Equivariant topological quantum field theory and symmetry protected topological phases

Energy Technology Data Exchange (ETDEWEB)

Kapustin, Anton [Division of Physics, California Institute of Technology,1200 E California Blvd, Pasadena, CA, 91125 (United States); Turzillo, Alex [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794 (United States)

2017-03-01

Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.

Topological quantization of gravitational fields

International Nuclear Information System (INIS)

Patino, Leonardo; Quevedo, Hernando

2005-01-01

We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes values in the Lie algebra of the Lorentz group. This result is generalized to include the case of gauge matter fields in multiple principal fiber bundles. We present several examples of gravitational configurations that include a gravitomagnetic monopole in linearized gravity, the C-energy of cylindrically symmetric fields, the Reissner-Nordstroem and the Kerr-Newman black holes. As a result of the application of the topological quantization procedure, in all the analyzed examples we obtain conditions implying that the parameters entering the metric in each case satisfy certain discretization relationships

Twistor-theoretic approach to topological field theories

International Nuclear Information System (INIS)

Ito, Kei.

1991-12-01

The two-dimensional topological field theory which describes a four-dimensional self-dual space-time (gravitational instanton) as a target space, which we constructed before, is shown to be deeply connected with Penrose's 'twistor theory'. The relations are presented in detail. Thus our theory offers a 'twistor theoretic' approach to topological field theories. (author)

Magnetic Field Topology in Jets

Science.gov (United States)

Gardiner, T. A.; Frank, A.

2000-01-01

We present results on the magnetic field topology in a pulsed radiative. jet. For initially helical magnetic fields and periodic velocity variations, we find that the magnetic field alternates along the, length of the jet from toroidally dominated in the knots to possibly poloidally dominated in the intervening regions.

Vector supersymmetry in topological field theories

International Nuclear Information System (INIS)

Gieres, F.; Grimstrup, J.; Pisar, T.; Schweda, M.

2000-01-01

We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges. (author)

On a characterization of path connected topological fields

OpenAIRE

Caicedo, Xavier; Mantilla-Soler, Guillermo

2017-01-01

The aim of this paper is to give a characterization of path connected topological fields, inspired by the classic Gelfand's correspondence between a compact Hausdorff topological space $X$ and the space of maximal ideals on the ring of real valued continuous functions $C(X,\\mathbb{R})$. More explicitly, our motivation is the following question: What is the essential property of the topological field $F=\\mathbb{R}$ that makes such correspondence valid for all compact Hausdorff spaces? It turns...

A general action for topological quantum field theories

International Nuclear Information System (INIS)

Dayi, O.F.

1989-03-01

Topological field theories can be formulated by beginning from a higher dimensional action. The additional dimension is an unphysical time parameter and the action is the derivative of a functional W with respect to this variable. In the d = 4 case, it produces actions which are shown to give topological quantum field theory after gauge fixing. In d = 3 this action leads to the Hamiltonian, which yields the Floer groups if the additional parameter is treated as physical when W is the pure Chern-Simons action. This W can be used to define a topological quantum field theory in d = 3 by treating the additional parameter as unphysical. The BFV-BRST operator quantization of this theory yields to an enlarged system which has only first class constraints. This is not identical to the previously introduced d = 3 topological quantum field theory, even if it is shown that the latter theory also gives the theory which we began with, after a partial gauge fixing. (author). 18 refs

Quantum transport in topological semimetals under magnetic fields

Science.gov (United States)

Lu, Hai-Zhou; Shen, Shun-Qing

2017-06-01

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.

Anisotropic quantum quench in the presence of frustration or background gauge fields: A probe of bulk currents and topological chiral edge modes

Science.gov (United States)

Killi, Matthew; Trotzky, Stefan; Paramekanti, Arun

2012-12-01

Bosons and fermions, in the presence of frustration or background gauge fields, can form many-body ground states that support equilibrium charge or spin currents. Motivated by the experimental creation of frustration or synthetic gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge-invariant route to probing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge modes in gapped topological states, such as quantum Hall or quantum spin Hall insulators.

Knots, topology and quantum field theories

International Nuclear Information System (INIS)

Lusanna, L.

1989-01-01

The title of the workshop, Knots, Topology and Quantum Field Theory, accurate reflected the topics discussed. There have been important developments in mathematical and quantum field theory in the past few years, which had a large impact on physicist thinking. It is historically unusual and pleasing that these developments are taking place as a result of an intense interaction between mathematical physicists and mathematician. On the one hand, topological concepts and methods are playing an increasingly important lead to novel mathematical concepts: for instance, the study of quantum groups open a new chapter in the deformation theory of Lie algebras. These developments at present will lead to new insights into the theory of elementary particles and their interactions. In essence, the talks dealt with three, broadly defined areas of theoretical physics. One was topological quantum field theories, the other the problem of quantum groups and the third one certain aspects of more traditional field theories, such as, for instance, quantum gravity. These topics, however, are interrelated and the general theme of the workshop defies rigid classification; this was evident from the cross references to be found in almo all the talks

Representation of magnetic fields with toroidal topology in terms of field-line invariants

International Nuclear Information System (INIS)

Lewis, H.R.

1990-01-01

Beginning with Boozer's representation of magnetic fields with toroidal topology [Phys. Fluids 26, 1288 (1983)], a general formalism is presented for the representation of any magnetic field with toroidal topology in terms of field-line invariants. The formalism is an application to the magnetic field case of results developed recently by Lewis et al. (submitted for publication to J. Phys. A) for arbitrary time-dependent Hamiltonian systems with one degree of freedom. Every magnetic field with toroidal topology can be associated with time-dependent Hamiltonian systems with one degree of freedom and every time-dependent Hamiltonian system with one degree of freedom can be associated with magnetic fields with toroidal topology. In the Hamiltonian context, given any particular function I(q,p,t), Lewis et al. derived those Hamiltonians for which I(q,p,t) is an invariant. In addition, for each of those Hamiltonians, they derived a function canonically conjugate to I(q,p,t) that is also an invariant. They applied this result to the case where I(q,p,t) is expressed as a function of two canonically conjugate functions. This general Hamiltonian formalism provides a basis for representing magnetic fields with toroidal topology in terms of field-line invariants. The magnetic fields usually contain plasma with flow and anisotropic pressure. A class of fields with or without rotational symmetry is identified for which there are magnetic surfaces. The formalism is developed for application to the case of vacuum magnetic fields

Gauge-field topology in two dimensions: θ-vacuum, topological phases and composite fields

International Nuclear Information System (INIS)

Ilieva, N.; Pervushin, V.N.

1990-06-01

In the framework of the minimal quantization method, the residual 'longitudinal' vacuum dynamics of the Abelian gauge field, that is described by a new pair of canonical variables, is revealed. This dynamics is shown to give origin to the θ-vacuum, thus providing a field analogy of the Josephson effect. The destructive interference of the topological phases - that the fermion fields are shown to acquire - is considered as a reason for the charge screening in the two-dimensional massless QED. (author). 11 refs

Anomalous resistivity and the evolution of magnetic field topology

Science.gov (United States)

Parker, E. N.

1993-01-01

This paper explores the topological restructuring of a force-free magnetic field caused by the hypothetical sudden onset of a localized region of strong anomalous resistivity. It is shown that the topological complexity increases, with the primitive planar force-free field with straight field lines developing field lines that wrap half a turn around each other, evidently providing a surface of tangential discontinuity in the wraparound region. It is suggested that the topological restructuring contributes to the complexity of the geomagnetic substorm, the aurora, and perhaps some of the flare activity on the sun, or other star, and the Galactic halo.

The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields

Science.gov (United States)

Buchholz, Detlev; Ciolli, Fabio; Ruzzi, Giuseppe; Vasselli, Ezio

2017-02-01

Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated regions, can appear in regular representations of the algebra only if the fields depend non-linearly on the mollifying test functions. On the other hand, examples of regular vacuum representations with non-trivial topological charges are constructed, where the underlying field still satisfies a weakened form of "spacelike linearity". Such representations also appear in the presence of electric currents. The status of topological charges in theories with several types of electromagnetic fields, which appear in the short distance (scaling) limit of asymptotically free non-abelian gauge theories, is also briefly discussed.

On the background independence of two-dimensional topological gravity

Science.gov (United States)

Imbimbo, Camillo

1995-04-01

We formulate two-dimensional topological gravity in a background covariant Lagrangian framework. We derive the Ward identities which characterize the dependence of physical correlators on the background world-sheet metric defining the gauge-slice. We point out the existence of an "anomaly" in Ward identitites involving correlators of observables with higher ghost number. This "anomaly" represents an obstruction for physical correlators to be globally defined forms on moduli space which could be integrated in a background independent way. Starting from the anomalous Ward identities, we derive "descent" equations whose solutions are cocycles of the Lie algebra of the diffeomorphism group with values in the space of local forms on the moduli space. We solve the descent equations and provide explicit formulas for the cocycles, which allow for the definition of background independent integrals of physical correlators on the moduli space.

Topological mass mechanism and exact fields mapping

International Nuclear Information System (INIS)

Amaral, R L P G; Ventura, O S; Buffon, L O; Costa, J V

2006-01-01

We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the other model in closed expressions. These expressions provide the mappings of their actions as well as the mappings of their propagators. For a general class of models in which the topological model becomes the BF model the mappings present arbitrary functions which otherwise are absent for Chern-Simons like actions. This work generalizes the results of (Ventura O S, Amaral R L P G, Costa J V, Buffon L O and Lemes V E R 2004 J. Phys. A: Math. Gen. 37 11711-23) for arbitrary dimensions

The topology of Double Field Theory

Science.gov (United States)

Hassler, Falk

2018-04-01

We describe the doubled space of Double Field Theory as a group manifold G with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so G only captures the topology of the doubled space. Strong Constraint solutions are maximal isotropic submanifold M in G. We construct them and their Generalized Geometry in Double Field Theory on Group Manifolds. In general, G admits different physical subspace M which are Poisson-Lie T-dual to each other. By studying two examples, we reproduce the topology changes induced by T-duality with non-trivial H-flux which were discussed by Bouwknegt, Evslin and Mathai [1].

On topological string theory with Calabi-Yau backgrounds

International Nuclear Information System (INIS)

Haghighat, Babak

2009-01-01

String theory represents a unifying framework for quantum field theory as well as for general relativity combining them into a theory of quantum gravity. The topological string is a subsector of the full string theory capturing physical amplitudes which only depend on the topology of the compactification manifold. Starting with a review of the physical applications of topological string theory we go on to give a detailed description of its theoretical framework and mathematical principles. Having this way provided the grounding for concrete calculations we proceed to solve the theory on three major types of Calabi-Yau manifolds, namely Grassmannian Calabi-Yau manifolds, local Calabi-Yau manifolds, and K3 fibrations. Our method of solution is the integration of the holomorphic anomaly equations and fixing the holomorphic ambiguity by physical boundary conditions. We determine the correct parameterization of the ambiguity and new boundary conditions at various singularity loci in moduli space. Among the main results of this thesis are the tables of degeneracies of BPS states in the appendices and the verification of the correct microscopic entropy interpretation for five dimensional extremal black holes arising from compactifications on Grassmannian Calabi-Yau manifolds. (orig.)

On topological string theory with Calabi-Yau backgrounds

International Nuclear Information System (INIS)

Haghighat, Babak

2010-06-01

String theory represents a unifying framework for quantum field theory as well as for general relativity combining them into a theory of quantum gravity. The topological string is a subsector of the full string theory capturing physical amplitudes which only depend on the topology of the compactification manifold. Starting with a review of the physical applications of topological string theory we go on to give a detailed description of its theoretical framework and mathematical principles. Having this way provided the grounding for concrete calculations we proceed to solve the theory on three major types of Calabi-Yau manifolds, namely Grassmannian Calabi-Yau manifolds, local Calabi-Yau manifolds, and K3 fibrations. Our method of solution is the integration of the holomorphic anomaly equations and fixing the holomorphic ambiguity by physical boundary conditions. We determine the correct parameterization of the ambiguity and new boundary conditions at various singularity loci in moduli space. Among the main results of this thesis are the tables of degeneracies of BPS states in the appendices and the veri cation of the correct microscopic entropy interpretation for five dimensional extremal black holes arising from compactifications on Grassmannian Calabi-Yau manifolds. (orig.)

On topological string theory with Calabi-Yau backgrounds

Energy Technology Data Exchange (ETDEWEB)

Haghighat, Babak

2010-06-15

String theory represents a unifying framework for quantum field theory as well as for general relativity combining them into a theory of quantum gravity. The topological string is a subsector of the full string theory capturing physical amplitudes which only depend on the topology of the compactification manifold. Starting with a review of the physical applications of topological string theory we go on to give a detailed description of its theoretical framework and mathematical principles. Having this way provided the grounding for concrete calculations we proceed to solve the theory on three major types of Calabi-Yau manifolds, namely Grassmannian Calabi-Yau manifolds, local Calabi-Yau manifolds, and K3 fibrations. Our method of solution is the integration of the holomorphic anomaly equations and fixing the holomorphic ambiguity by physical boundary conditions. We determine the correct parameterization of the ambiguity and new boundary conditions at various singularity loci in moduli space. Among the main results of this thesis are the tables of degeneracies of BPS states in the appendices and the veri cation of the correct microscopic entropy interpretation for five dimensional extremal black holes arising from compactifications on Grassmannian Calabi-Yau manifolds. (orig.)

On topological string theory with Calabi-Yau backgrounds

Energy Technology Data Exchange (ETDEWEB)

Haghighat, Babak

2009-10-29

String theory represents a unifying framework for quantum field theory as well as for general relativity combining them into a theory of quantum gravity. The topological string is a subsector of the full string theory capturing physical amplitudes which only depend on the topology of the compactification manifold. Starting with a review of the physical applications of topological string theory we go on to give a detailed description of its theoretical framework and mathematical principles. Having this way provided the grounding for concrete calculations we proceed to solve the theory on three major types of Calabi-Yau manifolds, namely Grassmannian Calabi-Yau manifolds, local Calabi-Yau manifolds, and K3 fibrations. Our method of solution is the integration of the holomorphic anomaly equations and fixing the holomorphic ambiguity by physical boundary conditions. We determine the correct parameterization of the ambiguity and new boundary conditions at various singularity loci in moduli space. Among the main results of this thesis are the tables of degeneracies of BPS states in the appendices and the verification of the correct microscopic entropy interpretation for five dimensional extremal black holes arising from compactifications on Grassmannian Calabi-Yau manifolds. (orig.)

The topology of moduli space and quantum field theory

International Nuclear Information System (INIS)

Montano, D.; Sonnenschein, J.

1989-01-01

We show how an SO(2,1) gauge theory with a fermionic symmetry may be used to describe the topology of the moduli space of curves. The observables of the theory correspond to the generators of the cohomology of moduli space. This is an extension of the topological quantum field theory introduced by Witten to investigate the cohomology of Yang-Mills instanton moduli space. We explore the basic structure of topological quantum field theories, examine a toy U(1) model, and then realize a full theory of moduli space topology. We also discuss why a pure gravity theory, as attempted in previous work, could not succeed. (orig.)

Topological field theory: zero-modes and renormalization

International Nuclear Information System (INIS)

Ouvry, S.; Thompson, G.

1989-09-01

We address the issue of the non-triviality of the observables in various Topological Field Theories by means of the explicit introduction of the zero-modes into the BRST algebra. Supersymmetric quantum mechanics and Topological Yang-Mills theory are dealt with in detail. It is shown that due to the presence of fermionic zero-modes the BRST algebra may be dynamically broken leading to non trivial observables albeit the local cohomology being trivial. However the metric and coupling constant independence of the observables are still valid. A renormalization procedure is given that correctly incorporates the zero-modes. Particular attention is given to the conventional gauge fixing in Topological Yang-Mills theories, with emphasis on the geometrical character of the fields and their role in the non-triviality of the observables

Topological gravity from a transgression gauge field theory

International Nuclear Information System (INIS)

Merino, N.; Perez, A.; Salgado, P.; Valdivia, O.

2010-01-01

It is shown that a topological action for gravity in even dimensions can be obtained from a gravity theory whose Lagrangian is given by a transgression form invariant under the Poincare group. The field φ a , which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d-1,1).

Topological phases in a three-dimensional topological insulator with a time-reversal invariant external field

International Nuclear Information System (INIS)

Guo, Xiaoyong; Ren, Xiaobin; Wang, Gangzhi; Peng, Jie

2014-01-01

We investigate the impact of a time-reversal invariant external field on the topological phases of a three-dimensional (3D) topological insulator. By taking the momentum k z as a parameter, we calculate the spin-Chern number analytically. It is shown that both the quantum spin Hall phase and the integer quantum Hall phase can be realized in our system. When the strength of the external field is varied, a series of topological phase transitions occurs with the closing of the energy gap or the spin-spectrum gap. In a tight-binding form, the surface modes are discussed numerically to confirm the analytically results. (paper)

Topological magnetoelectric effects in microwave far-field radiation

Energy Technology Data Exchange (ETDEWEB)

Berezin, M.; Kamenetskii, E. O.; Shavit, R. [Microwave Magnetic Laboratory, Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva (Israel)

2016-07-21

Similar to electromagnetism, described by the Maxwell equations, the physics of magnetoelectric (ME) phenomena deals with the fundamental problem of the relationship between electric and magnetic fields. Despite a formal resemblance between the two notions, they concern effects of different natures. In general, ME-coupling effects manifest in numerous macroscopic phenomena in solids with space and time symmetry breakings. Recently, it was shown that the near fields in the proximity of a small ferrite particle with magnetic-dipolar-mode (MDM) oscillations have the space and time symmetry breakings and the topological properties of these fields are different from the topological properties of the free-space electromagnetic fields. Such MDM-originated fields—called magnetoelectric (ME) fields—carry both spin and orbital angular momenta. They are characterized by power-flow vortices and non-zero helicity. In this paper, we report on observation of the topological ME effects in far-field microwave radiation based on a small microwave antenna with a MDM ferrite resonator. We show that the microwave far-field radiation can be manifested with a torsion structure where an angle between the electric and magnetic field vectors varies. We discuss the question on observation of the regions of localized ME energy in far-field microwave radiation.

Singular trajectories: space-time domain topology of developing speckle fields

Science.gov (United States)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

How to detect colour field topologies in hadronic interactions

International Nuclear Information System (INIS)

Andersson, B.; Bengtsson, H.U.

1987-06-01

We discuss the different colour field topologies of QCD interactions, and demonstrate how the existence of two different colour topologies in qg scattering will lead to an experimentally observable asymmetry in the production of K + K - pairs in hadron-hadron collisions. (authors)

Quantum field theory in topology changing spacetimes; Quantenfeldtheorie auf Raumzeiten mit Topologieaenderungen

Energy Technology Data Exchange (ETDEWEB)

Bauer, W.

2007-03-15

The goal of this diploma thesis is to present an overview of how to reduce the problem of topology change of general spacetimes to the investigation of elementary cobordisms. In the following we investigate the possibility to construct quantum fields on elementary cobordisms, in particular we discuss the trousers topology. Trying to avoid the problems occuring at spacetimes with instant topology change we use a model for simulating topology change. We construct the algebra of observables for a free scalar field with the algebraic approach to quantum field theory. Therefore we determine a fundamental solution of the eld equation. (orig.)

Abelian Chern endash Simons theory. I. A topological quantum field theory

International Nuclear Information System (INIS)

Manoliu, M.

1998-01-01

We give a construction of the Abelian Chern endash Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern endash Simons theory [J. Diff. Geom. 33, 787 endash 902 (1991); Topology 32, 509 endash 529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans 68, 175 endash 186 (1989)]. copyright 1998 American Institute of Physics

Planck 2015 results. XVIII. Background geometry & topology

CERN Document Server

Ade, P.A.R.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; De Rosa, A.; De Zotti, G.; Delabrouille, J.; Désert, F.X.; Diego, J.M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T.A.; Eriksen, H.K.; Feeney, S.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T.S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P.B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P.M.; Macías-Pérez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P.G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McEwen, J.D.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Nørgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pogosyan, D.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prézeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Tent, F. Van; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; Yvon, D.; Zacchei, A.; Zonca, A.

2016-01-01

Full-sky CMB maps from the 2015 Planck release allow us to detect departures from global isotropy on the largest scales. We present the first searches using CMB polarization for correlations induced by a non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance $\\chi_{rec}$). We specialize to flat spaces with toroidal and slab topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology at a scale below the diameter of the last scattering surface. The limits on the radius $R_i$ of the largest sphere inscribed in the topological domain (at log-likelihood-ratio $\\Delta\\ln{L}>-5$ relative to a simply-connected flat Planck best-fit model) are $R_i>0.97\\chi_{rec}$ for the cubic torus and $R_i>0.56\\chi_{rec}$ for the slab. The limit for the cubic torus from the matched-circles search is numerically equivalent, $R_i>0.97\\chi_{rec}...

Nobel Lecture: Topological quantum matter*

Science.gov (United States)

Haldane, F. Duncan M.

2017-10-01

Nobel Lecture, presented December 8, 2016, Aula Magna, Stockholm University. I will describe the history and background of three discoveries cited in this Nobel Prize: The "TKNN" topological formula for the integer quantum Hall effect found by David Thouless and collaborators, the Chern insulator or quantum anomalous Hall effect, and its role in the later discovery of time-reversal-invariant topological insulators, and the unexpected topological spin-liquid state of the spin-1 quantum antiferromagnetic chain, which provided an initial example of topological quantum matter. I will summarize how these early beginnings have led to the exciting, and currently extremely active, field of "topological matter."

Topological vortices in gauge models of graphene

Science.gov (United States)

Zhang, Xin-Hui; Li, Xueqin; Hao, Jin-Bo

2018-06-01

Graphene-like structure possessing the topological vortices and knots, and the magnetic flux of the vortices configuration quantized, are proposed in this paper. The topological charges of the vortices are characterized by Hopf indices and Brower degrees. The Abelian background field action (BF action) is a topological invariant for the knot family, which is just the total sum of all the self-linking numbers and all the linking numbers. Flux quantization opens the possibility of having Aharonov-Bohm-type effects in graphene without external electromagnetic field.

Monoidal categories and topological field theory

CERN Document Server

Turaev, Vladimir

2017-01-01

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery gr...

Topological defects in open string field theory

Science.gov (United States)

Kojita, Toshiko; Maccaferri, Carlo; Masuda, Toru; Schnabl, Martin

2018-04-01

We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism.

Lattice formulation of a two-dimensional topological field theory

International Nuclear Information System (INIS)

Ohta, Kazutoshi; Takimi, Tomohisa

2007-01-01

We investigate an integrable property and the observables of 2-dimensional N=(4,4) topological field theory defined on a discrete lattice by using the 'orbifolding' and 'deconstruction' methods. We show that our lattice model is integrable and, for this reason, the partition function reduces to matrix integrals of scalar fields on the lattice sites. We elucidate meaningful differences between a discrete lattice and a differentiable manifold. This is important for studying topological quantities on a lattice. We also propose a new construction of N=(2,2) supersymmetric lattice theory, which is realized through a suitable truncation of scalar fields from the N=(4,4) theory. (author)

Topological field theories and quantum mechanics on commutative space

International Nuclear Information System (INIS)

Lefrancois, M.

