, G.; Cossutti, F.; Crawley, H. B.; Crennell, D.; Crosetti, G.; Cuevas Maestro, J.; Czellar, S.; Dahl-Jensen, E.; Dahm, J.; Dalmagne, B.; Dam, M.; Damgaard, G.; Daum, A.; Dauncey, P. D.; Davenport, M.; da Silva, W.; Defoix, C.; Della Ricca, G.; Delpierre, P.; Demaria, N.; de Angelis, A.; de Boeck, H.; de Boer, W.; de Brabandere, S.; de Clercq, C.; de La Vaissiere, C.; de Lotto, B.; de Min, A.; de Paula, L.; de Saint-Jean, C.; Dijkstra, H.; di Ciaccio, L.; Djama, F.; Dolbeau, J.; Donszelmann, M.; Doroba, K.; Dracos, M.; Drees, J.; Drees, K. A.; Dris, M.; Dufour, Y.; Dupont, F.; Edsall, D.; Ehret, R.; Eigen, G.; Ekelof, T.; Ekspong, G.; Elsing, M.; Engel, J.-P.; Ershaidat, N.; Erzen, B.; Espirito Santo, M.; Falk, E.; Fassouliotis, D.; Feindt, M.; Ferrer, A.; Filippas, T. A.; Firestone, A.; Fischer, P. A.; Foeth, H.; Fokitis, E.; Fontanelli, F.; Formenti, F.; Franek, B.; Frenkiel, P.; Fries, D. C.; Frodesen, A. G.; Frhwirth, R.; Fulda-Quenzer, F.; Furstenau, H.; Fuster, J.; Galloni, A.; Gamba, D.; Gandelman, M.; Garcia, C.; Garcia, J.; Gaspar, C.; Gasparini, U.; Gavillet, Ph.; Gazis, E. N.; Gele, D.; Gerber, J.-P.; Gibbs, M.; Gillespie, D.; Gokieli, R.; Golob, B.; Gopal, G.; Gorn, L.; Gorski, M.; Gouz, Yu.; Gracco, V.; Graziani, E.; Grosdidier, G.; Gunnarsson, P.; Gunther, M.; Guy, J.; Haedinger, U.; Hahn, E.; Hahn, M.; Hahn, S.; Hajduk, Z.; Hallgren, A.; Hamacher, K.; Hao, W.; Harris, F. J.; Hedberg, V.; Henriques, R.; Hernandez, J. J.; Herquet, P.; Herr, H.; Hessing, T. L.; Higon, E.; Hilke, H. J.; Hill, T. S.; Holmgren, S.-O.; Holt, P. J.; Holthuizen, D.; Houlden, M.; Hrubec, J.; Huet, K.; Hultqvist, K.; Ioannou, P.; Jackson, J. N.; Jacobsson, R.; Jalocha, P.; Janik, R.; Jarlskog, G.; Jarry, P.; Jean-Marie, B.; Johansson, E. K.; Jonsson, L.; Jonsson, P.; Joram, C.; Juillot, P.; Kaiser, M.; Kalmus, G.; Kapusta, F.; Karlsson, M.; Karvelas, E.; Katsanevas, S.; Katsoufis, E. C.; Keranen, R.; Khomenko, B. A.; Khovanski, N. N.; King, B.; Kjaer, N. J.; Klein, H.; Klovning, A.; Kluit, P.; Koehne, J. H.; Koene, B.; Kokkinias, P.; Koratzinos, M.; Korcyl, K.; Kostioukhine, V.; Kourkoumelis, C.; Kouznetsov, O.; Kramer, P. H.; Krammer, M.; Kreuter, C.; Krolikowski, J.; Kronkvist, I.; Krumstein, Z.; Krupinski, W.; Kubinec, P.; Kucewicz, K.; Kurvinen, K.; Lacasta, C.; Laktineh, I.; Lamblot, S.; Lamsa, J. W.; Lanceri, L.; Lane, D. W.; Langefeld, P.; Lapin, V.; Last, I.; Laugier, J.-P.; Lauhakangas, R.; Leder, G.; Ledroit, F.; Lefebure, V.; Legan, C. K.; Leitner, R.; Lemoigne, Y.; Lemonne, J.; Lenzen, G.; Lepeltier, V.; Lesiak, T.; Liko, D.; Lindner, R.; Lipniacka, A.; Lippi, I.; Loerstad, B.; Lokajicek, M.; Loken, J. G.; Lopez, J. M.; Lopez-Fernandez, A.; Lopez Aguera, M. A.; Loukas, D.; Lutz, P.; Lyons, L.; MacNaughton, J.; Maehlum, G.; Maio, A.; Malychev, V.; Mandl, F.; Marco, J.; Marechal, B.; Margoni, M.; Marin, J.-C.; Mariotti, C.; Markou, A.; Maron, T.; Martinez-Rivero, C.; Martinez-Vidal, F.; Marti I Garcia, S.; Matorras, F.; Matteuzzi, C.; Matthiae, G.; Mazzucato, M.; Cubbin, M. Mc.; Kay, R. Mc; Nulty, R. Mc; Medbo, J.; Meroni, C.; Meyer, W. T.; Michelotto, M.; Migliore, E.; Mirabito, L.; Mitaroff, W. A.; Mjoernmark, U.; Moa, T.; Moeller, R.; Moenig, K.; Monge, M. R.; Morettini, P.; Mueller, H.; Mundim, L. M.; Murray, W. J.; Muryn, G.; Myatt, G.; Naraghi, F.; Navarria, F. L.; Navas, S.; Negri, P.
1995-09-01
The lifetimes of charged and neutral B hadrons have been measured using data collected by the DELPHI experiment at LEP between 1991 and 1993. B hadrons are tagged as jets with a secondary vertex and the charge of the B candidate is taken to be the sum of the charges of the particles in the secondary vertex. Approximately 1,434,000 multihadronic Z0 decays yielded 1817 B hadron candidates. The B purity was estimated to be around 99.1±0.3%, and 83% (70%) of the events measured as neutral (charged) came from neutral (charged) B's. The mean lifetimes of charged and neutral B hadrons were found to be 1.72±0.08 (stat.) ±0.06 (syst.) ps and 1.58±0.11 (stat.)±0.09 (syst.) ps respectively. The ratio of their lifertimes, ?charged/?neutral, was 1.09{-0.10/+0.11} (stat.)±0.08 (syst.). By making assumptions about the B{s/0} and ?{b/0} states, the B+ and B0 meson lifetimes were determined to be ?B+ = 1.72 ± 0.08 (stat.) ±0.06 (syst.) ps and ?B+ = 1.63 ± 0.14 (stat.)±0.13 (syst.) ps and the ratio of their lifetimes was: ?B+/?B0 = 1.06{-0.11/+0.13} ±0.10. The mean B lifetime was also deduced to be < ? > = 1.64 ±0.06 (stat.)±0.04 (syst.) ps.
Charge Topology of Coherent Dissociation of 11C and 12N Relativistic 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. Z.
2015-06-01
The charge topology of the events of coherent dissociation of 11C and 12N of an energy of 1.2A GeV in nuclear track emulsion is presented and its compared is given with the appropriate data on the nuclei 7Be, 8,10B, 9,10C and 14.
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.
Charge quantisation without magnetic poles: a topological approach to electromagnetism
Romero Solha
2015-08-08
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
NASA Astrophysics Data System (ADS)
Taguchi, Katsuhisa; Shintani, Kunitaka; Tanaka, Yukio
2015-07-01
We theoretically study the spin and charge generations along with the electron transport on a disordered surface of a doped three-dimensional topological insulator/magnetic insulator junction by using Green's function techniques. We find that the spin and charge currents are induced by not only local, but also nonlocal magnetization dynamics through nonmagnetic impurity scattering on the disordered surface of the doped topological insulator. We also clarify that the spin current as well as charge density are induced by spatially inhomogeneous magnetization dynamics, and the spin current diffusively propagates on the disordered surface. Using these results, we discuss both local and nonlocal spin torques before and after the spin and spin-current generations on the surface, and provide a procedure to detect the spin current.
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.
Charneski, Catherine A; Hurst, Laurence D
2014-01-01
In the great majority of genomes, the use of positive charge increases, on average, approaching protein N-termini. Such charged residues slow ribosomes by interacting with the negatively charged exit tunnel. This has been proposed to be selectively advantageous as it provides an elongation speed ramp at translational starts. Positive charges, however, are known to orientate proteins in membranes by the positive-inside rule whereby excess charge lies on the cytoplasmic side of the membrane. Which of these two models better explains the N-terminal loading of positively charged amino acids? We find strong evidence that the tendency for average positive charge use to increase at termini is exclusively due to membrane protein topology: 1) increasing N-terminal positive charge is not found in cytosolic proteins, but in transmembrane ones with cytosolic N-termini, with signal sequences contributing additional charge; 2) positive charge density at N-termini corresponds to the length of cytoplasmically exposed transmembrane tails, its usage increasing just up until the membrane; 3) membrane-related patterns are repeated at C-termini, where no ramp is expected; and 4) N-terminal positive charge patterns are no different from those seen internally in proteins in membrane-associated domains. The overall apparent increase in positive charge across all N-termini results from membrane proteins using positive charge adjacent to the cytosolic leaflet, combined with a skewed distribution of where N-termini cross the plasma membrane; 5) while Escherichia coli was predicted to have a 5' ribosomal occupancy ramp of at least 31 codons, in contrast to what is seen in yeast, we find in ribosomal footprinting data no evidence for such a ramp. In sum, we find no need to invoke a translational ramp to explain the rising positive charge densities at N-termini. The membrane orientation model makes a full account of the trend. PMID:24077849
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.
No P- V criticality for charged topological black holes in Ho?ava-Lifshitz gravity
NASA Astrophysics Data System (ADS)
Mo, Jie-Xiong
2015-04-01
Searching for the unusual characteristics of Ho?ava-Lifshitz gravity, we generalize our former research of charged topological black holes in Ho?ava-Lifshitz gravity to the extended phase space. By treating cosmological constant as thermodynamic pressure, thermodynamic volume is derived as the conjugate quantity. P- V criticality is investigated by carrying out analytic analysis not only for the uncharged case but also for the charged case. All the topologies are considered. Unfortunately, no physical critical point has been found in all the cases. The results suggests again that the van der Waals like P- V criticality is not a universal phenomenon by providing one more example other than BTZ black holes. Our results also show that the existence of cosmological constant in the black hole metric is not sufficient for the existence of van der Waals like P- V criticality.
Comparison of converter topologies for charging capacitors used in pulsed load applications
NASA Technical Reports Server (NTRS)
Nelms, R. M.; Schatz, J. E.; Pollard, Barry
1991-01-01
The authors present a qualitative comparison of different power converter topologies which may be utilized for charging capacitors in pulsed power applications requiring voltages greater than 1 kV. The operation of the converters in capacitor charging applications is described, and relevant advantages are presented. All of the converters except one may be classified in the high-frequency switching category. One of the benefits from high-frequency operation is a reduction in size and weight. The other converter discussed is a member of the command resonant changing category. The authors first describe a boost circuit which functions as a command resonant charging circuit and utilizes a single pulse of current to charge the capacitor. The discussion of high-frequency converters begins with the flyback and Ward converters. Then, the series, parallel, and series/parallel resonant converters are examined.
Charge and spin edge currents in two-dimensional Floquet topological superconductors
NASA Astrophysics Data System (ADS)
Sacramento, P. D.
2015-06-01
A time periodic driving on a topologically trivial system induces edge modes and topological properties. In this work we consider triplet and singlet superconductors subject to periodic variations of the chemical potential, spin-orbit coupling, and magnetization in both topologically trivial and nontrivial phases, and study their influence on the charge and spin currents that propagate along the edges of the two-dimensional system, for moderate to large driving frequencies. Currents associated with the edge modes are induced in the trivial phases and enhanced in the topological phases. In some cases there is a sign reversal of the currents as a consequence of the periodic driving. The edge states associated with the finite quasienergy states at the edge of the Floquet zone are in general robust, while the stability of the zero quasienergy states depends on the parameters. Also, the spin polarization of the Floquet spectrum quasienergies is strong as for the unperturbed topological phases. It is found that in some cases the unperturbed edge states are immersed in a continuum of states due to the perturbation, particularly if the driving frequency is not large enough. However, their contribution to the edge currents and spin polarization is still significant.
NASA Astrophysics Data System (ADS)
Zhai, Zhaohui; Li, Zhixiang; Xu, Jingjun; Zhang, Guoquan
2013-09-01
We verified that optical topological charges are conserved in a two-step light-pulse storage and retrieval process based on the electromagnetically-induced-transparency (EIT) effect in a Pr3+:Y2SiO5 crystal. Based on this conservation law, one could transfer topological charges from the interacting beams, which may not be overlapped in space and time domains, to the targeted output signal beam, and algebraic operations such as summation and subtraction of topological charges carried by the interacting beams were demonstrated via the EIT-assisted two-step light-pulse storage-retrieval process. The results may be useful for classical and quantum information processing based on optical topological charge buffer memory in EIT media.
Miyamoto, K., E-mail: k-miyamoto@faculty.chiba-u.jp [Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522 (Japan); Suizu, K.; Akiba, T. [Department of Electrical, Electronics and Computer Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016 (Japan); Omatsu, T. [Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522 (Japan); CREST Japan Science and Technology Agency, Sanbancho, Chiyoda-ku, Tokyo 102-0075 (Japan)
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.
The Geometry and Electronic Topology of Higher-Order Charged Möbius Annulenes
NASA Astrophysics Data System (ADS)
Wannere, Chaitanya S.; Rzepa, Henry S.; Rinderspacher, B. Christopher; Paul, Ankan; Allan, Charlotte S. M.; Schaefer, Henry F.; Schleyer, Paul V. R.
2009-07-01
Higher-order aromatic charged Möbius-type annulenes have been Lkrealized computationally. These charged species are based on strips with more than one electronic half-twist, as defined by their linking numbers. The B3LYP/6-311+G(d,p) optimized structures and properties of annulene rings with such multiple half-twists (C12H122+, C12H122-, C14H14, C18H182+, C18H182-, C21H21+, C24H242-, C28H282+, and C28H282-) have the nearly equal C-C bond lengths, small dihedral angles around the circuits, stabilization energies, and nucleus-independent chemical shift values associated with aromaticity. The topology and nature of Möbius annulene systems are analyzed in terms of the torus curves defined by electron density functions (?(r)?, ELF?) constructed using only the occupied ?-MOs. The ?-torus subdivides into a torus knot for annulenes defined by an odd linking number (Lk = 1, 3?) and a torus link for those with an even linking number (Lk = 2, 4?). The torus topology is shown to map onto single canonical ?-MOs only for even values of Lk. Incomplete and misleading descriptions of the topology of ?-electronic Möbius systems with an odd number of half twists result when only signed orbital diagrams are considered, as is often done for the iconic single half twist system.
Quark mass, scale and volume dependence of topological charge density correlator in Lattice QCD
Abhishek Chowdhury; Asit K. De; A. Harindranath; Jyotirmoy Maiti; Santanu Mondal
2012-11-30
We study the two-point Topological Charge Density Correlator (TCDC) in lattice QCD with two degenerate flavours of naive Wilson fermions and unimproved Wilson gauge action at two values of lattice spacings and different volumes, for a range of quark masses. Configurations are generated with DDHMC algorithm and smoothed with HYP smearing. In order to shed light on the mechanisms leading to the observed suppression of topological susceptibility with respect to the decreasing quark mass and decreasing volume, in this work, we carry out a detailed study of the two-point TCDC. We have shown that, (1) the TCDC is negative beyond a positive core and radius of the core shrinks as lattice spacing decreases, (2) as the volume decreases, the magnitude of the contact term and the radius of the positive core decrease and the magnitude of the negative peak increases resulting in the suppression of the topological susceptibility as the volume decreases, (3) the contact term and radius of the positive core decrease with decreasing quark mass at a given lattice spacing and the negative peak increases with decreasing quark mass resulting in the suppression of the topological susceptibility with decreasing quark mass, (4) increasing levels of smearing suppresses the contact term and the negative peak keeping the susceptibility intact and (5) both the contact term and the negative peak diverge in nonintegrable fashion as lattice spacing decreases.
$\\eta^\\prime$ meson mass from topological charge density correlator in QCD
Fukaya, H; Cossu, G; Hashimoto, S; Kaneko, T; Noaki, J
2015-01-01
The flavor-singlet component of the eta prime meson is related to the topological structure of the SU(3) gauge field through the chiral anomaly. We perform a 2+1-flavor lattice QCD calculation and demonstrate that the two-point function of a gluonically defined topological charge density after a short Yang-Mills gradient flow contains the propagation of the eta prime meson, by showing that its mass in the chiral and continuum limit is consistent with the experimental value. The gluonic correlator does not suffer from the contamination of the pion contribution, and the clean signal is obtained at significantly lower numerical cost compared to the conventional method with the quark bilinear operators.
The Ehrenfest force field: Topology and consequences for the definition of an atom in a molecule.
Martín Pendás, A; 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. PMID:23039579
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.
Two phase equilibrium in charged topological dilaton AdS black hole
Hui-Hua Zhao; Li-Chun Zhang; Meng-Sen Ma; Ren Zhao
2014-12-01
In this paper we discuss the phase transition of the charged topological dilaton AdS black holes by Maxwell equal area law. Using Maxwell equal area law we found the border of the region of two phase coexistence in $P-v$ diagrams and analyze the parameters which affect the extent of the region. We also plot the $P-T$ phase diagram and derive the Clapeyron equation for the black hole, and investigate the phase change latent heat. The results show the phase transition characteristic is similar to that of usual non-gravity thermodynamic systems.
Instability of a domain wall in electric current: Role of topological charge
NASA Astrophysics Data System (ADS)
Karashtin, E. A.; Fraerman, A. A.
2015-07-01
We theoretically show that the electric current applied in the plane of a Bloch domain wall introduces a mechanism of its stability or instability that is strongly connected to its topological charge. In the case of a wall in an infinite ferromagnet, applying a current in one direction leads to the instability, while a current in the opposite direction the wall is stable. This property is caused by the toroidal moment of the system and appears to be due to the magnetostatic energy of the domain wall. A more complicated case of a ferromagnetic slab is considered.
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.
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.
NSDL National Science Digital Library
Kaeley, Bhim S.
A unit designed to develop logical reasoning through topology, using sorting, classifying, and patterning. Topology is about points, lines, and the figures they make; but length, area, curvature and angle can be altered as much as you wish. Thus topology is sometimes called Rubber-Sheet Geometry. Topics chosen are presented in a way that requires a minimum mathematical background and maturity; it is not assumed that students who use this unit know how to solve even simple equations or that they have much acquaintance with geometric figures.
Li, Jinhong; Zeng, Jun; Duan, Meiling
2015-05-01
The analytical expressions for the cross-spectral density function of partially coherent sinh-Gaussian (ShG) vortex beams propagating through free space and non-Kolmogorov atmospheric turbulence are derived, and used to study the classification of coherent vortices creation and distance of topological charge conservation. With the increment of the general structure constant and the waist width, as well as the decrement of the general exponent, the inner scale of turbulence and spatial correlation length, the distance of topological charge conservation will decrease, whereas the outer scale of turbulence and the Sh-part parameter have no effect on the distance of topological charge conservation. According to the creation, the coherent vortices are grouped into three classes: the first is the inherent coherent vortices of the vortex beams, the second is created by the vortex beams when propagating through free space, and the third is created by the atmospheric turbulence inducing the vortex beams. PMID:25969249
Furusaki, Akira; Nomura, Kentaro; Ryu, Shinsei; Takayanagi, Tadashi
2012-01-01
We discuss the thermal (or gravitational) responses in topological superconductors and in topological phases in general. Such thermal responses (as well as electromagnetic responses for conserved charge) provide a definition of topological insulators and superconductors beyond the single-particle picture. In two-dimensional topological phases, the Str\\v{e}da formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the angular momentum and thermal polarization (entropy polarization). We also discuss a use of D-branes in string theory as a systematic tool to derive all such topological terms and topological responses. In particular, we relate the $\\mathbb{Z}_2$ index of topological insulators introduced by Kane and Mele (and its generalization to other symmetry classes and to arbitrary dimensions) to the K-theory charge of non-BPS D-...
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.
Dmitri E. Kharzeev; Larry D. McLerran; Harmen J. Warringa
2007-11-06
Quantum chromodynamics (QCD) contains field configurations which can be characterized by a topological invariant, the winding number Q_w. Configurations with nonzero Q_w break the charge-parity CP symmetry of QCD. We consider a novel mechanism by which these configurations can separate charge in the presence of a background magnetic field - the "Chiral Magnetic Effect". We argue that sufficiently large magnetic fields are created in heavy ion collisions so that the Chiral Magnetic Effect causes preferential emission of charged particles along the direction of angular momentum. Since separation of charge is CP-odd, any observation of the Chiral Magnetic Effect could provide a clear demonstration of the topological nature of the QCD vacuum. We give an estimate of the effect and conclude that it might be observed experimentally.
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.
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
Membranes with topological charge and AdS{sub 4}/CFT{sub 3} correspondence
Klebanov, Igor R. [Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544 (United States); Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544 (United States); Pufu, Silviu S.; Tesileanu, Tiberiu [Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544 (United States)
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}.
Submitted to Topology Proceedings
Mashburn, Joe
Submitted to Topology Proceedings A COMPARISON OF THREE TOPOLOGIES ON ORDERED SETS DRAFT OF FEBRUARY 2, 2007 JOE MASHBURN Abstract. We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very
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.
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.
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.
P. G. Grinevich; K. V. Kaipa
2009-04-23
The most basic characteristic of x-quasiperiodic solutions u(x,t) of the sine-Gordon equation u_{tt}-u_{xx}+\\sin u=0 is the topological charge density denoted $\\bar n$. The real finite-gap solutions u(x,t) are expressed in terms of the Riemann theta-functions of a non-singular hyperelliptic curve $\\Gamma$ and a positive generic divisor D of degree g on $\\Gamma$, where the spectral data $(\\Gamma, D)$ must satisfy some reality conditions. The problem addressed in note is: to calculate $\\bar n$ directly from the theta-functional expressions for the solution u(x,t). The problem is solved here by introducing what we call the multiscale or elliptic limit of real finite-gap sine-Gordon solutions. We deform the spectral curve to a singular curve, for which the calculation of topological charges reduces to two special easier cases.
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 ...
Barnes, Graham
activity is then quantified through the transfer of flux between regions of differing field line events. One approach to characterizing the topology that has had some success is magnetic charge topology, paying particular attention to distinguishing real evolution of the photospheric magnetic flux from
Abbott, Laurence
Volume 116B, number 4 PHYSICSLETTERS 14 October 1982 CHARGE DEFINITION IN NON-ABEL[AN GAUGE THEORIES ~ L.F. ABBOTT and S. DESER Brandeis University, Waltham, MA 02254, USA Received 9 June 1982 Conserved gauge-invariant electric and magnetic charges are defined for non-abelian gauge theories in terms
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.
Construction of a topological charge on fuzzy S{sup 2}xS{sup 2} via a Ginsparg-Wilson relation
Aoki, Hajime [Department of Physics, Saga University, Saga 840-8502 (Japan); Hirayama, Yoshiko [Miyazaki Information Processing Center Limited, Fukuoka 812-0011 (Japan); Iso, Satoshi [KEK Theory Center, High Energy Accelerator Research Organization (KEK) and the Graduate University for Advanced Studies (SOKENDAI), Ibaraki 305-0801 (Japan)
2009-12-15
We construct a topological charge of gauge field configurations on a fuzzy S{sup 2}xS{sup 2} by using a Dirac operator satisfying the Ginsparg-Wilson relation. The topological charge defined on the fuzzy S{sup 2}xS{sup 2} can be interpreted as a noncommutative (or matrix) generalization of the 2nd Chern character on S{sup 2}xS{sup 2}. We further calculate the number of chiral zero modes of the Dirac operator in topologically nontrivial gauge configurations. Generalizations of our formulation to fuzzy (S{sup 2}){sup k} are also discussed.
A. Skouroupathis; H. Panagopoulos
2006-01-02
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)
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.
Akira Furusaki; Naoto Nagaosa; Kentaro Nomura; Shinsei Ryu; Tadashi Takayanagi
2012-11-02
We discuss the thermal (or gravitational) responses in topological superconductors and in topological phases in general. Such thermal responses (as well as electromagnetic responses for conserved charge) provide a definition of topological insulators and superconductors beyond the single-particle picture. In two-dimensional topological phases, the Str\\v{e}da formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the angular momentum and thermal polarization (entropy polarization). We also discuss a use of D-branes in string theory as a systematic tool to derive all such topological terms and topological responses. In particular, we relate the $\\mathbb{Z}_2$ index of topological insulators introduced by Kane and Mele (and its generalization to other symmetry classes and to arbitrary dimensions) to the K-theory charge of non-BPS D-branes, and vice versa. We thus establish a link between the stability of non-BPS D-branes and the topological stability of topological insulators.
Peng Ye; Juven Wang
2013-11-13
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 SPT states at least with charge symmetry (U(1) or Z$_N$) or spin $S^z$ rotation symmetry (U(1) or Z$_N$) in 2D, 3D, and the surface of 3D. If both are U(1), we apply external electromagnetic field / `spin gauge field' to study the charge / spin response. For the SPT examples we consider (i.e. U$_c$(1)$\\rtimes$Z$^T_2$, U$_s$(1)$\\times$Z$^T_2$, U$_c$(1)$\\times$[U$_s$(1)$\\rtimes$Z$_2$]; subscripts $c$ and $s$ are short for charge and spin; Z$^T_2$ and Z$_2$ are time-reversal symmetry and $\\pi$-rotation about $S^y$, respectively), many variants of Witten effect in the 3D SPT bulk and various versions of anomalous surface quantum Hall effect are defined and systematically investigated. If charge or spin symmetry reduces to Z$_N$ by considering charge-$N$ or spin-$N$ condensate, instead of the linear response approach, we gauge the charge/spin symmetry, leading to a dynamical gauge theory with some remaining global symmetry. The 3D dynamical gauge theory describes a symmetry-enriched topological phase (SET), i.e. a topologically ordered state with global symmetry which admits nontrivial ground state degeneracy depending on spatial manifold topology. For the SPT examples we consider, the corresponding SET states are described by dynamical topological gauge theory with topological BF term and axionic $\\Theta$-term in 3D bulk. And the surface of SET is described by the chiral boson theory with quantum anomaly.
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
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 ...
Sigalov, Michael; Shavit, Reuven
2007-01-01
In microwaves, a TE-polarized rectangular-waveguide resonator with an inserted thin ferrite disk gives an example of a nonintegrable system. The interplay of reflection and transmission at the disk interfaces together with the material gyrotropy effect gives rise to whirlpool-like electromagnetic vortices in the proximity of the ferromagnetic resonance. Based on numerical simulation, we show that a character of microwave vortices in a cavity can be analyzed by means of consideration of equivalent magnetic currents. Maxwell equations allows introduction of a magnetic current as a source of the electromagnetic field. Specifically, we found that in such nonintegrable structures, magnetic gyrotropy and geometrical factors leads to the effect of symmetry breaking resulting in effective chiral magnetic currents and topological magnetic charges. As an intriguing fact, one can observe precessing behavior of the electric-dipole polarization inside a ferrite disk.
Michael Sigalov; E. O. Kamenetskii; Reuven Shavit
2007-07-09
In microwaves, a TE-polarized rectangular-waveguide resonator with an inserted thin ferrite disk gives an example of a nonintegrable system. The interplay of reflection and transmission at the disk interfaces together with the material gyrotropy effect gives rise to whirlpool-like electromagnetic vortices in the proximity of the ferromagnetic resonance. Based on numerical simulation, we show that a character of microwave vortices in a cavity can be analyzed by means of consideration of equivalent magnetic currents. Maxwell equations allows introduction of a magnetic current as a source of the electromagnetic field. Specifically, we found that in such nonintegrable structures, magnetic gyrotropy and geometrical factors leads to the effect of symmetry breaking resulting in effective chiral magnetic currents and topological magnetic charges. As an intriguing fact, one can observe precessing behavior of the electric-dipole polarization inside a ferrite disk.
NASA Astrophysics Data System (ADS)
Fonseca, J. M.; Moura-Melo, W. A.; Pereira, A. R.
2013-11-01
By coating a three-dimensional topological insulator (TI) with a ferromagnetic film supporting an in-plane magnetic vortex, one breaks the time-reversal symmetry (TRS) without generating a mass gap. It rather yields electronic states bound to the vortex center which have different probabilities associated with each spin mode. In addition, its associate current (around the vortex center) is partially polarized with an energy gap separating the most excited bound state from the scattered ones. Charged zero-modes also appear as fully polarized modes localized near the vortex center. From the magnetic point of view, the observation of such a special current in a TI-magnet sandwich comes about as an alternative technique for detecting magnetic vortices in magnetic thin films.
Bouchard, Frédéric; Schulz, Sebastian A; Upham, Jeremy; Karimi, Ebrahim; Boyd, Robert W
2014-01-01
Orbital angular momentum associated with the helical phase-front of optical beams provides an unbounded \\qo{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 OAM $\\ell$. 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 traverse...
NASA Astrophysics Data System (ADS)
Mahfouzi, Farzad; Nikoli?, Branislav K.; Chen, Son-Hsien; Chang, Ching-Ray
2010-11-01
We study heterostructures where a two-dimensional topological insulator (TI) is attached to two normal-metal (NM) electrodes while an island of a ferromagnetic insulator (FI) with precessing magnetization covers a portion of its lateral edges to induce time-dependent exchange field underneath via the magnetic proximity effect. When the FI island covers both lateral edges, such device pumps pure spin current in the absence of any bias voltage, thereby acting as an efficient spin battery with giant output current even at very small microwave power input driving the precession. When only one lateral edge is covered by the FI island, both charge and spin current are pumped into the NM electrodes. We delineate conditions for the corresponding conductances (current-to-microwave-frequency ratio) to be quantized in a wide interval of precession cone angles, which is robust with respect to weak disorder and can be further extended by changes in device geometry. The origin of the quantization is explained using spatial profiles of local spin and charge currents in the reference frame rotating with the magnetization, which concomitantly reveals how current exiting from the chiral spin-filtered edge states within the TI region remains largely confined to a narrow flux within the NM electrodes that is refracted at the TI?NM interface.
Anomalies, gauge field topology, and the lattice
NASA Astrophysics Data System (ADS)
Creutz, Michael
2011-04-01
Motivated by the connection between gauge field topology and the axial anomaly in fermion currents, I suggest that the fourth power of the naive Dirac operator can provide a natural method 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.
NASA Astrophysics Data System (ADS)
Bouchard, Frédéric; De Leon, Israel; Schulz, Sebastian A.; Upham, Jeremy; Karimi, Ebrahim; Boyd, Robert W.
2014-09-01
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 ? = ± 2 q ? 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.
Exclusive Muon-Neutrino Charged Current muon plus any number of protons topologies in ArgoNeuT
NASA Astrophysics Data System (ADS)
Partyka, Kinga Anna
Neutrinos remain among the least understood fundamental particles even after decades of study. As we enter the precision era of neutrino measurements bigger and more sophisticated detectors have emerged. The leading candidate among them is a Liquid Argon Time Projection Chamber (LArTPC) detector technology due to its bubble-like chamber imaging, superb background rejection and scalability. It is a perfect candidate that will aim to answer the remaining questions of the nature of neutrino and perhaps our existence. Studying neutrinos with a detector that employs detection via beautiful images of neutrino interactions can be bath illuminating and surprising. The analysis presented here takes the full advantage of the LArTPC power by exploiting the first topological analysis of charged current muon neutrino mu + Np, muon and any number of protons, interactions with the ArgoNeuT LArTPC experiment on an argon target. The results presented here are the first that address the proton multiplicity at the vertex and the proton kinematics. This study also addresses the importance of nuclear effects in neutrino interactions. Furthermore, the developed here reconstruction techniques present a significant step forward for this technology and can be employed in the future LArTPC detectors.
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.
M. Bordag; B. Geyer; G. L. Klimchitskaya; V. M. Mostepanenko
2009-11-17
We show that in the presence of free charge carriers the definition of the frequency-dependent dielectric permittivity requires additional regularization. As an example, the dielectric permittivity of the Drude model is considered and its time-dependent counterpart is derived and analyzed. The respective electric displacement cannot be represented in terms of the standard Fourier integral. The regularization procedure allowing to circumvent these difficulties is suggested. For purpose of comparison it is shown that the frequency-dependent dielectric permittivity of insulators satisfies all rigorous mathematical criteria. This permits us to conclude that in the presence of free charge carriers the concept of dielectric permittivity is not as well defined as for insulators and we make a link to widely discussed puzzles in the theory of thermal Casimir force which might be caused by the use of such kind permittivities.
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.
NSDL National Science Digital Library
Geometry and Topology is "a fully refereed international journal dealing with all aspects of geometry and topology and their applications." The publisher, Geometry & Topology Publications (GTP), is a non-profit organization based in the Mathematics Department of the University of Warwick at Coventry, UK. Visitors can browse the journal, available free of charge electronically, or search by keyword or author. The moderate collection within the Geometry and Topology Monographs series includes research monographs and refereed conference proceedings.
Ye, Peng
2013-01-01
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 SPT states at least with charge symmetry (U(1) or Z_N) or spin S^z rotation symmetry (U(1) or Z_N) in 2D, 3D, and the surface of 3D, which is physically much closer to possible realization in realistic physical systems. If both are U(1), we apply external electromagnetic field / spin gauge field to study the charge/spin response. For the SPT examples we consider, many variants of Witten effects and different versions of anomalous quantum Hall effect are found and systematically discussed in the 3D SPT bulk and its surface, respectively. With the same symmetry, the surface of 3D SPT bulk admits anomalous response theory compared to 2D SPT state, which is justified by the K_G-matrix Chern-Simons term for external gauge fields based on the hydrodynamical approach to topological liquids. If charge or spin symmetry reduces to Z_N by considering ...
Ikenaga, Bruce
6231999 The Product Topology If X and Y are topological spaces, the product topology on X \\Theta Y is the topology generated by the basis consisting of all sets U \\Theta V , where U is open in X. How do you define a topology on a product of infinitely many spaces? Definition. Let fX a g a2A
CHAPTER III TOPOLOGICAL VECTOR SPACES AND
Baggett, Lawrence W.
S discussed in Exercise 3.10. DEFINITION. A topological vector space is a real (or complex) vector space XCHAPTER III TOPOLOGICAL VECTOR SPACES AND CONTINUOUS LINEAR FUNCTIONALS The marvelous interaction, topological vector spaces whose topologies are defined as the weakest topologies making certain collections
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)
INNOVATIVE POSSIBILITIES FOR UNDERGRADUATE TOPOLOGY
Smith, Sam
INNOVATIVE POSSIBILITIES FOR UNDERGRADUATE TOPOLOGY Samuel Bruce Smith Saint Joseph's University Philadephia, PA 19131 smith@sju.edu 1. INTRODUCTION. The development of topology ranks as one of the great success stories of twentieth century mathematics. While the precise definition of a topological space
Spanning set of silica cluster isomer topologies from QTAIM.
Jenkins, Samantha; Rong, Chunying; Kirk, Steven R; Yin, Dulin; Liu, Shubin
2011-11-17
Structural and chemical properties of the building block of silica nanowires, (SiO(2))(6), are investigated with the theory of atoms and molecules (QTAIM). Twenty-five conformers have been analyzed, ten of which have not been reported before. We extend the silica (SiO(2))(6) topology phase space using QTAIM; the Poincaré-Hopf topological sum rules are applied and used to identify the spanning set of topologies, and this includes finding eight new distinct topologies that satisfy the Poincaré-Hopf relation. A simple phase diagram of the solutions of the Poincaré-Hopf relation is created with the aid of a new classification scheme to determine the boundary between topological stability and instability. Sum rules are then found to be applicable to any set of isomers. We determine that O-O bonding interactions exist for the silica (SiO(2))(6) conformers in regions where the energy surface is flattest. In addition, we identify unstable local minima in the topology of the charge density in order to further compare conformer instabilities. We quantify the dimensionality of a molecule using the Poincaré-Hopf relation instead of Euclidean geometry. This quantum topological definition of geometry shows that the four most energetically stable (SiO(2))(6) conformers are quantified as two-dimensional within the new quantum topology. PMID:21557588
Eon, Jean-Guillaume
2011-01-01
Crystal-structure topologies, represented by periodic nets, are described by labelled quotient graphs (or voltage graphs). Because the edge space of a finite graph is the direct sum of its cycle and co-cycle spaces, a Euclidian representation of the derived periodic net is provided by mapping a basis of the cycle and co-cycle spaces to a set of real vectors. The mapping is consistent if every cycle of the basis is mapped on its own net voltage. The sum of all outgoing edges at every vertex may be chosen as a generating set of the co-cycle space. The embedding maps the cycle space onto the lattice L. By analogy, the concept of the co-lattice L* is defined as the image of the generators of the co-cycle space; a co-lattice vector is proportional to the distance vector between an atom and the centre of gravity of its neighbours. The pair (L, L*) forms a complete geometric descriptor of the embedding, generalizing the concept of barycentric embedding. An algebraic expression permits the direct calculation of fractional coordinates. Non-zero co-lattice vectors allow nets with collisions, displacive transitions etc. to be dealt with. The method applies to nets of any periodicity and dimension, be they crystallographic nets or not. Examples are analyzed: ?-cristobalite, the seven unstable 3-periodic minimal nets etc. PMID:21173475
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.
A gauge theoretical view of the charge concept in Einstein gravity
Toussaint, M
2000-01-01
We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension $\\hbar/l^2$, the mass parameter of a particle dimension $\\hbar/l$, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi-electric monopole charge of the time translation whereas the NUT parameter is a quasi-magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpret...
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.
Banach Spaces 1) Basic definitions and Hahn Banach
Junge, Marius
Banach Spaces 1) Basic definitions and Hahn Banach Definition: 1) A vector space X equipped(x,y)=||x-y|| makes it a metric space, and hence a topological vector space. Definition: A Banach space is a complete Definition: Let (X,tau) be a topological vector space. Then L(X,K) is a again a topological vectors space
Schuster, David I; Cheng, Peng; Jarowski, Peter D; Guldi, Dirk M; Luo, Chuping; Echegoyen, Luis; Pyo, Soomi; Holzwarth, Alfred R; Braslavsky, Silvia E; Williams, René M; Klihm, Gudrun
2004-06-16
As part of a continuing investigation of the topological control of intramolecular electron transfer (ET) in donor-acceptor systems, a symmetrical parachute-shaped octaethylporphyrin-fullerene dyad has been synthesized. A symmetrical strap, attached to ortho positions of phenyl groups at opposing meso positions of the porphyrin, was linked to [60]-fullerene in the final step of the synthesis. The dyad structures were confirmed by (1)H, (13)C, and (3)He NMR, and MALDI-TOF mass spectra. The free-base and Zn-containing dyads were subjected to extensive spectroscopic, electrochemical and photophysical studies. UV-vis spectra of the dyads are superimposable on the sum of the spectra of appropriate model systems, indicating that there is no significant ground-state electronic interaction between the component chromophores. Molecular modeling studies reveal that the lowest energy conformation of the dyad is not the C(2)(v)() symmetrical structure, but rather one in which the porphyrin moves over to the side of the fullerene sphere, bringing the two pi-systems into close proximity, which enhances van der Waals attractive forces. To account for the NMR data, it is proposed that the dyad is conformationally mobile at room temperature, with the porphyrin swinging back and forth from one side of the fullerene to the other. The extensive fluorescence quenching in both the free base and Zn dyads is associated with an extremely rapid photoinduced electron-transfer process, k(ET) approximately 10(11) s(-)(1), generating porphyrin radical cations and C(60) radical anions, detected by transient absorption spectroscopy. Back electron transfer (BET) is slower than charge separation by up to 2 orders of magnitude in these systems. The BET rate is slower in nonpolar than in polar solvents, indicating that BET occurs in the Marcus inverted region, where the rate decreases as the thermodynamic driving force for BET increases. Transient absorption and singlet molecular oxygen sensitization data show that fullerene triplets are formed only with the free base dyad in toluene, where triplet formation from the charge-separated state is competitive with decay to the ground state. The photophysical properties of the P-C(60) dyads with parachute topology are very similar to those of structurally related rigid pi-stacked P-C(60) dyads, with the exception that there is no detectable charge-transfer absorption in the parachute systems, attributed to their conformational flexibility. It is concluded that charge separation in these hybrid systems occurs through space in unsymmetrical conformations, where the center-to-center distance between the component pi-systems is minimized. Analysis of the BET data using Marcus theory gives reorganization energies for these systems between 0.6 and 0.8 eV and electronic coupling matrix elements between 4.8 and 5.6 cm(-)(1). PMID:15186163
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)
S?raru, Silviu-Constantin
Topological field theories originate in the papers of Schwarz and Witten. Initially, Schwarz shown that one of the topological invariants, namely the Ray-Singer torsion, can be represented as the partition function of a certain quantum field theory. Subsequently, Witten constructed a framework for understanding Morse theory in terms of supersymmetric quantum mechanics. These two constructions represent the prototypes of all topological field theories. The model used by Witten has been applied to classical index theorems and, moreover, suggested some generalizations that led to new mathematical results on holomorphic Morse inequalities. Starting with these results, further developments in the domain of topological field theories have been achieved. The Becchi-Rouet-Stora-Tyutin (BRST) symmetry allowed for a new definition of topological ...eld theories as theories whose BRST-invariant Hamiltonian is also BRST-exact. An important class of topological theories of Schwarz type is the class of BF models. This type of models describes three-dimensional quantum gravity and is useful at the study of four-dimensional quantum gravity in Ashtekar-Rovelli-Smolin formulation. Two-dimensional BF models are correlated to Poisson sigma models from various two-dimensional gravities. The analysis of Poisson sigma models, including their relationship to two-dimensional gravity and the study of classical solutions, has been intensively studied in the literature. In this thesis we approach the problem of construction of some classes of interacting BF models in the context of the BRST formalism. In view of this, we use the method of the deformation of the BRST charge and BRST-invariant Hamiltonian. Both methods rely on specific techniques of local BRST cohomology. The main hypotheses in which we construct the above mentioned interactions are: space-time locality, Poincare invariance, smoothness of deformations in the coupling constant and the preservation of the number of derivatives on each field. The first two hypotheses implies that the resulting interacting theory must be local in space-time and Poincare invariant. The smoothness of deformations means that the deformed objects that contribute to the construction of interactions must be smooth in the coupling constant and reduce to the objects corresponding to the free theory in the zero limit of the coupling constant. The preservation of the number of derivatives on each field imp! lies two aspects that must be simultaneously fulfilled: (i) the differential order of each free field equation must coincide with that of the corresponding interacting field equation; (ii) the maximum number of space-time derivatives from the interacting vertices cannot exceed the maximum number of derivatives from the free Lagrangian. The main results obtained can be synthesized into: obtaining self-interactions for certain classes of BF models; generation of couplings between some classes of BF theories and matter theories; construction of interactions between a class of BF models and a system of massless vector fields.
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.
AdS Boundary Conditions and the Topologically Massive Gravity/CFT Correspondence
Skenderis, Kostas; Taylor, Marika; Rees, Balt C. van [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
2009-12-15
The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights obtained in this direction over the last decade and apply the new techniques to Topologically Massive Gravity. We show that this theory is dual to a non-unitary CFT for any value of its parameter mu and becomes a Logarithmic CFT at mu = 1.
NASA Astrophysics Data System (ADS)
Faulkner, Michael F.; Bramwell, Steven T.; Holdsworth, Peter C. W.
2015-04-01
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.
Topological index theorem on the lattice through the spectral flow of staggered fermions
NASA Astrophysics Data System (ADS)
Azcoiti, V.; Follana, E.; Vaquero, A.; Di Carlo, G.
2015-05-01
We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic (quenched) gauge configurations. We obtain clear numerical evidence that the definition works as expected: there is a clear separation between crossings near and far away from the origin, and the topological charge defined through the crossings near the origin agrees, for most configurations, with the one defined through the near-zero modes of large taste-singlet chirality of the staggered Dirac operator. The crossings are much closer to the origin if we improve the Dirac operator used in the definition, and they move towards the origin as we decrease the lattice spacing.
Topological activity in Bragg elliptical twisted fibers.
Alexeyev, Constantine N; Fadeyeva, Tatyana A; Lapin, Boris P; Yavorsky, Maxim A
2012-04-01
We have theoretically shown that Bragg twisted elliptical fibers manifest, in certain spectral regions, the property of topological activity--the ability to change in the reflected field the topological charge of incoming optical vortices and fundamental modes by two units. This property could be used for narrowband generation of optical vortices from Gaussian beams and for changing the topological charge of incoming optical vortices. PMID:22505114
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
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.
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.
Sinclair, D.K.
1992-11-20
The HTMCGC collaboration has been simulating lattice QCD with two light staggered quarks with masses m[sub q] = 0.0125 and also m[sub q] = 0.00625 on a 16[sup 3] [times] 8 lattice. We have been studying the behavior of the transition from hadronic matter to a quark-gluon plasma and the properties of that plasma. We have been measuring entropy densities, Debye and hadronic screening lengths, the spacial string tension and topological susceptibility in addition to the standard order parameters. The HEMCGC collaboration has simulated lattice QCD with two light staggered quarks,m[sub q] = 0.025 and m[sub q] = 0.010 on a 16[sup 3] [times] 32 lattice. We have measured the glueball spectrum and topological susceptibilities for these runs.
Sinclair, D.K.; HEMCGC collaboration; HTMCGC collaboration
1992-11-20
The HTMCGC collaboration has been simulating lattice QCD with two light staggered quarks with masses m{sub q} = 0.0125 and also m{sub q} = 0.00625 on a 16{sup 3} {times} 8 lattice. We have been studying the behavior of the transition from hadronic matter to a quark-gluon plasma and the properties of that plasma. We have been measuring entropy densities, Debye and hadronic screening lengths, the spacial string tension and topological susceptibility in addition to the standard order parameters. The HEMCGC collaboration has simulated lattice QCD with two light staggered quarks,m{sub q} = 0.025 and m{sub q} = 0.010 on a 16{sup 3} {times} 32 lattice. We have measured the glueball spectrum and topological susceptibilities for these runs.
Chiral condensate, quark charge and chiral density
Harald Markum; Wolfgang Sakuler; Stefan Thurner
1998-09-20
We study the topological and fermionic vacuum structure of four-dimensional QCD on the lattice by means of correlators of fermionic observables and topological densities. We show the existence of strong local correlations between the topological charge density and the quark condensate, charge and chiral density. By analysis of individual gauge configurations, we visualize that instantons (antiinstantons) carry positive (negative) chirality, whereas the quark charge density fluctuates in sign within instantons.
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
Topological Pumping over a Photonic Fibonacci Quasicrystal
Mor Verbin; Oded Zilberberg; Yoav Lahini; Yaacov E. Kraus; Yaron Silberberg
2014-03-27
Quasiperiodic lattices have recently been shown to be a non-trivial topological phase of matter. Charge pumping -- one of the hallmarks of topological states of matter -- was recently realized for photons in a one-dimensional (1D) off-diagonal Harper model implemented in a photonic waveguide array. The topologically nontrivial 1D Fibonacci quasicrystal (QC) is expected to facilitate a similar phenomenon, but its discrete nature and lack of pumping parameter hinder the experimental study of such topological effects. In this work we overcome these obstacles by utilizing a family of topologically equivalent QCs which ranges from the Fibonacci QC 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 QC.
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.