2005-12-01

In particle physics, the Standard Model describes the interactions between fundamental particles. However, it was not able till now to unify quantum field theory and general relativity. This thesis focuses on two different unification approaches, though they might show some compatibility: topological field theories and quantum mechanics on non-commutative space. Topological field theories have been introduced some twenty years ago and have a very strong link to mathematics: their observables are topological invariants of the manifold they are defined on. In this thesis, we first give interest to topological Yang-Mills. We develop a superspace formalism and give a systematic method for the determination of the observables. This approach allows, once projected on a particular super gauge (of Wess-Zumino type), to recover the existing results but it also gives a generalisation to the case of an unspecified super-gauge. We have then be able to show that the up-to-now known observables correspond to the most general form of the solutions. This superspace formalism can be applied to more complex models; the case of topological gravity is given here in example. Quantum mechanics on noncommutative space provides an extension of the Heisenberg algebra of ordinary quantum mechanics. What differs here is that the components of the position or momentum operators do not commute with each other anymore. This implies to introduce a fundamental length. The second part of this thesis focuses on the description of the commutation algebra. Applications are made to low-dimensional quantum systems (Landau system, harmonic oscillator...) and to supersymmetric systems. (author)

Magnetic-field induced semimetal in topological crystalline insulator thin films

International Nuclear Information System (INIS)

Ezawa, Motohiko

2015-01-01

We investigate electromagnetic properties of a topological crystalline insulator (TCI) thin film under external electromagnetic fields. The TCI thin film is a topological insulator indexed by the mirror-Chern number. It is demonstrated that the gap closes together with the emergence of a pair of gapless cones carrying opposite chirarities by applying in-plane magnetic field. A pair of gapless points have opposite vortex numbers. This is a reminiscence of a pair of Weyl cones in 3D Weyl semimetal. We thus present an a magnetic-field induced semimetal–semiconductor transition in 2D material. This is a giant-magnetoresistance, where resistivity is controlled by magnetic field. Perpendicular electric field is found to shift the gapless points and also renormalize the Fermi velocity in the direction of the in-plane magnetic field. - Highlights: • The band structure of topological crystalline insulator thin films can be controlled by applying in-plane magnetic field. • At the gap closing magnetic field, a pair of gapless cones carrying opposite chirarities emerge. • A pair of gapless points have opposite vortex numbers. • This is a reminiscence of a pair of Weyl cones in 3D Weyl semimetal. • A magnetic-field induced semimetal–semiconductor transition occurs in 2D material

Magnetic-field induced semimetal in topological crystalline insulator thin films

Energy Technology Data Exchange (ETDEWEB)

Ezawa, Motohiko, E-mail: ezawa@ap.t.u-tokyo.ac.jp

2015-06-19

We investigate electromagnetic properties of a topological crystalline insulator (TCI) thin film under external electromagnetic fields. The TCI thin film is a topological insulator indexed by the mirror-Chern number. It is demonstrated that the gap closes together with the emergence of a pair of gapless cones carrying opposite chirarities by applying in-plane magnetic field. A pair of gapless points have opposite vortex numbers. This is a reminiscence of a pair of Weyl cones in 3D Weyl semimetal. We thus present an a magnetic-field induced semimetal–semiconductor transition in 2D material. This is a giant-magnetoresistance, where resistivity is controlled by magnetic field. Perpendicular electric field is found to shift the gapless points and also renormalize the Fermi velocity in the direction of the in-plane magnetic field. - Highlights: • The band structure of topological crystalline insulator thin films can be controlled by applying in-plane magnetic field. • At the gap closing magnetic field, a pair of gapless cones carrying opposite chirarities emerge. • A pair of gapless points have opposite vortex numbers. • This is a reminiscence of a pair of Weyl cones in 3D Weyl semimetal. • A magnetic-field induced semimetal–semiconductor transition occurs in 2D material.

Topology of magnetic fields in particle physics, implications on the quark model

Energy Technology Data Exchange (ETDEWEB)

Jehle, H.

1977-01-01

The flux-loop model of quarks is considered covering electomagnetic gauge invariance, flux quantization, topological conditions for the magnetic field, the extended source model, the electric field, linkage of loop forms, topology and motion of flux loop forms, coalial loops of hadrons having weak interactions, magnetic moments of hadrons, strong interactions, some remarks about string models, and the implications of he topological quark model on the ground and excited states of mesons. 80 references. (JFP)

A Relation Between Topological Quantum Field Theory and the Kodama State

OpenAIRE

Oda, Ichiro

2003-01-01

We study a relation between topological quantum field theory and the Kodama (Chern-Simons) state. It is shown that the Kodama (Chern-Simons) state describes a topological state with unbroken diffeomorphism invariance in Yang-Mills theory and Einstein's general relativity in four dimensions. We give a clear explanation of "why" such a topological state exists.

Reconfigurable topological photonic crystal

Science.gov (United States)

Shalaev, Mikhail I.; Desnavi, Sameerah; Walasik, Wiktor; Litchinitser, Natalia M.

2018-02-01

Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topology of the band structure. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators are topologically protected from scattering due to structural defects and disorders. Recently, it was shown that photonic crystals (PCs) can serve as a platform for realizing a scatter-free propagation of light waves. In conventional PCs, imperfections, structural disorders, and surface roughness lead to significant losses. The breakthrough in overcoming these problems is likely to come from the synergy of the topological PCs and silicon-based photonics technology that enables high integration density, lossless propagation, and immunity to fabrication imperfections. For many applications, reconfigurability and capability to control the propagation of these non-trivial photonic edge states is essential. One way to facilitate such dynamic control is to use liquid crystals (LCs), which allow to modify the refractive index with external electric field. Here, we demonstrate dynamic control of topological edge states by modifying the refractive index of a LC background medium. Background index is changed depending on the orientation of a LC, while preserving the topology of the system. This results in a change of the spectral position of the photonic bandgap and the topological edge states. The proposed concept might be implemented using conventional semiconductor technology, and can be used for robust energy transport in integrated photonic devices, all-optical circuity, and optical communication systems.

Low-lying eigenmodes of the Wilson-Dirac operator and correlations with topological objects

International Nuclear Information System (INIS)

Kusterer, Daniel-Jens; Hedditch, John; Kamleh, Waseem; Leinweber, D.B.; Williams, Anthony G.

2002-01-01

The probability density of low-lying eigenvectors of the hermitian Wilson-Dirac operator H(κ)=γ 5 D W (κ) is examined. Comparisons in position and size between eigenvectors, topological charge and action density are made. We do this for standard Monte-Carlo generated SU(3) background fields and for single instanton background fields. Both hot and cooled SU(3) background fields are considered. An instanton model is fitted to eigenmodes and topological charge density and the sizes and positions of these are compared

Strings, conformal fields and topology

International Nuclear Information System (INIS)

Kaku, Michio

1991-01-01

String Theory has advanced at an astonishing pace in the last few years, and this book aims to acquaint the reader with the most active topics of research in the field. Building on the foundations laid in his Introduction to Superstrings, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, the non-polynominal closed string field theory, matrix models, and topological field theory. Several chapters review the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum. The book conveys the vitality of current research in string theory and places readers at its forefront. (orig.) With 40 figs. in 50 parts

Localization and diagonalization. A review of functional integral techniques for low-dimensional gauge theories and topological field theories

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1995-01-01

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory. (author). 83 refs

Supergravity and Yang-Mills theories as generalized topological fields with constraints

International Nuclear Information System (INIS)

Ling Yi; Tung Rohsuan; Guo Hanying

2004-01-01

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand

Topological insulators and topological superconductors

CERN Document Server

Bernevig, Andrei B

2013-01-01

This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topolo...

Orbifold line topology and the cosmic microwave background

Energy Technology Data Exchange (ETDEWEB)

Rathaus, Ben; Ben-David, Assaf; Itzhaki, Nissan, E-mail: ben.rathaus@gmail.com, E-mail: bd.assaf@gmail.com, E-mail: nitzhaki@post.tau.ac.il [Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978 (Israel)

2013-10-01

We extend our study of a universe with a non-classical stringy topology, and consider an orbifold line topology, R × R{sup 2}/Z{sub p}. This topology has a fixed line and identifies each point in space with p−1 other points. An observable imprint of an orbifold line on the CMB is the appearance of up to (p−1)/2 pairs of matching circles. Searching the WMAP data for matching circles, we can rule out an orbifold line topology with p up to 10, except for p = 8. While the significance of the peak at p = 8 varies between data releases of WMAP, it does not appear in Planck data, enabling us to rule out p = 8 as well.

Random fields, topology, and the Imry-Ma argument.

Science.gov (United States)

Proctor, Thomas C; Garanin, Dmitry A; Chudnovsky, Eugene M

2014-03-07

We consider an n-component fixed-length order parameter interacting with a weak random field in d=1, 2, 3 dimensions. Relaxation from the initially ordered state and spin-spin correlation functions are studied on lattices containing hundreds of millions of sites. At n ≤ d the presence of topological defects leads to strong metastability and glassy behavior, with the final state depending on the initial condition. At n=d+1, when topological structures are nonsingular, the system possesses a weak metastability. At n>d+1, when topological objects are absent, the final, lowest-energy state is independent of the initial condition. It is characterized by the exponential decay of correlations that agrees quantitatively with the theory based upon the Imry-Ma argument.

Microwave magnetoelectric fields: An analytical study of topological characteristics

Energy Technology Data Exchange (ETDEWEB)

Joffe, R., E-mail: ioffr1@gmail.com [Microwave Magnetic Laboratory, Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva (Israel); Department of Electrical and Electronics Engineering, Shamoon College of Engineering, Beer Sheva (Israel); Shavit, R.; Kamenetskii, E.O. [Microwave Magnetic Laboratory, Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva (Israel)

2015-10-15

The near fields originated from a small quasi-two-dimensional ferrite disk with magnetic-dipolar-mode (MDM) oscillations are the fields with broken dual (electric-magnetic) symmetry. Numerical studies show that such fields – called the magnetoelectric (ME) fields – are distinguished by the power-flow vortices and helicity parameters (E.O. Kamenetskii, R. Joffe, R. Shavit, Phys. Rev. E 87 (2013) 023201). These numerical studies can well explain recent experimental results with MDM ferrite disks. In the present paper, we obtain analytically topological characteristics of the ME-field modes. For this purpose, we used a method of successive approximations. In the second approximation we take into account the influence of the edge regions of an open ferrite disk, which are excluded in the first-approximation solving of the magnetostatic (MS) spectral problem. Based on the analytical method, we obtain a “pure” structure of the electric and magnetic fields outside the MDM ferrite disk. The analytical studies can display some fundamental features that are non-observable in the numerical results. While in numerical investigations, one cannot separate the ME fields from the external electromagnetic (EM) radiation, the present theoretical analysis allows clearly distinguish the eigen topological structure of the ME fields. Importantly, this ME-field structure gives evidence for certain phenomena that can be related to the Tellegen and bianisotropic coupling effects. We discuss the question whether the MDM ferrite disk can exhibit properties of the cross magnetoelectric polarizabilities. - Highlights: • We obtain analytically topological characteristics of the ME-field modes. • We take into account the influence of the edge regions of an open ferrite disk. • We obtain a “pure” structure of the electromagnetic fields outside the ferrite disk. • Analytical studies show features that are non-observable in the numerical results. • ME-field gives evidence for

Microwave magnetoelectric fields: An analytical study of topological characteristics

International Nuclear Information System (INIS)

Joffe, R.; Shavit, R.; Kamenetskii, E.O.

2015-01-01

The near fields originated from a small quasi-two-dimensional ferrite disk with magnetic-dipolar-mode (MDM) oscillations are the fields with broken dual (electric-magnetic) symmetry. Numerical studies show that such fields – called the magnetoelectric (ME) fields – are distinguished by the power-flow vortices and helicity parameters (E.O. Kamenetskii, R. Joffe, R. Shavit, Phys. Rev. E 87 (2013) 023201). These numerical studies can well explain recent experimental results with MDM ferrite disks. In the present paper, we obtain analytically topological characteristics of the ME-field modes. For this purpose, we used a method of successive approximations. In the second approximation we take into account the influence of the edge regions of an open ferrite disk, which are excluded in the first-approximation solving of the magnetostatic (MS) spectral problem. Based on the analytical method, we obtain a “pure” structure of the electric and magnetic fields outside the MDM ferrite disk. The analytical studies can display some fundamental features that are non-observable in the numerical results. While in numerical investigations, one cannot separate the ME fields from the external electromagnetic (EM) radiation, the present theoretical analysis allows clearly distinguish the eigen topological structure of the ME fields. Importantly, this ME-field structure gives evidence for certain phenomena that can be related to the Tellegen and bianisotropic coupling effects. We discuss the question whether the MDM ferrite disk can exhibit properties of the cross magnetoelectric polarizabilities. - Highlights: • We obtain analytically topological characteristics of the ME-field modes. • We take into account the influence of the edge regions of an open ferrite disk. • We obtain a “pure” structure of the electromagnetic fields outside the ferrite disk. • Analytical studies show features that are non-observable in the numerical results. • ME-field gives evidence for

Lattice topological field theory on nonorientable surfaces

International Nuclear Information System (INIS)

Karimipour, V.; Mostafazadeh, A.

1997-01-01

The lattice definition of the two-dimensional topological quantum field theory [Fukuma et al., Commun. Math. Phys. 161, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that there is a one-to-one correspondence between real associative *-algebras and the topological state sum invariants defined on such surfaces. The partition and n-point functions on all two-dimensional surfaces (connected sums of the Klein bottle or projective plane and g-tori) are defined and computed for arbitrary *-algebras in general, and for the group ring A=R[G] of discrete groups G, in particular. copyright 1997 American Institute of Physics

Topology optimization of nanoparticles for localized electromagnetic field enhancement

DEFF Research Database (Denmark)

Christiansen, Rasmus Ellebæk; Vester-Petersen, Joakim; Madsen, Søren Peder

2017-01-01

We consider the design of individual and periodic arrangements of metal or semiconductor nanoparticles for localized electromagnetic field enhancement utilizing a topology optimization based numerical framework as the design tool. We aim at maximizing a function of the electromagnetic field...

Opening the cusp. [using magnetic field topology

Science.gov (United States)

Crooker, N. U.; Toffoletto, F. R.; Gussenhoven, M. S.

1991-01-01

This paper discusses the magnetic field topology (determined by the superposition of dipole, image, and uniform fields) for mapping the cusp to the ionosphere. The model results are compared to both new and published observations and are then used to map the footprint of a flux transfer event caused by a time variation in the merging rate. It is shown that the cusp geometry distorts the field lines mapped from the magnetopause to yield footprints with dawn and dusk protrusions into the region of closed magnetic flux.

Topological Methods for Visualization

Energy Technology Data Exchange (ETDEWEB)

Berres, Anne Sabine [Los Alamos National Lab. (LANL), Los Alamos, NM (United Stat

2016-04-07

This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.

Topological geons with self-gravitating phantom scalar field

Science.gov (United States)

Kratovitch, P. V.; Potashov, I. M.; Tchemarina, Ju V.; Tsirulev, A. N.

2017-12-01

A topological geon is the quotient manifold M/Z 2 where M is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically at solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.

Protected gates for topological quantum field theories

International Nuclear Information System (INIS)

Beverland, Michael E.; Pastawski, Fernando; Preskill, John; Buerschaper, Oliver; Koenig, Robert; Sijher, Sumit

2016-01-01

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group

Representation and display of vector field topology in fluid flow data sets

Science.gov (United States)

Helman, James; Hesselink, Lambertus

1989-01-01

The visualization of physical processes in general and of vector fields in particular is discussed. An approach to visualizing flow topology that is based on the physics and mathematics underlying the physical phenomenon is presented. It involves determining critical points in the flow where the velocity vector vanishes. The critical points, connected by principal lines or planes, determine the topology of the flow. The complexity of the data is reduced without sacrificing the quantitative nature of the data set. By reducing the original vector field to a set of critical points and their connections, a representation of the topology of a two-dimensional vector field that is much smaller than the original data set but retains with full precision the information pertinent to the flow topology is obtained. This representation can be displayed as a set of points and tangent curves or as a graph. Analysis (including algorithms), display, interaction, and implementation aspects are discussed.

Topological and statistical properties of nonlinear force-free fields

Science.gov (United States)

Mangalam, A.; Prasad, A.

2018-01-01

We use our semi-analytic solution of the nonlinear force-free field equation to construct three-dimensional magnetic fields that are applicable to the solar corona and study their statistical properties for estimating the degree of braiding exhibited by these fields. We present a new formula for calculating the winding number and compare it with the formula for the crossing number. The comparison is shown for a toy model of two helices and for realistic cases of nonlinear force-free fields; conceptually the formulae are nearly the same but the resulting distributions calculated for a given topology can be different. We also calculate linkages, which are useful topological quantities that are independent measures of the contribution of magnetic braiding to the total free energy and relative helicity of the field. Finally, we derive new analytical bounds for the free energy and relative helicity for the field configurations in terms of the linking number. These bounds will be of utility in estimating the braided energy available for nano-flares or for eruptions.

Novel topological effects in dense QCD in a magnetic field

Science.gov (United States)

Ferrer, E. J.; de la Incera, V.

2018-06-01

We study the electromagnetic properties of dense QCD in the so-called Magnetic Dual Chiral Density Wave phase. This inhomogeneous phase exhibits a nontrivial topology that comes from the fermion sector due to the asymmetry of the lowest Landau level modes. The nontrivial topology manifests in the electromagnetic effective action via a chiral anomaly term θFμνF˜μν, with a dynamic axion field θ given by the phase of the Dual Chiral Density Wave condensate. The coupling of the axion with the electromagnetic field leads to several macroscopic effects that include, among others, an anomalous, nondissipative Hall current, an anomalous electric charge, magnetoelectricity, and the formation of a hybridized propagating mode known as an axion polariton. Connection to topological insulators and Weyls semimetals, as well as possible implications for heavy-ion collisions and neutron stars are all highlighted.

Lateral phase drift of the topological charge density in stochastic optical fields

CSIR Research Space (South Africa)

Roux, FS

2012-03-01

Full Text Available The statistical distributions of optical vortices or topological charge in stochastic optical fields can be inhomogeneous in both transverse directions. Such two-dimensional inhomogeneous vortex or topological charge distributions evolve in a...

At technique for visualizing electrostatic fields based on their topological structures

International Nuclear Information System (INIS)

Handa, Susumu

2004-01-01

In molecular science, visualization techniques based on computer graphics are now well established as a tool to interpret simulation results, since molecules are complicated in the structures and mutual interactions. As a probe to study such molecular interactions, electrostatic fields are considered to be useful. However, since they are given as 3D vector fields having complicated distributions, conventional drawing techniques are inadequate. In this article, a new approach based on topological structures in vector fields is presented to visualize the electrostatic fields of molecules. The scheme is to select regions of interest only from the topological structures of the fields. An example in applications to chemical reactions of an amino acid complex is presented to show how the scheme is used. (author)

Topological study of magnetic field near a neutral point

International Nuclear Information System (INIS)

Fukao, Shoichiro; Ugai, Masayuki; Tsuda, Takao.

1975-01-01

Configuration of magnetic fields near a neutral point is re-examined by a topological analysis. The so-called X-and 0-type magnetic fields respectively occupy their own seat in our classified table. Then the existence of the spiral and node types of configuration will be shown by the analysis. (auth.)

Searching for stringy topologies in the cosmic microwave background

International Nuclear Information System (INIS)

Ben-David, Assaf; Rathaus, Ben; Itzhaki, Nissan

2012-01-01

We consider a universe with a non-classical stringy topology that has fixed points. We concentrate on the simplest example, an orbifold point, and study its observable imprints on the cosmic microwave background (CMB). We show that an orbifold preserves the Gaussian nature of the temperature fluctuations, yet modifies the angular correlation function. A direct signature of an orbifold is a single circle in the CMB that is invariant under rotation by 180°. Searching the 7-year ILC map of WMAP, we find one candidate circle with high statistical significance. However, a closer look reveals that the temperature profile does not fit an orbifold. We place a lower bound on the distance to an orbifold point at ∼ 85% of the distance to the surface of last scattering

Searching for stringy topologies in the cosmic microwave background

Energy Technology Data Exchange (ETDEWEB)

Ben-David, Assaf; Rathaus, Ben; Itzhaki, Nissan, E-mail: bd.assaf@gmail.com, E-mail: ben.rathaus@gmail.com, E-mail: nitzhaki@post.tau.ac.il [Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, 69978 (Israel)

2012-11-01

We consider a universe with a non-classical stringy topology that has fixed points. We concentrate on the simplest example, an orbifold point, and study its observable imprints on the cosmic microwave background (CMB). We show that an orbifold preserves the Gaussian nature of the temperature fluctuations, yet modifies the angular correlation function. A direct signature of an orbifold is a single circle in the CMB that is invariant under rotation by 180°. Searching the 7-year ILC map of WMAP, we find one candidate circle with high statistical significance. However, a closer look reveals that the temperature profile does not fit an orbifold. We place a lower bound on the distance to an orbifold point at ∼ 85% of the distance to the surface of last scattering.

Topological vector spaces and distributions

CERN Document Server

Horvath, John

2012-01-01

""The most readable introduction to the theory of vector spaces available in English and possibly any other language.""-J. L. B. Cooper, MathSciNet ReviewMathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.The precise exposition o

Topological events on the lines of circular polarization in nonparaxial vector optical fields.

Science.gov (United States)

Freund, Isaac

2017-02-01

In nonparaxial vector optical fields, the following topological events are shown to occur in apparent violation of charge conservation: as one translates the observation plane along a line of circular polarization (a C line), the points on the line (C points) are seen to change not only the signs of their topological charges, but also their handedness, and, at turning points on the line, paired C points with the same topological charge and opposite handedness are seen to nucleate. These counter-intuitive events cannot occur in paraxial fields.

A Robust Algorithm to Determine the Topology of Space from the Cosmic Microwave Background Radiation

OpenAIRE

Weeks, Jeffrey R.

2001-01-01

Satellite measurements of the cosmic microwave back-ground radiation will soon provide an opportunity to test whether the universe is multiply connected. This paper presents a new algorithm for deducing the topology of the universe from the microwave background data. Unlike an older algorithm, the new algorithm gives the curvature of space and the radius of the last scattering surface as outputs, rather than requiring them as inputs. The new algorithm is also more tolerant of erro...

Topological currents in neutron stars: kicks, precession, toroidal fields, and magnetic helicity

International Nuclear Information System (INIS)

Charbonneau, James; Zhitnitsky, Ariel

2010-01-01

The effects of anomalies in high density QCD are striking. We consider a direct application of one of these effects, namely topological currents, on the physics of neutron stars. All the elements required for topological currents are present in neutron stars: degenerate matter, large magnetic fields, and parity violating processes. These conditions lead to the creation of vector currents capable of carrying momentum and inducing magnetic fields. We estimate the size of these currents for many representative states of dense matter in the neutron star and argue that they could be responsible for the large proper motion of neutron stars (kicks), the toroidal magnetic field and finite magnetic helicity needed for stability of the poloidal field, and the resolution of the conflict between type-II superconductivity and precession. Though these observational effects appear unrelated, they likely originate from the same physics — they are all P-odd phenomena that stem from a topological current generated by parity violation

Klein Topological Field Theories from Group Representations

Directory of Open Access Journals (Sweden)

Sergey A. Loktev

2011-07-01

Full Text Available We show that any complex (respectively real representation of finite group naturally generates a open-closed (respectively Klein topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.

Open and Closed String field theory interpreted in classical Algebraic Topology

OpenAIRE

Sullivan, Dennis

2003-01-01

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.

Topological sensitivity based far-field detection of elastic inclusions

Directory of Open Access Journals (Sweden)

Tasawar Abbas

2018-03-01

Full Text Available The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A L2-cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion. 2000 MSC: 35R30, 35L05, 74B05, 47A52, 65J20, Keywords: Inverse elastic scattering, Elasticity imaging, Topological derivative, Resolution analysis, Stability analysis

EFFECTS OF FIELD-LINE TOPOLOGY ON ENERGY PROPAGATION IN THE CORONA

Energy Technology Data Exchange (ETDEWEB)

Candelaresi, S.; Pontin, D. I.; Hornig, G. [Division of Mathematics, University of Dundee, Dundee, DD1 4HN (United Kingdom)

2016-12-01

We study the effect of photospheric footpoint motions on magnetic field structures containing magnetic nulls. The footpoint motions are prescribed on the photospheric boundary as a velocity field that entangles the magnetic field. We investigate the propagation of the injected energy, the conversion of energy, emergence of current layers, and other consequences of the nontrivial magnetic field topology in this situation. These boundary motions lead initially to an increase in magnetic and kinetic energy. Following this, the energy input from the photosphere is partially dissipated and partially transported out of the domain through the Poynting flux. The presence of separatrix layers and magnetic null points fundamentally alters the propagation behavior of disturbances from the photosphere into the corona. Depending on the field-line topology close to the photosphere, the energy is either trapped or free to propagate into the corona.

Non-perturbative background field calculations

International Nuclear Information System (INIS)

Stephens, C.R.; Department of Physics, University of Utah, Salt Lake City, Utah 84112)

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation: perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation. copyright 1988 Academic Press, Inc

Non-perturbative background field calculations

Science.gov (United States)

Stephens, C. R.

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

Planck 2015 results. XVIII. Background geometry and topology of the Universe

Science.gov (United States)

Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H. C.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Feeney, S.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A. A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J. E.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T. S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C. R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P. G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McEwen, J. D.; McGehee, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H. V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pogosyan, D.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Spencer, L. D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, F.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; Wehus, I. K.; Yvon, D.; Zacchei, A.; Zonca, A.

2016-09-01

Maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality full-sky view of the surface of last scattering available to date. This enables us to detect possible departures from a globally isotropic cosmology. We present the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χrec), both via a direct scan for matched circular patterns at the intersections and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology with a scale below the diameter of the last-scattering surface. The limits on the radius ℛI of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Δlnℒ > -5 relative to a simply-connected flat Planck best-fit model) are: ℛI > 0.97 χrec for the T3 cubic torus; and ℛI > 0.56 χrec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, ℛI > 0.97 χrec at 99% confidence level from polarization data alone. We also perform a Bayesian search for an anisotropic global Bianchi VIIh geometry. In the non-physical setting, where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of log-evidence. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to the Planck data requires an amplitude of -0.10 ± 0.04 compared to the value of + 1 if the

Planck 2015 results: XVIII. Background geometry and topology of the Universe

International Nuclear Information System (INIS)

Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Ashdown, M.; Aumont, J.

2016-01-01

We report that maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality full-sky view of the surface of last scattering available to date. This enables us to detect possible departures from a globally isotropic cosmology. We present the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χ rec ), both via a direct scan for matched circular patterns at the intersections and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology with a scale below the diameter of the last-scattering surface. The limits on the radius R i of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio ΔlnL > -5 relative to a simply-connected flat Planck best-fit model) are: R i > 0.97 χ rec for the T3 cubic torus; and R i > 0.56 χ rec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, R i > 0.97 χ rec at 99% confidence level from polarization data alone. We also perform a Bayesian search for an anisotropic global Bianchi VII h geometry. In the non-physical setting, where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of log-evidence. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to the Planck data requires an amplitude of -0.10 ± 0.04 compared to the

Discrete gravity as a topological field theorywith light-like curvature defects

Energy Technology Data Exchange (ETDEWEB)

Wieland, Wolfgang [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada)

2017-05-29

I present a model of discrete gravity as a topological field theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a number of intersecting null surfaces. At these null surfaces, the gravitational field can be singular, representing a curvature defect propagating at the speed of light. The underlying action is local and it is studied in both its Lagrangian and Hamiltonian formulation. The canonically conjugate variables on the null surfaces are a spinor and a spinor-valued two-surface density, which are coupled to a topological field theory for the Lorentz connection in the bulk. I discuss the relevance of the model for non-perturbative approaches to quantum gravity, such as loop quantum gravity, where similar variables have recently appeared as well.

One-and two-dimensional topological charge distributions in stochastic optical fields

CSIR Research Space (South Africa)

Roux, FS

2011-06-01

Full Text Available The presentation on topological charge distributions in stochastic optical fields concludes that by using a combination of speckle fields one can produce inhomogeneous vortex distributions that allow both analytical calculations and numerical...

Imprints of spherical nontrivial topologies on the cosmic microwave background.

Science.gov (United States)

Niarchou, Anastasia; Jaffe, Andrew

2007-08-24

The apparent low power in the cosmic microwave background (CMB) temperature anisotropy power spectrum derived from the Wilkinson Microwave Anisotropy Probe motivated us to consider the possibility of a nontrivial topology. We focus on simple spherical multiconnected manifolds and discuss their implications for the CMB in terms of the power spectrum, maps, and the correlation matrix. We perform a Bayesian model comparison against the fiducial best-fit cold dark matter model with a cosmological constant based both on the power spectrum and the correlation matrix to assess their statistical significance. We find that the first-year power spectrum shows a slight preference for the truncated cube space, but the three-year data show no evidence for any of these spaces.

Planck 2013 results. XXVI. Background geometry and topology of the Universe

Science.gov (United States)

Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R. C.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H. C.; Chiang, L.-Y.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Couchot, F.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.-M.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Dupac, X.; Efstathiou, G.; Enßlin, T. A.; Eriksen, H. K.; Fabre, O.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Ganga, K.; Giard, M.; Giardino, G.; Giraud-Héraud, Y.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huffenberger, K. M.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T. S.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Laureijs, R. J.; Lawrence, C. R.; Leahy, J. P.; Leonardi, R.; Leroy, C.; Lesgourgues, J.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Macías-Pérez, J. F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D. J.; Martin, P. G.; Martínez-González, E.; Masi, S.; Massardi, M.; Matarrese, S.; Matthai, F.; Mazzotta, P.; McEwen, J. D.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; Osborne, S.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H. V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pogosyan, D.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Riazuelo, A.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rusholme, B.; Sandri, M.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Spencer, L. D.; Starck, J.-L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L. A.; Wandelt, B. D.; Yvon, D.; Zacchei, A.; Zonca, A.

2014-11-01

The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky view of the surface of last scattering available to date. This allows us to detect possible departures from the standard model of a globally homogeneous and isotropic cosmology on the largest scales. We search for correlations induced by a possible non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance χrec), both via a direct search for matched circular patterns at the intersections and by an optimal likelihood search for specific topologies. For the latter we consider flat spaces with cubic toroidal (T3), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature spaces. These searches yield no detection of the compact topology with the scale below the diameter of the last scattering surface. For most compact topologies studied the likelihood maximized over the orientation of the space relative to the observed map shows some preference for multi-connected models just larger than the diameter of the last scattering surface. Since this effect is also present in simulated realizations of isotropic maps, we interpret it as the inevitable alignment of mild anisotropic correlations with chance features in a single sky realization; such a feature can also be present, in milder form, when the likelihood is marginalized over orientations. Thus marginalized, the limits on the radius ℛi of the largest sphere inscribed in topological domain (at log-likelihood-ratio Δln ℒ > -5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, ℛi> 0.92χrec for the T3 cubic torus; ℛi> 0.71χrec for the T2 chimney; ℛi> 0.50χrec for the T1 slab; and in a positively curved Universe, ℛi> 1.03χrec for the dodecahedral space; ℛi> 1

Topological phase transition in anisotropic square-octagon lattice with spin-orbit coupling and exchange field

Science.gov (United States)

Yang, Yuan; Yang, Jian; Li, Xiaobing; Zhao, Yue

2018-03-01

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin-orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.

Topological background on charmed and beauty particle pairs produced in high energy hadron interactions in nuclear emulsions

International Nuclear Information System (INIS)

Romano, G.

1984-01-01

This chapter demonstrates that by making use of the fact that new flavors must be produced in pairs in strong interactions and that beauty particles are expected to decay often into charmed particles, the contribution of background simulating decays can be computed from a pure topological point of view. Topics covered include the emulsion data, the search for charmed particles, the search for beauty particles, detection efficiency, and the evaluation of mean life-time. It is assumed that in the interaction of (350-400) GeV hadrons in emulsion the production rate of charmed particle pairs is 5X10 -3 /interaction. The corresponding figures for BB production are estimated to be 10 3 times smaller. It is noted that some neutral decay topology, like 4 or more charged prongs, are much less affected by background

Critical solutions of topologically gauged N=8 CFTs in three dimensions

International Nuclear Information System (INIS)

Nilsson, Bengt E.W.

2014-01-01

In this paper we discuss some special (critical) background solutions that arise in topological gauged N=8 three-dimensional CFTs with SO(N) gauge group. Depending on how many scalar fields are given a VEV the theory has background solutions for certain values of μl, where μ and l are parameters in the TMG Lagrangian. Apart from Minkowski, chiral round AdS 3 and null-warped AdS 3 (or Schrödinger(z=2)) we identify also a more exotic solution recently found in TMG by Ertl, Grumiller and Johansson. We also discuss the spectrum, symmetry breaking pattern and the supermultiplet structure in the various backgrounds and argue that some properties are due to their common origin in a conformal phase. Some of the scalar fields, including all higgsed ones, turn out to satisfy three-dimensional field equations similar to those of the singleton. Finally, we note that topologically gauged N=6 ABJ(M) theories have a similar, but more restricted, set of background solutions

THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. II. THE RECLOSING OF AN OPENED FIELD

International Nuclear Information System (INIS)

Low, B. C.; Janse, A. M.

2009-01-01

This is a study of the spontaneous formation of current sheets responding to the closing of an opened magnetic field by resistive reconnection in an electrically, highly conducting atmosphere outside a unit sphere. Pairs of initial-final equilibrium states are calculated explicitly, taking the field to be composed of three systems of untwisted flux in both states. In the initial state, two of the three flux systems are closed potential fields whereas the third system contains an equilibrium current sheet that keeps the potential fields on its two sides globally open. The final state is an everywhere potential field, with all three flux systems closed, produced by the resistive dissipation of the current sheet in the initial state. The unit sphere is taken to be a rigid, perfectly conducting wall during reconnection, so that the normal flux distribution is unchanged on the unit sphere. Field solutions subject to this unchanging boundary condition are obtained with and without the assumption of axisymmetry. The mathematical model has been designed to show that the topological changes produced by the current-sheet dissipation are simple under axisymmetry but radically different in the absence of axisymmetry, a fundamental point established in the first paper of this series. In the general case, the topological changes imply that other current sheets must have formed. Some of these current sheets form on the separatrix flux surfaces of the multipolar field. Others form throughout the closed-flux systems induced by volumetric changes. The opening and reclosing of magnetic fields during a solar coronal mass ejection may produce a multitude of current sheets not previously anticipated in the current understanding of this phenomenon. Basic to this study is a general topological property of magnetic flux tubes treated separately in the Appendix.

Quintessential quartic quasi-topological quartet

Energy Technology Data Exchange (ETDEWEB)

Ahmed, Jamil [Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada); Department of Mathematics, Quaid-i-Azam University,Islamabad (Pakistan); Hennigar, Robie A. [Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada); Mann, Robert B. [Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada); Perimeter Institute,31 Caroline Street North, Waterloo, ON, N2L 2Y5 (Canada); Mir, Mozhgan [Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada); School of Physics, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

2017-05-25

We construct the quartic version of generalized quasi-topological gravity, which was recently constructed to cubic order in https://arxiv.org/abs/1703.01631. This class of theories includes Lovelock gravity and a known form of quartic quasi-topological gravity as special cases and possess a number of remarkable properties: (i) In vacuum, or in the presence of suitable matter, there is a single independent field equation which is a total derivative. (ii) At the linearized level, the equations of motion on a maximally symmetric background are second order, coinciding with the linearized Einstein equations up to a redefinition of Newton’s constant. Therefore, these theories propagate only the massless, transverse graviton on a maximally symmetric background. (iii) While the Lovelock and quasi-topological terms are trivial in four dimensions, there exist four new generalized quasi-topological terms (the quartet) that are nontrivial, leading to interesting higher curvature theories in d≥4 dimensions that appear well suited for holographic study. We construct four dimensional black hole solutions to the theory and study their properties. A study of black brane solutions in arbitrary dimensions reveals that these solutions are modified from the ‘universal’ properties they possess in other higher curvature theories, which may lead to interesting consequences for the dual CFTs.

Localizing gauge fields on a topological Abelian string and the Coulomb law

International Nuclear Information System (INIS)

Torrealba S, Rafael S.

2010-01-01

The confinement of electromagnetic field is studied in axial symmetrical, warped, six-dimensional brane world, using a recently proposed topological Abelian string-vortex solution as background. It was found, that the massless gauge field fluctuations follow four-dimensional Maxwell equations in the Lorenz gauge. The massless zero mode is localized when the thickness of the string vortex is less than 5β/4πe 2 v 2 and there are no other localized massless modes. There is also an infinite of nonlocalized massive Fourier modes, that follow four-dimensional Proca equations with a continuous spectrum. To compute the corrections to the Coulomb potential, a radial cutoff was introduced, in order to achieve a discrete mass spectrum. As a main result, a (R o /βR 2 ) correction was found for the four-dimensional effective Coulomb law; the result is in correspondence with the observed behavior of the Coulomb potential at today's measurable distances.

Topology optimization based design of unilateral NMR for generating a remote homogeneous field.

Science.gov (United States)

Wang, Qi; Gao, Renjing; Liu, Shutian

2017-06-01

This paper presents a topology optimization based design method for the design of unilateral nuclear magnetic resonance (NMR), with which a remote homogeneous field can be obtained. The topology optimization is actualized by seeking out the optimal layout of ferromagnetic materials within a given design domain. The design objective is defined as generating a sensitive magnetic field with optimal homogeneity and maximal field strength within a required region of interest (ROI). The sensitivity of the objective function with respect to the design variables is derived and the method for solving the optimization problem is presented. A design example is provided to illustrate the utility of the design method, specifically the ability to improve the quality of the magnetic field over the required ROI by determining the optimal structural topology for the ferromagnetic poles. Both in simulations and experiments, the sensitive region of the magnetic field achieves about 2 times larger than that of the reference design, validating validates the feasibility of the design method. Copyright © 2017. Published by Elsevier Inc.

Phase transition and field effect topological quantum transistor made of monolayer MoS2

Science.gov (United States)

Simchi, H.; Simchi, M.; Fardmanesh, M.; Peeters, F. M.

2018-06-01

We study topological phase transitions and topological quantum field effect transistor in monolayer molybdenum disulfide (MoS2) using a two-band Hamiltonian model. Without considering the quadratic (q 2) diagonal term in the Hamiltonian, we show that the phase diagram includes quantum anomalous Hall effect, quantum spin Hall effect, and spin quantum anomalous Hall effect regions such that the topological Kirchhoff law is satisfied in the plane. By considering the q 2 diagonal term and including one valley, it is shown that MoS2 has a non-trivial topology, and the valley Chern number is non-zero for each spin. We show that the wave function is (is not) localized at the edges when the q 2 diagonal term is added (deleted) to (from) the spin-valley Dirac mass equation. We calculate the quantum conductance of zigzag MoS2 nanoribbons by using the nonequilibrium Green function method and show how this device works as a field effect topological quantum transistor.

Introduction to the background field method

International Nuclear Information System (INIS)

Abbott, L.F.; Brandeis Univ., Waltham, MA

1982-01-01

The background field approach to calculations in gauge field theories is presented. Conventional functional techniques are reviewed and the background field method is introduced. Feynman rules and renormalization are discussed and, as an example, the Yang-Mills β function is computed. (author)

Topological field theories and two-dimensional instantons

International Nuclear Information System (INIS)

Schaposnik, F.A.

1990-01-01

In this paper, the author discusses some topics related to the recently developed Topological Field Theories (TFTs). The first part is devoted to a discussion on how a TFT can be quantized using techniques which are well-known from the study of gauge theories. Then the author describes the results that we have obtained in collaboration with George Thompson in the study of a two-dimensional TFT related to the Abelian Higgs model

Cartan's equations define a topological field theory of the BF type

International Nuclear Information System (INIS)

Cuesta, Vladimir; Montesinos, Merced

2007-01-01

Cartan's first and second structure equations together with first and second Bianchi identities can be interpreted as equations of motion for the tetrad, the connection and a set of two-form fields T I and R J I . From this viewpoint, these equations define by themselves a field theory. Restricting the analysis to four-dimensional spacetimes (keeping gravity in mind), it is possible to give an action principle of the BF type from which these equations of motion are obtained. The action turns out to be equivalent to a linear combination of the Nieh-Yan, Pontrjagin, and Euler classes, and so the field theory defined by the action is topological. Once Einstein's equations are added, the resulting theory is general relativity. Therefore, the current results show that the relationship between general relativity and topological field theories of the BF type is also present in the first-order formalism for general relativity

Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

Science.gov (United States)

Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang

2015-01-23

The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.

Engineering Topological Surface State of Cr-doped Bi2Se3 under external electric field

Science.gov (United States)

Zhang, Jian-Min; Lian, Ruqian; Yang, Yanmin; Xu, Guigui; Zhong, Kehua; Huang, Zhigao

2017-03-01

External electric field control of topological surface states (SSs) is significant for the next generation of condensed matter research and topological quantum devices. Here, we present a first-principles study of the SSs in the magnetic topological insulator (MTI) Cr-doped Bi2Se3 under external electric field. The charge transfer, electric potential, band structure and magnetism of the pure and Cr doped Bi2Se3 film have been investigated. It is found that the competition between charge transfer and spin-orbit coupling (SOC) will lead to an electrically tunable band gap in Bi2Se3 film under external electric field. As Cr atom doped, the charge transfer of Bi2Se3 film under external electric field obviously decreases. Remarkably, the band gap of Cr doped Bi2Se3 film can be greatly engineered by the external electric field due to its special band structure. Furthermore, magnetic coupling of Cr-doped Bi2Se3 could be even mediated via the control of electric field. It is demonstrated that external electric field plays an important role on the electronic and magnetic properties of Cr-doped Bi2Se3 film. Our results may promote the development of electronic and spintronic applications of magnetic topological insulator.

Correlation between topological structure and its properties in dynamic singular vector fields.

Science.gov (United States)

Vasilev, Vasyl; Soskin, Marat

2016-04-20

A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 103  s order.

Two dimensional topological insulator in quantizing magnetic fields

Science.gov (United States)

Olshanetsky, E. B.; Kvon, Z. D.; Gusev, G. M.; Mikhailov, N. N.; Dvoretsky, S. A.

2018-05-01

The effect of quantizing magnetic field on the electron transport is investigated in a two dimensional topological insulator (2D TI) based on a 8 nm (013) HgTe quantum well (QW). The local resistance behavior is indicative of a metal-insulator transition at B ≈ 6 T. On the whole the experimental data agrees with the theory according to which the helical edge states transport in a 2D TI persists from zero up to a critical magnetic field Bc after which a gap opens up in the 2D TI spectrum.

Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields

Science.gov (United States)

Zhu, Xiaoyu

2018-05-01

A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We investigate a time-reversal-invariant topological superconductor in two dimensions and demonstrate that an in-plane magnetic field could transform it into a second-order topological superconductor. A detailed analysis reveals that the magnetic field gives rise to mass terms which take distinct values among the edges, and Majorana corner states naturally emerge at the intersection of two adjacent edges with opposite masses. With the rotation of the magnetic field, Majorana corner states localized around the boundary may hop from one corner to a neighboring one and eventually make a full circle around the system when the field rotates by 2 π . In the end, we briefly discuss physical realizations of this system.

Topological superconductivity, topological confinement, and the vortex quantum Hall effect

International Nuclear Information System (INIS)

Diamantini, M. Cristina; Trugenberger, Carlo A.

2011-01-01

Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.

Visualization of Morse connection graphs for topologically rich 2D vector fields.

Science.gov (United States)

Szymczak, Andrzej; Sipeki, Levente

2013-12-01

Recent advances in vector field topologymake it possible to compute its multi-scale graph representations for autonomous 2D vector fields in a robust and efficient manner. One of these representations is a Morse Connection Graph (MCG), a directed graph whose nodes correspond to Morse sets, generalizing stationary points and periodic trajectories, and arcs - to trajectories connecting them. While being useful for simple vector fields, the MCG can be hard to comprehend for topologically rich vector fields, containing a large number of features. This paper describes a visual representation of the MCG, inspired by previous work on graph visualization. Our approach aims to preserve the spatial relationships between the MCG arcs and nodes and highlight the coherent behavior of connecting trajectories. Using simulations of ocean flow, we show that it can provide useful information on the flow structure. This paper focuses specifically on MCGs computed for piecewise constant (PC) vector fields. In particular, we describe extensions of the PC framework that make it more flexible and better suited for analysis of data on complex shaped domains with a boundary. We also describe a topology simplification scheme that makes our MCG visualizations less ambiguous. Despite the focus on the PC framework, our approach could also be applied to graph representations or topological skeletons computed using different methods.

Critical solutions of topologically gauged N=8 CFTs in three dimensions

Energy Technology Data Exchange (ETDEWEB)

Nilsson, Bengt E.W. [Fundamental Physics, Chalmers University of Technology,SE-412 96 Göteborg (Sweden)

2014-04-16

In this paper we discuss some special (critical) background solutions that arise in topological gauged N=8 three-dimensional CFTs with SO(N) gauge group. Depending on how many scalar fields are given a VEV the theory has background solutions for certain values of μl, where μ and l are parameters in the TMG Lagrangian. Apart from Minkowski, chiral round AdS{sub 3} and null-warped AdS{sub 3} (or Schrödinger(z=2)) we identify also a more exotic solution recently found in TMG by Ertl, Grumiller and Johansson. We also discuss the spectrum, symmetry breaking pattern and the supermultiplet structure in the various backgrounds and argue that some properties are due to their common origin in a conformal phase. Some of the scalar fields, including all higgsed ones, turn out to satisfy three-dimensional field equations similar to those of the singleton. Finally, we note that topologically gauged N=6 ABJ(M) theories have a similar, but more restricted, set of background solutions.

Topological insulators

CERN Document Server

Franz, Marcel

2013-01-01

Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was

The new topological sectors associated with quantum electrodynamics

International Nuclear Information System (INIS)

Marino, E.C.

1994-01-01

A formulation of Quantum Electrodynamics in terms of an antisymmetric-tensor gauge field is presented. In this formulation the topological current of this field appears as a source for the electromagnetic field and the topological charge therefore acts physically as an electric charge. These nontrivial, electrically charged, sectors contain massless states orthogonal to the vacuum which are created by a gauge invariant operator can be interpreted as coherent states of photons. The new states do interact with the charged states of QCD in the usual way. It is argued that if these new sectors are in fact realized in nature then a very intense background electromagnetic field is necessary for the experimental observation of them. The order of magnitude of the intensity threshold is presented. (author). 2 refs

Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds

International Nuclear Information System (INIS)

Zois, I.P.

2016-01-01

We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry. (paper)

Edge topology and flows in the reversed-field pinch

International Nuclear Information System (INIS)

Spizzo, G.; Agostini, M.; Scarin, P.; Vianello, N.; Cappello, S.; Puiatti, M. E.; Valisa, M.; White, R. B.

2012-01-01

Edge topology and plasma flow deeply influence transport in the reversed-field pinch as well as in all fusion devices, playing an important role in many practical aspects of plasma performance, such as access to enhanced confinement regimes, the impact on global power balance and operative limits, such as the density limit (Spizzo G. et al 2010 Plasma Phys. Control. Fusion 52 095011). A central role is played by the edge electric field, which is determined by the ambipolar constraint guaranteeing quasi-neutrality in a sheath next to the plasma wall. Its radial component is experimentally determined in RFX over the whole toroidal angle by means of a diagnostic set measuring edge plasma potential and flow with different techniques (Scarin P. et al 2011 Nucl. Fusion 51 073002). The measured radial electric field is used to construct the potential in the form Φ(ψ p , θ, ζ) (ψ p radial coordinate, θ, ζ angles), by means of the Hamiltonian guiding-centre code ORBIT. Simulations show that a proper functional form of the potential can balance the differential radial diffusion of electrons and ions subject to m = 0 magnetic island O- and X-points. Electrons spend more time in the X-points of such islands than in O-points; ions have comparatively larger drifts and their radial motion is more uniform over the toroidal angle. The final spatial distribution of Φ(ψ p , θ, ζ) results in a complex 3D pattern, with convective cells next to the wall. Generally speaking, an edge topology dominating parallel transport with a given symmetry brings about an edge potential with the same symmetry. This fact helps us to build a first step of a unified picture of the effect of magnetic topology on the Greenwald limit, and, more generally, on flows in the edge of RFPs and tokamaks. (paper)

Chern-Simons-Rozansky-Witten topological field theory

Energy Technology Data Exchange (ETDEWEB)

Kapustin, Anton [California Institute of Technology, Minor Outlying Islands (United States); Saulina, Natalia [California Institute of Technology, Minor Outlying Islands (United States)], E-mail: saulina@theory.caltech.edu

2009-12-21

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4d=3 supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kaehler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern-Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.