Topological Pumping over a Photonic Fibonacci Quasicrystal
Verbin, Mor; Lahini, Yoav; Kraus, Yaacov E; Silberberg, Yaron
2014-01-01
Quasiperiodic lattices have recently been shown to be a non-trivial topological phase of matter. Charge pumping -- one of the hallmarks of topological states of matter -- was recently realized for photons in a one-dimensional (1D) off-diagonal Harper model implemented in a photonic waveguide array. The topologically nontrivial 1D Fibonacci quasicrystal (QC) is expected to facilitate a similar phenomenon, but its discrete nature and lack of pumping parameter hinder the experimental study of such topological effects. In this work we overcome these obstacles by utilizing a family of topologically equivalent QCs which ranges from the Fibonacci QC 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 QC.
V.1Semi-topological K-Theory Eric M. Friedlander and Mark E. Walker *
....................................................................................... 878 1.2 Definition of Semi-topological K-Theory ........................................ 881 SemiV.1Semi-topological K-Theory Eric M. Friedlander and Mark E. Walker * 1.1 Introduction-topological K-Theory of Projective Varieties: Ksemi ....................... 883 Semi-topological K-Theory
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.
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
NSDL National Science Digital Library
Hosted by York University, with support from University of Florida, University of Tennessee at Martin, Nipissing University, York University, and the University of Milan, the Topology Atlas Website calls itself a publisher of information related to topology. The site amounts to a vast repository of documents for mathematicians and others interested in topology. A preprints section offers documents dating from December 1995 to the present. An Invited Contributions section holds short surveys of specialized topics including titles like "On Variations of Continuity," and "Atlas of oriented knots and links." Also available at this site are abstracts (for books, published articles, and research announcements), journals, TopCom (a magazine for the topology community), and more.
NASA Astrophysics Data System (ADS)
Yang, Zhaoju; Gao, Fei; Shi, Xihang; Lin, Xiao; Gao, Zhen; Chong, Yidong; Zhang, Baile
2015-03-01
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.
Srivastava, Alka; Balaji, Petety V.
2014-01-01
This study explores the stabilities of single sheet parallel systems of three sequence variants of 1GNNQQNY7, N2D, N2S and N6D, with variations in aggregate size (5–8) and termini charge (charged or neutral). The aggregates were simulated at 300 and 330 K. These mutations decrease amyloid formation in the yeast prion protein Sup35. The present study finds that these mutations cause instability even in the peptide context. The protonation status of termini is found to be a key determinant of stabilities; other determinants are sequence, position of mutation and aggregate size. All systems with charged termini are unstable, whereas both stable and unstable systems are found when the termini are neutral. When termini are charged, the largest stable aggregate for the N2S and N6D systems has 3 to 4 peptides whereas N2D mutation supports oligomers of larger size (5-and 6-mers) as well. Mutation at 2nd position (N2S and N2D) results in fewer H-bonds at the mutated as well as neighboring (Gly1/Gln4) positions. However, no such effect is found if mutation is at 6th position (N6D). The effect of Asn?Asp mutation depends on the position and termini charge: it is more destabilizing at the 2nd position than at the 6th in case of neutral termini, however, the opposite is true in case of charged termini. Appearance of twist in stable systems and in smaller aggregates formed in unstable systems suggests that twist is integral to amyloid arrangement. Disorder, dissociation or rearrangement of peptides, disintegration or collapse of aggregates and formation of amorphous aggregates observed in these simulations are likely to occur during the early stages of aggregation also. The smaller aggregates formed due to such events have a variety of arrangements of peptides. This suggests polymorphic nature of oligomers and presence of a heterogeneous mixture of oligomers during early stages of aggregation. PMID:24817093
Symmetry, Defects, and Gauging of Topological Phases
Maissam Barkeshli; Parsa Bonderson; Meng Cheng; Zhenghan Wang
2014-11-12
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the topological symmetry group, which characterizes the symmetry of the emergent topological quantum numbers of a topological phase $\\mathcal{C}$, and we describe its relation with the microscopic symmetry of the underlying physical system. We derive a general framework to classify symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are anti-unitary. We develop a theory of extrinsic defects (fluxes) associated with elements of the symmetry group, which provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter $\\mathcal{C}$ with symmetry group $G$. The algebraic theory of the defects, known as a $G$-crossed braided tensor category $\\mathcal{C}_{G}^{\\times}$, allows one to compute many properties, such as the number of topologically distinct types of defects associated with each group element, their fusion rules, quantum dimensions, zero modes, braiding exchange transformations, a generalized Verlinde formula for the defects, and modular transformations of the $G$-crossed extensions of topological phases. We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic $G$-defects are turned into deconfined quasiparticle excitations, which results in a different topological phase $\\mathcal{C}/G$. A number of instructive and/or physically relevant examples are studied in detail.
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.
Philip Kremer; Grigori Mints
2005-01-01
Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, ? is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and ? can be understood
Philip Kremer; Grigori Mints
Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and can be understood as a
Shesh Narayan Vaishnav; H. Krishnaswami
2011-01-01
In this paper, an isolated bi-directional ac\\/dc con- verter with a single power conversion stage is proposed for both charging and Vehicle-to-Grid (V2G) applications of PHEV. The converter consists of two active bridges connected through a se- ries resonant tank and a high-frequency transformer. Steady-state analysis is presented for the proposed phase-shift modulation technique between active bridges, to control the
Measurement-only topological quantum computation via anyonic interferometry
Bonderson, Parsa Freedman, Michael Nayak, Chetan
2009-04-15
We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using 'forced measurement' protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems.
12 CFR 1026.4 - Finance charge.
Code of Federal Regulations, 2014 CFR
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...
Charged Unruh effect on geon spacetimes
David Edward Bruschi; Jorma Louko
2010-03-05
A topological geon black hole with gauge charges may have a gauge bundle that necessarily incorporates charge conjugation as a gauge symmetry. This happens for example for the Reissner-Nordstrom geon. We show that gauging the charge conjugation leaves an imprint in the Unruh effect: the geon's exterior region contains non-thermal correlations for particle pairs of the same, rather than opposite, charge. The phenomenon occurs also in topologically similar Rindler spacetimes with a background gauge field.
Dynamical overlap fermion at fixed topology
JLQCD collaboration; S. Hashimoto; S. Aoki; H. Fukaya; K. Kanaya; T. Kaneko; H. Matsufuru; M. Okamoto; T. Onogi; N. Yamada
2006-10-02
We launched a project to perform dymanical fermion simulations using the overlap fermion formulation for sea quarks. In order to avoid the appearace of near-zero modes of the hermitian Wilson-Dirac operator $H_W$, we introduce a pair of extra Wilson fermions with a large negative mass term. Crossing of the topological boundary is then strictly prohibited, and the topological charge is conserved during simulations. It makes the simulations substantially faster compared to the algorithms which allow the topology change. We discuss on the finite volume effects due to the fixed global topology.
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)
Bonneau, Philippe
Following a preceding paper showing how the introduction of a t.v.s. topology on quantum groups led to a remarkable unification and rigidification of the different definitions, we adapt here, in the same way, the definition of quantum double. This topological double is dualizable and reflexive (even for infinite dimensional algebras). In a simple case we show, considering the double as the "zero class" of an extension theory, the uniqueness of the double structure as a quasi-Hopf algebra. A la suite d'un précédent article montrant comment l'introduction d'une topologie d'e.v.t. sur les groupes quantiques permet une unification et une rigidification remarquables des différentes définitions, on adapte ici de la même manière la définition du double quantique. Ce double topologique est alors dualisable et reflexif (même pour des algèbres de dimension infinie). Dans un cas simple on montre, en considérant le double comme la "classe zéro" d'une théorie d'extensions, l'unicité de cette structure comme algèbre quasi-Hopf.
Influence of topology on the scale setting
Georg Bergner; Pietro Giudice; Istvan Montvay; Gernot Münster; Stefano Piemonte
2014-11-25
Recently a new method to set the scale in lattice gauge theories, based on the gradient flow generated by the Wilson action, has been proposed, and the systematic errors of the new scales t0 and w0 have been investigated by various groups. The Wilson flow provides also an interesting alternative smoothing procedure in particular useful for the measurement of the topological charge as a pure gluonic observable. We show the viability of this method for N=1 supersymmetric Yang-Mills theory by analysing the configurations produced by the DESY-Muenster collaboration. For increasing flow time the topological charge quickly approaches near-integer values. The topological susceptibility has been measured for different fermion masses and its value is observed to approach zero in the chiral limit. Finally, the relation between the scale defined by the Wilson flow and the topological charge has been investigated, demonstrating a correlation between these two quantities.
Charge varying sine-Gordon deformed defects
Alex E. Bernardini; Mariana Chinaglia; Roldao da Rocha
2015-04-28
Sine-Gordon deformed defects that exhibit unusual phenomenological features on the topological charge are investigated. The possibility of a smooth and continuous transition between topological (non null charge) and non-topological (null charge) scenarios of deformed defects supported by sine-Gordon structures is evinced by the analytical calculation of topological charges and localized energy distributions. By describing cyclic deformation chains, we show that a triggering sine-Gordon model simultaneously supports kink and lump-like defects, whose topological mass values are closed by trigonometric or hyperbolic successive deformations. In spite of preserving analytical closure relations constraining the topological masses of $3$-and $4$-cyclically deformed defects, the deformation chains produce kinks and lumps which exhibit non-monotonic behavior and extra inflection points, respectively. The outcome of our analysis suggests that cyclic deformations create novel scenarios of physical and mathematical applicability of defect structures supported by the sine-Gordon theory.
Target Space Symmetries in Topological Theories I
NASA Astrophysics Data System (ADS)
Baulieu, L.; Losev, A. S.; Nekrasov, N. A.
2002-03-01
We study realization of the target space diffeomorphisms in the type C topological string. We found that the charges, which generate transformations of the boundary observables, form an algebra, which differs from that of bulk charges by the contribution of the bubbled disks. We discuss applications to noncommutative field theories.
New class of non-topological solitons
Frieman, J.A.; Lynn, B.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.
1. Theory of CW-Complexes 1. Definitions.
Johannson, Klaus
1. Theory of CW-Complexes 1. Definitions. A CW-complex is a topological space which * *attaching maps. They are an important ingredient of the CW-structure. Here are better def* *initions. Definition. A CW-complex is a topological space X together with a filtration
Is a color superconductor topological?
Yusuke Nishida
2010-04-05
A fully gapped state of matter, whether insulator or superconductor, can be asked if it is topologically trivial or nontrivial. Here we investigate topological properties of superconducting Dirac fermions in 3D having a color superconductor as an application. In the chiral limit, when the pairing gap is parity even, the right-handed and left-handed sectors of the free space Hamiltonian have nontrivial topological charges with opposite signs. Accordingly, a vortex line in the superconductor supports localized gapless right-handed and left-handed fermions with the dispersion relations E=+/-vp_z (v is a parameter dependent velocity) and thus propagating in opposite directions along the vortex line. However, the presence of the fermion mass immediately opens up a mass gap for such localized fermions and the dispersion relations become E=+/-v(m^2+p_z^2)^(1/2). When the pairing gap is parity odd, the situation is qualitatively different. The right-handed and left-handed sectors of the free space Hamiltonian in the chiral limit have nontrivial topological charges with the same sign and therefore the presence of the small fermion mass does not open up a mass gap for the fermions localized around the vortex line. When the fermion mass is increased further, there is a topological phase transition at m=(\\mu^2+\\Delta^2)^(1/2) and the localized gapless fermions disappear. We also elucidate the existence of gapless surface fermions localized at a boundary when two phases with different topological charges are connected. A part of our results is relevant to the color superconductivity of quarks.
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)
Hamann, Bernd
, and we provide the definitions only for this case. Definition 1.1 A planar vector field is a map Ú Ê ¾ Ê ÓÐÐÑ ÒÒ Ù Ú ×º Ù Keywords: vector field, flow, topology, visualization Abstract The topology of vector fields offers a well known way to show a "condensed" view of the stream line behavior of a vector field
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.
NSDL National Science Digital Library
2014-09-12
In this activity, learners construct three math puzzles out of simple materials like wood, string, and Styrofoam. The first two puzzles, called "Remove the Loop" and "Two Washers," are examples of topology, an area of math about how geometric figures are different and similar. The third puzzle, "Towers of Hanoi," uses a mathematical tool called an algorithm and is also a good example of an exponential function.
Computational Topology: An Introduction
Vegter, Gert
7 Computational Topology: An Introduction G¨unter Rote and Gert Vegter 7.1 Introduction Topology, the distance between points, or the curvature of a surface, are irrelevant to topology. Com- putational topology deals with the complexity of topological problems, and with the design of efficient algorithms
Topological properties in topological insulators and superconductors
Chunbo Zhao
2013-09-09
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter physics that issuing TSM. Fiber bundle theory is a powerful concept to describe the non-trivial topology properties underlying the physical system. So we briefly present some motivation of fiber bundle theory and following that several effective topological methods have been introduced to judge whether a fiber bundle is trivial or not. Next, we give some topological invariants that characterizes the non-trivial TSM in the non-interacting systems in all dimensions, which is called topological band theory. Following that, we review and generalize the topological response using topological field theory called Chern-Simons effective theory. Finally, the classification of free-fermion systems have been studied by loop space and K-theory.
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.
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.
Extracting Physics from Topologically Frozen Markov Chains
Urs Gerber; Irais Bautista; Wolfgang Bietenholz; Héctor Mejía-Díaz; Christoph P. Hofmann
2014-10-02
In Monte Carlo simulations with a local update algorithm, the auto-correlation with respect to the topological charge tends to become very long. In the extreme case one can only perform reliable measurements within fixed sectors. We investigate approaches to extract physical information from such topologically frozen simulations. Recent results in a set of sigma-models and gauge theories are encouraging. In a suitable regime, the correct value of some observable can be evaluated to a good accuracy. In addition there are ways to estimate the value of the topological susceptibility.
Nagpal, Radhika; Patel, Ankit; Gibson, Matthew C
2008-03-01
It is universally accepted that genetic control over basic aspects of cell and molecular biology is the primary organizing principle in development and homeostasis of living systems. However, instances do exist where important aspects of biological order arise without explicit genetic instruction, emerging instead from simple physical principles, stochastic processes, or the complex self-organizing interaction between random and seemingly unrelated parts. Being mostly resistant to direct genetic dissection, the analysis of such emergent processes falls into a grey area between mathematics, physics and molecular cell biology and therefore remains very poorly understood. We recently proposed a mathematical model predicting the emergence of a specific non-Gaussian distribution of polygonal cell shapes from the stochastic cell division process in epithelial cell sheets; this cell shape distribution appears to be conserved across a diverse set of animals and plants.1 The use of such topological models to study the process of cellular morphogenesis has a long history, starting almost a century ago, and many insights from those original works influence current experimental studies. Here we review current and past literature on this topic while exploring some new ideas on the origins and implications of topological order in proliferating epithelia. PMID:18293365
Exotic topological types of Majorana zero modes and their universal quantum manipulation
NASA Astrophysics Data System (ADS)
Zhao, Y. X.; Wang, Z. D.
2014-09-01
From our general index theorem, which characterizes faithfully the topological intrinsic boundary-bulk correspondence of topological superconductors and insulators, we reveal rigorously that four topologically distinct types of Majorana zero modes can emerge at the ends of superconducting wires of various symmetry classes. More intriguingly, we establish three exotic one-dimensional models that have different types of topological charge of Majorana zero modes and disclose exactly the corresponding topological properties, whose distinct topological essences may be tested experimentally. Moreover, we also address their application in universal quantum manipulation, which is promising for realizing universal topological quantum computation.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 2010-01-01 false Definitions. 120.420 Section 120...Financings § 120.420 Definitions. (a) 7(a) Loans...entered against it for felony or fraud, or charges relating...against him for, a felony or fraud, or charges relating...
D-brane charge, flux quantisation and relative (co)homology
NASA Astrophysics Data System (ADS)
Figueroa-O'Farrill, José Miguel; Stanciu, Sonia
2001-01-01
We reconsider the problem of U(1) flux and D0-charge for D-branes in the WZW model and investigate the relationship between the different definitions that have been proposed recently. We identify the D0-charge as a particular reduction of a class in the relative cohomology of the group modulo the D-submanifold. We investigate under which conditions this class is equivalent to the first Chern class of a line bundle on the D-submanifold and we find that in general there is an obstruction given by the cohomology class of the NS 3-form. Therefore we conclude that for topologically nontrivial B-fields, there is strictly speaking no U(1) gauge field on the D-submanifold. Nevertheless the ambiguity in the flux is not detected by the D0-charge. This has a natural interpretation in terms of gerbes.
Orbifolds and Topological Defects
NASA Astrophysics Data System (ADS)
Brunner, Ilka; Carqueville, Nils; Plencner, Daniel
2014-12-01
We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory, as well as bulk-boundary correlators from a novel, universal perspective. This entails a structure somewhat weaker than ordinary TFT, which however still describes a sector of the underlying conformal theory. The case of B-twisted Landau-Ginzburg models is discussed in detail, where we compute charge vectors and superpotential terms for B-type branes. Our construction also works in the absence of supersymmetry and for generalised "orbifolds" that need not arise from symmetry groups. In general, this involves a natural appearance of Hochschild (co)homology in a 2-categorical setting, in which among other things we provide simple presentations of Serre functors and a further generalisation of the Cardy condition.
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2010 CFR
2010-01-01
...Section 226.4 Banks and Banking FEDERAL RESERVE SYSTEM (CONTINUED) BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM TRUTH IN LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is...
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2011 CFR
2011-01-01
...Section 226.4 Banks and Banking FEDERAL RESERVE SYSTEM (CONTINUED) BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM TRUTH IN LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is...
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2012 CFR
2012-01-01
...Section 226.4 Banks and Banking FEDERAL RESERVE SYSTEM (CONTINUED) BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM TRUTH IN LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is...
Topological insulators and superconductors from string theory
Ryu, Shinsei; Takayanagi, Tadashi [Department of Physics, University of California, Berkeley, California 94720 (United States); Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, Kashiwa, Chiba 277-8582 (Japan)
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 Insulators and Superconductors from String Theory
Shinsei Ryu; Tadashi Takayanagi
2010-08-01
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 supercondutors, 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 non-interacting 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).
Localization of overlap eigenmodes and topological charge
;massless Neuberger overlap operator D(0) = a 1 + DW D W DW , DW = M - a with the Wilson Dirac operator DW with negative mass term /a To implement the sign function we use the Minmax polynomial the condition numer of DW , · project out some low eigenmodes of the Wilson-Kernel and treat the sign function
Deficient topological measures and functionals generated by them
Svistula, Marina G [Samara State University, Samara (Russian Federation)
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.
Gapped symmetry preserving surface state for the electron topological insulator
Wang, Chong
It is well known that the three-dimensional (3D) electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often ...
Submitted to Topology Proceedings
Short, Jon W.
Submitted to Topology Proceedings DENSE ARC COMPONENTS IN WEAKENED TOPOLOGICAL GROUPS JON W. SHORT Abstract. We will show how to construct metrizable group topologies on the subgroups and quotient groups of R that are weaker than the standard topologies. Even though these groups can be very complicated, we
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.
- 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.
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
Section 3: Topology of Introduction
Choi, Suhyoung
Section 3: Topology of orbifolds S. Choi Introduction Topology of 2-orbifolds Topology of 2-approach to the universal covering spaces 2-orbifolds, triangulations, and topological constructions and covering spaces 3: Topology of orbifolds S. Choi Introduction Topology of 2-orbifolds Topology of 2-orbifolds Smooth
Nontrivial topology and the chiral Schwinger model
Dias, S.A. (Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150, 22290 Rio de Janeiro, Rio de Janeiro (Brazil)); Linhares, C.A. (Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150, 22290 Rio de Janeiro, Rio de Janeiro (Brazil) Instituto de Estudos Avancados, Centro Tecnico Aeroespacial, Rodovia dos Tamoios, km 5,5, 12231 Sao Jose dos Campos, Sao Paulo (Brazil))
1993-02-15
We analyze the chiral Schwinger model in nontrivial topological sectors, performing its complete bosonization. In order to do this, we propose a prescription for evaluating the fermion determinant in the presence of the zero modes, valid for non-Hermitian Dirac operators, in general. By taking fermionic external sources into account in every step of the calculation, we discover a phase ambiguity which affects the effective action and can be used to render the result invariant with respect to particular choices of the topologically charged background configuration. Consistency requirements on the bosonization procedure fix the phase ambiguity and determine a unique value for the Jackiw-Rajaraman regularization parameter in all sectors with a nonzero topological charge. We thus find that nontrivial sectors have a null contribution to all fermionic correlation functions. Our method is also checked against the analogous results for the Schwinger model.
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.
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.
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.
A hierarchy of topological tensor network states
Buerschaper, Oliver [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5 (Canada) [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5 (Canada); Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching (Germany); Mombelli, Juan Martin [Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Medina Allende s/n, Ciudad Universitaria, 5000 Cordoba (Argentina)] [Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Medina Allende s/n, Ciudad Universitaria, 5000 Cordoba (Argentina); Christandl, Matthias [Institute for Theoretical Physics, ETH Zurich, 8093 Zurich (Switzerland)] [Institute for Theoretical Physics, ETH Zurich, 8093 Zurich (Switzerland); Aguado, Miguel [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching (Germany)] [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching (Germany)
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.
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
Periodic table for topological insulators and superconductors
Alexei Kitaev; Alexei
2009-01-01
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
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\
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.
Code of Federal Regulations, 2013 CFR
2013-01-01
... § 7.4001 Charging interest at rates permitted competing institutions; charging interest to corporate borrowers...Definition. The term “interest” as used in 12 U...includes, among other things, the...
Code of Federal Regulations, 2014 CFR
2014-01-01
... § 7.4001 Charging interest at rates permitted competing institutions; charging interest to corporate borrowers...Definition. The term “interest” as used in 12 U...includes, among other things, the...
Code of Federal Regulations, 2012 CFR
2012-01-01
... § 7.4001 Charging interest at rates permitted competing institutions; charging interest to corporate borrowers...Definition. The term “interest” as used in 12 U...includes, among other things, the...
Momentum polarization of non-Abelian topologically ordered states
NASA Astrophysics Data System (ADS)
Zhang, Yi; Qi, Xiao-Liang
2014-03-01
We study momentum polarization of non-Abelian topologically ordered states for the Gutzwiller projected Chern insulator wave function with Chern number C=2. The resulting quasiparticle topological spin and edge central charge confirm the field theory description of an SU(2) gauge field coupled to ? = 2 fermions and rule out other candidate theories. We also discuss characteristic differences and the quantum phase transition between this non-Abelian topological phase and an Abelian topological phase described by the projected wave function of two C=1 Chern insulators.
Topological insulators and superconductors from D-brane
NASA Astrophysics Data System (ADS)
Ryu, Shinsei; Takayanagi, Tadashi
2010-09-01
Realization of topological insulators (TIs) and superconductors (TSCs), such as the quantum spin Hall effect and the Z2 topological insulator, in terms of D-branes in string theory is proposed. We establish a one-to-one correspondence between the K-theory classification of TIs/TSCs and D-brane charges. The string theory realization of TIs and TSCs comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature. This sheds light on TIs and TSCs beyond non-interacting systems, and the underlying topological field theory description thereof.