Planck 2015 results: XVIII. Background geometry and topology of the Universe

DEFF Research Database (Denmark)

Ade, P. A R; Aghanim, N.; Arnaud, M.

2016-01-01

and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology...... the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χrec), both via a direct scan for matched circular patterns at the intersections...... with a scale below the diameter of the last-scattering surface. The limits on the radius i of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Δlnℒ>-5 relative to a simply-connected flat Planck best-fit model) are: i > 0.97 χrec for the T3 cubic torus; and i > 0.56 χrec for the T...

Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions

Energy Technology Data Exchange (ETDEWEB)

Shiozaki, Ken [Department of Physics, University of Illinois at Urbana Champaign,1110 West Green Street, Urbana, IL 61801 (United States); Ryu, Shinsei [James Franck Institute and Kadanoff Center for Theoretical Physics, University of Chicago,5640 South Ellis Ave, Chicago, IL 60637 (United States)

2017-04-18

Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases — symmetry-protected topological (SPT) phases in particular — defined in one dimensional lattices. On the other hand, it is natural to expect that gapped quantum phases in the limit of zero correlation length are described by topological quantum field theories (TFTs or TQFTs). In this paper, for (1+1)-dimensional bosonic SPT phases protected by symmetry G, we bridge their descriptions in terms of MPSs, and those in terms of G-equivariant TFTs. In particular, for various topological invariants (SPT invariants) constructed previously using MPSs, we provide derivations from the point of view of (1+1) TFTs. We also discuss the connection between boundary degrees of freedom, which appear when one introduces a physical boundary in SPT phases, and “open” TFTs, which are TFTs defined on spacetimes with boundaries.

Topology optimized and 3D printed polymer-bonded permanent magnets for a predefined external field

Science.gov (United States)

Huber, C.; Abert, C.; Bruckner, F.; Pfaff, C.; Kriwet, J.; Groenefeld, M.; Teliban, I.; Vogler, C.; Suess, D.

2017-08-01

Topology optimization offers great opportunities to design permanent magnetic systems that have specific external field characteristics. Additive manufacturing of polymer-bonded magnets with an end-user 3D printer can be used to manufacture permanent magnets with structures that had been difficult or impossible to manufacture previously. This work combines these two powerful methods to design and manufacture permanent magnetic systems with specific properties. The topology optimization framework is simple, fast, and accurate. It can also be used for the reverse engineering of permanent magnets in order to find the topology from field measurements. Furthermore, a magnetic system that generates a linear external field above the magnet is presented. With a volume constraint, the amount of magnetic material can be minimized without losing performance. Simulations and measurements of the printed systems show very good agreement.

On local frame fields and fermion dynamics in space with nontrivial topologies

International Nuclear Information System (INIS)

Fomin, P.I.; Zemlyakov, A.T.

1991-01-01

The covariant operators of total angular momentum of fermion in spaces which possess Killing vector fields are defined. The classification of local frame fields in a closed world with S 3 topology is carried out. The vortex-type solution to Dirac equation in Minkowskii space is obtained by means of cylindrical local frame field. 7 refs. (author)

Lateral diffusion of the topological charge density in stochastic optical fields

CSIR Research Space (South Africa)

Roux, FS

2010-01-01

Full Text Available Stochastic (i.e. random and quasi-random) optical fields may contain distributions of optical vortices that are represented by non-uniform topological charge densities. Numerical simulations are used to investigate the evolution under free...

Acoustic inverse scattering using topological derivative of far-field measurements-based L2 cost functionals

International Nuclear Information System (INIS)

Bellis, Cédric; Bonnet, Marc; Cakoni, Fioralba

2013-01-01

Originally formulated in the context of topology optimization, the concept of topological derivative has also proved effective as a qualitative inversion tool for a wave-based identification of finite-sized objects. This approach remains, however, largely based on a heuristic interpretation of the topological derivative, whereas most other qualitative approaches to inverse scattering are backed by a mathematical justification. As an effort toward bridging this gap, this study focuses on a topological derivative approach applied to the L 2 -norm of the misfit between far-field measurements. Either an inhomogeneous medium or a finite number of point-like scatterers are considered, using either the Born approximation or a full-scattering model. Topological derivative-based imaging functionals are analyzed using a suitable factorization of the far-field operator, for each of the considered cases, in order to characterize their behavior and assess their ability to reconstruct the unknown scatterer(s). Results include the justification of the usual sign heuristic underpinning the method for (i) the Born approximation and (ii) full-scattering models limited to moderately strong scatterers. Semi-analytical and numerical examples are presented. Within the chosen framework, the topological derivative approach is finally discussed and compared to other well-known qualitative methods. (paper)

Quantum computation with topological codes from qubit to topological fault-tolerance

CERN Document Server

Fujii, Keisuke

2015-01-01

This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.

The Background-Field Method and Noninvariant Renormalization

International Nuclear Information System (INIS)

Avdeev, L.V.; Kazakov, D.I.; Kalmykov, M.Yu.

1994-01-01

We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional σ model it is demonstrated that the background-field method gives incorrect results when the regularization (and/or renormalization) is noninvariant. In particular, it is found that the cut-off regularization and the differential renormalization belong to this class and are incompatible with the background-field method in theories with nonlinear symmetries. 17 refs

L lines, C points and Chern numbers: understanding band structure topology using polarization fields

Science.gov (United States)

Fösel, Thomas; Peano, Vittorio; Marquardt, Florian

2017-11-01

Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an important quantity in this field. Another example of topology, in polarization physics, are polarization singularities, called L lines and C points. By establishing a connection between these two theories, we develop a novel technique to visualize and potentially measure the Chern number: it can be expressed either as the winding of the polarization azimuth along L lines in reciprocal space, or in terms of the handedness and the index of the C points. For mechanical systems, this is directly connected to the visible motion patterns.

Anomalous quantum numbers and topological properties of field theories

International Nuclear Information System (INIS)

Polychronakos, A.P.

1987-01-01

We examine the connection between anomalous quantum numbers, symmetry breaking patterns and topological properties of some field theories. The main results are the following: In three dimensions the vacuum in the presence of abelian magnetic field configurations behaves like a superconductor. Its quantum numbers are exactly calculable and are connected with the Atiyah-Patodi-Singer index theorem. Boundary conditions, however, play a nontrivial role in this case. Local conditions were found to be physically preferable than the usual global ones. Due to topological reasons, only theories for which the gauge invariant photon mass in three dimensions obeys a quantization condition can support states of nonzero magnetic flux. For similar reasons, this mass induces anomalous angular momentum quantum numbers to the states of the theory. Parity invariance and global flavor symmetry were shown to be incompatible in such theories. In the presence of mass less flavored fermions, parity will always break for an odd number of fermion flavors, while for even fermion flavors it may not break but only at the expense of maximally breaking the flavor symmetry. Finally, a connection between these theories and the quantum Hall effect was indicated

Topology optimized permanent magnet systems

DEFF Research Database (Denmark)

Bjørk, Rasmus; Bahl, Christian; Insinga, Andrea Roberto

2017-01-01

Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. The Halbach cylinder is topology optimized with iron...... and an increase of 15% in magnetic efficiency is shown. A topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111%. Finally, a permanent magnet with alternating high and low field regions is topology optimized and a ΛcoolΛcool figure of merit of 0...

Comparing topological charge definitions using topology fixing actions

International Nuclear Information System (INIS)

Bruckmann, Falk; Gruber, Florian; Jansen, Karl; Marinkovic, Marina; Urbach, Carsten; Wagner, Marc

2009-05-01

We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical situation fixed. At the same time the agreement between different definitions of topological charge - the field theoretic and the index definition - is directly correlated to the degree topology is fixed. Moreover, it turns out that the two definitions agree very well. We also study finite volume effects arising in the static potential and related quantities due to topology fixing. (orig.)

Planck 2013 results. XXVI. Background geometry and topology of the Universe

DEFF Research Database (Denmark)

Planck Collaboration,; Ade, P. A. R.; Aghanim, N.

2013-01-01

Planck CMB temperature maps allow us to detect departures from homogeneity and isotropy on the largest scales. We search for topology with a fundamental domain (nearly) intersecting the last scattering surface (comoving distance X_r). For most topologies studied the likelihood maximized over the ...

Solving topological field theories on mapping tori

International Nuclear Information System (INIS)

Blau, M.; Jermyn, I.; Thompson, G.

1996-05-01

Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1 modul 1) model of Rozansky and Saleur on Σ x S 1 , both directly and using equivalent two-dimensional theories. We also derive the partition function on a certain non-abelian generalization of the U(1 modul 1) model on mapping tori and hence obtain explicit expressions for the Ray-Singer torsion on these manifolds. Extensions of these results to BF and Chern-Simons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two- dimensional theories we find have the interesting property of depending explicitly on the diffeomorphism defining the mapping torus while the quantum field theory is sensitive only to its isomorphism class defining the mapping torus as a smooth manifold. (author). 20 refs

The Mathai-Quillen formalism and topological field theory

International Nuclear Information System (INIS)

Blau, Matthias.

1992-01-01

These lecture notes give an introductory account of an approach to cohomological field theory due to Atiyah and Jeffrey which is based on the construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics covered are: an explanation of regularized Euler numbers of infinite dimensional vector bundles; interpretation of supersymmetric quantum mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey interpretation of Donaldson theory; the construction of topological gauge theories from infinite dimensional vector bundles over space of connections. (author). 44 refs

Phase-Field Simulations of Topological Structures and Topological Phase Transitions in Ferroelectric Oxide Heterostructures

Science.gov (United States)

Zijian Hong

Ferroelectrics are materials that exhibit spontaneous electric polarization which can be switched between energy-degenerated states by external stimuli (e.g., mechanical force and electric field) that exceeds a critical value. They have wide potential applications in memories, capacitors, piezoelectric and pyroelectric sensors, and nanomechanical systems. Topological structures and topological phase transitions have been introduced to the condensed matter physics in the past few decades and have attracted broad attentions in various disciplines due to the rich physical insights and broad potential applications. Ferromagnetic topological structures such as vortex and skyrmion are known to be stabilized by the antisymmetric chiral interaction (e.g., Dzyaloshinskii-Moriya interaction). Without such interaction, ferroelectric topological structures (i.e., vortex, flux-closure, skyrmions, and merons) have been studied only recently with other designing strategies, such as reducing the dimension of the ferroelectrics. The overarching goal of this dissertation is to investigate the topological structures in ferroelectric oxide perovskites as well as the topological phase transitions under external applied forces. Pb(Zr,Ti)O3 (PZT) with morphotropic phase boundary is widely explored for high piezoelectric and dielectric properties. The domain structure of PZT tetragonal/rhombohedral (T/R) bilayer is investigated. Strong interfacial coupling is shown, with large polarization rotation to a lower symmetry phase near the T/R interface. Interlayer domain growth can also be captured, with T-domains in the R layer and R-domains in the T layer. For thin PZT bilayer with 5nm of T-layer and 20 nm of R-layer, the a1/a 2 twin domain structure is formed in the top T layer, which could be fully switched to R domains under applied bias. While a unique flux-closure pattern is observed both theoretically and experimentally in the thick bilayer film with 50 nm of thickness for both T and R

Topics in general topology

CERN Document Server

Morita, K

1989-01-01

Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments.The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.

Non-topological non-commutativity in string theory

International Nuclear Information System (INIS)

Guttenberg, S.; Herbst, M.; Kreuzer, M.; Rashkov, R.

2008-01-01

Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topological sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born-Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR-fields are also discussed. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

Topology optimized permanent magnet systems

Science.gov (United States)

Bjørk, R.; Bahl, C. R. H.; Insinga, A. R.

2017-09-01

Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. The Halbach cylinder is topology optimized with iron and an increase of 15% in magnetic efficiency is shown. A topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111%. Finally, a permanent magnet with alternating high and low field regions is topology optimized and a Λcool figure of merit of 0.472 is reached, which is an increase of 100% compared to a previous optimized design.

Heat kernel expansion in the background field formalism

CERN Document Server

Barvinsky, Andrei

2015-01-01

Heat kernel expansion and background field formalism represent the combination of two calculational methods within the functional approach to quantum field theory. This approach implies construction of generating functionals for matrix elements and expectation values of physical observables. These are functionals of arbitrary external sources or the mean field of a generic configuration -- the background field. Exact calculation of quantum effects on a generic background is impossible. However, a special integral (proper time) representation for the Green's function of the wave operator -- the propagator of the theory -- and its expansion in the ultraviolet and infrared limits of respectively short and late proper time parameter allow one to construct approximations which are valid on generic background fields. Current progress of quantum field theory, its renormalization properties, model building in unification of fundamental physical interactions and QFT applications in high energy physics, gravitation and...

Generalized Mathai-Quillen Topological Sigma Models

OpenAIRE

Llatas, Pablo M.

1995-01-01

A simple field theoretical approach to Mathai-Quillen topological field theories of maps $X: M_I \\to M_T$ from an internal space to a target space is presented. As an example of applications of our formalism we compute by applying our formulas the action and Q-variations of the fields of two well known topological systems: Topological Quantum Mechanics and type-A topological Sigma Model.

Algebraic characterization of vector supersymmetry in topological field theories

International Nuclear Information System (INIS)

Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G.; Sorella, S.P.

1997-01-01

An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author)

Photoinduced Topological Phase Transitions in Topological Magnon Insulators.

Science.gov (United States)

Owerre, S A

2018-03-13

Topological magnon insulators are the bosonic analogs of electronic topological insulators. They are manifested in magnetic materials with topologically nontrivial magnon bands as realized experimentally in a quasi-two-dimensional (quasi-2D) kagomé ferromagnet Cu(1-3, bdc), and they also possess protected magnon edge modes. These topological magnetic materials can transport heat as well as spin currents, hence they can be useful for spintronic applications. Moreover, as magnons are charge-neutral spin-1 bosonic quasiparticles with a magnetic dipole moment, topological magnon materials can also interact with electromagnetic fields through the Aharonov-Casher effect. In this report, we study photoinduced topological phase transitions in intrinsic topological magnon insulators in the kagomé ferromagnets. Using magnonic Floquet-Bloch theory, we show that by varying the light intensity, periodically driven intrinsic topological magnetic materials can be manipulated into different topological phases with different sign of the Berry curvatures and the thermal Hall conductivity. We further show that, under certain conditions, periodically driven gapped topological magnon insulators can also be tuned to synthetic gapless topological magnon semimetals with Dirac-Weyl magnon cones. We envision that this work will pave the way for interesting new potential practical applications in topological magnetic materials.

Background Independent Open String Field Theory and Constant B-Field

OpenAIRE

Nemeschansky, D.; Yasnov, V.

2000-01-01

We calculate the background independent action for bosonic and supersymmetric open string field theory in a constant B-field. We also determine the tachyon effective action in the presence of constant B-field.

Background geometries in string and M-theory

International Nuclear Information System (INIS)

Jeschek, C.

2005-01-01

In this thesis we consider background geometries resulting from string theory compactifications. In particular, we investigate supersymmetric vacuum spaces of supergravity theories and topological twisted sigma models by means of classical and generalised G-structures. In the first part we compactify 11d supergravity on seven-dimensional manifolds due to phenomenological reasons. A certain amount of supersymmetry forces the internal background to admit a classical SU(3)- or G 2 -structure. Especially, in the case that the four-dimensional space is maximally symmetric and four form fluxes are present we calculate the relation to the intrinsic torsion. The second and main part is two-fold. Firstly, we realise that generalised geometries on six-dimensional manifolds are a natural framework to study T-duality and mirror symmetry, in particular if the B-field is non-vanishing. An explicit mirror map is given and we apply this idea to the generalised formulation of a topological twisted sigma model. Implications of mirror symmetry are studied, e.g. observables and topological A- and B-branes. Secondly, we show that seven-dimensional NS-NS backgrounds in type II supergravity theories can be described by generalised G 2 -geometries. A compactification on six manifolds leads to a new structure. We call this geometry a generalised SU(3)-structure. We study the relation between generalised SU(3)- and G 2 -structures on six- and seven-manifolds and generalise the Hitchin-flow equations. Finally, we further develop the generalised SU(3)- and G 2 -structures via a constrained variational principle to incorporate also the remaining physical R-R fields. (Orig.)

(Non-)Abelian Kramers-Wannier duality and topological field theory

CERN Document Server

Severa, Pavol

2002-01-01

We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincare duality), and a similar formulation is given for higher-dimensional cases. In this form they lead to simple TFTs with boundary coloured in two colours. The statistical models live on the boundary of these TFTs, as in the CS/WZW or AdS/CFT correspondence. Classical models (Poisson-Lie T-duality) suggest a non-abelian generalization in the 2dcase, with abelian groups replaced by quantum groups. Amazingly, the TFT formulation solves the problem without computation: quantum groups appear in pictures, independently of the classical motivation. Connection with Chern-Simons theory appears at the symplectic level, and also in the pictures of the Drinfeld double: Reshetikhin-Turaev invariants of links in 3-manifolds, computed from the double, are included in these TFTs. All this suggests nice phenomena in higher dimensions.

Topological pregauge-pregeometry

International Nuclear Information System (INIS)

Akama, Keiichi; Oda, Ichiro.

1990-12-01

The pregauge-pregeometric action, i.e. the fundamental matter action whose quantum fluctuations give rise to the Einstein-Hilbert and the Yang-Mills actions is investigated from the viewpoint of the topological field theory. We show that the scalar pregauge-pregeometric action is a topological invariant for appropriate choices of the internal gauge group. This model realizes the picture that the gravitational and internal gauge theory at the low energy scale is induced as the quantum effects of the topological field theory at the Planck scale. (author)

Quantum capacitance in topological insulators under strain in a tilted magnetic field

KAUST Repository

Tahir, M.

2012-12-06

Topological insulators exhibit unique properties due to surface states of massless Dirac fermions with conserved time reversal symmetry. We consider the quantum capacitance under strain in an external tilted magnetic field and demonstrate a minimum at the charge neutrality point due to splitting of the zeroth Landau level. We also find beating in the Shubnikov de Haas oscillations due to strain, which originate from the topological helical states. Varying the tilting angle from perpendicular to parallel washes out these oscillations with a strain induced gap at the charge neutrality point. Our results explain recent quantum capacitance and transport experiments.

Quantum capacitance in topological insulators under strain in a tilted magnetic field

KAUST Repository

Tahir, M.; Schwingenschlö gl, Udo

2012-01-01

Topological insulators exhibit unique properties due to surface states of massless Dirac fermions with conserved time reversal symmetry. We consider the quantum capacitance under strain in an external tilted magnetic field and demonstrate a minimum at the charge neutrality point due to splitting of the zeroth Landau level. We also find beating in the Shubnikov de Haas oscillations due to strain, which originate from the topological helical states. Varying the tilting angle from perpendicular to parallel washes out these oscillations with a strain induced gap at the charge neutrality point. Our results explain recent quantum capacitance and transport experiments.

Geometrisation of electromagnetic field and topological interpretation of quantum mechanics formalism

International Nuclear Information System (INIS)

Olkhov, O.A.

2001-01-01

We consider interacting electromagnetic and electron-positron fields as a nonmetrized space-time 4-manifold. The Dirac and Maxwell equations is found to be a relationships expressing topological and metric properties of this manifold. A new equation for the weak interaction is proposed that explains geometrical mechanism of CP-violation

FIELD TOPOLOGY ANALYSIS OF A LONG-LASTING CORONAL SIGMOID

International Nuclear Information System (INIS)

Savcheva, A. S.; Van Ballegooijen, A. A.; DeLuca, E. E.

2012-01-01

We present the first field topology analysis based on nonlinear force-free field (NLFFF) models of a long-lasting coronal sigmoid observed in 2007 February with the X-Ray Telescope on Hinode. The NLFFF models are built with the flux rope insertion method and give the three-dimensional coronal magnetic field as constrained by observed coronal loop structures and photospheric magnetograms. Based on these models, we have computed horizontal maps of the current and the squashing factor Q for 25 different heights in the corona for all six days of the evolution of the region. We use the squashing factor to quantify the degree of change of the field line linkage and to identify prominent quasi-separatrix layers (QSLs). We discuss the major properties of these QSL maps and devise a way to pick out important QSLs since our calculation cannot reach high values of Q. The complexity in the QSL maps reflects the high degree of fragmentation of the photospheric field. We find main QSLs and current concentrations that outline the flux rope cavity and that become characteristically S-shaped during the evolution of the sigmoid. We note that, although intermittent bald patches exist along the length of the sigmoid during its whole evolution, the flux rope remains stable for several days. However, shortly after the topology of the field exhibits hyperbolic flux tubes (HFT) on February 7 and February 12 the sigmoid loses equilibrium and produces two B-class flares and associated coronal mass ejections (CMEs). The location of the most elevated part of the HFT in our model coincides with the inferred locations of the two flares. Therefore, we suggest that the presence of an HFT in a coronal magnetic configuration may be an indication that the system is ready to erupt. We offer a scenario in which magnetic reconnection at the HFT drives the system toward the marginally stable state. Once this state is reached, loss of equilibrium occurs via the torus instability, producing a CME.

Undergraduate topology a working textbook

CERN Document Server

McCluskey, Aisling

2014-01-01

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp i

Algebraic characterization of vector supersymmetry in topological field theories

Energy Technology Data Exchange (ETDEWEB)

Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Sorella, S.P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica. Dept. de Fisica Teorica

1997-01-01

An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact anti-field dependent cocycles with negative ghost number, according to the cohomological reformulation of the Noether theorem given by M. Henneaux et al. (author). 32 refs., 5 tabs.

A topologically twisted index for three-dimensional supersymmetric theories

International Nuclear Information System (INIS)

Benini, Francesco; Zaffaroni, Alberto

2015-01-01

We provide a general formula for the partition function of three-dimensional N=2 gauge theories placed on S 2 ×S 1 with a topological twist along S 2 , which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to Ω-backgrounds, as well as two-dimensional theories on S 2 and four-dimensional theories on S 2 ×T 2 . In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants.

Topics in two dimensional conformal field theory and three dimensional topological lattice field theory

International Nuclear Information System (INIS)

Chung, Stephen-wei.

1993-01-01

The authors first construct new parafermions in two-dimensional conformal field theory, generalizing the Z L parafermion theories from integer L to rational L. These non-unitary parafermions have some novel features: an infinite number of currents with negative conformal dimensions for most (if not all) of them. String functions of these new parafermion theories are calculated. They also construct new representations of N = 2 superconformal field theories, whose characters are obtained in terms of these new string functions. They then generalize Felder's BRST cohomology method to construct the characters and branching functions of the SU(2) L x SU(2) K /SU(2) K+L coset theories, where one of the (K,L) is an integer. This method of obtaining the branching functions also serves as a check of their new Z L parafermion theories. The next topic is the Lagrangian formulation of conformal field theory. They construct a chiral gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R , which can be different groups. This new construction is beyond the ordinary vector gauged WZW theory, whose gauge group H is a subgroup of both G L and G R . In the special case where H L = H R , the quantum theory of chiral gauged WZW theory is equivalent to that of the vector gauged WZW theory. It can be further shown that the chiral gauged WZW theory is equivalent to [G L /H L ](z) direct-product [G R /H R ](bar z) coset models in conformal field theory. In the second half of this thesis, they construct topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, they impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two local lattice moves. Invariant solutions are in one-to-one correspondence with Hopf algebras satisfying a certain constraint

Quantum magnetotransport for the surface states of three-dimensional topological insulators in the presence of a Zeeman field

KAUST Repository

Tahir, Muhammad; Schwingenschlö gl, Udo

2013-01-01

We show that the surface states of magnetic topological insulators realize an activated behavior and Shubnikov de Haas oscillations. Applying an external magnetic field perpendicular to the surface of the topological insulator in the presence

Topological signatures of interstellar magnetic fields - I. Betti numbers and persistence diagrams

Science.gov (United States)

Makarenko, Irina; Shukurov, Anvar; Henderson, Robin; Rodrigues, Luiz F. S.; Bushby, Paul; Fletcher, Andrew

2018-04-01

The interstellar medium (ISM) is a magnetized system in which transonic or supersonic turbulence is driven by supernova explosions. This leads to the production of intermittent, filamentary structures in the ISM gas density, whilst the associated dynamo action also produces intermittent magnetic fields. The traditional theory of random functions, restricted to second-order statistical moments (or power spectra), does not adequately describe such systems. We apply topological data analysis (TDA), sensitive to all statistical moments and independent of the assumption of Gaussian statistics, to the gas density fluctuations in a magnetohydrodynamic simulation of the multiphase ISM. This simulation admits dynamo action, so produces physically realistic magnetic fields. The topology of the gas distribution, with and without magnetic fields, is quantified in terms of Betti numbers and persistence diagrams. Like the more standard correlation analysis, TDA shows that the ISM gas density is sensitive to the presence of magnetic fields. However, TDA gives us important additional information that cannot be obtained from correlation functions. In particular, the Betti numbers per correlation cell are shown to be physically informative. Magnetic fields make the ISM more homogeneous, reducing the abundance of both isolated gas clouds and cavities, with a stronger effect on the cavities. Remarkably, the modification of the gas distribution by magnetic fields is captured by the Betti numbers even in regions more than 300 pc from the mid-plane, where the magnetic field is weaker and correlation analysis fails to detect any signatures of magnetic effects.