Bringing Definitions into High Definition
ERIC Educational Resources Information Center
Mason, John
2010-01-01
Why do definitions play such a central role in mathematics? It may seem obvious that precision about the terms one uses is necessary in order to use those terms reasonably (while reasoning). Definitions are chosen so as to be definite about the terms one uses, but also to make both the statement of, and the reasoning to justify, theorems as…
Ling-Yan Hung; Xiao-Gang Wen
2012-11-12
We consider a weakly coupled gauge theory where charged particles all have large gaps (ie no Higgs condensation to break the gauge "symmetry") and the field strength fluctuates only weakly. We ask what kind of topological terms can be added to the Lagrangian of such a weakly coupled gauge theory. In this paper, we systematically construct quantized topological terms which are generalization of the Chern-Simons terms and $F\\wedge F$ terms, in space-time dimensions $d$ and for any gauge groups (continuous or discrete), using each element of the topological cohomology classes $H^{d+1}(BG,\\Z)$ on the classifying space $BG$ of the gauge group $G$. In 3$d$ or for finite gauge groups above 3$d$, the weakly coupled gauge theories are gapped. So our results on topological terms can be viewed as a systematic construction of gapped topologically ordered phases of weakly coupled gauge theories. In other cases, the weakly coupled gauge theories are gapless. So our results can be viewed as an attempt to systematically construct different gapless phases of weakly coupled gauge theories. Amazingly, the bosonic symmetry protected topological (SPT) phases with a finite on-site symmetry group $G$ are also classified by the same $H^{d+1}(BG,\\Z)$. (SPT phases are gapped quantum phases with a symmetry and trivial topological order.) In this paper, we show an explicit duality relation between topological gauge theories with the quantized topological terms and the bosonic SPT phases, for any finite group $G$ and in any dimensions; a result first obtained by Levin and Gu. We also study the relation between topological lattice gauge theory and the string-net states with non-trivial topological order and no symmetry.
4D topological mass by gauging spin
NASA Astrophysics Data System (ADS)
Choudhury, I. D.; Diamantini, M. Cristina; Guarnaccia, Giuseppe; Lahiri, A.; Trugenberger, Carlo A.
2015-06-01
We propose a spin gauge field theory in which the curl of a Dirac fermion current density plays the role of the pseudovector charge density. In this field-theoretic model, spin interactions are mediated by a single scalar gauge boson in its antisymmetric tensor formulation. We show that these long range spin interactions induce a gauge invariant photon mass in the one-loop effective action. The fermion loop generates a coupling between photons and the spin gauge boson, which acquires thus charge. This coupling represents also an induced, gauge invariant, topological mass for the photons, leading to the Meissner effect. The one-loop effective equations of motion for the charged spin gauge boson are the London equations. We propose thus spin gauge interactions as an alternative, topological mechanism for superconductivity in which no spontaneous symmetry breaking is involved.
Volovik, G E
2013-01-01
Topology in momentum space is the main characteristics of the ground states of a system at zero temperature, the quantum vacua. The gaplessness of fermions in bulk, on the surface or inside the vortex core is protected by topology. Irrespective of the deformation of the parameters of the microscopic theory, the energy spectrum of these fermions remains strictly gapless. This solves the main hierarchy problem in particle physics. The quantum vacuum of Standard Model is one of the representatives of topological matter alongside with topological superfluids and superconductors, topological insulators and semi-metals, etc. There is a number of of topological invariants in momentum space of different dimensions. They determine universality classes of the topological matter and the type of the effective theory which emerges at low energy, give rise to emergent symmetries, including the effective Lorentz invariance, and emergent gauge and gravitational fields. The topological invariants in extended momentum and coor...
On Zeeman Topology in Kaluza-Klein and Gauge Theories
I. Struchiner; M. Rosa
2005-04-23
E. C. Zeeman [1] has criticized the fact that in all articles and books until that moment (1967) the topology employed to work with the Minkowski space was the Euclidean one. He has proposed a new topology, which was generalized for more general space-times by Goebel [2]. In the Zeeman and Goebel topologies for the space-time, the unique continuous curves are polygonals composed by time-like straight lines and geodesics respectively. In his paper, Goebel proposes a topology for which the continuous curves are polygonals composed by motions of charged particles. Here we obtain in a very simple way a generalization of this topology, valid for any gauge fields, by employing the projection theorem of Kaluza-Klein theories (page 144 of Bleecker [3]). This approach relates Zeeman topologies and Kaluza-Klein, therefore Gauge Theories, what brings insights and points in the direction of a completely geometric theory.
Topological wave functions and the 4D-5D lift
Peng Gao; Boris Pioline
2008-07-14
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'' 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 K\\"ahler 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.
Topological membrane theory from Mathai-Quillen formalism
Lilia Anguelova; Paul de Medeiros; Annamaria Sinkovics
2005-09-21
It is suggested that topological membranes play a fundamental role in the recently proposed topological M-theory. We formulate a topological theory of membranes wrapping associative three-cycles in a seven-dimensional target space with G_2 holonomy. The topological BRST rules and BRST invariant action are constructed via the Mathai-Quillen formalism. In a certain gauge we show this theory to be equivalent to a membrane theory with two BRST charges found by Beasley and Witten. We argue that at the quantum level an additional topological term should be included in the action, which measures the contributions of membrane instantons. We construct a set of local and non-local observables for the topological membrane theory. As the BRST cohomology of local operators turns out to be isomorphic to the de Rham cohomology of the G_2 manifold, our observables agree with the spectrum of d=4, N=1 G_2 compactifications of M-theory.
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.
NASA Technical Reports Server (NTRS)
Lieberman, R. N.
1972-01-01
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Completeness of topological groups
M. G. Tkachenko
1984-01-01
UDC 513.831 Introduction. In this paper we define a certain Hausdorff group topology p on the free algebraic group F(X) generated by the set X for every completely regular space X. The group F(X) equipped with the topology @ will be denoted by Fp(X). It turns out that the topology induced on X by Fp(X) coincides with the original topology
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.
Computer Science Computational topology
Peters, Thomas J.
Part 6 Computer Science #12;#12;Computational topology Denis Blackmore and Thomas J. Peters 1. Introduction The emphasis here will be upon how point-set topology can be applied to computing on geometric objects embedded in R3 . The fundamental topological concept of a neighborhood generalizes limits over
Computational Topology Afra Zomorodian
Zomorodian, Afra
Computational Topology Afra Zomorodian Dartmouth College November 3, 2009 1 Introduction According to the Oxford English Dictionary, the word topology is derived of topos (Ø ÔÓ ) meaning place, and -logy (ÐÓ ), a variant of the verb Ð´ Ò, meaning to speak. As such, topology speaks about places: how local neighborhoods
Cosmic topology affects dynamics
Boudewijn F. Roukema
2012-01-04
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic Newtonian-like arguments suggest a topological acceleration effect that differs for differing spatial sections. A relativistic spacetime solution solution shows that the effect is not just a Newtonian artefact.
K. I. Calvert; M. B. Doar; E. W. Zegura
1997-01-01
The topology of a network, or a group of networks such as the Internet, has a strong bearing on many management and performance issues. Good models of the topological structure of a network are essential for developing and analyzing internetworking technology. This article discusses how graph-based models can be used to represent the topology of large networks, particularly aspects of
Composition of Topological Relations
Egenhofer, Max J.
Composition of Topological Relations #12;Goal For all combinations of topological relations, derive from · A topRel1 B and B topRel2 C the result · A topRel3 C #12;Composition Example A B C Topological relation between A and C? disjoint A meets B and B contains C #12;How to Derive all Compositions? · Draw
Topological Structure of the SU(3) Vacuum
Douglas A. Smith; Michael J. Teper
1998-01-09
We investigate the topological structure of the vacuum in SU(3) lattice gauge theory. We use under-relaxed cooling to remove the high-frequency fluctuations and a variety of "filters" to identify the topological charges in the resulting smoothened field configurations. We find a densely packed vacuum with an average instanton size, in the continuum limit, of about 0.5 fm. The density at large sizes decreases as a large inverse power of the size. At small sizes we see some sign of a trend towards the asymptotic perturbative behaviour. We find that an interesting polarisation phenomenon occurs: the large topological charges tend to have, on the average, the same sign and are over-screened by the smaller charges which tend to have, again on the average, the opposite sign to the larger instantons. We also calculate the topological susceptibility for which we obtain a continuum value of about 187 MeV. We perform the calculations for various volumes, lattice spacings and numbers of cooling sweeps, so as to obtain some control over the associated systematic errors. The coupling range is from beta=6.0 to beta=6.4 and the lattice volumes range from 16x16x16x48 to 32x32x32x64.
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.
A Remark on Gapped Domain Walls Between Topological Phases
NASA Astrophysics Data System (ADS)
Kawahigashi, Yasuyuki
2015-05-01
We give a mathematical definition of a gapped domain wall between topological phases and a gapped boundary of a topological phase. We then provide answers to some recent questions studied by Lan, Wang and Wen in condensed matter physics based on works of Davydov, Müger, Nikshych and Ostrik. In particular, we identify their tunneling matrix and a coupling matrix of Rehren, and show that their conjecture does not hold.
A Remark on Gapped Domain Walls Between Topological Phases
NASA Astrophysics Data System (ADS)
Kawahigashi, Yasuyuki
2015-07-01
We give a mathematical definition of a gapped domain wall between topological phases and a gapped boundary of a topological phase. We then provide answers to some recent questions studied by Lan, Wang and Wen in condensed matter physics based on works of Davydov, Müger, Nikshych and Ostrik. In particular, we identify their tunneling matrix and a coupling matrix of Rehren, and show that their conjecture does not hold.
Quartic Quasi-Topological-Born-Infeld Gravity
Mohammad Ghanaatian
2015-03-30
In this paper, quartic quasi-topological black holes in the presence of a nonlinear electromagnetic Born-Infeld field is presented. By using the metric parameters, the charged black hole solutions of quasi-topological Born-Infeld gravity is considered. The thermodynamics of these black holes are investigated and I show that the thermodynamics and conserved quantities verify the first law of thermodynamics. I also introduce the thermodynamics of asymptotically AdS rotating black branes with flat horizon of these class of solutions and I calculate the finite action by use of the counterterm method inspired by AdS/CFT correspondence.
Nexus and Dirac lines in topological materials
NASA Astrophysics Data System (ADS)
Heikkilä, T. T.; Volovik, G. E.
2015-09-01
We consider the Z2 topology of the Dirac lines, i.e., lines of band contacts, on an example of graphite. Four lines—three with topological charge {N}1=1 each and one with {N}1=-1—merge together near the H-point and annihilate due to summation law 1+1+1-1=0. The merging point is similar to the real-space nexus, an analog of the Dirac monopole at which the Z2 strings terminate.
Quartic quasi-topological-Born-Infeld gravity
NASA Astrophysics Data System (ADS)
Ghanaatian, Mohammad
2015-09-01
In this paper, quartic quasi-topological black holes in the presence of a nonlinear electromagnetic Born-Infeld field is presented. By using the metric parameters, the charged black hole solutions of quasi-topological Born-Infeld gravity is considered. The thermodynamics of these black holes are investigated and I show that the thermodynamics and conserved quantities verify the first law of thermodynamics. I also introduce the thermodynamics of asymptotically AdS rotating black branes with flat horizon of these class of solutions and I calculate the finite action by use of the counterterm method inspired by AdS/CFT correspondence.
TRANSITING TOPOLOGICAL SECTORS WITH THE OVERLAP.
CREUTZ,M.
2002-06-29
The overlap operator provides an elegant definition for the winding number of lattice gauge field configurations. Only for a set of configurations of measure zero is this procedure undefined. Without restrictions on the lattice fields, however, the space of gauge fields is simply connected. I present a simple low dimensional illustration of how the eigenvalues of a truncated overlap operator flow as one travels between different topological sectors.
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.
Time-Reversal-Invariant Topological Superconductivity in n-type Doped BiH
NASA Astrophysics Data System (ADS)
Yang, Fan; Liu, Cheng-Cheng; Zhang, Yu-Zhong; Yao, Yugui; Lee, Dung-Hai
2015-03-01
Intrinsic and symmetry protected topological states have attracted lots of interest in condensed matter physics recently. In particular, time reversal symmetry protected fermion topological insulators have been theoretically predicted and experimentally verified. However despite considerable experimental and theoretical works, definitive evidence for time reversal invariant topological superconductivity is still lacking. Here we propose that upon electron doping the hydrogenated single bilayer Bi, namely BiH, will exhibit time reversal invariant topological superconductivity. If confirmed experimentally this material will constitute the first example of TRI topological superconductor.
NASA Astrophysics Data System (ADS)
Pardo, V.; Smith, J. C.; Pickett, W. E.
2012-06-01
It was reported earlier [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.056401 106, 056401 (2011)] that the skutterudite structure compound CoSb3 displays a unique band structure with a topological transition versus a symmetry-preserving sublattice (Sb) displacement very near the structural ground state. The transition is through a massless Dirac-Weyl semimetal, point Fermi surface phase which is unique in that (1) it appears in a three-dimensional crystal, (2) the band critical point occurs at k=0, and (3) linear bands are degenerate with conventional (massive) bands at the critical point (before inclusion of spin-orbit coupling). Further interest arises because the critical point separates a conventional (trivial) phase from a topological phase. In the native cubic structure this is a zero-gap topological semimetal; we show how spin-orbit coupling and uniaxial strain converts the system to a topological insulator (TI). We also analyze the origin of the linear band in this class of materials, which is the characteristic that makes them potentially useful in thermoelectric applications or possibly as transparent conductors. We characterize the formal charge as Co+ d8, consistent with the gap, with its 3¯ site symmetry, and with its lack of moment. The Sb states are characterized as px (separately, py) ?-bonded Sb4 ring states occupied and the corresponding antibonding states empty. The remaining (locally) pz orbitals form molecular orbitals with definite parity centered on the empty 2a site in the skutterudite structure. Eight such orbitals must be occupied; the one giving the linear band is an odd orbital singlet A2u at the zone center. We observe that the provocative linearity of the band within the gap is a consequence of the aforementioned near-degeneracy, which is also responsible for the small band gap.
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.
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.
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
Code of Federal Regulations, 2013 CFR
2013-07-01
...PARTY PAYERS OF REASONABLE CHARGES FOR HEALTHCARE SERVICES § 220.14 Definitions...beneficiaries. Covered beneficiaries are all healthcare beneficiaries under chapter 55 of...Facilities” or “USTFs”). Healthcare services. Healthcare services...
Code of Federal Regulations, 2014 CFR
2014-07-01
...PARTY PAYERS OF REASONABLE CHARGES FOR HEALTHCARE SERVICES § 220.14 Definitions...beneficiaries. Covered beneficiaries are all healthcare beneficiaries under chapter 55 of...Facilities” or “USTFs”). Healthcare services. Healthcare services...
Code of Federal Regulations, 2011 CFR
2011-07-01
...PARTY PAYERS OF REASONABLE CHARGES FOR HEALTHCARE SERVICES § 220.14 Definitions...beneficiaries. Covered beneficiaries are all healthcare beneficiaries under chapter 55 of...Facilities” or “USTFs”). Healthcare services. Healthcare services...
Code of Federal Regulations, 2012 CFR
2012-07-01
...PARTY PAYERS OF REASONABLE CHARGES FOR HEALTHCARE SERVICES § 220.14 Definitions...beneficiaries. Covered beneficiaries are all healthcare beneficiaries under chapter 55 of...Facilities” or “USTFs”). Healthcare services. Healthcare services...
Effective charge of colloidal particles Alexandre Diehla)
Levin, Yan
Effective charge of colloidal particles Alexandre Diehla) Departamento de Fi´sica, Universidade While the bare charge of a colloidal particle can be eas- ily measured by chemical methods 23 August 2004; accepted 1 October 2004 A new dynamical definition of the effective colloidal charge
Ciocan-Fontanine, Ionut
Definitions Calibration Parameter Dynamics Monte Carlo Simulation Concluding Remarks Using the SABR Model Jason Vinar Ameriprise Workshop 2012 Jason Vinar Using the SABR Model #12;Definitions Calibration which attempts to capture the volatility smile. This project will consist of Calibrating the SABR model
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.
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.
Topological insulators and topological nonlinear {sigma} models
Yao Hong; Lee, Dung-Hai [Department of Physics, University of California at Berkeley, Berkeley, California 94720 (United States) and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2010-12-15
In this paper we link the physics of topological nonlinear {sigma} models with that of Chern-Simons insulators. We show that corresponding to every 2n-dimensional Chern-Simons insulator there is a (n-1)-dimensional topological nonlinear {sigma} model with the Wess-Zumino-Witten term. Breaking internal symmetry in these nonlinear {sigma} models leads to nonlinear {sigma} models with the {theta} term. [This is analogous to the dimension reduction leading from 2n-dimensional Chern-Simons insulators to (2n-1) and (2n-2)-dimensional topological insulators protected by discrete symmetries.] The correspondence described in this paper allows one to derive the topological term in a theory involving fermions and order parameters (we shall referred to them as ''fermion-{sigma} models'') when the conventional gradient-expansion method fails. We also discuss the quantum number of solitons in topological nonlinear {sigma} model and the electromagnetic action of the (2n-1)-dimensional topological insulators. Throughout the paper we use a simple model to illustrate how things work.
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.
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
POTLUCK FOOD SAFETY 1. Definition
POTLUCK FOOD SAFETY 1. Definition: (i) Campus Potluck is a closed food event that is privately funded by the participants, where all group members bring food dishes to share with others in the group. All food provided for the potluck event shall be consumed by members of the group at no charge
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.
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
Topological mirror superconductivity.
Zhang, Fan; Kane, C L; Mele, E J
2013-08-01
We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z(2) index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out. PMID:23952424
Variable Topology on Fractal Manifold
Helene Porchon
2012-11-15
In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we prove that using the fractal manifold as model for the universe dynamic, the universe expansion is intimately correlated to the variation of the topology.
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.
Black hole attractors and the topological string
Ooguri, Hirosi [California Institute of Technology, Pasadena, California 91125 (United States); Strominger, Andrew; Vafa, Cumrun [Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138 (United States)
2004-11-15
A simple relationship of the form Z{sub BH}= vertical bar Z{sub top} vertical bar{sup 2} is conjectured, where Z{sub BH} is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Z{sub top} is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wave function defined by the topological string partition function.
Topological Pair-Density-Wave Superconducting States
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Soto-Garrido, Rodrigo; Fradkin, Eduardo
2014-12-01
We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg-Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform d -wave one-dimensional superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the PDW state is a charge-2 e field with finite momentum. However, the order parameter here is a quartic electron operator and conventional mean-field theory cannot be applied to study this state. We use bosonization to show that the 1D PDW state has a MZM at a boundary. This superconducting state is an exotic topological phase supporting Majorana fermions with finite-momentum pairing fields and charge-4 e superconductivity.
Bogovic, John A.; Bazin, Pierre-Louis; Prince, Jerry L.
2012-01-01
Methodology for fusing multiple segmentations to produce an improved result has been useful in computational anatomical studies. Although obtaining segmentations of anatomy having a particular topology are essential to studies using diffeomorphic deformation based analyses, no methods of label fusion presented to date have incorporated information regarding the topology of the anatomy. In this paper, we introduce “Topology STAPLE”, a novel method that statistically fuses multiple rater segmentations into a topologically correct segmentation. We evaluate the method on both simulated data and real delineations of the cerebellum produced by human raters.
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 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.
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 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.
Black hole attractors and the topological string
Hirosi Ooguri; Andrew Strominger; Cumrun Vafa
2004-01-01
A simple relationship of the form ZBH=|Ztop|2 is conjectured, where ZBH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Ztop is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a
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.
Experimental Discovery of Topological Insulators and Related Superconductors
Hasan, M. Zahid (Princeton) [Princeton
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.
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.
Ground State Degeneracy of Topological Phases on Open Surfaces
Ling-Yan Hung; Yidun Wan
2015-02-22
We relate the ground state degeneracy (GSD) of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase to a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence to the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The GSD resulting from a particular boundary condition coincides with the number of confined topological sectors due to the corresponding condensation. These lead to a generalization of the Laughlin-Wu-Tao (LWT) charge-pumping argument for Abelian fractional quantum Hall states (FQHS) to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a non-trivial cycle can pump a condensate from one boundary to another. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation.
Destroying a topological quantum bit by condensing Ising vortices.
Hao, Zhihao; Inglis, Stephen; Melko, Roger
2014-01-01
The imminent realization of topologically protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbours what is known as a Z2 liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called spinons, or Ising flux vortices called visons. At zero temperature, a Z2 liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum-phase transition destroying the topological order. Here we use quantum Monte Carlo to study a vison-induced transition from a Z2 liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is beyond the description of the standard Landau paradigm. PMID:25488132
Topological dynamics in supramolecular rotors.
Palma, Carlos-Andres; Björk, Jonas; Rao, Francesco; Kühne, Dirk; Klappenberger, Florian; Barth, Johannes V
2014-08-13
Artificial molecular switches, rotors, and machines are set to establish design rules and applications beyond their biological counterparts. Herein we exemplify the role of noncovalent interactions and transient rearrangements in the complex behavior of supramolecular rotors caged in a 2D metal-organic coordination network. Combined scanning tunneling microscopy experiments and molecular dynamics modeling of a supramolecular rotor with respective rotation rates matching with 0.2 kcal mol(-1) (9 meV) precision, identify key steps in collective rotation events and reconfigurations. We notably reveal that stereoisomerization of the chiral trimeric units entails topological isomerization whereas rotation occurs in a topology conserving, two-step asynchronous process. In supramolecular constructs, distinct displacements of subunits occur inducing a markedly lower rotation barrier as compared to synchronous mechanisms of rigid rotors. Moreover, the chemical environment can be instructed to control the system dynamics. Our observations allow for a definition of mechanical cooperativity based on a significant reduction of free energy barriers in supramolecules compared to rigid molecules. PMID:25078022
Topological susceptibility with the asqtad action
Van de Water, R.; Bernard, C.; Laiho, J.; Billeter, B.; DeTar, C.; Levkova, L.; Oktay, M.B.; Gottlieb, S.; Heller, U.M.; Hetrick, J.E.; Osborn, J.; Sugar, R.L.
2010-06-15
Chiral perturbation theory predicts that in quantum chromodynamics (QCD), light dynamical quarks suppress the gauge-field topological susceptibility of the vacuum. The degree of suppression depends on quark multiplicity and masses. It provides a strong consistency test for fermion formulations in lattice QCD. Such tests are especially important for staggered fermion formulations that lack a full chiral symmetry and use the 'fourth-root' procedure to achieve the desired number of sea quarks. Over the past few years we have measured the topological susceptibility on a large database of 18 gauge field ensembles, generated in the presence of 2+1 flavors of dynamical asqtad quarks with up and down quark masses ranging from 0.05 to 1 in units of the strange quark mass and lattice spacings ranging from 0.045 fm to 0.12 fm. Our study also includes three quenched ensembles with lattice spacings ranging from 0.06 to 0.12 fm. We construct the topological susceptibility from the integrated point-to-point correlator of the discretized topological charge density F{tilde F}. To reduce its variance, we model the asymptotic tail of the correlator. The continuum extrapolation of our results for the topological susceptibility agrees nicely at small quark mass with the predictions of lowest-order SU(3) chiral perturbation theory, thus lending support to the validity of the fourth-root procedure.
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
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...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...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....Finally, we give a synthetic account of Topological Domain Theory. We show that Topological Domain Theory is a specific model of Synthetic Domain Theory in the realizability topos over Scott's graph model. We give internal characterisations 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-calculus, and to obtain a richer collection of free algebras than those constructed earlier....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....
G. E. Volovik
2012-07-04
Topology in momentum space is the main characteristics of the ground states of a system at zero temperature, the quantum vacua. The gaplessness of fermions in bulk, on the surface or inside the vortex core is protected by topology. Irrespective of the deformation of the parameters of the microscopic theory, the energy spectrum of these fermions remains strictly gapless. This solves the main hierarchy problem in particle physics. The quantum vacuum of Standard Model is one of the representatives of topological matter alongside with topological superfluids and superconductors, topological insulators and semi-metals, etc. There is a number of of topological invariants in momentum space of different dimensions. They determine universality classes of the topological matter and the type of the effective theory which emerges at low energy, give rise to emergent symmetries, including the effective Lorentz invariance, and emergent gauge and gravitational fields. The topological invariants in extended momentum and coordinate space determine the bulk-surface and bulk-vortex correspondence, connecting the topology in bulk with the real space. The momentum space topology gives some lessons for quantum gravity. In effective gravity emerging at low energy, the collective variables are the tetrad field and spin connections, while the metric is the composite object of tetrad field. This suggests that the Einstein-Cartan-Sciama-Kibble theory with torsion field is more relevant. There are also several scenarios of Lorentz invariance violation governed by topology, including splitting of Fermi point and development of the Dirac points with quadratic and cubic spectrum. The latter leads to the natural emergence of the Horava-Lifshitz gravity.
42 CFR 405.509 - Determining the inflation-indexed charge.
Code of Federal Regulations, 2010 CFR
2010-10-01
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48 CFR 552.232-77 - Payment By Government Charge Card.
Code of Federal Regulations, 2010 CFR
2010-10-01
... false Payment By Government Charge Card. 552.232-77 Section 552.232-77...232-77 Payment By Government Charge Card. As prescribed in 532.7003, insert...clause: Payment By Government Charge Card (NOV 2009) (a) Definitions....
Wlodzimierz Piechocki
1999-10-15
General relativity is unable to determine the topology of the Universe. We propose to apply quantum approach. Quantization of dynamics of a test particle is sensitive to the spacetime topology. Presented results for a particle in de Sitter spacetimes favor a finite universe.
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
Superconductors are topologically ordered
Hans Hansson; Vadim Oganesyan; Shivaji Sondhi
2003-01-01
We revisit a venerable question: what is the nature of the ordering in a superconductor? We find that the answer is properly that the superconducting state exhibits topological order in the sense of Wen, i.e. that while it lacks a local order parameter, it is sensitive to the (global) topology of the underlying manifold. We show that this perspective unifies
Introduction to topological analysis
NASA Astrophysics Data System (ADS)
Letellier, Christophe; Gilmore, Robert
2013-01-01
The topological analysis of chaotic attractors is briefly reviewed. The main concept on which this book is based is thus introduced with a simple case (the attractor solution to the Sprott D system) explicitly treated. Then some perspectives to extend the topological analysis are discussed.
Topologically Adaptable Snakes
Tim Mcinerney; Demetri Terzopoulos
1995-01-01
This paper presents a topologically adaptable snakes model for image segmentation and object representation. The model is embedded in the framework of domain subdi- vision using simplicial decomposition. This framework ex- tends the geometric and topological adaptability of snakes while retaining all of the features of traditional snakes, s uch as user interaction, and overcoming many of the limitations of
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.
Internet Topology Benoit Donnet
Bonaventure, Olivier
.]) - iPlane ([Madhyasta et al.]) - Rocketfuel ([Spring et al.]) 7 #12;INL Seminar - Internet Topology.]) - Rocketfuel ([Spring et al.]) - ... 7 #12;INL Seminar - Internet Topology Discovery IP Level - Projects 7]) - RIPE TTM ([Georgatos et al.]) - iPlane ([Madhyasta et al.]) - Rocketfuel ([Spring et al
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.
NASA Astrophysics Data System (ADS)
Petkova, V. B.
2013-10-01
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.
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
Spin-3 topologically massive gravity
NASA Astrophysics Data System (ADS)
Chen, Bin; Long, Jiang; Wu, Jun-bao
2011-11-01
In this Letter, we study the spin-3 topologically massive gravity (TMG), paying special attention to its properties at the chiral point. We propose an action describing the higher spin fields coupled to TMG. We discuss the traceless spin-3 fluctuations around the AdS3 vacuum and find that there is an extra local massive mode, besides the left-moving and right-moving boundary massless modes. At the chiral point, such extra mode becomes massless and degenerates with the left-moving mode. We show that at the chiral point the only degrees of freedom in the theory are the boundary right-moving graviton and spin-3 field. We conjecture that spin-3 chiral gravity with generalized Brown-Henneaux boundary condition is holographically dual to 2D chiral CFT with classical W3 algebra and central charge cR=3l/G.
The electric charge and magnetic moment of neutral fundamental particles
Kaushik Bhattacharya
2009-05-27
The article focuses on the issue of the two definitions of charge, mainly the gauge charge and the effective charge of fundamental particles. Most textbooks on classical electromagnetism and quantum field theory only works with the gauge charges while the concept of the induced charge remains unattended. In this article it has been shown that for intrinsically charged particles both of the charges remain the same but there can be situations where an electrically neutral particle picks up some electrical charge from its plasma surrounding. The physical origin and the scope of application of the induced charge concept has been briefly discussed in the article.
Geometry of complex networks and topological centrality
NASA Astrophysics Data System (ADS)
Ranjan, Gyan; Zhang, Zhi-Li
2013-09-01
We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L). The squared distance of a node i to the origin in this n-dimensional space (lii+), yields a topological centrality index, defined as C?(i)=1/lii+. In turn, the sum of reciprocals of individual node centralities, ?i1/C?(i)=?ilii+, or the trace of L, yields the well-known Kirchhoff index (K), an overall structural descriptor for the network. To put into context this geometric definition of centrality, we provide alternative interpretations of the proposed indices that connect them to meaningful topological characteristics - first, as forced detour overheads and frequency of recurrences in random walks that has an interesting analogy to voltage distributions in the equivalent electrical network; and then as the average connectedness of i in all the bi-partitions of the graph. These interpretations respectively help establish the topological centrality (C?(i)) of node i as a measure of its overall position as well as its overall connectedness in the network; thus reflecting the robustness of i to random multiple edge failures. Through empirical evaluations using synthetic and real world networks, we demonstrate how the topological centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchhoff index, is appropriately sensitive to perturbations/re-wirings in the network.
Time-reversal-invariant topological superconductivity in n -doped BiH
NASA Astrophysics Data System (ADS)
Yang, Fan; Liu, Cheng-Cheng; Zhang, Yu-Zhong; Yao, Yugui; Lee, Dung-Hai
2015-04-01
Despite intense interest and considerable works, definitive experimental evidence for time-reversal-invariant topological superconductivity is still lacking. Hence searching for such superconductivity in real materials remains one of the main challenges in the field of topological material. Previously it has been shown that in the buckled honeycomb lattice structure, hydrogenated single bilayer Bi, namely BiH, is a topological insulator. Here we predict that upon n -type doping, BiH is a time-reversal-invariant topological superconductor. Interestingly the edge states of such a superconductor consist of both helical complex fermion modes and helical Majorana fermion modes.
NASA Astrophysics Data System (ADS)
Kimme, Lukas; Hyart, Timo; Rosenow, Bernd
2015-06-01
We address the question of whether individual nonmagnetic impurities can induce zero-energy states in time-reversal-invariant topological superconductors, and define a class of symmetries which guarantee the existence of such states for a specific value of the impurity strength. These symmetries allow the definition of a position-space topological Z2 invariant, which is related to the standard bulk topological Z2 invariant. Our general results are applied to the time-reversal-invariant p -wave phase of the doped Kitaev-Heisenberg model, where we demonstrate how a lattice of impurities can drive a topologically trivial system into the nontrivial phase.
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, ...
Wild topology, hyperbolic geometry and fusion algebra of high energy particle physics
M. S. El Naschie
2002-01-01
The relation between Wild Topology, Hyperbolic Geometry and Fusion Algebra on the one side and the charge and coupling constants of the standard model and quantum gravity on the other is examined.The close connection found between E(?) theory and the Topological theory of four manifolds as well as the theory of fundamental groups is elucidated using various classical theories and
NASA Astrophysics Data System (ADS)
Meidan, Dganit; Micklitz, Tobias; Brouwer, Piet W.
2010-10-01
We study the recently introduced Z2 pump consisting of a family of one-dimensional bulk insulators with time-reversal restriction on the pumping cycle. We find that the scattering matrices of these pumps are dichotomized by a topological index. We show that the class of pumps characterized by a nontrivial topological index allows, in contrast to its topologically trivial counterpart, for the noiseless pumping of quantized spin, even in the absence of spin conservation. This distinction sheds light on the Z2 classification of two-dimensional time-reversal invariant insulators.
Multiresolution Topological Simplification.
Xia, Kelin; Zhao, Zhixiong; Wei, Guo-Wei
2015-09-01
Persistent homology has been advocated as a new strategy for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for tackling large datasets. Our basic idea is to match the resolution with the scale of interest so as to create a topological microscopy for the underlying data. We adjust the resolution via a rigidity density-based filtration. The proposed multiresolution topological analysis is validated by the study of a complex RNA molecule. PMID:26222626
Topological properties of hypercubes
Saad, Y.; Schultz, M.H.
1988-07-01
The n-dimensional hypercube is a highly concurrent loosely coupled multiprocessor based on the binary n-cube topology. Machines based on the hypercube topology have been advocated as ideal parallel architectures for their powerful interconnection features. In this paper, the authors examine the hypercube from the graph theory point of view and consider those features that make its connectivity so appealing. Among other things, they propose a theoretical characterization of the n-cube as a graph and show how to map various other topologies into a hypercube.
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.
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
Seeing the magnetic monopole through the mirror of topological surface states
Qi, Xiao-Liang; Li, Rundong; /Stanford U., Phys. Dept.; Zang, Jiadong; /Fudan U.; 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.
S. Reucroft
2015-05-01
We investigate the hypothesis that the core of a galaxy has a positive electrical charge with an equal and opposite negative charge distributed over the galactic periphery. We present a determination of the amount of charge needed to explain the apparent anomalous rotation behaviour.
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.
Helical topological exciton condensates
NASA Astrophysics Data System (ADS)
Michetti, Paolo; Budich, Jan C.; Trauzettel, Björn
2014-03-01
We investigate a bilayer system of critical HgTe quantum wells each featuring a spin-degenerate pair of massless Dirac fermions. In the presence of an electrostatic inter-layer Coulomb coupling, we determine the exciton condensate order parameter of the system self-consistently. Calculating the bulk topological Z2 invariant of the resulting mean field Hamiltonian, we discover a novel time reversal symmetric topological exciton condensate state coined the helical topological exciton condensate. We argue that this phase can exist for experimentally relevant parameters. Interestingly, due to its multi-band nature, the present bilayer model exhibits a nontrivial interplay between spontaneous symmetry breaking and topology: Depending on which symmetry the condensate order parameter spontaneously picks in combined orbital and spin space, stable minima in the free energy corresponding to both trivial and nontrivial gapped states can be found.
Bombin, Hector
We introduce a family of two-dimensional (2D) topological subsystem quantum error-correcting codes. The gauge group is generated by two-local Pauli operators, so that two-local measurements are enough to recover the error ...
Sumati Surya
2008-09-17
The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,set. In order to obtain a well defined continuum approximation, the causal set must possess the requisite intrinsic topological and geometric properties that characterise a continuum spacetime in the large. The continuum approximation thus sets the stage for the study of topology in CST. We review the status of causal set topology and present some new results relating poset and spacetime topologies. The hope is that in the process, some of the ideas and questions arising from CST will be made accessible to the larger community of computer scientists and mathematicians working on posets.
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
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
The nonmodular topological phase and phase singularities
NASA Astrophysics Data System (ADS)
Bhandari, Rajendra
2011-09-01
Generalizing an earlier definition of the noncyclic geometric phase [R. Bhandari, Phys. Lett. A 157 (1991) 221], a nonmodular topological phase is defined with reference to a generic time-dependent two-slit interference experiment involving particles with N internal states in which the internal state of both the beams undergoes unitary evolution. A simple proof of the shorter geodesic rule for closure of the open path is presented and several useful new insights into the behavior of the dynamical and geometrical components of the phase shift presented. An effective Hamiltonian interpretation of the observable phase shifts is also presented.
Topologically protected quantum computation
John Preskill
2003-01-01
I describe the properties of surface codes, topological quantum error-correcting codes such that qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. Protocols for error recovery are formulated, and their efficacy studied. An order-disorder phase transition occurs in this system at a nonzero
Eric Dennis; Alexei Kitaev; Andrew Landahl; John Preskill
2002-01-01
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in
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.
Recipe for Topological Polaritons
NASA Astrophysics Data System (ADS)
Karzig, Torsten; Bardyn, Charles-Edouard; Lindner, Netanel; Refael, Gil
2015-03-01
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 non-trivial 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 spin-orbit coupling in the electronic system and an applied Zeeman field. We discuss the requirements for obtaining a sizable topological gap in the polariton spectrum. Funded by the Institute for Quantum Information and Matter, the Bi-National Science Foundation and I-Core: the Israeli Excellence Center ``Circle of Light'', and Darpa under funding for FENA, and the Swiss National Science Foundation.
Topology of Event Horizons and Topological Censorship
Ted Jacobson; Shankar Venkataramani
1994-10-31
We prove that, under certain conditions, the topology of the event horizon of a four dimensional asymptotically flat black hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let $M$ be a four dimensional asymptotically flat spacetime satisfying the averaged null energy condition, and suppose that the domain of outer communication $\\C_K$ to the future of a cut $K$ of $\\Sm$ is globally hyperbolic. Suppose further that a Cauchy surface $\\Sigma$ for $\\C_K$ is a topological 3-manifold with compact boundary $\\partial\\S$ in $M$, and $\\S'$ is a compact submanifold of $\\bS$ with spherical boundary in $\\S$ (and possibly other boundary components in $M/\\S$). Then we prove that the homology group $H_1(\\Sigma',Z)$ must be finite. This implies that either $\\partial\\S'$ consists of a disjoint union of 2-spheres, or $\\S'$ is nonorientable and $\\partial\\S'$ contains a projective plane. Further, $\\partial\\S=\\partial\\Ip[K]\\cap\\partial\\Im[\\Sp]$, and $\\partial \\Sigma$ will be a cross section of the horizon as long as no generator of $\\partial\\Ip[K]$ becomes a generator of $\\partial\\Im[\\Sp]$. In this case, if $\\S$ is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.}
Order Topology and Frink Ideal Topology of Effect Algebras
Lei Qiang; Wu Junde; Li Ronglu
2009-12-15
In this paper, the following results are proved: (1) $ $ If $E$ is a complete atomic lattice effect algebra, then $E$ is (o)-continuous iff $E$ is order-topological iff $E$ is totally order-disconnected iff $E$ is algebraic. (2) $ $ If $E$ is a complete atomic distributive lattice effect algebra, then its Frink ideal topology $\\tau_{id}$ is Hausdorff topology and $\\tau_{id}$ is finer than its order topology $\\tau_{o}$, and $\\tau_{id}=\\tau_o$ iff 1 is finite iff every element of $E$ is finite iff $\\tau_{id}$ and $\\tau_o$ are both discrete topologies. (3) $ $ If $E$ is a complete (o)-continuous lattice effect algebra and the operation $\\oplus$ is order topology $\\tau_o$ continuous, then its order topology $\\tau_{o}$ is Hausdorff topology. (4) $ $ If $E$ is a (o)-continuous complete atomic lattice effect algebra, then $\\oplus$ is order topology continuous.
Finite temperature topological order in 2D topological color codes
Mehdi Kargarian
2009-07-19
In this work the topological order at finite temperature in two-dimensional color code is studied. The topological entropy is used to measure the behavior of the topological order. Topological order in color code arises from the colored string-net structures. By imposing the hard constrained limit the exact solution of the entanglement entropy becomes possible. For finite size systems, by raising the temperature, one type of string-net structure is thermalized and the associative topological entropy vanishes. In the thermodynamic limit the underlying topological order is fragile even at very low temperatures. Taking first the thermodynamic limit and then the zero-temperature limit and vice versa does not commute, and their difference is related only to the topology of regions. The contribution of the colors and symmetry of the model in the topological entropy is also discussed. It is shown how the gauge symmetry of the color code underlies the topological entropy.
Finite temperature topological order in 2D topological color codes
Kargarian, Mehdi
2009-01-01
In this work the topological order at finite temperature in two-dimensional color code is studied. The topological entropy is used to measure the behavior of the topological order. Topological order in color code arises from the string-net structures. By imposing the hard constrained limit the exact solution of the entanglement entropy becomes possible. For finite size system by rising the temperature one type of string-net structures is thermalized and the associative topological entropy vanishes. In the thermodynamic limit the underlying topological order is fragile even at very low temperatures. Taking first thermodynamic limit and then zero-temperature limit and vice versa don't commute, and their difference is related only to the topology of regions. The contribution of the colors and symmetry of the model in the topological entropy is also discussed. It is shown how the gauge symmetry of the color code underlies the topological entropy.
Topological Aspects of Fermions on a Honeycomb Lattice
Dipankar Chakrabarti; Simon Hands; Antonio Rago
2009-07-25
We formulate a model of relativistic fermions moving in two Euclidean dimensions based on a tight-binding model of graphene. The eigenvalue spectrum of the resulting Dirac operator is solved numerically in smooth U(1) gauge field backgrounds carrying an integer-valued topological charge Q, and it is demonstrated that the resulting number of zero-eigenvalue modes is in accord with the Atiyah-Singer index theorem applied to two continuum flavors. A bilinear but gauge non-invariant chirality operator appropriate for distinguishing the topological zero modes is identified. When this operator is used to calculate Q, it is found that the maximum topological charge capable of being measured in this fashion scales with the perimeter of the lattice. Some concluding remarks compare these results to what is known for staggered lattice fermions.
Topological Insulators and Superconductors from D-branes
Shinsei Ryu; Tadashi Takayanagi
2010-08-08
Realization of topological insulators (TIs) and superconductors (TSCs), such as the quantum spin Hall effect and the Z_2 topological insulator, in terms of D-branes in string theory is proposed. We establish a one-to-one correspondence between the K-theory classification of TIs/TSCs and D-brane charges. The string theory realization of TIs and TSCs comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature. This sheds light on TIs and TSCs beyond non-interacting 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.
Topological Insulators and Superconductors from D-branes
Ryu, Shinsei
2010-01-01
Realization of topological insulators (TIs) and superconductors (TSCs), such as the quantum spin Hall effect and the Z_2 topological insulator, in terms of D-branes in string theory is proposed. We establish a one-to-one correspondence between the K-theory classification of TIs/TSCs and D-brane charges. The string theory realization of TIs and TSCs comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature. This sheds light on TIs and TSCs beyond non-interacting 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.
Symmetry Protected Josephson Supercurrents in Three-Dimensional Topological Insulators
Sungjae Cho; Brian Dellabetta; Alina Yang; John Schneeloch; Zhijun Xu; Tonica Valla; Genda Gu; Matthew J. Gilbert; Nadya Mason
2012-09-27
Coupling the surface state of a topological insulator (TI) to an s-wave superconductor is predicted to produce the long-sought Majorana quasiparticle excitations. However, superconductivity has not been measured in surface states when the bulk charge carriers are fully depleted, i.e., in the true topological regime that is relevant for investigating Majorana modes. Here, we report measurements of DC Josephson effects in TI-superconductor junctions as the chemical potential is moved from the bulk bands into the band gap, or through the true topological regime characterized by the presence of only surface currents. We examine the relative behavior of the system at different bulk/surface ratios, determining the effects of strong bulk/surface mixing, disorder, and magnetic field. We compare our results to 3D quantum transport simulations to conclude that the supercurrent is largely carried by surface states, due to the inherent topology of the bands, and that it is robust against disorder.
TOPPER: Topology Prediction of Transmembrane Protein Based on Evidential Reasoning
Deng, Xinyang; Liu, Qi; Hu, Yong; Deng, Yong
2013-01-01
The topology prediction of transmembrane protein is a hot research field in bioinformatics and molecular biology. It is a typical pattern recognition problem. Various prediction algorithms are developed to predict the transmembrane protein topology since the experimental techniques have been restricted by many stringent conditions. Usually, these individual prediction algorithms depend on various principles such as the hydrophobicity or charges of residues. In this paper, an evidential topology prediction method for transmembrane protein is proposed based on evidential reasoning, which is called TOPPER (topology prediction of transmembrane protein based on evidential reasoning). In the proposed method, the prediction results of multiple individual prediction algorithms can be transformed into BPAs (basic probability assignments) according to the confusion matrix. Then, the final prediction result can be obtained by the combination of each individual prediction base on Dempster's rule of combination. The experimental results show that the proposed method is superior to the individual prediction algorithms, which illustrates the effectiveness of the proposed method. PMID:23401665
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.
Stringy instanton counting and topological strings
NASA Astrophysics Data System (ADS)
Manabe, Masahide
2015-07-01
We study the stringy instanton partition function of four dimensional U( N) supersymmetric gauge theory which was obtained by Bonelli et al. in 2013. In type IIB string theory on , the stringy U( N) instantons of charge k are described by k D1-branes wrapping around the bound to N D5-branes on . The KK corrections induced by compactification of the give the stringy corrections. We find a relation between the stringy instanton partition function whose quantum stringy corrections have been removed and the K-theoretic instanton partition function, or by geometric engineering, the refined topological A-model partition function on a local toric Calabi-Yau threefold. We also study the quantum stringy corrections in the stringy instanton partition function which is not captured by the refined topological strings.
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
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
Aharonov-Bohm interference in topological insulator nanoribbons.
Peng, Hailin; Lai, Keji; Kong, Desheng; Meister, Stefan; Chen, Yulin; Qi, Xiao-Liang; Zhang, Shou-Cheng; Shen, Zhi-Xun; Cui, Yi
2010-03-01
Topological insulators represent unusual phases of quantum matter with an insulating bulk gap and gapless edges or surface states. The two-dimensional topological insulator phase was predicted in HgTe quantum wells and confirmed by transport measurements. Recently, Bi(2)Se(3) and related materials have been proposed as three-dimensional topological insulators with a single Dirac cone on the surface, protected by time-reversal symmetry. The topological surface states have been observed by angle-resolved photoemission spectroscopy experiments. However, few transport measurements in this context have been reported, presumably owing to the predominance of bulk carriers from crystal defects or thermal excitations. Here we show unambiguous transport evidence of topological surface states through periodic quantum interference effects in layered single-crystalline Bi(2)Se(3) nanoribbons, which have larger surface-to-volume ratios than bulk materials and can therefore manifest surface effects. Pronounced Aharonov-Bohm oscillations in the magnetoresistance clearly demonstrate the coherent propagation of two-dimensional electrons around the perimeter of the nanoribbon surface, as expected from the topological nature of the surface states. The dominance of the primary h/e oscillation, where h is Planck's constant and e is the electron charge, and its temperature dependence demonstrate the robustness of these states. Our results suggest that topological insulator nanoribbons afford promising materials for future spintronic devices at room temperature. PMID:20010826
Dundas, BjÃ¸rn Ian
Definitions and constructions Homotopy theory Maps Golod 25th Nordic and 1st British of Mathematicians #12;Definitions and constructions Homotopy theory Maps Golod TORIC TOPOLOGY from a homotopy of Mathematicians #12;Definitions and constructions Homotopy theory Maps Golod Combinatorics: Simplicial complex V
Lattice Topological Field Theory on Non-Orientable Surfaces
Vahid Karimipour; Ali Mostafazadeh
1995-01-01
The lattice definition of the two-dimensional topological quantum field\\u000atheory [Fukuma, {\\\\em et al}, Commun.~Math.~Phys.\\\\ {\\\\bf 161}, 157 (1994)] is\\u000ageneralized to arbitrary (not necessarily orientable) compact surfaces. It is\\u000ashown that there is a one-to-one correspondence between real associative\\u000a$*$-algebras and the topological state sum invariants defined on such surfaces.\\u000aThe partition and $n$-point functions on all two-dimensional surfaces
Hadron masses from fixed topology simulations: parity partners and SU(2) Yang-Mills results
Arthur Dromard; Christopher Czaban; Marc Wagner
2014-10-20
Lattice QCD simulations tend to get stuck in a single topological sector at fine lattice spacing, or when using chirally symmetric quarks. In such cases computed observables differ from their full QCD counterparts by finite size effects, which need to be understood on a quantitative level. We discuss extensions of existing relations from the literature between correlation functions at fixed topology and hadron masses at unfixed topology. Particular focus is put on disentangling positive and negative parity states, which mix, when the topological charge is fixed. We also present numerical results for SU(2) Yang-Mills Theory.