A novel background field removal method for MRI using projection onto dipole fields (PDF).

Science.gov (United States)

Liu, Tian; Khalidov, Ildar; de Rochefort, Ludovic; Spincemaille, Pascal; Liu, Jing; Tsiouris, A John; Wang, Yi

2011-11-01

For optimal image quality in susceptibility-weighted imaging and accurate quantification of susceptibility, it is necessary to isolate the local field generated by local magnetic sources (such as iron) from the background field that arises from imperfect shimming and variations in magnetic susceptibility of surrounding tissues (including air). Previous background removal techniques have limited effectiveness depending on the accuracy of model assumptions or information input. In this article, we report an observation that the magnetic field for a dipole outside a given region of interest (ROI) is approximately orthogonal to the magnetic field of a dipole inside the ROI. Accordingly, we propose a nonparametric background field removal technique based on projection onto dipole fields (PDF). In this PDF technique, the background field inside an ROI is decomposed into a field originating from dipoles outside the ROI using the projection theorem in Hilbert space. This novel PDF background removal technique was validated on a numerical simulation and a phantom experiment and was applied in human brain imaging, demonstrating substantial improvement in background field removal compared with the commonly used high-pass filtering method. Copyright © 2011 John Wiley & Sons, Ltd.

Topological gravity with minimal matter

International Nuclear Information System (INIS)

Li Keke

1991-01-01

Topological minimal matter, obtained by twisting the minimal N = 2 supeconformal field theory, is coupled to two-dimensional topological gravity. The free field formulation of the coupled system allows explicit representations of BRST charge, physical operators and their correlation functions. The contact terms of the physical operators may be evaluated by extending the argument used in a recent solution of topological gravity without matter. The consistency of the contact terms in correlation functions implies recursion relations which coincide with the Virasoro constraints derived from the multi-matrix models. Topological gravity with minimal matter thus provides the field theoretic description for the multi-matrix models of two-dimensional quantum gravity. (orig.)

Ordered groups and topology

CERN Document Server

Clay, Adam

2016-01-01

This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.

Lepton-photon interactions in external background fields

Energy Technology Data Exchange (ETDEWEB)

Akal, Ibrahim [Theory Group, Deutsches Elektronen-Synchrotron (DESY), Notkestrasse 85, D-22607 Hamburg (Germany); Moortgat-Pick, Gudrid [II. Institute for Theoretical Physics, University of Hamburg, Luruper Chaussee 149, D-22761 Hamburg (Germany)

2016-07-01

We investigate lepton-photon interactions in a class of generalized external background fields with periodic plane-wave character. Considering the full interaction with the background, S-matrix elements are calculated exactly. We apply those general expressions to interaction schemes like Compton scattering in specific field configurations, as for instance provided in modern laser facilities, or in high intense regions of future linear colliders. Results are extended to the case of frontal colliding high-energy field photons with leptons such that new insights beyond the usual soft terms become accessible.

Stochastic quantization of topological field theory: generalized Langevin equation with memory kernel

International Nuclear Information System (INIS)

Menezes, G.; Svaiter, N.F.

2006-04-01

We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. (author)

Antiferromagnetic and topological states in silicene: A mean field study

Science.gov (United States)

Liu, Feng; Liu, Cheng-Cheng; Yao, Yu-Gui

2015-08-01

It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron-electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling (SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K‧ for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state. Project supported by the National Key Basic Research Program of China (Grant Nos. 2014CB920903, 2013CB921903, 2011CBA00108, and 2012CB937500), the National Natural Science Foundation of China (Grant Nos. 11021262, 11172303, 11404022, 11225418, and 11174337), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20121101110046), the Excellent Young Scholars Research Fund of Beijing Institute of Technology (Grant No. 2014CX04028), and the Basic Research Funds of Beijing Institute of Technology (Grant No. 20141842001).

MAGNETIC FIELD TOPOLOGY IN LOW-MASS STARS: SPECTROPOLARIMETRIC OBSERVATIONS OF M DWARFS

International Nuclear Information System (INIS)

Phan-Bao, Ngoc; Lim, Jeremy; Donati, Jean-Francois; Johns-Krull, Christopher M.; MartIn, Eduardo L.

2009-01-01

The magnetic field topology plays an important role in the understanding of stellar magnetic activity. While it is widely accepted that the dynamo action present in low-mass partially convective stars (e.g., the Sun) results in predominantly toroidal magnetic flux, the field topology in fully convective stars (masses below ∼0.35 M sun ) is still under debate. We report here our mapping of the magnetic field topology of the M4 dwarf G 164-31 (or Gl 490B), which is expected to be fully convective, based on time series data collected from 20 hr of observations spread over three successive nights with the ESPaDOnS spectropolarimeter. Our tomographic imaging technique applied to time series of rotationally modulated circularly polarized profiles reveals an axisymmetric large-scale poloidal magnetic field on the M4 dwarf. We then apply a synthetic spectrum fitting technique for measuring the average magnetic flux on the star. The flux measured in G 164-31 is |Bf| = 3.2 ± 0.4 kG, which is significantly greater than the average value of 0.68 kG determined from the imaging technique. The difference indicates that a significant fraction of the stellar magnetic energy is stored in small-scale structures at the surface of G 164-31. Our Hα emission light curve shows evidence for rotational modulation suggesting the presence of localized structure in the chromosphere of this M dwarf. The radius of the M4 dwarf derived from the rotational period and the projected equatorial velocity is at least 30% larger than that predicted from theoretical models. We argue that this discrepancy is likely primarily due to the young nature of G 164-31 rather than primarily due to magnetic field effects, indicating that age is an important factor which should be considered in the interpretation of this observational result. We also report here our polarimetric observations of five other M dwarfs with spectral types from M0 to M4.5, three of them showing strong Zeeman signatures.

New topological invariants for non-abelian antisymmetric tensor fields from extended BRS algebra

International Nuclear Information System (INIS)

Boukraa, S.; Maillet, J.M.; Nijhoff, F.

1988-09-01

Extended non-linear BRS and Gauge transformations containing Lie algebra cocycles, and acting on non-abelian antisymmetric tensor fields are constructed in the context of free differential algebras. New topological invariants are given in this framework. 6 refs

On the background independence of string field theory

International Nuclear Information System (INIS)

Sen, A.

1990-01-01

Given a solution Ψ cl of the classical equations of motion in either closed or open string field theory formulated around a given conformal field theory background, we can construct a new operator Q B in the corresponding two-dimensional field theory such that (Q B ) 2 =0. It is shown that in the limit when the background field Ψ cl is weak, Q B can be identified with the BRST charge of a new local conformal field theory. This indicates that the string field theories formulated around these two different conformal field theories are actually the same theory, and that these two conformal field theories may be regarded as different classical solutions of this string field theory. (orig.)

Topological Foundations of Electromagnetism

CERN Document Server

Barrett, Terrence W

2008-01-01

Topological Foundations of Electromagnetism seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in certain precisely defined topological conditions, electromagnetic theory (Maxwell's theory) must be extended or generalized in order to provide an explanation and understanding of, until now, unusual electromagnetic phenomena. Key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical effects. Basic to the approach taken is that the topological composition of electromagnetic field

From topological quantum field theories to supersymmetric gauge theories

International Nuclear Information System (INIS)

Bossard, G.

2007-10-01

This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the β function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)

Measurement of the topological charge and index of vortex vector optical fields with a space-variant half-wave plate.

Science.gov (United States)

Liu, Gui-Geng; Wang, Ke; Lee, Yun-Han; Wang, Dan; Li, Ping-Ping; Gou, Fangwang; Li, Yongnan; Tu, Chenghou; Wu, Shin-Tson; Wang, Hui-Tian

2018-02-15

Vortex vector optical fields (VVOFs) refer to a kind of vector optical field with an azimuth-variant polarization and a helical phase, simultaneously. Such a VVOF is defined by the topological index of the polarization singularity and the topological charge of the phase vortex. We present a simple method to measure the topological charge and index of VVOFs by using a space-variant half-wave plate (SV-HWP). The geometric phase grating of the SV-HWP diffracts a VVOF into ±1 orders with orthogonally left- and right-handed circular polarizations. By inserting a polarizer behind the SV-HWP, the two circular polarization states project into the linear polarization and then interfere with each other to form the interference pattern, which enables the direct measurement of the topological charge and index of VVOFs.

A short course on topological insulators band structure and edge states in one and two dimensions

CERN Document Server

Asbóth, János K; Pályi, András

2016-01-01

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.

Topological insulators in cold-atom gases with non-Abelian gauge fields: the role of interactions

Energy Technology Data Exchange (ETDEWEB)

Orth, Peter Philipp [Institut fuer Theorie der Kondensierten Materie, Karlsruher Institut fuer Technologie, 76128 Karlsruhe (Germany); Cocks, Daniel; Buchhold, Michael; Hofstetter, Walter [Institut fuer Theoretische Physik, Goethe Universitaet, 60438 Frankfurt am Main (Germany); Rachel, Stephan [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States); Le Hur, Karyn [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States); Center for Theoretical Physics, Ecole Polytechnique, 91128 Palaiseau Cedex (France)

2012-07-01

With the recent technological advance of creating (non)-Abelian gauge fields for ultracold atoms in optical lattices, it becomes possible to study the interplay of topological phases and interactions in these systems. Specifically, we consider a spinful and time-reversal invariant version of the Hofstadter problem. In addition, we allow for a hopping term which does not preserve S{sub z} spin symmetry and a staggered sublattice potential. Without interactions, the parameters can be tuned such that the system is a topological insulator. Using a combination of analytical techniques and the powerful real-space dynamical mean-field (R-DMFT) method, we discuss the effect of interactions and determine the interacting phase diagram.

Toric topology

CERN Document Server

Buchstaber, Victor M

2015-01-01

This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric v

The Topological Field Theory of Data: a program towards a novel strategy for data mining through data language

Science.gov (United States)

Rasetti, M.; Merelli, E.

2015-07-01

This paper aims to challenge the current thinking in IT for the 'Big Data' question, proposing - almost verbatim, with no formulas - a program aiming to construct an innovative methodology to perform data analytics in a way that returns an automaton as a recognizer of the data language: a Field Theory of Data. We suggest to build, directly out of probing data space, a theoretical framework enabling us to extract the manifold hidden relations (patterns) that exist among data, as correlations depending on the semantics generated by the mining context. The program, that is grounded in the recent innovative ways of integrating data into a topological setting, proposes the realization of a Topological Field Theory of Data, transferring and generalizing to the space of data notions inspired by physical (topological) field theories and harnesses the theory of formal languages to define the potential semantics necessary to understand the emerging patterns.

Planck 2013 results. XXVI. Background geometry and topology of the Universe

CERN Document Server

Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Dupac, X.; Efstathiou, G.; Ensslin, T.A.; Eriksen, H.K.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Ganga, K.; Giard, M.; Giardino, G.; Giraud-Heraud, Y.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F.K.; Hanson, D.; Harrison, D.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Jaffe, T.R.; Jaffe, A.H.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Laureijs, R.J.; Lawrence, C.R.; Leahy, J.P.; Leonardi, R.; Leroy, C.; Lesgourgues, J.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; McEwen, J.D.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Pogosyan, D.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Riazuelo, A.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rowan-Robinson, M.; Rusholme, B.; Sandri, M.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; Yvon, D.; Zacchei, A.; Zonca, A.

2014-01-01

Planck CMB temperature maps allow detection of large-scale departures from homogeneity and isotropy. We search for topology with a fundamental domain nearly intersecting the last scattering surface (comoving distance $\\chi_r$). For most topologies studied the likelihood maximized over orientation shows some preference for multi-connected models just larger than $\\chi_r$. This effect is also present in simulated realizations of isotropic maps and we interpret it as the alignment of mild anisotropic correlations with chance features in a single realization; such a feature can also exist, in milder form, when the likelihood is marginalized over orientations. Thus marginalized, the limits on the radius $R_i$ of the largest sphere inscribed in a topological domain (at log-likelihood-ratio -5) are: in a flat Universe, $R_i>0.9\\chi_r$ for the cubic torus (cf. $R_i>0.9\\chi_r$ at 99% CL for a matched-circles search); $R_i>0.7\\chi_r$ for the chimney; $R_i>0.5\\chi_r$ for the slab; in a positively curved Universe, $R_i>1...

On the renormalization of topological Yang-Mills field theory in N=1 superspace

Energy Technology Data Exchange (ETDEWEB)

Oliveira, M.W. de; Penna Firme, A.B.

1996-03-01

We discuss the renormalization aspects of topological super-Yang-Mills field theory in N=1 superspace. Our approach makes use of the regularization independent BRS algebraic technique adapted to the case of a N=1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be BRS-coboundary, implying that the co-homological properties of the super topological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik {beta}-function of the model by employing a recently discovered supersymmetric antighost Ward identity. (author). 30 refs.

On the renormalization of topological Yang-Mills field theory in N=1 superspace

International Nuclear Information System (INIS)

Oliveira, M.W. de; Penna Firme, A.B.

1996-03-01

We discuss the renormalization aspects of topological super-Yang-Mills field theory in N=1 superspace. Our approach makes use of the regularization independent BRS algebraic technique adapted to the case of a N=1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be BRS-coboundary, implying that the co-homological properties of the super topological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik β-function of the model by employing a recently discovered supersymmetric antighost Ward identity. (author). 30 refs

Two-dimensional topological photonics

Science.gov (United States)

Khanikaev, Alexander B.; Shvets, Gennady

2017-12-01

Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.

Towards Noncommutative Topological Quantum Field Theory: Tangential Hodge-Witten cohomology

International Nuclear Information System (INIS)

Zois, I P

2014-01-01

Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called ''tangential cohomology'' of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for tangential cohomology of foliations by mimicing Witten's approach to ordinary Morse theory by perturbations of the Laplacian

The Status of Cosmic Topology after Planck Data

Directory of Open Access Journals (Sweden)

Jean-Pierre Luminet

2016-01-01

Full Text Available In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB obtained by WMAP and Planck telescopes. Cosmic Topology involves both global topological features and more local geometrical properties such as curvature. It deals with questions such as whether space is finite or infinite, simply-connected or multi-connected, and smaller or greater than its observable counterpart. A striking feature of some relativistic, multi-connected small universe models is to create multiples images of faraway cosmic sources. While the last CMB (Planck data fit well the simplest model of a zero-curvature, infinite space model, they remain consistent with more complex shapes such as the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. We review the theoretical and observational status of the field.

Quasinormal modes, stability analysis and absorption cross section for 4-dimensional topological Lifshitz black hole

International Nuclear Information System (INIS)

Gonzalez, P.A.; Moncada, Felipe; Vasquez, Yerko

2012-01-01

We study scalar perturbations in the background of a topological Lifshitz black hole in four dimensions. We compute analytically the quasinormal modes and from these modes we show that topological Lifshitz black hole is stable. On the other hand, we compute the reflection and transmission coefficients and the absorption cross section and we show that there is a range of modes with high angular momentum which contributes to the absorption cross section in the low frequency limit. Furthermore, in this limit, we show that the absorption cross section decreases if the scalar field mass increases, for a real scalar field mass. (orig.)

Quasinormal modes, stability analysis and absorption cross section for 4-dimensional topological Lifshitz black hole

Energy Technology Data Exchange (ETDEWEB)

Gonzalez, P.A. [Universidad Central de Chile, Escuela de Ingenieria Civil en Obras Civiles, Facultad de Ciencias Fisicas y Matematicas, Santiago (Chile); Universidad Diego Portales, Santiago (Chile); Moncada, Felipe; Vasquez, Yerko [Universidad de La Frontera, Departamento de Ciencias Fisicas, Facultad de Ingenieria, Ciencias y Administracion, Temuco (Chile)

2012-12-15

We study scalar perturbations in the background of a topological Lifshitz black hole in four dimensions. We compute analytically the quasinormal modes and from these modes we show that topological Lifshitz black hole is stable. On the other hand, we compute the reflection and transmission coefficients and the absorption cross section and we show that there is a range of modes with high angular momentum which contributes to the absorption cross section in the low frequency limit. Furthermore, in this limit, we show that the absorption cross section decreases if the scalar field mass increases, for a real scalar field mass. (orig.)

A topological derivative method for topology optimization

DEFF Research Database (Denmark)

Norato, J.; Bendsøe, Martin P.; Haber, RB

2007-01-01

resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void......We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric...... regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures....

Comparison of serial field bus topologies at high transmission rates; Topologievergleich serieller Feldbusse bei hohen Uebertragungsraten

Energy Technology Data Exchange (ETDEWEB)

Meier, U. [Fachhochschule Lippe, Lemgo (Germany); Meinhardt, S. [Eltromat Gesellschaft fuer Industrieelektronik mbH, Leopoldshoehe (Germany)

1999-11-01

This paper investigates the maximum transmission rate of serial field-busses for different line topologies. The unidirectional point-to-point topology (e.g. INTERBUS-S) and the bidirectional multi-drop topology (e.g. PROFIBUS-DP) are compared. Developed simulation models and their results will be presented and causes of different transmission ranges will be discussed. (orig.) [Deutsch] Dieser Beitrag untersucht die maximal nutzbare Uebertragungsrate serieller Feldbusse unter Beruecksichtigung ihrer unterschiedlichen Leitungstopologien. Vergleichend gegenuebergstellt werden eine unidirektionale Punkt-zu-Punkt-Topologie (z.B. INTERBUS-S) und eine bidirektionale Multi-Drop-Topologie (z.B. PROFIBUS-DP). Entwickelte Simulationsmodelle und deren Ergebnisse werden vorgestellt und die Ursachen der unterschiedlichen Uebertragungsreichweiten eroertert. (orig.)

Phase-Field Relaxation of Topology Optimization with Local Stress Constraints

DEFF Research Database (Denmark)

Stainko, Roman; Burger, Martin

2006-01-01

inequality constraints. We discretize the problem by finite elements and solve the arising finite-dimensional programming problems by a primal-dual interior point method. Numerical experiments for problems with local stress constraints based on different criteria indicate the success and robustness......We introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase-field method. In the basic formulation we have a PDE-constrained optimization problem, where the finite element and design analysis are solved simultaneously...

Effect of the topology of the universe on the cosmic microwave background radiation

International Nuclear Information System (INIS)

Caillerie, Samuel

2005-01-01

Whereas geometrical problems of cosmology related to the local shape of the Universe are well described, this research thesis, after some recalls on cosmology, addresses the issue of Universe topology. The author explains how topology can be described by using the conventional image of 'ghost objects', and then shows that topology intervenes at the level of Eigenmodes of different physical values which describe the content of the Universe by discretizing them. Thus, the author proposes a reinterpretation of the behaviour of the power spectrum, and notably the weak quadrupole, in a topological effect related to the lack of modes for this scale. However, the problem of the shape of the Universe remains open as few estimators are actually reliable with respect to present observations. But the author states that some models can be discarded (like non simply connected non Euclidean models), and that some strong constraints can be obtained on the remaining models [fr

Nonperturbative quantum electrodynamics in a photon-condensate background field

International Nuclear Information System (INIS)

Kikuchi, Y.; Ng, Y.J.

1988-01-01

Analyses of the Schwinger-Dyson (SD) equation for the fermion self-energy have revealed the existence of a QED ultraviolet nonperturbative fixed point which separates a strong-coupling regime from a weak-coupling regime. Here we study the SD equation in the presence of a weak constant photon-condensate background field. This background field does not seem to affect the fixed point. Better approximations or some more realistic background fields may change the result. The investigation is partly motivated by recent heavy-ion experiments

QCD as a topologically ordered system

International Nuclear Information System (INIS)

Zhitnitsky, Ariel R.

2013-01-01

We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called “deformed QCD” which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial θ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological “BF” action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1) A problem where the would be η ′ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the U(1) A problem). Finally, we elaborate on relation between “string-net” condensation in topologically ordered condensed matter systems and long range coherent configurations, the “skeletons”, studied in QCD lattice simulations. -- Highlights: •QCD may belong to a topologically ordered phase similar to condensed matter (CM) systems. •We identify the non-propagating topological field in deformed QCD with the Veneziano ghost. •Relation between “string-net” condensates in CM systems and the “skeletons” in QCD lattice simulations is studied

Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topological interactions

KAUST Repository

Haskovec, Jan

2013-10-01

We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called "topological distance" in previous works), which is the number of intermediate individuals separating them. This makes the model scale-free and is motivated by recent extensive observations of starling flocks, suggesting that the interaction ruling animal collective behavior depends on topological rather than the metric distance. We study the conditions leading to asymptotic flocking in the topological model, defined as the convergence of the agents\\' velocities to a common vector. The shift from metric to topological interactions requires development of new analytical methods, taking into account the graph-theoretical nature of the problem. Moreover, we provide a rigorous derivation of the mean-field limit of large populations, recovering kinetic and hydrodynamic descriptions. In particular, we introduce the novel concept of relative separation in continuum descriptions, which is applicable to a broad variety of models of collective behavior. As an example, we shortly discuss a topological modification of the attraction-repulsion model and illustrate with numerical simulations that the modified model produces interesting new pattern dynamics. © 2013 Elsevier B.V. All rights reserved.

The Topological Field Theory of Data: a program towards a novel strategy for data mining through data language

International Nuclear Information System (INIS)

Rasetti, M; Merelli, E

2015-01-01

This paper aims to challenge the current thinking in IT for the 'Big Data' question, proposing - almost verbatim, with no formulas - a program aiming to construct an innovative methodology to perform data analytics in a way that returns an automaton as a recognizer of the data language: a Field Theory of Data. We suggest to build, directly out of probing data space, a theoretical framework enabling us to extract the manifold hidden relations (patterns) that exist among data, as correlations depending on the semantics generated by the mining context. The program, that is grounded in the recent innovative ways of integrating data into a topological setting, proposes the realization of a Topological Field Theory of Data, transferring and generalizing to the space of data notions inspired by physical (topological) field theories and harnesses the theory of formal languages to define the potential semantics necessary to understand the emerging patterns. (paper)

Defects in G/H coset, G/G topological field theory and discrete Fourier–Mukai transform

DEFF Research Database (Denmark)

Sarkissian, Gor

2011-01-01

with Wilson lines are established. Special attention to topological coset G/G has been paid. We prove that a G/G theory on a cylinder with N defects coincides with Chern–Simons theory on a torus times the time-line R with 2N Wilson lines. We have shown also that a G/G theory on a strip with N defects...... coincides with Chern–Simons theory on a sphere times the time-line R with 2N+4 Wilson lines. This particular example of topological field theory enables us to penetrate into a general picture of defects in semisimple 2D topological field theory. We conjecture that defects in this case described by a 2...

 Topological quantum field theory: 20 years later

DEFF Research Database (Denmark)

Reshetikhin, Nicolai

2008-01-01

This article is an overview of the developments in topological quantum field theory, and, in particular on the progress in the Chern–Simons theory.......This article is an overview of the developments in topological quantum field theory, and, in particular on the progress in the Chern–Simons theory....