Gregory Gabadadze; Rachel A. Rosen
2007-08-24
We consider Bose-Einstein condensation of massive electrically charged scalars in a uniform background of charged fermions. We focus on the case when the scalar condensate screens the background charge, while the net charge of the system resides on its boundary surface. A distinctive signature of this substance is that the photon acquires a Lorentz-violating mass in the bulk of the condensate. Due to this mass, the transverse and longitudinal gauge modes propagate with different group velocities. We give qualitative arguments that at high enough densities and low temperatures a charged system of electrons and helium-4 nuclei, if held together by laboratory devices or by force of gravity, can form such a substance. We briefly discuss possible manifestations of the charged condensate in compact astrophysical objects.
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.
Topological Susceptibility in Two Flavors Lattice QCD with the Optimal Domain-Wall Fermion
Ting-Wai Chiu; Tung-Han Hsieh; Yao-Yuan Mao
2011-06-29
We determine the topological susceptibility of the gauge configurations generated by lattice simulations using two flavors of optimal domain-wall fermion on the $ 16^3 \\times 32 $ lattice with length 16 in the fifth dimension, at the lattice spacing $ a \\simeq 0.1 $ fm. Using the adaptive thick-restart Lanczos algorithm, we project the low-lying eigenmodes of the overlap Dirac operator, and obtain the topological charge of each configuration, for eight ensembles with pion masses in the range $ 220-550 $ MeV. From the topological charge, we compute the topological susceptibility and the second normalized cumulant. Our result of the topological susceptibility agrees with the sea-quark mass dependence predicted by the chiral perturbation theory and provides a determination of the chiral condensate, $\\Sigma^{\\bar{MS}}(2 GeV)=[259(6)(7) MeV]^3 $, and the pion decay constant $F_\\pi = 92(12)(2)$ MeV.
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.
Conserved charges in 3D gravity
Blagojevic, M.; Cvetkovic, B.
2010-06-15
The covariant canonical expression for the conserved charges, proposed by Nester, is tested on several solutions in three-dimensional gravity with or without torsion and topologically massive gravity. In each of these cases, the calculated values of energy momentum and angular momentum are found to satisfy the first law of black hole thermodynamics.
Charged Particles' Acceleration through Multiple Reconnecting Regions
C. Gontikakis; A. C. Anastasiadis Efthymiopoulos
2008-01-01
We study the acceleration of charged particles (electrons and protons) in steady Reconnecting Current Sheets and X-points in the Solar Corona. We compute the orbits of test particles in simplified magnetic and electric field topologies where a longitudinal magnetic field component is included. We study the particles' kinetic energy gain as a function of the field parameters. The kinetic energy
a Torsional Topological Invariant
NASA Astrophysics Data System (ADS)
Nieh, H. T.
2008-12-01
Curvature and torsion are the two tensors characterizing a general Riemannian space-time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space-time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space-time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.
Adiabatic topological quantum computing
NASA Astrophysics Data System (ADS)
Cesare, Chris; Landahl, Andrew J.; Bacon, Dave; Flammia, Steven T.; Neels, Alice
2015-07-01
Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.
Topology improves phylogenetic motif functional site predictions.
Kc, Dukka B; Livesay, Dennis R
2011-01-01
Prediction of protein functional sites from sequence-derived data remains an open bioinformatics problem. We have developed a phylogenetic motif (PM) functional site prediction approach that identifies functional sites from alignment fragments that parallel the evolutionary patterns of the family. In our approach, PMs are identified by comparing tree topologies of each alignment fragment to that of the complete phylogeny. Herein, we bypass the phylogenetic reconstruction step and identify PMs directly from distance matrix comparisons. In order to optimize the new algorithm, we consider three different distance matrices and 13 different matrix similarity scores. We assess the performance of the various approaches on a structurally nonredundant data set that includes three types of functional site definitions. Without exception, the predictive power of the original approach outperforms the distance matrix variants. While the distance matrix methods fail to improve upon the original approach, our results are important because they clearly demonstrate that the improved predictive power is based on the topological comparisons. Meaning that phylogenetic trees are a straightforward, yet powerful way to improve functional site prediction accuracy. While complementary studies have shown that topology improves predictions of protein-protein interactions, this report represents the first demonstration that trees improve functional site predictions as well. PMID:21071810
Topology Preserving SOM with Transductive Confidence Machine
NASA Astrophysics Data System (ADS)
Tong, Bin; Qin, Zhiguang; Suzuki, Einoshin
We propose a novel topology preserving self-organized map (SOM) classifier with transductive confidence machine (TPSOM-TCM). Typically, SOM acts as a dimension reduction tool for mapping training samples from a high-dimensional input space onto a neuron grid. However, current SOM-based classifiers can not provide degrees of classification reliability for new unlabeled samples so that they are difficult to be used in risk-sensitive applications where incorrect predictions may result in serious consequences. Our method extends a typical SOM classifier to allow it to supply such reliability degrees. To achieve this objective, we define a nonconformity measurement with which a randomness test can predict how nonconforming a new unlabeled sample is with respect to the training samples. In addition, we notice that the definition of nonconformity measurement is more dependent on the quality of topology preservation than that of quantization error reduction. We thus incorporate the grey relation coefficient (GRC) into the calculation of neighborhood radii to improve the topology preservation without increasing the quantization error. Our method is able to improve the time efficiency of a previous method kNN-TCM, when the number of samples is large. Extensive experiments on both the UCI and KDDCUP 99 data sets show the effectiveness of our method.
Bibliography. P. Alexandroff, Elementary concepts of topology,
Johannson, Klaus
Bibliography. · P. Alexandroff, Elementary concepts of topology, Dover (1961) · C.W. Baker, Introduction to Topology, Brown (1991) · M. Barnsley, Fractals everywhere, Academic Press (1988) · N. Bourbaki, Elements of Mathematics: General topology, Addison Wesley Verlag (1966) · J. Dugundji, Topology, Ally
Topological Insulators with SU(2) Landau Levels
NASA Astrophysics Data System (ADS)
Li, Yi; Zhang, Shou-Cheng; Wu, Congjun
2013-11-01
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 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.
Raghu, S.
2010-03-02
We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.
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 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.
An Introduction to Finitesimal Topology #
Selinger, Peter
An Introduction to Finitesimal Topology # M.Kegelmann, P.Selinger March 27, 1992 1 Motivation Since with the complex notions of infinite topological spaces, the authors hope that this humble exposition will serve into the depths of classical topology. Of course we assume some familiarity with basic concepts like the notions
Topology with Dynamical Overlap Fermions
G. I. Egri; Z. Fodor; S. D. Katz; K. K. Szabo
2005-10-28
We perform dynamical QCD simulations with $n_f=2$ overlap fermions by hybrid Monte-Carlo method on $6^4$ to $8^3\\times 16$ lattices. We study the problem of topological sector changing. A new method is proposed which works without topological sector changes. We use this new method to determine the topological susceptibility at various quark masses.
Computational Topology for Geometric Design
Peters, Thomas J.
"mi03 2005/ page i i i i i i i i Computational Topology for Geometric Design and Molecular Design Edward L. F. Moore , Thomas J. Peters Abstract The nascent field of computational topology holds great. Commercial CAGD packages depend upon complementary geometric and topological algorithms. The emergence of geo
An Introduction to Finitesimal Topology
Selinger, Peter
An Introduction to Finitesimal Topology M.Kegelmann, P.Selinger March 27, 1992 1 Motivation Since with the complex notions of infinite topological spaces, the authors hope that this humble exposition will serve into the depths of classical topology. Of course we assume some familiarity with basic concepts like the notions
Topology verification for isosurface extraction.
Etiene, Tiago; Nonato, L Gustavo; Scheidegger, Carlos; Tierny, Julien; Peters, Thomas J; Pascucci, Valerio; Kirby, Robert M; Silva, Cláudio T
2012-06-01
The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes. PMID:21690649
Noncommuting Momenta of Topological Solitons
NASA Astrophysics Data System (ADS)
Watanabe, Haruki; Murayama, Hitoshi
2014-05-01
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.
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 T-duality for torus bundles with monodromy
NASA Astrophysics Data System (ADS)
Baraglia, David
2015-05-01
We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological conditions for T-duals are shown to follow. We determine necessary and sufficient conditions for existence of a T-dual in the case of affine torus bundles. This is general enough to include all principal torus bundles as well as torus bundles with arbitrary monodromy representations. We show that isomorphisms in twisted cohomology, twisted K-theory and of Courant algebroids persist in this general setting. We also give an example where twisted K-theory groups can be computed by iterating T-duality.
Spectroscopy of Cosmic topology
Tarun Souradeep
2006-09-07
Einstein's theory of gravitation that governs the geometry of space-time, coupled with spectacular advance in cosmological observations, promises to deliver a `standard model' of cosmology in the near future. However, local geometry of space constrains, but does not dictate the topology of the cosmos. hence, Cosmic topology has remained an enigmatic aspect of the `standard model' of cosmology. Recent advance in the quantity and quality of observations has brought this issue within the realm of observational query. The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic consequence of non trivial cosmic topology arising from to the imposed `crystallographic' periodicity on the eigenstates of the Laplacian. The sky maps of Cosmic Microwave Background (CMB) anisotropy and polarization most promising observations that would carry signatures of a violation of statistical isotropy and homogeneity. Hence, a measurable spectroscopy of cosmic topology is made possible using the Bipolar power spectrum (BiPS) of the temperature and polarization that quantifies violation of statistical isotropy.
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
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....
Order, topology and preference
NASA Technical Reports Server (NTRS)
Sertel, M. R.
1971-01-01
Some standard order-related and topological notions, facts, and methods are brought to bear on central topics in the theory of preference and the theory of optimization. Consequences of connectivity are considered, especially from the viewpoint of normally preordered spaces. Examples are given showing how the theory of preference, or utility theory, can be applied to social analysis.
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.
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.
Homotopy theory of strong and weak topological insulators
NASA Astrophysics Data System (ADS)
Kennedy, Ricardo; Guggenheim, Charles
2015-06-01
We use homotopy theory to extend the notion of strong and weak topological insulators to the nonstable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d -dimensional," i.e., not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required outside the stable regime. However, this does not exclude weak topological insulators from being "truly d -dimensional," which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of the parameter space replacements Td?Sd and Tdk×Sdx?Sdk+dx used widely in the current literature.
Homotopy Theory of Strong and Weak Topological Insulators
Ricardo Kennedy; Charles Guggenheim
2014-09-08
We use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d-dimensional", i.e. not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required. However, this does not exclude weak topological insulators from being "truly d-dimensional", which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of replacing $T^d$ by $S^d$ and $T^{d_k}\\times S^{d_x}$ by $S^{d_k+d_x}$ as is common in the current literature.
Helical Spin Order from Topological Dirac and Weyl Semimetals.
Sun, Xiao-Qi; Zhang, Shou-Cheng; Wang, Zhong
2015-08-14
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. PMID:26317739
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
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.
Lawson topology of the space of formal balls and the hyperbolic topology
Tsuiki, Hideki
Lawson topology of the space of formal balls and the hyperbolic topology Hideki Tsuiki a,,1 investigate the topological structures of BX, in particular the relations between the Lawson topology and the product topology. We show that the Lawson topology coincides with the product topology if (X, d
Topological Hall Effect in Skyrmions: A Nonequilibrium Coherent Transport Approach
NASA Astrophysics Data System (ADS)
Yin, Gen; Zang, Jiadong; Lake, Roger
2014-03-01
Skyrmion is a topological spin texture recently observed in many materials with broken inversion symmetry. In experiments, one effective method to detect the skyrmion crystal phase is the topological Hall measurement. At adiabatic approximation, previous theoretical studies show that the Hall signal is provided by an emergent magnetic field, which explains the topological Hall effect in the classical level. Motivated by the potential device application of skyrmions as digital bits, it is important to understand the topological Hall effect in the mesoscopic level, where the electron coherence should be considered. In this talk, we will discuss the quantum aspects of the topological Hall effect on a tight binding setup solved by nonequilibrium Green's function (NEGF). The charge distribution, Hall potential distribution, thermal broadening effect and the Hall resistivity are investigated in detail. The relation between the Hall resistance and the DM interaction is investigated. Driven by the spin transferred torque (SST), Skyrmion dynamics is previously studied within the adiabatic approximation. At the quantum transport level, this talk will also discuss the non-adiabatic effect in the skyrmion motion with the presence of the topological Hall effect. This material is based upon work supported by the National Science Foundation under Grant Nos. NSF 1128304 and NSF 1124733. It was also supported in part by FAME, one of six centers of STARnet, an SRC program sponsored by MARCO and DARPA.
Topological aspects of fermions on hyperdiamond
Saidi, E. H. [Hassan II Academy of Science and Technology, Avenue Mohammed VI, KM 4, Souissi, Rabat (Morocco); Lab Of High Energy Physics, Modeling and Simulations, Faculty of Science, University Mohammed V-Agdal, Rabat (Morocco); Fassi-Fehri, O.; Bousmina, M. [Hassan II Academy of Science and Technology, Avenue Mohammed VI, KM 4, Souissi, Rabat (Morocco)
2012-07-15
Motivated by recent results on the index of the Dirac operator D={gamma}{sup {mu}}D{sub {mu}} of QCD on lattice and also by results on topological features of electrons and holes of two-dimensional graphene, we compute in this paper the index of D for fermions living on a family of even-dimensional lattices denoted as L{sub 2N} and describing the 2N-dimensional generalization of the graphene honeycomb. The calculation of this topological index is done by using the direct method based on solving explicitly the gauged Dirac equation and also by using specific properties of the lattices L{sub 2N}, which are shown to be intimately linked with the weight lattices of SU(2N+ 1). The index associated with the two leading N= 1 and N= 2 elements of this family describe precisely the chiral anomalies of graphene and QCD{sub 4}. Comments on the method using the spectral flow approach as well as the computation of the topological charges on 2-cycles of 2N-dimensional compact supercell in L{sub 2N} and applications to QCD{sub 4} are also given.
Topological phases reviewed: The Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases
McKellar, B. H. J. [ARC Centre of Excellence for Particle Physics at the Terrascale, School of Physics, University of Melbourne (Australia); He, X-G. [Department of Physics, National Taiwan University, Taipei, Taiwan (China); Klein, A. G. [School of Physics, University of Melbourne (Australia)
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.
7 CFR 62.301 - Payment of fees and other charges.
Code of Federal Regulations, 2010 CFR
2010-01-01
... AGRICULTURAL MARKETING SERVICE (Standards, Inspections...AGRICULTURAL COMMODITIES (QUALITY SYSTEMS VERIFICATION PROGRAMS) Quality Systems Verification Programs Definitions Charges for Service § 62.301 Payment of...
Flat bands in topological media
Heikkila, T T; Volovik, G E
2010-01-01
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 Dirac or Majorana fermions on the surface of the system and/or inside the vortex core. 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 the three-dimensional topological media with protected nodal lines and in the vortex core in the systems with topologically protected Dirac points. Flat band has an extremely singular density of states, which may give rise in particular to surface superconductivity with an unusually high transition temperature.
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.
J. Albrecht; M. Artuso; K. Babu; R. H. Bernstein; T. Blum; D. N. Brown; B. C. K. Casey; C. -h. Cheng; V. Cirigliano; A. Cohen; A. Deshpande; E. C. Dukes; B. Echenard; A. Gaponenko; D. Glenzinski; M. Gonzalez-Alonso; F. Grancagnolo; Y. Grossman; R. C. Group; R. Harnik; D. G. Hitlin; B. Kiburg; K. Knoepfe; K. Kumar; G. Lim; Z. -T. Lu; D. McKeen; J. P. Miller; M. Ramsey-Musolf; R. Ray; B. L. Roberts; M. Rominsky; Y. Semertzidis; D. Stoeckinger; R. Talman; R. Van De Water; P. Winter
2013-11-24
This is the report of the Intensity Frontier Charged Lepton Working Group of the 2013 Community Summer Study "Snowmass on the Mississippi", summarizing the current status and future experimental opportunities in muon and tau lepton studies and their sensitivity to new physics. These include searches for charged lepton flavor violation, measurements of magnetic and electric dipole moments, and precision measurements of the decay spectrum and parity-violating asymmetries.
Kim D Blake; Chitra Prasad
2006-01-01
CHARGE syndrome was initially defined as a non-random association of anomalies (Coloboma, Heart defect, Atresia choanae, Retarded growth and development, Genital hypoplasia, Ear anomalies\\/deafness). In 1998, an expert group defined the major (the classical 4C's: Choanal atresia, Coloboma, Characteristic ears and Cranial nerve anomalies) and minor criteria of CHARGE syndrome. Individuals with all four major characteristics or three major and
Role of dipole charges in black hole thermodynamics
Copsey, Keith; Horowitz, Gary T. [Department of Physics, UCSB, Santa Barbara, California 93106 (United States)
2006-01-15
Modern derivations of the first law of black holes appear to show that the only charges that arise are monopole charges that can be obtained by surface integrals at infinity. However, the recently discovered five dimensional black ring solutions empirically satisfy a first law in which dipole charges appear. We resolve this contradiction and derive a general form of the first law for black rings. Dipole charges do appear together with a corresponding potential. We also include theories with Chern-Simons terms and generalize the first law to other horizon topologies and more generic local charges.
Code of Federal Regulations, 2013 CFR
2013-07-01
...Inorganic Arsenic Emissions From Primary Copper Smelters § 61.171 Definitions...addition of a molten or solid material to a copper converter. Control device means...rate at which arsenic is charged to the copper converters in the copper converter...
Code of Federal Regulations, 2012 CFR
2012-07-01
...Inorganic Arsenic Emissions From Primary Copper Smelters § 61.171 Definitions...addition of a molten or solid material to a copper converter. Control device means...rate at which arsenic is charged to the copper converters in the copper converter...
Code of Federal Regulations, 2014 CFR
2014-07-01
...Inorganic Arsenic Emissions From Primary Copper Smelters § 61.171 Definitions...addition of a molten or solid material to a copper converter. Control device means...rate at which arsenic is charged to the copper converters in the copper converter...
Bazant, Martin Z.
Electrokinetic motion of heterogeneous particles Synonyms Electrophoresis, induced-charge electrophoresis, transverse electrophoresis. Definition The electrokinetic motion of heterogeneous particles due to the combined effects of electrophoresis, induced-charge electrophoresis, and dielectrophoresis
EDITORIAL: Topological data analysis Topological data analysis
NASA Astrophysics Data System (ADS)
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
The Ehrenfest force topology: a physically intuitive approach for analyzing chemical interactions.
Maza, Julio R; Jenkins, Samantha; Kirk, Steven R; Anderson, James S M; Ayers, Paul W
2013-11-01
Modified ANO-RCC basis sets are used to determine twelve molecular graphs of the Ehrenfest force for H2, CH4, CH2O, CH3NO, C2H2, C2H4, C3H3NO, N4H4, H2O, (H2O)2, (H2O)4 and (H2O)6. The molecular graphs include all types of topological critical points and a mix of bonding types is chosen to include sigma-, ?- and hydrogen-bonding. We then compare a wide range of point properties: charge density, trace of the Hessian, eigenvalues, ellipticity, stiffness, total local energy and the eigenvectors are calculated at the bond critical points (BCPs) and compared for the Ehrenfest, QTAIM and stress tensor schemes. QTAIM is found to be the only partitioning scheme that can differentiate between shared- and closed-shell chemical bond types. Only the results from the Ehrenfest force partitioning, however, are demonstrated to be physically intuitive. This is demonstrated for the water molecule, the water-dimer and the water clusters (H2O)4 and (H2O)6. In particular, both the stiffness and the trace of the Hessians of the appropriate quantities of the sigma-bond BCPs for the water clusters are found to depend on the quantum topology dimension of the molecular graph. The behavior of all the stress tensor point properties is found to be erratic. This is explained by the ambiguity in the theoretical definition of the stress tensor. As a complementary approach the Ehrenfest force provides a new indicator of the mixed chemical character of the hydrogen-bond BCP, which arises from the collinear donor sigma-bond donating a degree of covalent character to the hydrogen-bond. This indicator takes the form of the relative orientation of the shallowest direction of the Ehrenfest potential of the hydrogen-bond BCPs and the corresponding direction for the collinear sigma-bond BCP. PMID:24045853
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.
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.
Critical charge calculations for a bipolar SRAM array
Leo B. Freeman
1996-01-01
The critical charge, Q{sub crit}, of a memory array storage cell is defined as the largest charge that can be injected without changing the cell`s logic state. The Q{sub crit} of a Schottky-coupled complementary bipolar SRAM array is evaluated in detail. An operational definition of critical charge is made, and the critical charge for the cell is determined by circuit
Topological invariant quintessence
NASA Astrophysics Data System (ADS)
de Laurentis, Mariafelicia
2015-03-01
The issues of quintessence and cosmic acceleration can be discussed in the framework of F(R,G) theories of gravity where R is the Ricci curvature scalar and G is the Gauss-Bonnet topological invariant. It is possible to show that such an approach exhausts all the curvature content related to the Riemann tensor giving rise to a fully geometric approach to dark energy.
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.
Gods as Topological Invariants
Schoch, Daniel
2012-01-01
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.
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.
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 lim- itations 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 struc- ture. A remarkably simple relation emerges between the Coulomb and weak potentials.
Topological Quantum Glassiness
Claudio Castelnovo; Claudio Chamon
2011-10-24
Quantum tunneling often allows pathways to relaxation past energy barriers which are otherwise hard to overcome classically at low temperatures. However, this is not always the case. In this paper we provide simple exactly solvable examples where the barriers each system encounters on its approach to lower and lower energy states become increasingly large and eventually scale with the system size. If the environment couples locally to the physical degrees of freedom in the system, tunnelling under large barriers requires processes whose order in perturbation theory is proportional to the width of the barrier. This results in quantum relaxation rates that are exponentially suppressed in system size: For these quantum systems, no physical bath can provide a mechanism for relaxation that is not dynamically arrested at low temperatures. The examples discussed here are drawn from three dimensional generalizations of Kitaev's toric code, originally devised in the context of topological quantum computing. They are devoid of any local order parameters or symmetry breaking and are thus examples of topological quantum glasses. We construct systems that have slow dynamics similar to either strong or fragile glasses. The example with fragile-like relaxation is interesting in that the topological defects are neither open strings or regular open membranes, but fractal objects with dimension $d^* = ln 3/ ln 2$.
Estrada, Rolando; Tomasi, Carlo; Schmidler, Scott C; Farsiu, Sina
2015-08-01
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 data sets show that our methodology is both accurate and efficient. PMID:26353004
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
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.
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.
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.
Topological gap states of semiconducting armchair graphene ribbons
Jeong, Y H; Yang, S -R Eric
2015-01-01
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.
A Comparative Study of Power Supply Architectures In Wireless Electric Vehicle Charging Systems
NASA Astrophysics Data System (ADS)
Esteban, Bryan
Wireless inductive power transfer is a transformational and disruptive technology that enables the reliable and efficient transfer of electrical power over large air gaps for a host of unique applications. One such application that is now gaining much momentum worldwide is the wireless charging of electric vehicles (EVs). This thesis examines two of the primary power supply topologies being predominantly used for EV charging, namely the SLC and the LCL resonant full bridge inverter topologies. The study of both of these topologies is presented in the context of designing a 3 kW, primary side controlled, wireless EV charger with nominal operating parameters of 30 kHz centre frequency and range of coupling in the neighborhood of .18-.26. A comparison of both topologies is made in terms of their complexity, cost, efficiency, and power quality. The aim of the study is to determine which topology is better for wireless EV charging.
40 CFR 98.430 - Definition of the source category.
Code of Federal Regulations, 2011 CFR
2011-07-01
...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...
40 CFR 98.430 - Definition of the source category.
Code of Federal Regulations, 2013 CFR
2013-07-01
...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...
40 CFR 98.430 - Definition of the source category.
Code of Federal Regulations, 2012 CFR
2012-07-01
...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...
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.
Topology of dynamical lattice configurations including results from dynamical overlap fermions
Falk Bruckmann; Nigel Cundy; Florian Gruber; Thomas Lippert; Andreas Schäfer
2011-11-10
We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry in different fermion actions. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to vanish in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10 %. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for this specific observable related to topology, both among themselves and compared to overlap fermions.