D-string fluid in conifold, I: Topological gauge model

International Nuclear Information System (INIS)

Ahl Laamara, R.; Drissi, L.B.; Saidi, E.H.

2006-01-01

Motivated by similarities between quantum Hall systems a la Susskind and aspects of topological string theory on conifold as well as results obtained in [E.H. Saidi, Topological SL(2) gauge theory on conifold and noncommutative geometry, hep-th/0601020], we study the dynamics of D-string fluids running in deformed conifold in presence of a strong and constant RR background B-field. We first introduce the basis of D-string system in fluid approximation and then derive the holomorphic noncommutative gauge invariant field action describing its dynamics in conifold. This study may be also viewed as embedding Susskind description for Laughlin liquid in type IIB string theory. FQH systems on real manifolds RxS 2 and S 3 are shown to be recovered by restricting conifold to its Lagrangian sub-manifolds. Aspects of quantum behaviour of the string fluid are discussed. ring fluid are discussed

Topology and geometry for physicists

CERN Document Server

Nash, Charles

1983-01-01

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr

Lagrangian statistics and flow topology in forced two-dimensional turbulence.

Science.gov (United States)

Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K

2011-03-01

A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.

Coronal Heating Topology: The Interplay of Current Sheets and Magnetic Field Lines

Energy Technology Data Exchange (ETDEWEB)

Rappazzo, A. F.; Velli, M. [Department of Earth, Planetary, and Space Sciences, UCLA, Los Angeles, CA 90095 (United States); Matthaeus, W. H. [Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (United States); Ruffolo, D. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Servidio, S., E-mail: rappazzo@ucla.edu [Dipartimento di Fisica, Università della Calabria, Cosenza I-87036 (Italy)

2017-07-20

The magnetic topology and field line random walk (FLRW) properties of a nanoflare-heated and magnetically confined corona are investigated in the reduced magnetohydrodynamic regime. Field lines originating from current sheets form coherent structures, called current sheet connected (CSC) regions, which extend around them. CSC FLRW is strongly anisotropic, with preferential diffusion along the current sheets’ in-plane length. CSC FLRW properties remain similar to those of the entire ensemble but exhibit enhanced mean square displacements and separations due to the stronger magnetic field intensities in CSC regions. The implications for particle acceleration and heat transport in the solar corona and wind, and for solar moss formation are discussed.

Two-dimensional Topology of the Two-Degree Field Galaxy Redshift Survey

Science.gov (United States)

Hoyle, Fiona; Vogeley, Michael S.; Gott, J. Richard, III

2002-05-01

We study the topology of the publicly available data released by the Two Degree Field Galaxy Redshift Survey team (2dF GRS). The 2dF GRS data contain over 100,000 galaxy redshifts with a magnitude limit of bJ=19.45 and is the largest such survey to date. The data lie over a wide range of right ascension (75° strips) but only within a narrow range of declination (10° and 15° strips). This allows measurements of the two-dimensional genus to be made. We find that the genus curves of the north Galactic pole (NGP) and south Galactic pole (SGP) are slightly different. The NGP displays a slight meatball shift topology, whereas the SGP displays a bubble-like topology. The current SGP data also have a slightly higher genus amplitude. In both cases, a slight excess of overdense regions is found over underdense regions. We assess the significance of these features using mock catalogs drawn from the Virgo Consortium's Hubble volume ΛCDM z=0 simulation. We find that differences between the NGP and SGP genus curves are only significant at the 1 σ level. The average genus curve of the 2dF GRS agrees well with that extracted from the ΛCDM mock catalogs. We also use the simulations to assess how the current incompleteness of the survey (the strips are not completely filled in) affects the measurement of the genus and find that we are not sensitive to the geometry; there are enough data in the current sample to trace the isolated high- and low-density regions. We compare the amplitude of the 2dF GRS genus curve to the amplitude of the genus curve of a Gaussian random field that we construct to have the same power spectrum as the 2dF GRS. In previous three-dimensional analyses, it was found that the genus curve of observed samples was lower than the Gaussian random field curve, presumably because of high-order correlations present in the data. However, we find that the 2dF GRS genus curve has an amplitude that is slightly higher than that of the power-spectrum-matched Gaussian

Topologies on the algebra of test functions in quantum field theory

International Nuclear Information System (INIS)

Hofmann, G.

1982-01-01

The algebraic structure of the tensor algebra over the Schwartz spce defines two topologies. The properties of the locally convex topologies situated between the topologies defined above are studied and the families of topologies for which the positive cone is normal or non-normal are constructed

Topological Higgs mechanism with ordinary Higgs mechanism

International Nuclear Information System (INIS)

Oda Ichiro; Yahikozawa Shigeaki.

1989-12-01

Topological Higgs mechanism in higher dimensions is analyzed when ordinary Higgs potential exists. It is shown that if one-form B-field becomes massive by the ordinary Higgs mechanism, another D-2 form C-field also becomes massive through topological term in addition to the topological mass generation by the topological Higgs mechanism. Moreover we investigate this mechanism in three dimensional theories, that is to say, Chern-Simons theory and more general theory. (author). 10 refs

Topological phases of silicene and germanene in an external magnetic field: Quantitative results

KAUST Repository

Singh, Nirpendra; Schwingenschlö gl, Udo

2014-01-01

We investigate the topological phases of silicene and germanene that arise due to the strong spin-orbit interaction in an external perpendicular magnetic field. Below and above a critical field of 10 T, respectively, we demonstrate for silicene under 3% tensile strain quantum spin Hall and quantum anomalous Hall phases. Not far above the critical field, and therefore in the experimentally accessible regime, we obtain an energy gap in the meV range, which shows that the quantum anomalous Hall phase can be realized experimentally in silicene, in contrast to graphene (tiny energy gap) and germanene (enormous field required). © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Topological phases of silicene and germanene in an external magnetic field: Quantitative results

KAUST Repository

Singh, Nirpendra

2014-03-17

We investigate the topological phases of silicene and germanene that arise due to the strong spin-orbit interaction in an external perpendicular magnetic field. Below and above a critical field of 10 T, respectively, we demonstrate for silicene under 3% tensile strain quantum spin Hall and quantum anomalous Hall phases. Not far above the critical field, and therefore in the experimentally accessible regime, we obtain an energy gap in the meV range, which shows that the quantum anomalous Hall phase can be realized experimentally in silicene, in contrast to graphene (tiny energy gap) and germanene (enormous field required). © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Few remarks on chiral theories with sophisticated topology

International Nuclear Information System (INIS)

Golo, V.L.; Perelomov, A.M.

1978-01-01

Two classes of the two-dimensional Euclidean chiral field theoreties are singled out: 1) the field phi(x) takes the values in the compact Hermitiam symmetric space 2) the field phi(x) takes the values in an orbit of the adjoint representation of the comcompact Lie group. The theories have sophisticated topological and rich analytical structures. They are considered with the help of topological invariants (topological charges). Explicit formulae for the topological charges are indicated, and the lower bound extimate for the action is given

Magnetic field topology and chemical abundance distributions of the young, rapidly rotating, chemically peculiar star HR 5624

Science.gov (United States)

Kochukhov, O.; Silvester, J.; Bailey, J. D.; Landstreet, J. D.; Wade, G. A.

2017-09-01

Context. The young, rapidly rotating Bp star HR 5624 (HD 133880) shows an unusually strong non-sinusoidal variability of its longitudinal magnetic field. This behaviour was previously interpreted as the signature of an exceptionally strong, quadrupole-dominated surface magnetic field geometry. Aims: We studied the magnetic field structure and chemical abundance distributions of HR 5624 with the aim to verify the unusual quadrupolar nature of its magnetic field and to investigate correlations between the field topology and chemical spots. Methods: We analysed high-resolution, time series Stokes parameter spectra of HR 5624 with the help of a magnetic Doppler imaging inversion code based on detailed polarised radiative transfer modelling of the line profiles. Results: We refined the stellar parameters, revised the rotational period, and obtained new longitudinal magnetic field measurements. Our magnetic Doppler inversions reveal that the field structure of HR 5624 is considerably simpler and the field strength is much lower than proposed by previous studies. We find a maximum local field strength of 12 kG and a mean field strength of 4 kG, which is about a factor of three weaker than predicted by quadrupolar field models. Our model implies that overall large-scale field topology of HR 5624 is better described as a distorted, asymmetric dipole rather than an axisymmetric quadrupole. The chemical abundance maps of Mg, Si, Ti, Cr, Fe, and Nd obtained in our study are characterised by large-scale, high-contrast abundance patterns. These structures correlate weakly with the magnetic field geometry and, in particular, show no distinct element concentrations in the horizontal field regions predicted by theoretical atomic diffusion calculations. Conclusions: We conclude that the surface magnetic field topology of HR 5624 is not as unusual as previously proposed. Considering these results together with other recent magnetic mapping analyses of early-type stars suggests that

Nonabelian gauge fields in the background of magnetic strings

International Nuclear Information System (INIS)

Wieczorek, E.

1993-01-01

Quantized nonabelian gauge fields are studied in the external classical background of a linear magnetic string. The determination of the gauge field propagator demands a specification of the string by suitable physical limiting procedures. The vacuum energy density is obtained after transforming the background problem into a Casimir problem. (orig.)

On the topology of flux transfer events

Science.gov (United States)

Hesse, Michael; Birn, Joachim; Schindler, Karl

1990-01-01

A topological analysis is made of a simple model magnetic field of a perturbation at the magnetopause that shares magnetic properties with flux transfer events. The aim is to clarify a number of topological aspects that arise in the case of fully three-dimensional magnetic fields. It is shown that a localized perturbation at the magnetopause can in principle open a closed magnetosphere by establishing magnetic connections across the magnetopause by the formation of a ropelike magnetic field structure. For this purpose a global topological model of a closed magnetosphere is considered as the unperturbed state. The topological substructure of the model flux rope is discussed in detail.

Leader propagation in uniform background fields in SF6

International Nuclear Information System (INIS)

Seeger, M; Niemeyer, L; Bujotzek, M

2009-01-01

The breakdown mechanism of compressed SF 6 in gas insulation is known to be controlled by stepped leader propagation. This process is still not well understood in uniform and weakly non-uniform background fields with small electrode protrusions, such as particles or surface roughness. In a previous publication an investigation of partial discharges and breakdown in uniform background fields that focused on streamer and leader inception mechanisms was presented (Seeger et al 2008 J. Phys. D: Appl. Phys. 41 185204). In this paper we present for the first time a physical leader propagation model that consistently describes the observed phenomena in uniform background fields in SF 6 . The model explains two different types of leader breakdown; these can be associated with the precursor and the stem mechanisms. It also yields the parameters of stepped leader propagation, which include step lengths, associated step charges, step times and fields and temperatures in the leader channel. Further, it explains the features of arrested leaders in uniform background fields. The model predicts the range of parameters under which arrested and breakdown leaders occur in good agreement with the experimental data.

Dirichlet topological defects

International Nuclear Information System (INIS)

Carroll, S.M.; Trodden, M.

1998-01-01

We propose a class of field theories featuring solitonic solutions in which topological defects can end when they intersect other defects of equal or higher dimensionality. Such configurations may be termed open-quotes Dirichlet topological defects,close quotes in analogy with the D-branes of string theory. Our discussion focuses on defects in scalar field theories with either gauge or global symmetries, in 3+1 dimensions; the types of defects considered include walls ending on walls, strings on walls, and strings on strings. copyright 1998 The American Physical Society

Contact and symplectic topology

CERN Document Server

Colin, Vincent; Stipsicz, András

2014-01-01

Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

Cosmic Topology

Science.gov (United States)

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.

On deformations and quantization in topological string theory

International Nuclear Information System (INIS)

Kay, Michael

2014-01-01

The study of moduli spaces of N=(2,2) superconformal field theories and more generally of N=(2,2) supersymmetric quantum field theories, has been a longstanding, multifaceted area of research. In this thesis we focus on certain selected general aspects of this study and develop general techniques within the framework of topological string theory. This work is naturally divided into two parts. The first is concerned with aspects of closed topological string theory, and culminates with a theory, where the geometrical structure of the topological anti-topological moduli spaces of N=(2,2) superconformal field theories with central charge c=9 is rediscovered in the light of quantization, within a general framework. The second part is concerned with aspects of the study of the open and closed moduli space of topological conformal field theories at genus zero. In particular, it contains an exposition of a paper, where general results on the classification and computation of bulk-induced deformations of open topological conformal field theories were obtained from a coherent algebraic approach, drawing from the defining L ∞ and A ∞ structures involved. In part, the latter investigation is restricted to arbitrary affine B-twisted Landau Ginzburg models. Subsequently, further original work is presented that completes the topological string field theory structure of B-twisted Landau Ginzburg models.

Chameleon scalar fields in relativistic gravitational backgrounds

Energy Technology Data Exchange (ETDEWEB)

Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Tamaki, Takashi [Department of Physics, Waseda University, Okubo 3-4-1, Tokyo 169-8555 (Japan); Tavakol, Reza, E-mail: shinji@rs.kagu.tus.ac.jp, E-mail: tamaki@gravity.phys.waseda.ac.jp, E-mail: r.tavakol@qmul.ac.uk [Astronomy Unit, School of Mathematical Sciences, Queen Mary University of London, London E1 4NS (United Kingdom)

2009-05-15

We study the field profile of a scalar field {phi} that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential {Phi}{sub c} at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V({phi}) = M{sup 4+n}{phi}{sup -n} by employing the information provided by our analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential {Phi}{sub c} is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for {Phi}{sub c}{approx}

Chameleon scalar fields in relativistic gravitational backgrounds

International Nuclear Information System (INIS)

Tsujikawa, Shinji; Tamaki, Takashi; Tavakol, Reza

2009-01-01

We study the field profile of a scalar field φ that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential Φ c at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials V(φ) = M 4+n φ −n by employing the information provided by our analytical solutions to set the boundary conditions around the centre of the object and show that thin-shell solutions in fact exist if the gravitational potential Φ c is smaller than 0.3, which marginally covers the case of neutron stars. Thus the chameleon mechanism is present in the relativistic gravitational backgrounds, capable of reducing the effective coupling. Since thin-shell solutions are sensitive to the choice of boundary conditions, our analytic field profile is very helpful to provide appropriate boundary conditions for Φ c ∼< O(0.1)

Ambipolar field effect in the ternary topological insulator (BixSb1–x)2Te3 by composition tuning

KAUST Repository

Kong, Desheng

2011-10-02

Topological insulators exhibit a bulk energy gap and spin-polarized surface states that lead to unique electronic properties 1-9, with potential applications in spintronics and quantum information processing. However, transport measurements have typically been dominated by residual bulk charge carriers originating from crystal defects or environmental doping 10-12, and these mask the contribution of surface carriers to charge transport in these materials. Controlling bulk carriers in current topological insulator materials, such as the binary sesquichalcogenides Bi 2Te 3, Sb 2Te 3 and Bi 2Se 3, has been explored extensively by means of material doping 8,9,11 and electrical gating 13-16, but limited progress has been made to achieve nanostructures with low bulk conductivity for electronic device applications. Here we demonstrate that the ternary sesquichalcogenide (Bi xSb 1-x) 2Te 3 is a tunable topological insulator system. By tuning the ratio of bismuth to antimony, we are able to reduce the bulk carrier density by over two orders of magnitude, while maintaining the topological insulator properties. As a result, we observe a clear ambipolar gating effect in (Bi xSb 1-x) 2Te 3 nanoplate field-effect transistor devices, similar to that observed in graphene field-effect transistor devices 17. The manipulation of carrier type and density in topological insulator nanostructures demonstrated here paves the way for the implementation of topological insulators in nanoelectronics and spintronics. © 2011 Macmillan Publishers Limited. All rights reserved.

Topological superconductivity in metallic nanowires fabricated with a scanning tunneling microscope

International Nuclear Information System (INIS)

Rodrigo, J G; Crespo, V; Suderow, H; Vieira, S; Guinea, F

2013-01-01

We report on several low-temperature experiments supporting the presence of Majorana fermions in superconducting lead nanowires fabricated with a scanning tunneling microscope (STM). These nanowires are the connecting bridges between the STM tip and the sample resulting from indentation–retraction processes. We show here that by a controlled tuning of the nanowire region, in which superconductivity is confined by applied magnetic fields, the conductance curves obtained in these situations are indicative of topological superconductivity and Majorana fermions. The most prominent feature of this behavior is the emergence of a zero bias peak in the conductance curves, superimposed on a background characteristic of the conductance between a normal metal and a superconductor in the Andreev regime. The zero bias peak emerges in some nanowires when a magnetic field larger than the lead bulk critical field is applied. This field drives one of the electrodes into the normal state while the other, the tip, remains superconducting on its apex. Meanwhile a topological superconducting state appears in the connecting nanowire of nanometric size. (paper)

Topological Insulators Dirac Equation in Condensed Matters

CERN Document Server

Shen, Shun-Qing

2012-01-01

Topological insulators are insulating in the bulk, but process metallic states around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, Topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological in...

Topology optimization of the permanent magnet type MRI considering the magnetic field homogeneity

International Nuclear Information System (INIS)

Lee, Junghoon; Yoo, Jeonghoon

2010-01-01

This study is to suggest a concept design of the permanent magnet (PM) type magnetic resonance imaging (MRI) device based on the topology optimization method. The pulse currents in the gradient coils in the MRI device will introduce the effect of eddy currents in ferromagnetic material and it may worsen the quality of imaging. To equalize the magnetic flux in the PM type MRI device for good imaging, the eddy current effect in the ferromagnetic material must be reduced. This study attempts to use the topology optimization scheme for equalizing the magnetic flux in the measuring domain of the PM type MRI device using that the magnetic flux can be calculated directly by a commercial finite element analysis package. The density method is adopted for topology optimization and the sensitivity of the objective function is computed according to the density change of each finite element in the design domain. As a result, optimal shapes of the pole of the PM type MRI device can be obtained. The commercial package, ANSYS, is used for analyzing the magnetic field problem and obtaining the resultant magnetic flux.

Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks

International Nuclear Information System (INIS)

Hasan, M Zahid; Xu, Su-Yang; Bian, Guang

2015-01-01

Unlike string theory, topological physics in lower dimensional condensed matter systems is an experimental reality since the bulk-boundary correspondence can be probed experimentally in lower dimensions. In addition, recent experimental discoveries of non-quantum-Hall-like topological insulators, topological superconductors, Weyl semimetals and other topological states of matter also signal a clear departure from the quantum-Hall-effect-like transport paradigm that has dominated the field since the 1980s. It is these new forms of matter that enabled realizations of topological-Dirac, Weyl cones, helical-Cooper-pairs, Fermi-arc-quasiparticles and other emergent phenomena in fine-tuned photoemission (ARPES) experiments since ARPES experiments directly allow the study of bulk-boundary (topological) correspondence. In this proceeding we provide a brief overview of the key experiments and discuss our perspectives regarding the new research frontiers enabled by these experiments. Taken collectively, we argue in favor of the emergence of ‘topological-condensed-matter-physics’ in laboratory experiments for which a variety of theoretical concepts over the last 80 years paved the way. (review)

Focus on topological quantum computation

International Nuclear Information System (INIS)

Pachos, Jiannis K; Simon, Steven H

2014-01-01

Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances in the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This ‘focus on’ collection brings together several of the latest developments in the field and facilitates the synergy between different approaches. (editorial)

Form factors and excitations of topological solitons

International Nuclear Information System (INIS)

Weir, David J.; Rajantie, Arttu

2011-01-01

We show how the interaction properties of topological solitons in quantum field theory can be calculated with lattice Monte Carlo simulations. Topologically nontrivial field configurations are key to understanding the nature of the QCD vacuum through, for example, the dual superconductor picture. Techniques that we have developed to understand the excitations and form factors of topological solitons, such as kinks and 't Hooft-Polyakov monopoles, should be equally applicable to chromoelectric flux tubes. We review our results for simple topological solitons and their agreement with exact results, then discuss our progress towards studying objects of interest to high energy physics.

Topological insulators and superconductors from string theory

International Nuclear Information System (INIS)

Ryu, Shinsei; Takayanagi, Tadashi

2010-01-01

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 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 θ 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).

An extended topological Yang-Mills theory

International Nuclear Information System (INIS)

Deguchi, Shinichi

1992-01-01

Introducing infinite number of fields, we construct an extended version of the topological Yang-Mills theory. The properties of the extended topological Yang-Mills theory (ETYMT) are discussed from standpoint of the covariant canonical quantization. It is shown that the ETYMT becomes a cohomological topological field theory or a theory equivalent to a quantum Yang-Mills theory with anti-self-dual constraint according to subsidiary conditions imposed on state-vector space. On the basis of the ETYMT, we may understand a transition from an unbroken phase to a physical phase (broken phase). (author)

Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale

Science.gov (United States)

Fang, Yiqi; Lu, Qinghong; Wang, Xiaolei; Zhang, Wuhong; Chen, Lixiang

2017-02-01

The study of vortex dynamics is of fundamental importance in understanding the structured light's propagation behavior in the realm of singular optics. Here, combining with the large-angle holographic lithography in photoresist, a simple experiment to trace and visualize the vortex birth and splitting of light fields induced by various fractional topological charges is reported. For a topological charge M =1.76 , the recorded microstructures reveal that although it finally leads to the formation of a pair of fork gratings, these two vortices evolve asynchronously. More interestingly, it is observed on the submicron scale that high-order topological charges M =3.48 and 3.52, respectively, give rise to three and four characteristic forks embedded in the samples with one-wavelength resolution of about 450 nm. Numerical simulations based on orbital angular momentum eigenmode decomposition support well the experimental observations. Our method could be applied effectively to study other structured matter waves, such as the electron and neutron beams.

Topological strings from Liouville gravity

International Nuclear Information System (INIS)

Ishibashi, N.; Li, M.

1991-01-01

We study constrained SU(2) WZW models, which realize a class of two-dimensional conformal field theories. We show that they give rise to topological gravity coupled to the topological minimal models when they are coupled to Liouville gravity. (orig.)

Two-time physics with gravitational and gauge field backgrounds

International Nuclear Information System (INIS)

Bars, Itzhak

2000-01-01

It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d dimensions (one time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained by generalizing the world line formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from d+2 dimensions to (d-1)+1 dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target (d+2)-dimensional spacetime. The gravitational background obeys a closed homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher (d+2)-dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden

Topological field theories and quantum mechanics on commutative space; Theories des champs topologiques et mecanique quantique en espace non-commutatif

Energy Technology Data Exchange (ETDEWEB)

Lefrancois, M

2005-12-15

In particle physics, the Standard Model describes the interactions between fundamental particles. However, it was not able till now to unify quantum field theory and general relativity. This thesis focuses on two different unification approaches, though they might show some compatibility: topological field theories and quantum mechanics on non-commutative space. Topological field theories have been introduced some twenty years ago and have a very strong link to mathematics: their observables are topological invariants of the manifold they are defined on. In this thesis, we first give interest to topological Yang-Mills. We develop a superspace formalism and give a systematic method for the determination of the observables. This approach allows, once projected on a particular super gauge (of Wess-Zumino type), to recover the existing results but it also gives a generalisation to the case of an unspecified super-gauge. We have then be able to show that the up-to-now known observables correspond to the most general form of the solutions. This superspace formalism can be applied to more complex models; the case of topological gravity is given here in example. Quantum mechanics on noncommutative space provides an extension of the Heisenberg algebra of ordinary quantum mechanics. What differs here is that the components of the position or momentum operators do not commute with each other anymore. This implies to introduce a fundamental length. The second part of this thesis focuses on the description of the commutation algebra. Applications are made to low-dimensional quantum systems (Landau system, harmonic oscillator...) and to supersymmetric systems. (author)

Towards topological quantum computer

Science.gov (United States)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Towards topological quantum computer

Directory of Open Access Journals (Sweden)

D. Melnikov

2018-01-01

Full Text Available Quantum R-matrices, the entangling deformations of non-entangling (classical permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern–Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

Topological Susceptibility from Slabs

CERN Document Server

Bietenholz, Wolfgang; Gerber, Urs

2015-01-01

In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.

Magnetic topology and the problem of its invariant definition

International Nuclear Information System (INIS)

Hornig, G.; Schindler, K.