Measuring the Topological Susceptibility in a Fixed Sector: Results for Sigma Models
Irais Bautista; Wolfgang Bietenholz; Arthur Dromard; Urs Gerber; Christoph P. Hofmann; Héctor Mejía-Díaz; Marc Wagner
2015-03-23
For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility chi_t = ( - ^2 ) / V. If we manage to perform a Monte Carlo simulation where Q changes frequently, chi_t can be evaluated directly. However, for local update algorithms and fine lattices, the auto-correlation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of chi_t is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in non-linear sigma-models yield accurate results for chi_t, which confirm that the method is applicable. Unfortunately, for increasing volume the wanted signal gets rapidly suppressed, and this method requires huge statistics.
Measuring the Topological Susceptibility in a Fixed Sector: Results for Sigma Models
Bautista, Irais; Dromard, Arthur; Gerber, Urs; Hofmann, Christoph P; Mejía-Díaz, Héctor; Wagner, Marc
2015-01-01
For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility chi_t = ( - ^2 ) / V. If we manage to perform a Monte Carlo simulation where Q changes frequently, chi_t can be evaluated directly. However, for local update algorithms and fine lattices, the auto-correlation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of chi_t is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in non-linear sigma-models yield accurate results for chi_t, which confirm that the method is applicable. Unfortunately, for increasing volume the wanted signal gets rapidly suppressed, and this method requires huge statistics.
Transfer of planar orders onto a sphere: formation and properties of complex topological defects
D. S. Roshal; C. Yu. Petrov; A. E. Myasnikova; S. B. Rochal
2013-09-30
General topological principles how to transfer the planar orders onto a sphere are considered. Formation of extended topological defects (ETDs), which have a reconstructed inner structure surrounded by perfect initial order, is discussed. Topological charge of the ETD can be determined from the shape of a characteristic polygon bounding the defect. Relation between the total topological charge of all defects in the spherical structure and the type of initial planar order is found. It is also demonstrated that in the spherical hexagonal crystal a dislocation located in the ETD area is actually absorbed by it, because the order outside the defect doesn't display existence of dislocation in any way. For the case of singly connected spherical hexagonal order arising from mutual repulsion of N particles (N < 1000) only triangulation of the order inside the ETD regions recovers the linear scars which represent a narrow parts of wider ETD areas.
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.
Visualizing vector field topology in fluid flows
NASA Technical Reports Server (NTRS)
Helman, James L.; Hesselink, Lambertus
1991-01-01
Methods of automating the analysis and display of vector field topology in general and flow topology in particular are discussed. Two-dimensional vector field topology is reviewed as the basis for the examination of topology in three-dimensional separated flows. The use of tangent surfaces and clipping in visualizing vector field topology in fluid flows is addressed.
Topology Basic Course List of Topics
Topology Basic Course List of Topics I. Elementary Concepts 1. Topological spaces. Basis and final topology. Subspace, quotient, sum and product topologies. 4. Compact spaces. Tychonoff theorem spaces and second-countable space topologies. Succession convergence. 7. Urysohn lemma and Tietze theorem
Topology Qualifying Exam Syllabus and Suggested Reading
Topology Qualifying Exam Syllabus and Suggested Reading The students taking a topology qualifying, ordinal numbers, axiom of choice, well- ordered sets, transfinite induction, Zorn lemma. 2. Topological Spaces · Topological spaces, open and closed sets, bases of topology, closures and interiors of sets
The Topological Open String Wavefunction
NASA Astrophysics Data System (ADS)
Grassi, Alba; Källén, Johan; Mariño, Marcos
2015-09-01
We show that, in local Calabi-Yau manifolds, the topological open string partition function transforms as a wavefunction under modular transformations. Our derivation is based on the topological recursion for matrix models, and it generalizes in a natural way the known result for the closed topological string sector. As an application, we derive results for vacuum expectation values of 1/2 BPS Wilson loops in ABJM theory at all genera in a strong coupling expansion, for various representations.
The topological open string wavefunction
Alba Grassi; Johan Kallen; Marcos Marino
2015-03-02
We show that, in local Calabi-Yau manifolds, the topological open string partition function transforms as a wavefunction under modular transformations. Our derivation is based on the topological recursion for matrix models, and it generalizes in a natural way the known result for the closed topological string sector. As an application, we derive results for vevs of 1/2 BPS Wilson loops in ABJM theory at all genera in a strong coupling expansion, for various representations.
Optical conductivity of bismuth-based topological insulators
NASA Astrophysics Data System (ADS)
Di Pietro, P.; Vitucci, F. M.; Nicoletti, D.; Baldassarre, L.; Calvani, P.; Cava, R.; Hor, Y. S.; Schade, U.; Lupi, S.
2012-07-01
The optical conductivity ?1(?) and the spectral weight SW of four topological insulators with increasing chemical compensation (Bi2Se3,Bi2Se2Te,Bi2-xCaxSe3, and Bi2Te2Se) have been measured from 5 to 300 K and from subterahertz to visible frequencies. The effect of compensation is clearly observed in the infrared spectra through the suppression of an extrinsic Drude term and the appearance of strong absorption peaks that we assign to electronic transitions among localized states. From the far-infrared spectral weight SW of the most compensated sample (Bi2Te2Se), one can estimate a density of charge carriers on the order of 1017/cm3 in good agreement with transport data. Those results demonstrate that the low-energy electrodynamics in single crystals of topological insulators, even at the highest degree of compensation presently achieved, is still influenced by three-dimensional charge excitations.
Z2 anomaly and boundaries of topological insulators
NASA Astrophysics Data System (ADS)
Ringel, Zohar; Stern, Ady
2013-09-01
We study the edge and surface theories of topological insulators from the perspective of anomalies and identify a Z2 anomaly associated with charge conservation. The anomaly is manifested through a two-point correlation function involving creation and annihilation operators on two decoupled boundaries. Although charge conservation on each boundary requires this quantity to vanish, we find that it diverges. A corollary result is that under an insertion of a flux quantum, the ground state evolves to an exactly orthogonal state independent of the rate at which the flux is inserted. The anomaly persists in the presence of disorder and imposes sharp restrictions on possible low-energy theories. Being formulated in a many-body, field-theoretical language, the anomaly allows one to test the robustness of topological insulators to interactions in a concise way.
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.
Architectures for Parafermionic Topological Matter in Two Dimensions
NASA Astrophysics Data System (ADS)
Burrello, Michele; van Heck, Bernard; Cobanera, Emilio
2013-03-01
Recent proposals exploit edge modes of fractional topological insulators (FTIs), induced superconducting pairing, and back-scattering to realize one-dimensional systems of parafermions. We extend these proposals to two dimensions and analyze the effect of the superconducting islands' charging energy on the parafermions they host. We focus on two two-dimensional architectures, the tile and stripe configurations, characterized by different distributions of FTIs and derive the associated parafermionic effective Hamiltonians. The tile model realizes the Z2 m toric code in low-order perturbation theory and hence possesses full topological quantum order. By exploiting dualities, we obtain the phase diagram and generalized order parameters for both the tile and stripe models of parafermions. Recent proposals exploit edge modes of fractional topological insulators (FTIs), induced superconducting pairing, and back-scattering to realize one-dimensional systems of parafermions. We extend these proposals to two dimensions and analyze the effect of the superconducting islands' charging energy on the parafermions they host. We focus on two two-dimensional architectures, the tile and stripe configurations, characterized by different distributions of FTIs and derive the associated parafermionic effective Hamiltonians. The tile model realizes the Z2 m toric code in low-order perturbation theory and hence possesses full topological quantum order. By exploiting dualities, we obtain the phase diagram and generalized order parameters for both the tile and stripe models of parafermions. This work was supported by the Dutch Science Foundation NWO/FOM and an ERC Advanced Investigator grant.
Topological modular forms and conformal nets
Christopher L. Douglas; André G. Henriques
2011-03-22
We describe the role conformal nets, a mathematical model for conformal field theory, could play in a geometric definition of the generalized cohomology theory TMF of topological modular forms. Inspired by work of Segal and Stolz-Teichner, we speculate that bundles of boundary conditions for the net of free fermions will be the basic underlying objects representing TMF-cohomology classes. String structures, which are the fundamental orientations for TMF-cohomology, can be encoded by defects between free fermions, and we construct the bundle of fermionic boundary conditions for the TMF-Euler class of a string vector bundle. We conjecture that the free fermion net exhibits an algebraic periodicity corresponding to the 576-fold cohomological periodicity of TMF; using a homotopy-theoretic invariant of invertible conformal nets, we establish a lower bound of 24 on this periodicity of the free fermions.
Topological modular forms and conformal nets
Douglas, Christopher L
2011-01-01
We describe the role conformal nets, a mathematical model for conformal field theory, could play in a geometric definition of the generalized cohomology theory TMF of topological modular forms. Inspired by work of Segal and Stolz-Teichner, we speculate that bundles of boundary conditions for the net of free fermions will be the basic underlying objects representing TMF-cohomology classes. String structures, which are the fundamental orientations for TMF-cohomology, can be encoded by defects between free fermions, and we construct the bundle of fermionic boundary conditions for the TMF-Euler class of a string vector bundle. We conjecture that the free fermion net exhibits an algebraic periodicity corresponding to the 576-fold cohomological periodicity of TMF; using a homotopy-theoretic invariant of invertible conformal nets, we establish a lower bound of 24 on this periodicity of the free fermions.
Detecting Communities Based on Network Topology
Liu, Wei; Pellegrini, Matteo; Wang, Xiaofan
2014-01-01
Network methods have had profound influence in many domains and disciplines in the past decade. Community structure is a very important property of complex networks, but the accurate definition of a community remains an open problem. Here we defined community based on three properties, and then propose a simple and novel framework to detect communities based on network topology. We analyzed 16 different types of networks, and compared our partitions with Infomap, LPA, Fastgreedy and Walktrap, which are popular algorithms for community detection. Most of the partitions generated using our approach compare favorably to those generated by these other algorithms. Furthermore, we define overlapping nodes that combine community structure with shortest paths. We also analyzed the E. Coli. transcriptional regulatory network in detail, and identified modules with strong functional coherence. PMID:25033828
Entangled Networks, Synchronization, and Optimal Network Topology
NASA Astrophysics Data System (ADS)
Donetti, Luca; Hurtado, Pablo I.; Muñoz, Miguel A.
2005-10-01
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.
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
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.
Semi Compactness in Multiset Topology
J. Mahanta; D. Das
2014-11-21
In this paper, we introduce and study the concepts of semi open SOM) and semi closed (SCM) M-sets in multiset topological spaces.With this generalization of the notions of open and closed sets in M-topology, we generalize the concept of compactness in M-topology as semi compactness. Further semi compactness is generalized as semi whole compactness, semi partial whole compactness and semi full compactness. Some characterizations of these compact spaces are studied in the setting of multiset theory. In each step, several remarks with proper justifications are provided taking the well existing theories of general topology as the base of our study.
Path-integral bosonization in topologically nontrivial sectors: The non-Abelian case
Cabra, D.; Manias, M.V. (Departamento de Fisica, Universidad Nacional de La Plata, CC 67, 1900 La Plata, Argentina (AR) Consejo Nacional de Investigaciones Cientificas y Tecnicas, Argentina (AR)); Schaposnik, F.A. (Laboratoire de Physique Theorique Particules Elementaires, Universite de Paris 7, Tour 24-5 et., 2 Place Jussieu, 75251 Paris CEDEX 05, France (FR) Departamento de Fisica, Universidad Nacional de La Plata, CC67 1900 La Plata, Argentina (AR) Comision de Investigaciones Cientificas Buenos Aires (CICBA), Buenos Aires, Argentina (AR)); Trobo, M. (Departamento de Fisica, Universidad Nacional de La Plata, CC 67, 1900 La Plata, Argentina Consejo Nacional de Investigaciones Cientificas y Tecnicas, Argentina (AR))
1991-05-15
We present a path-integral bosonization approach which allows us to take into account nontrivial topological sectors in two-dimensional models such as two-dimensional QCD. Because of the existence of fermionic zero modes, the partition function receives a contribution only from the topologically trivial ({ital n}=0) sector. However, certain fermionic correlation functions (constructed from chiral-charge-nonconserving operators) become nonvanishing when one takes into account {ital n}{ne}0 sectors.
WHEN IS THE ISBELL TOPOLOGY A GROUP TOPOLOGY? SZYMON DOLECKI AND FRDRIC MYNARD
Dolecki, Szymon
WHEN IS THE ISBELL TOPOLOGY A GROUP TOPOLOGY? SZYMON DOLECKI AND FRÉDÉRIC MYNARD Abstract. Conditions on a topological space X under which the space C(X; R) of continuous real-valued maps with the Isbell topology is a topological group (topological vector space) are investigated. It is proved
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 ...
Black hole mass and angular momentum in topologically massive gravity
NASA Astrophysics Data System (ADS)
Bouchareb, Adel; Clément, Gérard
2007-11-01
We extend the Abbott Deser Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.
Perfect valley filter in a topological domain wall
NASA Astrophysics Data System (ADS)
Pan, Hui; Li, Xin; Zhang, Fan; Yang, Shengyuan A.
2015-07-01
We propose a realization of perfect valley filters based on the chiral domain-wall channels between a quantum anomalous Hall insulator and a quantum valley Hall insulator. Uniquely, all these channels reside in the same valley and propagate unidirectionally, 100 % valley-polarizing passing-by carriers without backscattering. The valley index, the chirality, and the number of the channels are protected by topological charges, controllable by external fields, and detectable by circular dichroism.
NSDL National Science Digital Library
Eric Muller
1995-01-01
In this trick, learners discover how to stick a straw to the palm of their hand, window door, or anywhere using static electricity. This activity introduces learners to negative and positive charges and shows how opposites attract. Note: this trick works best in low humidity (dry air).
Blobbed topological recursion: properties and applications
Gaëtan Borot; Sergey Shadrin
2015-02-18
We study the set of solutions $(\\omega_{g,n})_{g \\geq 0,n \\geq 1}$ of abstract loop equations. We prove that $\\omega_{g,n}$ is determined by its purely holomorphic part: this results in a decomposition that we call "blobbed topological recursion". This is a generalization of the theory of the topological recursion, in which the initial data $(\\omega_{0,1},\\omega_{0,2})$ is enriched by non-zero symmetric holomorphic forms in $n$ variables $(\\phi_{g,n})_{2g - 2 + n > 0}$. In particular, we establish for any solution of abstract loop equations: (1) a graphical representation of $\\omega_{g,n}$ in terms of $\\phi_{g,n}$; (2) a graphical representation of $\\omega_{g,n}$ in terms of intersection numbers on the moduli space of curves; (3) variational formulae under infinitesimal transformation of $\\phi_{g,n}$ ; (4) a definition for the free energies $\\omega_{g,0} = F_g$ respecting the variational formulae. We discuss in detail the application to the multi-trace matrix model and enumeration of stuffed maps.
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.
Topologically clean distance fields.
Gyulassy, Attila; Duchaineau, Mark; Natarajan, Vijay; Pascucci, Valerio; Bringa, Eduardo; Higginbotham, Andrew; Hamann, Bernd
2007-01-01
Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material. We focus on distance fields defined on a volumetric domain considering the distance to a given surface embedded within the domain. Topological features of the field are characterized by its critical points. Our first method begins with a distance field that is computed using a standard approach, and simplifies this field using ideas from Morse theory. We present a procedure for identifying and extracting a feature set through analysis of the MS complex, and apply it to find the invariants in the clean distance field. Our second method proceeds by advancing a front, beginning at the surface, and locally controlling the creation of new critical points. We demonstrate the value of topologically clean distance fields for the analysis of filament structures in porous solids. Our methods produce a curved skeleton representation of the filaments that helps material scientists to perform a detailed qualitative and quantitative analysis of pores, and hence infer important material properties. Furthermore, we provide a set of criteria for finding the "difference" between two skeletal structures, and use this to examine how the structure of the porous solid changes over several timesteps in the simulation of the particle impact. PMID:17968094
OPTIMAL NETWORK TOPOLOGY DESIGN
NASA Technical Reports Server (NTRS)
Yuen, J. H.
1994-01-01
This program was developed as part of a research study on the topology design and performance analysis for the Space Station Information System (SSIS) network. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. It is intended that this new design technique consider all important performance measures explicitly and take into account the constraints due to various technical feasibilities. In the current program, technical constraints are taken care of by the user properly forming the starting set of candidate components (e.g. nonfeasible links are not included). As subsets are generated, they are tested to see if they form an acceptable network by checking that all requirements are satisfied. Thus the first acceptable subset encountered gives the cost-optimal topology satisfying all given constraints. The user must sort the set of "feasible" link elements in increasing order of their costs. The program prompts the user for the following information for each link: 1) cost, 2) connectivity (number of stations connected by the link), and 3) the stations connected by that link. Unless instructed to stop, the program generates all possible acceptable networks in increasing order of their total costs. The program is written only to generate topologies that are simply connected. Tests on reliability, delay, and other performance measures are discussed in the documentation, but have not been incorporated into the program. This program is written in PASCAL for interactive execution and has been implemented on an IBM PC series computer operating under PC DOS. The disk contains source code only. This program was developed in 1985.
Sivakumar, Raghupathy
#12;Â· Â· Â· Â· #12;Â· Â· f1 f2 f3 f2 f3 f1 #12;comp 1 comp 2 f1 f2 f3 #12;f2 f2 Toy Topology f1 f1 1 1. Flows 0 50 100 150 200 250 300 350 400 450 500 F1 F2 F3 F1 F2 F3 F1 F2 F3 Component Flow Single Flow Identifier Throughput(KB/s) Average Throughput (KB/s) vs. Flows 0 100 200 300 400 500 600 F1 F2 F3 F1 F2 F3 F
Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces
Sergei Alexandrov; Daniel Persson; Boris Pioline
2015-03-27
We investigate quantum corrections to the hypermultiplet moduli space M in Calabi-Yau compactifications of type II string theories, with particular emphasis on instanton effects from Euclidean NS5-branes. Based on the consistency of D- and NS5-instanton corrections, we determine the topology of the hypermultiplet moduli space at fixed string coupling, as previewed in arXiv:1009.3026. On the type IIB side, we compute corrections from (p,k)-fivebrane instantons to the metric on M (specifically, the correction to the complex contact structure on its twistor space Z) by applying S-duality to the D-instanton sum. For fixed fivebrane charge k, the corrections can be written as a non-Gaussian theta series, whose summand for k=1 reduces to the topological A-model amplitude. By mirror symmetry, instanton corrections induced from the chiral type IIA NS5-brane are similarly governed by the wave function of the topological B-model. In the course of this investigation we clarify charge quantization for coherent sheaves and find hitherto unnoticed corrections to the Heisenberg, monodromy and S-duality actions on M, as well as to the mirror map for Ramond-Ramond fields and D-brane charges.
Topologically induced local P and CP violation in hot QCD
Kharzeev,D.E.
2009-02-01
Very stringent experimental bounds exist on the amount of P and CP violation in strong interactions. Nevertheless, the presence of non-Abelian topological solutions and the axial anomaly make the issue of CP invariance in QCD non-trivial ('the strong CP problem'). Even in the absence of a global P and CP violation the fluctuations of topological charge in the QCD vacuum are expected to play an important role in the breaking of chiral symmetry, and in the mass spectrum and other properties of hadrons. Here I argue that topological fluctuations in hot QCD matter can become directly observable in the presence of a very intense external magnetic field by inducing local P- and CP-odd effects. These local parity-violating phenomena can be described by using the Maxwell-Chern-Simons, or axion, electrodynamics as an effective theory. Local P and CP violation in hot QCD matter can be observed in experiment through the 'chiral magnetic effect' - the separation of electric charge along the axis of magnetic field that is created by the colliding relativistic ions. There is a recent evidence for the electric charge separation relative to the reaction plane of heavy ion collisions from the STAR Collaboration at RHIC.
Screening and atomic-scale engineering of the potential at a topological insulator surface
NASA Astrophysics Data System (ADS)
Löptien, P.; Zhou, L.; Wiebe, J.; Khajetoorians, A. A.; Mi, J. L.; Iversen, B. B.; Hofmann, Ph.; Wiesendanger, R.
2014-02-01
The electrostatic behavior of a prototypical three-dimensional topological insulator, Bi2Se3(111), is investigated by a scanning tunneling microscopy (STM) study of the distribution of Rb atoms adsorbed on the surface. The positively charged ions are screened by both free electrons residing in the topological surface state as well as band bending induced quantum well states of the conduction band, leading to a surprisingly short screening length. Combining a theoretical description of the potential energy with STM-based atomic manipulation, we demonstrate the ability to create tailored electronic potential landscapes on topological surfaces with atomic-scale control.
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.
Topology of sensor networks Population protocols
Aspnes, James
Topology of sensor networks Population protocols Protocols on graphs Getting organized protocols Protocols on graphs Getting organized Is it practical? Topology of sensor networks Consider Properties of Network Graphs #12;Topology of sensor networks Population protocols Protocols on graphs Getting
AUGMENTED LAGRANGIAN FOR CONE CONSTRAINED TOPOLOGY OPTIMIZATION
Samuel, Amstutz
AUGMENTED LAGRANGIAN FOR CONE CONSTRAINED TOPOLOGY OPTIMIZATION SAMUEL AMSTUTZ Abstract. Algorithmic aspects for the solution of topological shape optimization problems subject to a cone constraint of topological derivative is proposed. It is illustrated by some numerical experiments in structural optimization
String winding modes from charge non-conservation in compact Chern-Simons theory
Leith Cooper; Ian I. Kogan; Lee Kai-Ming
1997-01-01
In this letter we show how string winding modes can be constructed using topological membranes. We use the fact that monopole-instantons in compact topologically massive gauge theory lead to charge non-conservation inside the membrane which, in turn, enables us to construct string vertex operators with different left and right momenta. The amount of charge non-conservation inside the membrane is interpreted
Communication: An approximation to Bader's topological atom.
Salvador, Pedro; Ramos-Cordoba, Eloy
2013-08-21
A new, more flexible definition of fuzzy Voronoi cells is proposed as a computationally efficient alternative to Bader's Quantum Theory of Atoms in Molecules (QTAIM) partitioning of the physical space for large-scale routine calculations. The new fuzzy scheme provides atomic charges, delocalization indices, and molecular energy components very close to those obtained using QTAIM. The method is flexible enough to either ignore the presence of spurious non-nuclear attractors or to readily incorporate them by introducing additional fuzzy Voronoi cells. PMID:23968064
Charge separation induced by P-odd bubbles in QCD matter
D. Kharzeev; A. Zhitnitsky
2007-10-01
We examine the recent suggestion that P- and CP-odd effects in QCD matter can induce electric charge asymmetry with respect to reaction plane in relativistic heavy ion collisions. General arguments are given which confirm that the angular momentum of QCD matter in the presence of non-zero topological charge should induce an electric field aligned along the axis of the angular momentum. A simple formula relating the magnitude of charge asymmetry to the angular momentum and topological charge is derived. The expected asymmetry is amenable to experimental observation at RHIC and LHC; we discuss the recent preliminary STAR result in light of our findings.