1996-01-01

The evolution of an ideal plasma conserves magnetic lines of force and hence magnetic topology. However, magnetic topology, i.e. the structure and linkage of magnetic flux, is a property of the magnetic field alone. Therefore, the conservation of topology can also be a property of non-ideal plasmas for which the plasma flow is not line conserving. A general definition of magnetic topology is given and it is shown that it yields a large set of non-ideal topology-conserving systems. In the application of the notion of magnetic topology to real plasmas problems arise concerning the stability of topology. Instability may inhibit one from defining the topology of a given real, i.e. not exactly prescribed, magnetic field configuration and makes it difficult to detect changes of magnetic topology, such as reconnection processes. This problem of structural instability of magnetic topology also appears in connection with changes of the frame of reference. A change of the frame of reference may lead to a transition in topology especially for topological unstable, non-ideal systems. copyright 1996 American Institute of Physics

Multiphoton amplitude in a constant background field

Science.gov (United States)

Ahmad, Aftab; Ahmadiniaz, Naser; Corradini, Olindo; Kim, Sang Pyo; Schubert, Christian

2018-01-01

In this contribution, we present our recent compact master formulas for the multiphoton amplitudes of a scalar propagator in a constant background field using the worldline fomulation of quantum field theory. The constant field has been included nonperturbatively, which is crucial for strong external fields. A possible application is the scattering of photons by electrons in a strong magnetic field, a process that has been a subject of great interest since the discovery of astrophysical objects like radio pulsars, which provide evidence that magnetic fields of the order of 1012G are present in nature. The presence of a strong external field leads to a strong deviation from the classical scattering amplitudes. We explicitly work out the Compton scattering amplitude in a magnetic field, which is a process of potential relevance for astrophysics. Our final result is compact and suitable for numerical integration.

Open bosonic string in background electromagnetic field

International Nuclear Information System (INIS)

Nesterenko, V.V.

1987-01-01

The classical and quantum dynamics of an open string propagating in the D-dimensional space-time in the presence of a background electromagnetic field is investigated. An important point in this consideration is the use of the generalized light-like gauge. There are considered the strings of two types; the neutral strings with charges at their ends obeying the condition q 1 +q 2 =0 and the charged strings having a net charge q 1 +q 2 ≠ 0. The consistency of theory demands that the background electric field does not exceed its critical value. The distance between the mass levels of the neutral open string decreases (1-e 2 ) times in comparison with the free string, where e is the dimensionless strength of the electric field. The magnetic field does not affect this distance. It is shown that at a classical level the squared mass of the neutral open string has a tachyonic contribution due to the motion of the string as a whole in transverse directions. The tachyonic term disappears if one considers, instead of M 2 , the string energy in a special reference frame where the projection of the total canonical momentum of the string onto the electric field vanishes. The contributions due to zero point fluctuations to the energy spectrum of the neutral string and to the Virasoro operators in the theory of charged string are found

Broadband Control of Topological Nodes in Electromagnetic Fields

Science.gov (United States)

Song, Alex Y.; Catrysse, Peter B.; Fan, Shanhui

2018-05-01

We study topological nodes (phase singularities) in electromagnetic wave interactions with structures. We show that, when the nodes exist, it is possible to bind certain nodes to a specific plane in the structure by a combination of mirror and time-reversal symmetry. Such binding does not rely on any resonances in the structure. As a result, the nodes persist on the plane over a wide wavelength range. As an implication of such broadband binding, we demonstrate that the topological nodes can be used for hiding of metallic objects over a broad wavelength range.

Relativity of topology and dynamics

International Nuclear Information System (INIS)

Finkelstein, D.; Rodriguez, E.

1984-01-01

Recent developments in quantum set theory are used to formulate a program for quantum topological physics. The world is represented in Hilbert space whose psi vectors represent abstract complexes generated from the null set by one bracket operator and the usual Grassmann (or Clifford) product. Such a theory may be more basic than field theory, in that it may generate its own natural topology, time, kinematics and dynamics, without benefit of an absolute time-space dimension, topology, or Hamiltonian. For example there is a natural expression for the quantum gravitational field in terms of quantum topological operators. In such a theory the usual spectrum of possible dimensions describes only one of an indefinite hierarchy of levels, each with a similar spectrum, describing nonspatial infrastructure. While c simplices have no continuous symmetry, the q simplex has an orthogonal group (O(m,n). Because quantum theory cannot take the universe as physical system, a ''third relativity'' is proposed. The division between observer and observed is arbitrary. Then it is wrong to ask for ''the'' topology and dynamics of a system, in the same sense that it is wrong to ask for the ''the'' psi vectors of a system; topology and dynamics, like psi vectors, are not absolute but relative to the observer. (author)

On background-independent open-string field theory

International Nuclear Information System (INIS)

Witten, E.

1992-01-01

A framework for background-independent open-string field theory is proposed. The approach involves using the Batalin-Vilkovisky formalism, in a way suggested by recent developments in closed-string field theory, to implicitly define a gauge-invariant Lagrangian in a hypothetical ''space of all open-string world-sheet theories.'' It is built into the formalism that classical solutions of the string field theory are Becchi-Rouet-Stora-Tyutin- (BRST-) invariant open-string world-sheet theories and that, when expanding around a classical solution, the infinitesimal gauge transformations are generated by the world-sheet BRST operator

Towards Noncommutative Topological Quantum Field Theory – Hodge theory for cyclic cohomology

International Nuclear Information System (INIS)

Zois, I P

2014-01-01

Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called ''tangential cohomology'' of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for cyclic and Hochschild cohomology for the corresponding C*-algebra of a foliation

Effect of a background electric field on the Hagedorn temperature

International Nuclear Information System (INIS)

Ferrer, E.J.; Incera, V. de la; Fradkin, E.S.

1990-07-01

We compute the one-loop free energy of the open neutral string gas in a constant electromagnetic background. Starting from this result we show that the Hagedorn temperature of this hot string gas depends on the background electric field. The larger the electric field, the lower the Hagedorn temperature is. (author). 13 refs

Topological rings

CERN Document Server

Warner, S

1993-01-01

This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn''s Lemma, is also expected.

Background field coils for the High Field Test Facility

International Nuclear Information System (INIS)

Zbasnik, J.P.; Cornish, D.N.; Scanlan, R.M.; Jewell, A.M.; Leber, R.L.; Rosdahl, A.R.; Chaplin, M.R.

1980-01-01

The High Field Test Facility (HFTF), presently under construction at LLNL, is a set of superconducting coils that will be used to test 1-m-o.d. coils of prototype conductors for fusion magnets in fields up to 12 T. The facility consists of two concentric sets of coils; the outer set is a stack of Nb-Ti solenoids, and the inner set is a pair of solenoids made of cryogenically-stabilized, multifilamentary Nb 3 Sn superconductor, developed for use in mirror-fusion magnets. The HFTF system is designed to be parted along the midplane to allow high-field conductors, under development for Tokamak fusion machines, to be inserted and tested. The background field coils were wound pancake-fashion, with cold-welded joints at both the inner and outer diameters. Turn-to-turn insulation was fabricated at LLNL from epoxy-fiberglass strip. The coils were assembled and tested in our 2-m-diam cryostat to verify their operation

Topological anomalies for Seifert 3-manifolds

Energy Technology Data Exchange (ETDEWEB)

Imbimbo, Camillo [Dipartimento di Fisica, Università di Genova,Via Dodecaneso 33, 16146 Genova (Italy); INFN - Sezione di Genova,Via Dodecaneso 33, 16146, Genova (Italy); Rosa, Dario [School of Physics and Astronomy andCenter for Theoretical Physics Seoul National University,Seoul 151-747 (Korea, Republic of); Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN - Sezione di Milano-Bicocca,I-20126 Milano (Italy)

2015-07-14

We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach, the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the BRST transformations of topological gravity. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context the Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.

Introduction to topological quantum matter & quantum computation

CERN Document Server

Stanescu, Tudor D

2017-01-01

What is -topological- about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-know...

Subquantum nonlocal correlations induced by the background random field

Energy Technology Data Exchange (ETDEWEB)

Khrennikov, Andrei, E-mail: Andrei.Khrennikov@lnu.s [International Center for Mathematical Modelling in Physics and Cognitive Sciences, Linnaeus University, Vaexjoe (Sweden); Institute of Information Security, Russian State University for Humanities, Moscow (Russian Federation)

2011-10-15

We developed a purely field model of microphenomena-prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction-the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology-for Gaussian random fields with covariance operators corresponding to factorizable quantum states).

Subquantum nonlocal correlations induced by the background random field

International Nuclear Information System (INIS)

Khrennikov, Andrei

2011-01-01

We developed a purely field model of microphenomena-prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction-the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology-for Gaussian random fields with covariance operators corresponding to factorizable quantum states).

Topological symmetry breaking of self-interacting fractional Klein-Gordon field theories on toroidal spacetime

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2008-01-01

Quartic self-interacting fractional Klein-Gordon scalar massive and massless field theories on toroidal spacetime are studied. The effective potential and topologically generated mass are determined using zeta-function regularization technique. Renormalization of these quantities are derived. Conditions for symmetry breaking are obtained analytically. Simulations are carried out to illustrate regions or values of compactified dimensions where symmetry-breaking mechanisms appear

Quantum capacitance of an ultrathin topological insulator film in a magnetic field

KAUST Repository

Tahir, M.; Sabeeh, K.; Schwingenschlö gl, Udo

2013-01-01

We present a theoretical study of the quantum magnetocapacitance of an ultrathin topological insulator film in an external magnetic field. The study is undertaken to investigate the interplay of the Zeeman interaction with the hybridization between the upper and lower surfaces of the thin film. Determining the density of states, we find that the electron-hole symmetry is broken when the Zeeman and hybridization energies are varied relative to each other. This leads to a change in the character of the magnetocapacitance at the charge neutrality point. We further show that in the presence of both Zeeman interaction and hybridization the magnetocapacitance exhibits beating at low and splitting of the Shubnikov de Haas oscillations at high perpendicular magnetic field. In addition, we address the crossover from perpendicular to parallel magnetic field and find consistency with recent experimental data.

The graph representation approach to topological field theory in 2 + 1 dimensions

International Nuclear Information System (INIS)

Martin, S.P.

1991-02-01

An alternative definition of topological quantum field theory in 2+1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but non-local observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wavefunctions in this ''graph representation'' approach are functionals on an appropriate set of graphs. This is in contrast to the usual ''connection representation'' approach in which the theory is defined in terms of a gauge field and the wavefunctions are functionals on the space of flat spatial connections modulo gauge transformations

Quantum capacitance of an ultrathin topological insulator film in a magnetic field

KAUST Repository

Tahir, M.

2013-02-12

We present a theoretical study of the quantum magnetocapacitance of an ultrathin topological insulator film in an external magnetic field. The study is undertaken to investigate the interplay of the Zeeman interaction with the hybridization between the upper and lower surfaces of the thin film. Determining the density of states, we find that the electron-hole symmetry is broken when the Zeeman and hybridization energies are varied relative to each other. This leads to a change in the character of the magnetocapacitance at the charge neutrality point. We further show that in the presence of both Zeeman interaction and hybridization the magnetocapacitance exhibits beating at low and splitting of the Shubnikov de Haas oscillations at high perpendicular magnetic field. In addition, we address the crossover from perpendicular to parallel magnetic field and find consistency with recent experimental data.

The Topological Vertex

CERN Document Server

Aganagic, M; Marino, M; Vafa, C; Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun

2005-01-01

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kahler classes of Calabi-Yau. We interpret this result as an operator computation of the amplitudes in the B-model mirror which is the Kodaira-Spencer quantum theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.

Charged Hadron Properties in Background Electric Fields

International Nuclear Information System (INIS)

Detmold, William; Tiburzi, Brian C.; Walker-Loud, Andre

2010-01-01

We report on a lattice calculation demonstrating a novel new method to extract the electric polarizability of charged pseudo-scalar mesons by analyzing two point correlation functions computed in classical background electric fields. A staple component of any electrodynamics or quantum mechanics course is the electric polarizability. Neutral material immersed in a weak external field polarizes, internally setting up an electric dipole moment, aligned so as to minimize the energy. At the atomic level, the electron clouds are distorted creating these microscopic dipole moments. The same process occurs at the hadronic level but the polarization effects are now constrained by the strong force. Polarizabilities of these bound QCD states can be viewed as a distortion of the charged pion cloud of a given hadron. One can use lattice QCD to non-perturbatively compute the quark and gluon interactions in the presence of background electric (or magnetic) fields. For sufficiently weak background fields, the low energy properties of the hadrons can be rigorously computed using effective field theory. With this treatment, a picture of hadrons emerges from chiral dynamics: that of a hadronic core surrounded by a pseudoscalar meson cloud. As some pseudoscalar mesons are charged, polarizabilities of hadrons encode the stiffness of the charged meson cloud (as well as that of the core). The form of pseudoscalar meson polarizabilities is consequently strongly constrained by chiral dynamics. However, beyond the leading order, the results depend upon essentially unknown low-energy constants, which must currently be estimated in a model-dependent fashion. In the case of the charged pion, the experimental measurement of the polarizability has proven difficult, both in the original measurement as well as the most recent published result. Currently, there is a 2-3 sigma discrepancy between the two-loop cPT prediction and the measured charged pion polarizability. New results with higher

Topological susceptibility from slabs

Energy Technology Data Exchange (ETDEWEB)

Bietenholz, Wolfgang [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Forcrand, Philippe de [Institute for Theoretical Physics, ETH Zürich,CH-8093 Zürich (Switzerland); CERN, Physics Department, TH Unit, CH-1211 Geneva 23 (Switzerland); Gerber, Urs [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo,Edificio C-3, Apdo. Postal 2-82, Morelia, Michoacán, C.P. 58040 (Mexico)

2015-12-14

In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ{sub t}. In principle it seems straightforward to measure χ{sub t} by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ{sub t} even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ{sub t}, as we demonstrate with numerical results for non-linear σ-models.

Streamline topology of axisymmetric flows

DEFF Research Database (Denmark)

Brøns, Morten

Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...... and interact follow the topological classification and that the complete set of patterns found is contained in a codimension-4 unfolding of the most simple singular configuration....

Impact of topology in foliated quantum Einstein gravity.

Science.gov (United States)

Houthoff, W B; Kurov, A; Saueressig, F

2017-01-01

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology [Formula: see text]. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology [Formula: see text] (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.

Quantum magnetotransport for the surface states of three-dimensional topological insulators in the presence of a Zeeman field

KAUST Repository

Tahir, Muhammad

2013-05-01

We show that the surface states of magnetic topological insulators realize an activated behavior and Shubnikov de Haas oscillations. Applying an external magnetic field perpendicular to the surface of the topological insulator in the presence of Zeeman interaction, we investigate the opening of a gap at the Dirac point, making the surface Dirac fermions massive, and the effects on the transport properties. Analytical expressions are derived for the collisional conductivity for elastic impurity scattering in the first Born approximation. We also calculate the Hall conductivity using the Kubo formalism. Evidence for a transition from gapless to gapped surface states at n = 0 and activated transport is found from the temperature and magnetic-field dependence of the collisional and Hall conductivities. © Copyright EPLA, 2013.

Topological twist in four dimensions, R-duality and hyperinstantons

International Nuclear Information System (INIS)

Anselmi, D.; Fre, P.

1993-01-01

In this paper we continue the programme of topologically twisting N=2 theories in D=4, focusing on the coupling of vector multiplets to N=2 supergravity. We show that in the minimal case, namely when the special gometry prepotential F(X) is a quadratic polynomial, the theory has a so far unknown on-shell U(1) symmetry, that we name R-duality. R-duality is a generalization of the chiral-dual on-shell symmetry of N=2 pure supergravity and of the R-symmetry of N=2 super Yang-Mills theory. Thanks to this, the theory can be topologically twisted and topologically shifted, precisely as pure N=2 supergravity, to yield a natural coupling of topological gravity to topological Yang-Mills theory. The gauge-fixing condition that emerges from the twisting is the self-duality condition on the gauge field strength and on the spin connection. Hence our theory reduces to intersection theory in the moduli-space of gauge instantons living in gravitational instanton backgrounds. We remark that, for deep properties of the parent N=2 theory, the topological Yang-Mills theory we obtain by taking the flat space limit of our gravity-coupled lagrangian is different from the Donaldson theory constructed by Witten. Whether this difference is substantial and what its geometrical implications may be is yet to be seen. We also discuss the topological twist of the hypermultiplets leading to topological quaternionic sigma-models. The instantons of these models, named by us hyperinstantons, correspond to a notion of triholomorphic mappings discussed in the paper. In all cases the new ghost number is the sum of the old ghost number plus the R-duality charge. The observables described by the theory are briefly discussed. In conclusion, the topological twist of the complete N=2 theory defines intersection theory in the moduli-space of gauge instantons plus gravitational instantons plus hyperinstantons. This is possibly a new subject for further mathematical investigation. (orig.)

Tunable Topological Phononic Crystals

KAUST Repository

Chen, Zeguo

2016-05-27

Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.

Tunable Topological Phononic Crystals

KAUST Repository

Chen, Zeguo; Wu, Ying

2016-01-01

Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.

Magnetic Measurements of the Background Field in the Undulator Hall

International Nuclear Information System (INIS)

Fisher, Andrew

2010-01-01

The steel present in the construction of the undulator hall facility has the potential for changing the ambient fields present in the undulator hall. This note describes a measurement done to make a comparison between the fields in the hall and in the Magnetic Measurement Facility. In order for the undulators to have the proper tuning, the background magnetic field in the Undulator Hall should agree with the background field in the Magnetic Measurements Facility within .5 gauss. In order to verify that this was the case measurements were taken along the length of the undulator hall, and the point measurements were compared to the mean field which was measured on the MMF test bench.

Lattice worldline representation of correlators in a background field

International Nuclear Information System (INIS)

Epelbaum, Thomas; Gelis, François; Wu, Bin

2015-01-01

We use a discrete worldline representation in order to study the continuum limit of the one-loop expectation value of dimension two and four local operators in a background field. We illustrate this technique in the case of a scalar field coupled to a non-Abelian background gauge field. The first two coefficients of the expansion in powers of the lattice spacing can be expressed as sums over random walks on a d-dimensional cubic lattice. Using combinatorial identities for the distribution of the areas of closed random walks on a lattice, these coefficients can be turned into simple integrals. Our results are valid for an anisotropic lattice, with arbitrary lattice spacings in each direction.

Topological charge on the lattice: a field theoretical view of the geometrical approach

International Nuclear Information System (INIS)

Rastelli, L.; Rossi, P.; Vicari, E.

1997-01-01

We construct sequences of ''field theoretical'' lattice topological charge density operators which formally approach geometrical definitions in 2D CP N-1 models and 4D SU(N) Yang-Mills theories. The analysis of these sequences of operators suggests a new way of looking at the geometrical method, showing that geometrical charges can be interpreted as limits of sequences of field theoretical (analytical) operators. In perturbation theory, renormalization effects formally tend to vanish along such sequences. But, since the perturbative expansion is asymptotic, this does not necessarily lead to well-behaved geometrical limits. It indeed leaves open the possibility that non-perturbative renormalizations survive. (orig.)

On the topological vacuum degeneracy in gauge theories

International Nuclear Information System (INIS)

Pervushin, V.N.

1982-01-01

It is shown that the nontrivial topology of gauge fields leads to the Josephson effect in the field space, i. e., to nonvanishing vacuum fields. The same definition is proposed for the physical (infrared) vacuum for Abelian (QED) and nonAbelian (QCD) theories. The equations and the topological Josephson effect for the gluon vacuum are discussed

Self-ordering of nontrivial topological polarization structures in nanoporous ferroelectrics.

Science.gov (United States)

Van Lich, Le; Shimada, Takahiro; Wang, Jie; Kitamura, Takayuki

2017-10-19

Topological field structures, such as skyrmions, merons, and vortices, are important features found in ordered systems with spontaneously broken symmetry. A plethora of topological field structures have been discovered in magnetic and ordered soft matter systems due to the presence of inherent chiral interactions, and this has provided a fruitful platform for unearthing additional groundbreaking functionalities. However, despite being one of the most important classes of ordered systems, ferroelectrics scarcely form topological polarization structures due to their lack of intrinsic chiral interactions. In the present study, we demonstrate using multiphysics phase-field modelling based on the Ginzburg-Landau theory that a rich assortment of nontrivial topological polarization structures, including hedgehogs, antivortices, multidirectional vortices, and vortex arrays, can be spontaneously formed in three-dimensional nanoporous ferroelectric structures. We realize that confining ferroelectrics to trivial geometries that are incompatible with the orientation symmetry may impose extrinsic frustration to the polarization field through the enhancement of depolarization fields at free porous surfaces. This frustration gives rise to symmetry breaking, resulting in the formation of nontrivial topological polarization structures as the ground state. We further topologically characterize the local accommodation of polarization structures by viewing them in a new perspective, in which polarization ordering can be mapped on the order parameter space, according to the topological theory of defects and homotopy theory. The results indicate that the nanoporous structures contain composite topological objects composed of two or more elementary topological polarization structures. The present study therefore offers a playground for exploring novel physical phenomena in ferroelectric systems as well as a novel nanoelectronics characterization platform for future topology

Things Fall Apart: Topology Change From Winding Tachyons

Energy Technology Data Exchange (ETDEWEB)

Adams, A.

2005-02-04

We argue that closed string tachyons drive two spacetime topology changing transitions--loss of genus in a Riemann surface and separation of a Riemann surface into two components. The tachyons of interest are localized versions of Scherk-Schwarz winding string tachyons arising on Riemann surfaces in regions of moduli space where string-scale tubes develop. Spacetime and world-sheet renormalization group analyses provide strong evidence that the decay of these tachyons removes a portion of the spacetime, splitting the tube into two pieces. We address the fate of the gauge fields and charges lost in the process, generalize it to situations with weak flux backgrounds, and use this process to study the type 0 tachyon, providing further evidence that its decay drives the theory sub-critical. Finally, we discuss the time-dependent dynamics of this topology-changing transition and find that it can occur more efficiently than analogous transitions on extended supersymmetric moduli spaces, which are limited by moduli trapping.

Topological fluid mechanics of Axisymmetric Flow

DEFF Research Database (Denmark)

Brøns, Morten

1998-01-01

Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...

Fold maps and positive topological quantum field theories

Energy Technology Data Exchange (ETDEWEB)

Wrazidlo, Dominik Johannes

2017-04-12

The notion of positive TFT as coined by Banagl is specified by an axiomatic system based on Atiyah's original axioms for TFTs. By virtue of a general framework that is based on the concept of Eilenberg completeness of semirings from computer science, a positive TFT can be produced rigorously via quantization of systems of fields and action functionals - a process inspired by Feynman's path integral from classical quantum field theory. The purpose of the present dissertation thesis is to investigate a new differential topological invariant for smooth manifolds that arises as the state sum of the fold map TFT, which has been constructed by Banagl as a example of a positive TFT. By eliminating an internal technical assumption on the fields of the fold map TFT, we are able to express the informational content of the state sum in terms of an extension problem for fold maps from cobordisms into the plane. Next, we use the general theory of generic smooth maps into the plane to improve known results about the structure of the state sum in arbitrary dimensions, and to determine it completely in dimension two. The aggregate invariant of a homotopy sphere, which is derived from the state sum, naturally leads us to define a filtration of the group of homotopy spheres in order to understand the role of indefinite fold lines beyond a theorem of Saeki. As an application, we show how Kervaire spheres can be characterized by indefinite fold lines in certain dimensions.

Machine learning topological states

Science.gov (United States)

Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.

2017-11-01

Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.

Accounting for the contributions of topological excitations in phase transitions through dual actions

International Nuclear Information System (INIS)

Ramos, Rudnei O.