Geometric background charge: dislocations on capillary bridges
William Irvine; Vincenzo Vitelli
2012-06-19
Recent experiments have shown that colloidal crystals confined to weakly curved capillary bridges introduce groups of dislocations organized into `pleats' as means to relieve the stress caused by the Gaussian curvature of the surface. We consider the onset of this curvature-screening mechanism, by examining the energetics of isolated dislocations and interstitials on capillary bridges with free boundaries. The boundary provides an essential contribution to the problem, akin to a background charge that "neutralizes" the unbalanced integrated curvature of the surface. This makes it favorable for topologically neutral dislocations and groups of dislocations - rather than topologically charged disclinations and scars - to relieve the stress caused by the unbalanced gaussian curvature of the surface. This effect applies to any crystal on a surface with non-vanishing integrated Gaussian curvature and stress-free boundary conditions. We corroborate the analytic results by numerically computing the energetics of a defected lattice of springs confined to surfaces with weak positive and negative curvature
Independent group topologies on Abelian groups
Mikhail Tkachenko; Ivan Yaschenko
2002-01-01
Two non-discrete T1 topologies ?1,?2 on a set X are called independent if their intersection ?1??2 is the cofinite topology on X. We show that a countable group does not admit a pair of independent group topologies. We use MA to construct group topologies on the additive groups R and T independent of their usual interval topologies. These topologies have necessarily to
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
Topological Insulator Nanowires and Nanoribbons
Cui, Yi
Topological Insulator Nanowires and Nanoribbons Desheng Kong, Jason C. Randel,,| Hailin Peng,, Judy and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025 material show that it is a three-dimensional topological insulator possessing conductive surface states
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.
Erik Verlinde
1990-01-01
We calculate correlation functions in minimal topological eld theories. These twisted version of N = 2 minimal models have recently been proposed to describe d < 1 matrix models, once coupled to topological gravity. In our calculation we make use of the Landau-Ginzburg formulation of the N = 2 models, and we nd a direct relation between the Landau-Ginzburg superpotential
Robbert Dijkgraaf; Herman Verlinde; Erik Verlinde
1991-01-01
We calculate correlation functions in minimal topological field theories. These twisted versions of N = 2 minimal models have recently been proposed to describe d < 1 matrix models, once coupled to topological gravity. In our calculation we make use of the Landau-Ginzburg formulation of the N = 2 models, and we find a direct relation between the Landau-Ginzburg superpotential
Topology, connectedness, and modal logic
Kontchakov, Roman
of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the e Logic and Modal Logic In their seminal paper The algebra of topology [40], McKinsey and Tarski sought as the topological interior operator. As McKinsey and Tarski showed, a modal formula # is an S4validity if and only
On Topological Properties of Functions.
ERIC Educational Resources Information Center
Hazzan, Orit
1996-01-01
Focuses on the understanding of the concept of function and presents discussions of the topological properties of functions and of students' mathematical thinking when they are asked to determine whether a property of a function is a topological property or not. Contains 15 references. (DDR)
Topology Change in General Relativity
Gary T. Horowitz
1991-09-18
A review is given of recent work on topology changing solutions to the first order form of general relativity. These solutions have metrics which are smooth everywhere, invertible almost everywhere, and have bounded curvature. The importance of considering degenerate metrics is discussed, and the possibility that quantum effects can suppress topology change is briefly examined.
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
Topological Insulators with Ultracold Atoms Indubala I. Satija and Erhai Zhao
Satija, Indu
general working definition of TI, applicable to the case of neutral atoms, is that they are bandChapter 12 Topological Insulators with Ultracold Atoms Indubala I. Satija and Erhai Zhao Abstract Ultracold atom research presents many avenues to study problems at the forefront of physics. Due
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+vk Example #12;#12;CA as Dynamical Systems Cantor distance: D(x, y)= dist. to center of the 1st cell where x
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.
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.
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.
Net charge fluctuations and local charge compensation
Fu Jinghua
2006-12-15
We propose net charge fluctuation as a measure of local charge correlation length. It is demonstrated that, in terms of a schematic multiperipheral model, net charge fluctuation satisfies the same Quigg-Thomas relation as satisfied by charge transfer fluctuation. Net charge fluctuations measured in finite rapidity windows depend on both the local charge correlation length and the size of the observation window. When the observation window is larger than the local charge correlation length, the net charge fluctuation only depends on the local charge correlation length, while forward-backward charge fluctuations always have strong dependence on the observation window size. Net charge fluctuations and forward-backward charge fluctuations measured in the present heavy ion experiments show characteristic features similar to those from multiperipheral models. But the data cannot all be understood within this simple model.
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...
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.
... and Stings Eating Well While Eating Out Melanoma Thyroid Disease Definitions KidsHealth > Teens > Diseases & Conditions > Growth, Hormones & Diabetes > Thyroid Disease Definitions Print A A A Text Size ...
Olgyay, Victor W. (Victor Wayne)
1986-01-01
Home is an elusive concept. In one manner it is highly specific and individual in its definition, and in other aspects it is ubiquitous, present in our every act. In this thesis I explore several possible definitions of ...
On the computational content of the Lawson topology
Escardó, Martín
On the computational content of the Lawson topology the Lawson topology is finer than the Scott topology, a stronger notion of computability is obtained. 1 Introduction The Lawson topology has its origins in topological algebra [8, 7]. A Lawson
A symmetry reduction method for continuum structural topology optimization
Swan Jr., Colby Corson
A symmetry reduction method for continuum structural topology optimization Iku Kosakaa, 1 , Colby C. All rights reserved. Keywords: Topology; Topology optimization; Continuum topology; Design sensitivity and motivation Continuum structural topology optimization is an increasingly powerful design tool which can
Surface conduction in encapsulated topological gated structures
NASA Astrophysics Data System (ADS)
Deshko, Yury; Korzhovska, Inna; Zhao, Lukas; Arefe, Ghidewon; Konczykowski, Marcin; Krusin-Elbaum, Lia
2015-03-01
In three-dimensional (3D) topological insulators (TIs), the surface Dirac fermions intermix with the conducting bulk, thereby complicating access to the low-energy surface charge transport or magnetic response. The subsurface 2D states of bulk origin are vulnerable to bandbending due to surface adatoms, a band modification thought to be responsible for the `ageing' effect. To minimize this effect, we have developed an inert environment mechanical exfoliation technique to fabricate transistor-like gated structures in which prototypical binary TIs as well as ultra-low bulk carrier density ternaries (such as Bi2Te2Se) were encapsulated by thin h-BN layers, with electrical contacts made using exfoliated graphene. The effects of electrostatic tuning by the gate bias voltage on surface conductivity as a function of thickness of the TI layers and the variation with disorder will be presented. Supported by NSF-DMR-1312483, and DOD-W911NF-13-1-0159.
Electric-Magnetic Duality and Topological Insulators
Karch, A. [Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)
2009-10-23
We work out the action of the SL(2,Z) electric-magnetic duality group for an insulator with a nontrivial permittivity, permeability, and theta angle. This theory has recently been proposed to be the correct low-energy effective action for topological insulators. As applications, we give manifestly SL(2,Z) covariant expressions for the Faraday rotation at orthogonal incidence at the interface of two such materials, as well as for the induced magnetic and electric charges, slightly clarifying the meaning of expressions previously derived in the literature. We also use electric-magnetic duality to find a gravitational dual for a strongly coupled version of this theory using the gauge/gravity correspondence.
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.
The mosaic of surface charge in contact electrification.
Baytekin, H T; Patashinski, A Z; Branicki, M; Baytekin, B; Soh, S; Grzybowski, B A
2011-07-15
When dielectric materials are brought into contact and then separated, they develop static electricity. For centuries, it has been assumed that such contact charging derives from the spatially homogeneous material properties (along the material's surface) and that within a given pair of materials, one charges uniformly positively and the other negatively. We demonstrate that this picture of contact charging is incorrect. Whereas each contact-electrified piece develops a net charge of either positive or negative polarity, each surface supports a random "mosaic" of oppositely charged regions of nanoscopic dimensions. These mosaics of surface charge have the same topological characteristics for different types of electrified dielectrics and accommodate significantly more charge per unit area than previously thought. PMID:21700838
AB effect and Aharonov-Susskind charge non-superselection
Erez, Noam
2010-01-01
We consider a particle in a coherent superposition of states with different electric charge moving in the vicinity of a magnetic flux. Formally, it should acquire a (gauge-dependent) AB relative phase between the charge states, even for an incomplete loop. If measureable, such a geometric, rather than topological, AB-phase would seem to break gauge invariance. Wick, Wightman and Wigner argued that since (global) charge-dependent phase transformations are physically unobservable, charge state superpositions are unphysical (`charge superselection rule'). This would resolve the apparent paradox in a trivial way. However, Aharonov and Susskind disputed this superselection rule: they distinguished between such global charge-dependent transformations, and transformations of the relative inter-charge phases of two particles, and showed that the latter \\emph{could} in principle be observable! Finally, the paradox again disappears once we considers the `calibration' of the phase measured by the Aharonov-Susskind phase...
G. Reid Lyon; Sally E. Shaywitz; Bennett A. Shaywitz
2003-01-01
This paper elaborates on the components of a working definition of developmental dyslexia. It follows the general format of\\u000a a paper by Lyon published in Annals of Dyslexia in 1995, which elaborated on a working definition proposed in 1994 (Lyon,\\u000a 1995). The current definition agreed on by the work group updates and expands on the working definition from 1994.
Spin-transfer torque generated by a topological insulator
NASA Astrophysics Data System (ADS)
Mellnik, A. R.; Lee, J. S.; Richardella, A.; Grab, J. L.; Mintun, P. J.; Fischer, M. H.; Vaezi, A.; Manchon, A.; Kim, E.-A.; Samarth, N.; Ralph, D. C.
2014-07-01
Magnetic devices are a leading contender for the implementation of memory and logic technologies that are non-volatile, that can scale to high density and high speed, and that do not wear out. However, widespread application of magnetic memory and logic devices will require the development of efficient mechanisms for reorienting their magnetization using the least possible current and power. There has been considerable recent progress in this effort; in particular, it has been discovered that spin-orbit interactions in heavy-metal/ferromagnet bilayers can produce strong current-driven torques on the magnetic layer, via the spin Hall effect in the heavy metal or the Rashba-Edelstein effect in the ferromagnet. In the search for materials to provide even more efficient spin-orbit-induced torques, some proposals have suggested topological insulators, which possess a surface state in which the effects of spin-orbit coupling are maximal in the sense that an electron's spin orientation is fixed relative to its propagation direction. Here we report experiments showing that charge current flowing in-plane in a thin film of the topological insulator bismuth selenide (Bi2Se3) at room temperature can indeed exert a strong spin-transfer torque on an adjacent ferromagnetic permalloy (Ni81Fe19) thin film, with a direction consistent with that expected from the topological surface state. We find that the strength of the torque per unit charge current density in Bi2Se3 is greater than for any source of spin-transfer torque measured so far, even for non-ideal topological insulator films in which the surface states coexist with bulk conduction. Our data suggest that topological insulators could enable very efficient electrical manipulation of magnetic materials at room temperature, for memory and logic applications.
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.
Punishment: Problems in Definition.
ERIC Educational Resources Information Center
Myers, Carmel
This paper examines the problems in definition of punishment at the construct level, comparing the common use meaning of the term with a behavioral definition and contrasting two definitions used within the field of psychology. The paper discusses whether punishing stimuli must be physically painful, the appropriate use of painful stimuli, and…
ERIC Educational Resources Information Center
Herrmann, Douglas J.; Chaffin, Roger
The relation definition theory proposed in this paper is explicitly different from previous semantic memory theories since it is the first to make a relation's definition the basis of semantic processing. The paper suggests that this relation definition theory successfully predicts relation similarity on the basis of one key primary assumption:…
Heubach, Silvia
Background Definitions Main Result Special Types of Patterns Summary Avoidance of partially ordered Avoidance of partially ordered patterns in compositions #12;Background Definitions Main Result Special Types of Patterns Summary Outline 1 Background 2 Definitions 3 Main Result Preliminaries Main Result 4 Special Types
Phase Diagrams of Binary Mixtures of Oppositely Charged Colloids
Markus Bier; Rene van Roij; Marjolein Dijkstra
2010-05-21
Phase diagrams of binary mixtures of oppositely charged colloids are calculated theoretically. The proposed mean-field-like formalism interpolates between the limits of a hard-sphere system at high temperatures and the colloidal crystals which minimize Madelung-like energy sums at low temperatures. Comparison with computer simulations of an equimolar mixture of oppositely charged, equally sized spheres indicate semi-quantitative accuracy of the proposed formalism. We calculate global phase diagrams of binary mixtures of equally sized spheres with opposite charges and equal charge magnitude in terms of temperature, pressure, and composition. The influence of the screening of the Coulomb interaction upon the topology of the phase diagram is discussed. Insight into the topology of the global phase diagram as a function of the system parameters leads to predictions on the preparation conditions for specific binary colloidal crystals.
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.
Topological Josephson ?0 junctions
NASA Astrophysics Data System (ADS)
Dolcini, Fabrizio; Houzet, Manuel; Meyer, Julia S.
2015-07-01
We study the effect of a magnetic field on the current-phase relation of a topological Josephson junction formed by connecting two superconductors through the helical edge states of a quantum spin-Hall insulator. We predict that the Zeeman effect along the spin quantization axis of the helical edges results in an anomalous Josephson relation that allows for a supercurrent to flow in the absence of superconducting phase bias. We relate the associated field-tunable phase shift ?0 in the Josephson relation of such a ?0 junction to the existence of a so-called helical superconductivity, which may result from the interplay of the Zeeman effect and spin-orbit coupling. We analyze the dependence of the magneto-supercurrent on the junction length and discuss its observability in suitably designed hybrid structures subject to an in-plane magnetic field.
Lee Smolin
1994-04-07
The canonical theory of quantum gravity in the loop representation can be extended to incorporate topology change, in the simple case that this refers to the creation or annihilation of "minimalist wormholes" in which two points of the spatial manifold are identified. Furthermore, if the states of the wormholes threaded by loop states are taken to be antisymmetrized under the permutation of wormhole mouths, as required by the relation between spin and statistics, then the quantum theory of pure general relativity, without matter but with minimalist wormholes, is shown to be equivalent to the quantum theory of general relativity coupled to a single Weyl fermion field, at both the kinematical and diffeomorphism invariant levels. The correspondence is also shown to extend to the action of the dynamics generated by the Hamiltonian constraint, on a large subspace of the physical state space, and is thus conjectured to be completely general.
Probing Topological Superconductors
NASA Astrophysics Data System (ADS)
Schmeltzer, David
2015-03-01
The presence of attractive interaction on the surface of a 3D topological insulator which is characterized by spinors carrying a Berry phase of ? gives rise to superconductivity that support space time half vortices (Majorana zero modes). We construct the effective dual action for the superconductor with the vortices, and show that the 2 n Majorana fermions are localized and can be replaced with n spinless fermions. The effect of the Majorana zero modes can be observed trough the the Andreev cross reflection when metallic leads are attached to the superconductor. The presence of the Majorana fermions can be detected with transverse sound waves. We have computed the effect of elastic strain fields and obtain an anomalous response indicating the presence of the Majorana fermions.
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.
Topological Phase Transition in Antimony
NASA Astrophysics Data System (ADS)
Wong, Man-Hong; Bian, Guang; Xu, Caizhi; Miller, Thomas; Chiang, Tai-Chang
2014-03-01
Spin-orbit coupling (SOC) is believed to cause the parity exchange that drives normal band insulators into the topological regime. Changing the strength of the effective SOC can also induce quantum phase transitions in materials. We performed a first-principles calculation to elucidate the quantum phase transition from a topologically trivial to nontrivial system in a 15-bilayer Sb film. We increased the k-space sampling relative to previous studies and varied the effective SOC in order to observe the changes in the bulk band gap and topological surface states. A transition from a metal to a semimetal is observed as the SOC is tuned from 0% to 100%. At a SOC value near 300%, a transition from a nontrivial topological semimetal to a topological insulator occurs. Varying the effective SOC strength can be realized experimentally by alloy substitution with elements in the same column in the periodic table. Increasing the effective SOC of the Sb film to values above 100% is a model of the Bi1-xSbx alloy, the first three-dimensional topological insulator. Further studies using this method on different systems may lead to the discovery of new topological insulators. This work is supported by the U.S. Department of Energy (Grant No. DE-FG02-07ER46383 for T-CC).
Aspects of photonic topological insulators
NASA Astrophysics Data System (ADS)
Rechtsman, Mikael
2015-03-01
Great excitement surrounding optical topological protection has recently emerged from the promise of endowing photonic devices with quantum Hall-like robustness. Here, I will present the prediction and realization of a photonic topological insulator for light. Topological insulators (TIs) are solid-state materials that are insulators in the bulk, but conduct electricity along their surfaces - and are intrinsically robust to disorder. In particular, when a surface electron in a TI encounters a defect, it simply goes around it without scattering, always exhibiting - quite strikingly - perfect transmission. The structure is composed of an array of coupled helical waveguides; the helicity generates an artificial circularly-polarized force on the photons that breaks time-reversal symmetry. This leads to bands with non-zero Chern number, and thus topologically-protected edge states (protected in the quantum Hall sense - not by any symmetry). Due to the time-dependent force, the band structure must be solved in the Floquet sense; the result bears close resemblance to that of the quantum anomalous Hall effect. I will also present experimental results on the first realization of a ``topological Anderson insulator'' (in a similar setting), where the addition of disorder can make a trivial system topological. Time permitting, I will discuss the question of what it means to have topological interface states in non-Hermitian systems, and show new experiments exploring their properties.
NSDL National Science Digital Library
Integrated Teaching and Learning Program,
Students are introduced to the idea of electrical energy. They learn about the relationships between charge, voltage, current and resistance. They discover that electrical energy is the form of energy that powers most of their household appliances and toys. In the associated activities, students learn how a circuit works and test materials to see if they conduct electricity. Building upon a general understanding of electrical energy, they design their own potato power experiment. In two literacy activities, students learn about the electrical power grid and blackouts.
NSDL National Science Digital Library
Jack D. Thatcher (Lewisburg; West Virginia School of Osteopathic Medicine REV)
2013-04-16
This Teaching Resource provides three animated lessons that describe the storage and utilization of energy across plasma membranes. The “Na,K ATPase” animation explains how these pumps establish the electrochemical gradient that stores energy across plasma membranes. The “ATP synthesizing complexes” animation shows how these complexes transfer energy from the inner mitochondrial membrane to adenosine triphosphate (ATP). The “action potential” lesson explains how charged membranes are used to propagate signals along the axons of neurons. These animations serve as valuable resources for any collegiate-level course that describes these important factors. Courses that might employ them include introductory biology, biochemistry, biophysics, cell biology, pharmacology, and physiology.
On the definition of entanglement entropy in lattice gauge theories
NASA Astrophysics Data System (ADS)
Aoki, Sinya; Iritani, Takumi; Nozaki, Masahiro; Numasawa, Tokiro; Shiba, Noburo; Tasaki, Hal
2015-06-01
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the Z N gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the Z N gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.
Characterization of heterocyclic rings through quantum chemical topology.
Griffiths, Mark Z; Popelier, Paul L A
2013-07-22
Five-membered rings are found in a myriad of molecules important in a wide range of areas such as catalysis, nutrition, and drug and agrochemical design. Systematic insight into their largely unexplored chemical space benefits from first principle calculations presented here. This study comprehensively investigates a grand total of 764 different rings, all geometry optimized at the B3LYP/6-311+G(2d,p) level, from the perspective of Quantum Chemical Topology (QCT). For the first time, a 3D space of local topological properties was introduced, in order to characterize rings compactly. This space is called RCP space, after the so-called ring critical point. This space is analogous to BCP space, named after the bond critical point, which compactly and successfully characterizes a chemical bond. The relative positions of the rings in RCP space are determined by the nature of the ring scaffold, such as the heteroatoms within the ring or the number of ?-bonds. The summed atomic QCT charges of the five ring atoms revealed five features (number and type of heteroatom, number of ?-bonds, substituent and substitution site) that dictate a ring's net charge. Each feature independently contributes toward a ring's net charge. Each substituent has its own distinct and systematic effect on the ring's net charge, irrespective of the ring scaffold. Therefore, this work proves the possibility of designing a ring with specific properties by fine-tuning it through manipulation of these five features. PMID:23795608
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.
Loop Variables in Topological Gravity
Y. Bi; J. Gegenberg
1993-07-22
We examine the relationship between covariant and canonical (Ashtekar/Rovelli/Smolin) loop variables in the context of BF type topological field theories in 2+1 and 3+1 dimensions, with respective gauge groups SO(2,1) and SO(3,1). The latter model can be considered as the simplest topological gravity theory in 3+1 dimensions. We carry out the canonical quantization of this model in both the connection and loop representations, for the two spatial topologies $T^3$ and $S^2\\times S^1$.
Topology of Chaotic Mixing Patterns
Jean-Luc Thiffeault; Matthew D. Finn; Emmanuelle Gouillart; Toby Hall
2008-08-26
A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at least a minimum amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.
Color confinement from fluctuating topology
Dmitri E. Kharzeev
2015-09-01
QCD possesses a compact gauge group, and this implies a non-trivial topological structure of the vacuum. In this contribution to the Gribov-85 Memorial volume, we first discuss the origin of Gribov copies and their interpretation in terms of fluctuating topology in the QCD vacuum. We then describe the recent work with E. Levin that links the confinement of gluons and color screening to the fluctuating topology, and discuss implications for spin physics, high energy scattering, and the physics of quark-gluon plasma.
Inexistence of Zeeman's fine topology
Norberto Sainz
2010-03-19
The family of topologies that induce the Euclidean metric space on every time axis and every space axis exhibits no maximal element when partially ordered by the relation ``finer than'', as demonstrated in this article. One conclusion and two reflections emerge and are addressed herein: Conclusion: a. Zeeman's fine topology [1] and G\\"{o}bel's extension to arbitrary spacetimes [2] do not exist. Reflections: a. Both authors' attempts may be classified as type-2 strategies, within the taxonomy of [3]. b. How could these inexistent topologies be used for decades?
Topological mirror symmetry with fluxes
NASA Astrophysics Data System (ADS)
Tomasiello, Alessandro
2005-06-01
Motivated by SU(3) structure compactifications, we show explicitly how to construct half-flat topological mirrors to Calabi-Yau manifolds with NS fluxes. Units of flux are exchanged with torsion factors in the cohomology of the mirror; this is the topological complement of previous differential-geometric mirror rules. The construction modifies explicit SYZ fibrations for compact Calabi-Yaus. The results are of independent interest for SU(3) compactifications. For example one can exhibit explicitly which massive forms should be used for Kaluza-Klein reduction, proving previous conjectures. Formality shows that these forms carry no topological information; this is also confirmed by infrared limits and old classification theorems.
Color confinement from fluctuating topology
Kharzeev, Dmitri E
2015-01-01
QCD possesses a compact gauge group, and this implies a non-trivial topological structure of the vacuum. In this contribution to the Gribov-85 Memorial volume, we first discuss the origin of Gribov copies and their interpretation in terms of fluctuating topology in the QCD vacuum. We then describe the recent work with E. Levin that links the confinement of gluons and color screening to the fluctuating topology, and discuss implications for spin physics, high energy scattering, and the physics of quark-gluon plasma.
Does Zeeman's Fine Topology Exist?
Norberto Sainz
2012-01-23
We work on the family of topologies for the Minkowski manifold M. We partially order this family by inclusion to form the lattice \\Sigma(M), and focus on the sublattice Z of topologies that induce the Euclidean metric space on every time axis and every space axis. We analyze the bounds of Z in the lattice \\Sigma(M), in search for its supremum. Our conclusion --that such a supremum does not belong in Z-- is compared with constructive proofs of existence of the fine topology, defined as the maximum of Z and conceived to play an essential role in contemporary physical theories. Essential mathematical and physical questions arise.
Collapsing Flow Topology Using Area Metrics
Liere, Robert van
Collapsing Flow Topology Using Area Metrics Wim de Leeuw, Robert van Liere Center for Mathematics with the original topology. We apply the collapsing topology technique to a turbulent flow field. Keywords: multi topological information in fluid flows is well known. However, when applied to turbulent flows, the result
THE UNIVERSITY OF MANCHESTER INTRODUCTION TO TOPOLOGY
Lionheart, Bill
MATH31051 Two hours THE UNIVERSITY OF MANCHESTER INTRODUCTION TO TOPOLOGY 20 January 2015 14 by a topology on a set X. (b) Define what is meant by saying that a function f : X Y between topological spaces = { x R2 | 1 |x| 2 } with the usual topology is homeomorphic to the cylinder S1 × [0, 1] R2 × R = R3