2006-01-01

Topological excitations are believed to play an important role in different areas of physics. For example, cases of topical interest are the study of contributions of nonhomogeneous field configurations, in particular those of topological nature (like kinks, vortices and monopoles) in phase transitions associated to spontaneous symmetry breaking, the use of topological excitations in dual models of QCD to understand properties of its vacuum and confinement through the condensation of magnetic monopoles and vortices and also the relevance of these nonhomogeneous type of configurations in cosmology, again associated to possible phase transitions that are expected to have happened in the early universe. Here we show a derivation of a model dual to the scalar Abelian Higgs model where its topological excitations, namely vortex-strings, become manifest and can be treated in a quantum field theory way. The contribution of these nontrivial vacuum excitations in the phase transition for the scalar Abelian Higgs model in a thermal background is then studied and the results interpreted from the computation of the partition function taking into account the vortice-strings in the functional integration. This is made possible from the derived dual action. The relevance of the obtained results in cosmology, the analogy with phase transitions in superconductors, the relevance also for the study of confinement and other extensions of our calculations are briefly discussed here. (author)

Topological recursion for Gaussian means and cohomological field theories

Science.gov (United States)

Andersen, J. E.; Chekhov, L. O.; Norbury, P.; Penner, R. C.

2015-12-01

We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M g,s disc (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M g,1 for all g in three ways: using the refined Harer-Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.

Vision-based topological map building and localisation using persistent features

CSIR Research Space (South Africa)

Sabatta, DG

2008-11-01

Full Text Available stream_source_info Sabatta_2008.pdf.txt stream_content_type text/plain stream_size 32284 Content-Encoding UTF-8 stream_name Sabatta_2008.pdf.txt Content-Type text/plain; charset=UTF-8 Vision-based Topological Map... of topological mapping was introduced into the field of robotics following studies of human cogni- tive mapping undertaken by Kuipers [8]. Since then, much progress has been made in the field of vision-based topologi- cal mapping. Topological mapping lends...

Wave Manipulation by Topology Optimization

DEFF Research Database (Denmark)

Andkjær, Jacob Anders

topology optimization can be used to design structures for manipulation of the electromagnetic and acoustic waves. The wave problems considered here fall within three classes. The first class concerns the design of cloaks, which when wrapped around an object will render the object undetectable...... for the cloak is to delay the waves in regions of higher permittivity than the background and subsequently phase match them to the waves outside. Directional acoustic cloaks can also be designed using the topology optimization method. Aluminum cylinders constitutes the design and their placement and size...... concerns the design of planar Fresnel zone plate lenses for focusing electromagnetic waves. The topology optimized zone plates improve the focusing performance compared to results known from the literature....

Surface charge conductivity of a topological insulator in a magnetic field: The effect of hexagonal warping

Science.gov (United States)

Akzyanov, R. S.; Rakhmanov, A. L.

2018-02-01

We investigate the influence of hexagonal warping on the transport properties of topological insulators. We study the charge conductivity within Kubo formalism in the first Born approximation using low-energy expansion of the Hamiltonian near the Dirac point. The effects of disorder, magnetic field, and chemical-potential value are analyzed in detail. We find that the presence of hexagonal warping significantly affects the conductivity of the topological insulator. In particular, it gives rise to the growth of the longitudinal conductivity with the increase of the disorder and anisotropic anomalous in-plane magnetoresistance. Hexagonal warping also affects the quantum anomalous Hall effect and anomalous out-of-plane magnetoresistance. The obtained results are consistent with the experimental data.

Topological aspect of disclinations in two-dimensional crystals

International Nuclear Information System (INIS)

Wei-Kai, Qi; Tao, Zhu; Yong, Chen; Ji-Rong, Ren

2009-01-01

By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given. (the physics of elementary particles and fields)

Non-topological solitons in field theories with kinetic self-coupling

International Nuclear Information System (INIS)

Diaz-Alonso, Joaquin; Rubiera-Garcia, Diego

2007-01-01

We investigate some fundamental features of a class of non-linear relativistic Lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which are finite-energy and stable. We determine general conditions for the existence and stability of these non-topological soliton solutions. In particular, we perform a linear stability analysis that goes beyond the usual Derrick-like criteria. On the basis of these considerations we obtain a complete characterization of the soliton-supporting members of the aforementioned class of non-linear field theories. We then classify the family of soliton-supporting theories according to the central and asymptotic behaviors of the soliton field, and provide illustrative explicit examples of models belonging to each of the corresponding sub-families. In the present work we restrict most of our considerations to one and many-components scalar models. We show that in these cases the finite-energy static spherically symmetric solutions are stable against charge-preserving perturbations, provided that the vacuum energy of the model vanishes and the energy density is positive definite. We also discuss briefly the extension of the present approach to models involving other types of fields, but a detailed study of this more general scenario will be addressed in a separate publication

Entanglement entropy in integrable field theories with line defects II. Non-topological defect

Science.gov (United States)

Jiang, Yunfeng

2017-08-01

This is the second part of two papers where we study the effect of integrable line defects on bipartite entanglement entropy in integrable field theories. In this paper, we consider non-topological line defects in Ising field theory. We derive an infinite series expression for the entanglement entropy and show that both the UV and IR limits of the bulk entanglement entropy are modified by the line defect. In the UV limit, we give an infinite series expression for the coefficient in front of the logarithmic divergence and the exact defect g-function. By tuning the defect to be purely transmissive and reflective, we recover correctly the entanglement entropy of the bulk and with integrable boundary respectively.

On non-perturbative effects of background fields

International Nuclear Information System (INIS)

Hosoda, Masataka; Yamakoshi, Hitoshi; Shimizu, Tadayoshi.

1986-01-01

APS-index of the Abelian Higgs model is at first obtained in a bounded domain of a disk with radius R. It is shown that the APS-index depends strongly on the behavior of the background fields and becomes integer when boundary effects are taken into account. Next, the electric charge of the vacuum is reconsidered in the momopole field coupled to a massive Dirac particle. It is reconfirmed that the monopole ground state has an electric charge θ/π which changes discontinuously to zero when the fermion mass is zero. (author)

Closed string emission from unstable D-brane with background electric field

International Nuclear Information System (INIS)

Nagami, Kenji

2004-01-01

We study the closed string emission from an unstable Dp-brane with constant background electric field in bosonic string theory. The average total number density and the average total energy density of emitted closed strings are explicitly calculated in the presence of electric field. It is explicitly shown that the energy density in the UV region becomes finite whenever the background electric field is switched on. The energy density converted into closed strings in the presence of electric field is negligibly small compared with the D-brane tension in the weak string coupling limit. (author)

Impact of topology in foliated quantum Einstein gravity

Energy Technology Data Exchange (ETDEWEB)

Houthoff, W.B.; Saueressig, F. [Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Nijmegen (Netherlands); Kurov, A. [Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Nijmegen (Netherlands); Moscow State University, Department of Theoretical Physics, Moscow (Russian Federation)

2017-07-15

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology S{sup 1} x S{sup d}. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of ''gravitational instability'', modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology S{sup 1} x T{sup d} (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology. (orig.)

Recent Progress in the Study of Topological Semimetals

Science.gov (United States)

Bernevig, Andrei; Weng, Hongming; Fang, Zhong; Dai, Xi

2018-04-01

The topological semimetal is a new, theoretically predicted and experimentally discovered, topological state of matter. In one of its several realizations, the topological semimetal hosts Weyl fermions, elusive particles predicted more than 85 years ago, sought after in high-energy experiments, but only recently found in a condensed-matter setting. In the present review, we catalogue the most recent progress in this fast-developing research field. We give special attention to topological invariants and the material realization of three different types of topological semimetal. We also discuss various photo emission, transport and optical experimental observables that characterize the appearance of topological semimetal phases.

Novel topological invariants and anomalies

International Nuclear Information System (INIS)

Hirayama, M.; Sugimasa, N.

1987-01-01

It is shown that novel topological invariants are associated with a class of Dirac operators. Trace formulas which are similar to but different from Callias's formula are derived. Implications of these topological invariants to anomalies in quantum field theory are discussed. A new class of anomalies are calculated for two models: one is two dimensional and the other four dimensional

Topology of helical fluid flow

DEFF Research Database (Denmark)

Andersen, Morten; Brøns, Morten

2014-01-01

function for the topology of the streamline pattern in incompressible flows. On this basis, we perform a comprehensive study of the topology of the flow field generated by a helical vortex filament in an ideal fluid. The classical expression for the stream function obtained by Hardin (Hardin, J. C. 1982...... the zeroes of a single real function of one variable, and we show that three different flow topologies can occur, depending on a single dimensionless parameter. By including the self-induced velocity on the vortex filament by a localised induction approximation, the stream function is slightly modified...... and an extra parameter is introduced. In this setting two new flow topologies arise, but not more than two critical points occur for any combination of parameters....

Nonperturbative summation over 3D discrete topologies

International Nuclear Information System (INIS)

Freidel, Laurent; Louapre, David

2003-01-01

The group field theories realizing the sum over all triangulations of all topologies of 3D discrete gravity amplitudes are known to be nonuniquely Borel summable. We modify these models to construct a new group field theory which is proved to be uniquely Borel summable, defining in an unambiguous way a nonperturbative sum over topologies in the context of 3D dynamical triangulations and spin foam models. Moreover, we give some arguments to support the fact that, despite our modification, this new model is similar to the original one, and therefore could be taken as a definition of the sum over topologies of 3D quantum gravity amplitudes

Chemistry explained by topology: an alternative approach.

Science.gov (United States)

Galvez, Jorge; Villar, Vincent M; Galvez-Llompart, Maria; Amigó, José M

2011-05-01

Molecular topology can be considered an application of graph theory in which the molecular structure is characterized through a set of graph-theoretical descriptors called topological indices. Molecular topology has found applications in many different fields, particularly in biology, chemistry, and pharmacology. The first topological index was introduced by H. Wiener in 1947 [1]. Although its very first application was the prediction of the boiling points of the alkanes, the Wiener index has demonstrated since then a predictive capability far beyond that. Along with the Wiener index, in this paper we focus on a few pioneering topological indices, just to illustrate the connection between physicochemical properties and molecular connectivity.

Robustness of edge states in topological quantum dots against global electric field

Science.gov (United States)

Qu, Jin-Xian; Zhang, Shu-Hui; Liu, Ding-Yang; Wang, Ping; Yang, Wen

2017-07-01

The topological insulator has attracted increasing attention as a new state of quantum matter featured by the symmetry-protected edge states. Although the qualitative robustness of the edge states against local perturbations has been well established, it is not clear how these topological edge states respond quantitatively to a global perturbation. Here, we study the response of topological edge states in a HgTe quantum dot to an external in-plane electric field—a paradigmatic global perturbation in solid-state environments. We find that the stability of the topological edge state could be larger than that of the ground bulk state by several orders of magnitudes. This robustness may be verified by standard transport measurements in the Coulomb blockage regime. Our work may pave the way towards utilizing these topological edge states as stable memory devices for charge and/or spin information and stable emitter of single terahertz photons or entangled terahertz photon pairs for quantum communication.

Thermodynamics of quasi-topological cosmology

International Nuclear Information System (INIS)

Dehghani, M.H.; Sheykhi, A.; Dehghani, R.

2013-01-01

In this Letter, we study thermodynamical properties of the apparent horizon in a universe governed by quasi-topological gravity. Our aim is twofold. First, by using the variational method we derive the general form of Friedmann equation in quasi-topological gravity. Then, by applying the first law of thermodynamics on the apparent horizon, after using the entropy expression associated with the black hole horizon in quasi-topological gravity, and replacing the horizon radius, r + , with the apparent horizon radius, r -tilde A , we derive the corresponding Friedmann equation in quasi-topological gravity. We find that these two different approaches yield the same result which shows the profound connection between the first law of thermodynamics and the gravitational field equations of quasi-topological gravity. We also study the validity of the generalized second law of thermodynamics in quasi-topological cosmology. We find that, with the assumption of the local equilibrium hypothesis, the generalized second law of thermodynamics is fulfilled for the universe enveloped by the apparent horizon for the late time cosmology

Elastic energy for reflection-symmetric topologies

International Nuclear Information System (INIS)

Majumdar, A; Robbins, J M; Zyskin, M

2006-01-01

Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with reflection-symmetric topologies, we derive a new lower bound for the one-constant elastic energy. For certain topologies, called conformal and anticonformal, the lower bound agrees with a previous result. For the remaining topologies, called nonconformal, the new bound is an improvement. For nonconformal topologies we derive an upper bound, which differs from the lower bound by a factor depending only on the aspect ratios of the prism

Proceeding of the workshop on quantum gravity and topology

International Nuclear Information System (INIS)

Oda, Ichiro

1991-10-01

The workshop on Quantum Gravity and Topology was held at INS on February 21-23, 1991. Several introductory lectures and more than 15 talks were delivered for about 100 participants. The main subjects discussed were i) Topological quantum field theories and topological gravity ii) Low dimensional and four dimensional gravity iii) Topology change iv) Superstring theories etc. (J.P.N.)

Signature of Topological Phases in Zitterbewegung

KAUST Repository

Ghosh, Sumit

2016-09-02

We have studied the Zitterbewegung effect on an infinite two-dimensional sheet with honeycomb lattice. By tuning the perpendicular electric field and the magnetization of the sheet, it can enter different topological phases. We have shown that the phase and magnitude of Zitterbewegung effect, i.e., the jittering motion of electron wavepackets, correlates with the various topological phases. The topological phase diagram can be reconstructed by analyzing these features. Our findings are applicable to materials like silicene, germanene, stanene, etc.

Signature of Topological Phases in Zitterbewegung

KAUST Repository

Ghosh, Sumit; Manchon, Aurelien

2016-01-01

We have studied the Zitterbewegung effect on an infinite two-dimensional sheet with honeycomb lattice. By tuning the perpendicular electric field and the magnetization of the sheet, it can enter different topological phases. We have shown that the phase and magnitude of Zitterbewegung effect, i.e., the jittering motion of electron wavepackets, correlates with the various topological phases. The topological phase diagram can be reconstructed by analyzing these features. Our findings are applicable to materials like silicene, germanene, stanene, etc.

The Gribov problem in presence of background field for SU(2) Yang–Mills theory

Energy Technology Data Exchange (ETDEWEB)

Canfora, Fabrizio, E-mail: canfora@cecs.cl [Centro de Estudios Científicos (CECS), Casilla 1469, Valdivia (Chile); Hidalgo, Diego, E-mail: dhidalgo@cecs.cl [Centro de Estudios Científicos (CECS), Casilla 1469, Valdivia (Chile); Departamento de Física, Universidad de Concepción, Casilla 160, Concepción (Chile); Pais, Pablo, E-mail: pais@cecs.cl [Centro de Estudios Científicos (CECS), Casilla 1469, Valdivia (Chile); Physique Théorique et Mathématique, Univérsite de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium)

2016-12-10

The Gribov problem in the presence of a background field is analyzed: in particular, we study the Gribov copies equation in the Landau–De Witt gauge as well as the semi-classical Gribov gap equation. As background field, we choose the simplest non-trivial one which corresponds to a constant gauge potential with non-vanishing component along the Euclidean time direction. This kind of constant non-Abelian background fields is very relevant in relation with (the computation of) the Polyakov loop but it also appears when one considers the non-Abelian Schwinger effect. We show that the Gribov copies equation is affected directly by the presence of the background field, constructing an explicit example. The analysis of the Gribov gap equation shows that the larger the background field, the smaller the Gribov mass parameter. These results strongly suggest that the relevance of the Gribov copies (from the path integral point of view) decreases as the size of the background field increases.

Change of the Magnetic-Field Topology by an Ergodic Divertor and the Effect on the Plasma Structure and Transport

International Nuclear Information System (INIS)

Jakubowski, M.W.; Schmitz, O.; Abdullaev, S.S.; Brezinsek, S.; Finken, K.H.; Kraemer-Flecken, A.; Lehnen, M.; Samm, U.; Unterberg, B.; Wolf, R.C.; Spatschek, K.H.

2006-01-01

The magnetic-field perturbation produced by the dynamic ergodic divertor in TEXTOR changes the topology of the magnetic field in the plasma edge, creating an open chaotic system. The perturbation spectrum contains only a few dominant harmonics and therefore it can be described by an analytical model. The modeling is performed in the vacuum approximation without assuming a backreaction of the plasma and does not rely on any experimentally obtained parameters. It is shown that this vacuum approximation predicts in many details the experimentally observed plasma structure. Several experiments have been performed to prove that the plasma edge behavior is defined mostly by the magnetic topology of the perturbed volume. The change in the transport can be explained with the knowledge of only the magnetic structures; i.e., the ergodic pattern dominates the plasma properties

Geometric model of topological insulators from the Maxwell algebra

Science.gov (United States)

Palumbo, Giandomenico

2017-11-01

We propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincaré algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.

Algebra and topology for applications to physics

Science.gov (United States)

Rozhkov, S. S.

1987-01-01

The principal concepts of algebra and topology are examined with emphasis on applications to physics. In particular, attention is given to sets and mapping; topological spaces and continuous mapping; manifolds; and topological groups and Lie groups. The discussion also covers the tangential spaces of the differential manifolds, including Lie algebras, vector fields, and differential forms, properties of differential forms, mapping of tangential spaces, and integration of differential forms.

Tunable topological phases in photonic and phononic crystals

KAUST Repository

Chen, Zeguo

2018-01-01

Topological photonics/phononics, inspired by the discovery of topological insulators, is a prosperous field of research, in which remarkable one-way propagation edge states are robust against impurities or defect without backscattering

Background rejection in NEXT using deep neural networks

CERN Document Server

Renner, J.

2017-01-01

We investigate the potential of using deep learning techniques to reject background events in searches for neutrinoless double beta decay with high pressure xenon time projection chambers capable of detailed track reconstruction. The differences in the topological signatures of background and signal events can be learned by deep neural networks via training over many thousands of events. These networks can then be used to classify further events as signal or background, providing an additional background rejection factor at an acceptable loss of efficiency. The networks trained in this study performed better than previous methods developed based on the use of the same topological signatures by a factor of 1.2 to 1.6, and there is potential for further improvement.

Background rejection in NEXT using deep neural networks

International Nuclear Information System (INIS)

Renner, J.; Farbin, A.; Vidal, J. Muñoz; Benlloch-Rodríguez, J. M.; Botas, A.

2017-01-01

Here, we investigate the potential of using deep learning techniques to reject background events in searches for neutrinoless double beta decay with high pressure xenon time projection chambers capable of detailed track reconstruction. The differences in the topological signatures of background and signal events can be learned by deep neural networks via training over many thousands of events. These networks can then be used to classify further events as signal or background, providing an additional background rejection factor at an acceptable loss of efficiency. The networks trained in this study performed better than previous methods developed based on the use of the same topological signatures by a factor of 1.2 to 1.6, and there is potential for further improvement.

The Uncertainty of Local Background Magnetic Field Orientation in Anisotropic Plasma Turbulence

Energy Technology Data Exchange (ETDEWEB)

Gerick, F.; Saur, J.; Papen, M. von, E-mail: felix.gerick@uni-koeln.de [Institute of Geophysics and Meteorology, University of Cologne, Cologne (Germany)

2017-07-01

In order to resolve and characterize anisotropy in turbulent plasma flows, a proper estimation of the background magnetic field is crucially important. Various approaches to calculating the background magnetic field, ranging from local to globally averaged fields, are commonly used in the analysis of turbulent data. We investigate how the uncertainty in the orientation of a scale-dependent background magnetic field influences the ability to resolve anisotropy. Therefore, we introduce a quantitative measure, the angle uncertainty, that characterizes the uncertainty of the orientation of the background magnetic field that turbulent structures are exposed to. The angle uncertainty can be used as a condition to estimate the ability to resolve anisotropy with certain accuracy. We apply our description to resolve the spectral anisotropy in fast solar wind data. We show that, if the angle uncertainty grows too large, the power of the turbulent fluctuations is attributed to false local magnetic field angles, which may lead to an incorrect estimation of the spectral indices. In our results, an apparent robustness of the spectral anisotropy to false local magnetic field angles is observed, which can be explained by a stronger increase of power for lower frequencies when the scale of the local magnetic field is increased. The frequency-dependent angle uncertainty is a measure that can be applied to any turbulent system.

The Uncertainty of Local Background Magnetic Field Orientation in Anisotropic Plasma Turbulence

International Nuclear Information System (INIS)

Gerick, F.; Saur, J.; Papen, M. von

2017-01-01

In order to resolve and characterize anisotropy in turbulent plasma flows, a proper estimation of the background magnetic field is crucially important. Various approaches to calculating the background magnetic field, ranging from local to globally averaged fields, are commonly used in the analysis of turbulent data. We investigate how the uncertainty in the orientation of a scale-dependent background magnetic field influences the ability to resolve anisotropy. Therefore, we introduce a quantitative measure, the angle uncertainty, that characterizes the uncertainty of the orientation of the background magnetic field that turbulent structures are exposed to. The angle uncertainty can be used as a condition to estimate the ability to resolve anisotropy with certain accuracy. We apply our description to resolve the spectral anisotropy in fast solar wind data. We show that, if the angle uncertainty grows too large, the power of the turbulent fluctuations is attributed to false local magnetic field angles, which may lead to an incorrect estimation of the spectral indices. In our results, an apparent robustness of the spectral anisotropy to false local magnetic field angles is observed, which can be explained by a stronger increase of power for lower frequencies when the scale of the local magnetic field is increased. The frequency-dependent angle uncertainty is a measure that can be applied to any turbulent system.

Even-dimensional topological gravity from Chern-Simons gravity

International Nuclear Information System (INIS)

Merino, N.; Perez, A.; Salgado, P.

2009-01-01

It is shown that the topological action for gravity in 2n-dimensions can be obtained from the (2n+1)-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a (2n+1)-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field φ a , which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d-1,1).

Braiding knots with topological strings

International Nuclear Information System (INIS)

Gu, Jie

2015-08-01

For an arbitrary knot in a three-sphere, the Ooguri-Vafa conjecture associates to it a unique stack of branes in type A topological string on the resolved conifold, and relates the colored HOMFLY invariants of the knot to the free energies on the branes. For torus knots, we use a modified version of the topological recursion developed by Eynard and Orantin to compute the free energies on the branes from the Aganagic-Vafa spectral curves of the branes, and find they are consistent with the known colored HOMFLY knot invariants a la the Ooguri-Vafa conjecture. In addition our modified topological recursion can reproduce the correct closed string free energies, which encode the information of the background geometry. We conjecture the modified topological recursion is applicable for branes associated to hyperbolic knots as well, encouraged by the observation that the modified topological recursion yields the correct planar closed string free energy from the Aganagic-Vafa spectral curves of hyperbolic knots. This has implications for the knot theory concerning distinguishing mutant knots with colored HOMFLY invariants. Furthermore, for hyperbolic knots, we present methods to compute colored HOMFLY invariants in nonsymmetric representations of U(N). The key step in this computation is computing quantum 6j-symbols in the quantum group U q (sl N ).

Aspects of NT ≥ 2 topological gauge theories and D-branes

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1996-12-01

Recently, topological field theories with extended N T > 1 topological symmetries have appeared in various contexts, e.g. in the discussion of S-duality in supersymmetry gauge theories, as world volume theories of Dirichlet p-branes in string theory, and in a general discussion of 'balanced' or critical topological theories. Here we will comment on, explain, or expand on various aspects of these theories, thus complementing the already existing discussions of such models in the literature. We comment on various aspects of topological gauge theories possessing N T ≥ 2 topological symmetry: 1. We show that the construction of Vafa-Witten and Dijkgraaf-Moore of 'balanced' topological field theories is equivalent to an earlier construction in terms of N T = 2 superfields inspired by supersymmetric quantum mechanics. 2. We explain the relation between topological field theories calculating signed and unsigned sums of Euler numbers of moduli spaces. 3. We show that the topological twist of N = 4 d = 4 Yang-Mills theory recently constructed by Marcus is formally a deformation of four-dimensional super-BF theory. 4. We construct a novel N T = 2 topological twist of N = 4 d = 3 Yang-Mills theory, a 'mirror' of the Casson invariant model, with certain unusual features (e.g. no bosonic scalar field and hence no underlying equivariant cohomology). 5. We give a complete classification of the topological twists of N = 8 d = 3 Yang-Mills theory and show that they are realized as world-volume theories of Dirichlet two-brane instantons wrapping supersymmetric three-cycles of Calabi-Yau three-folds and G 2 -holonomy Joyce manifolds. 6. We describe the topological gauge theories associated to D-string instantons on holomorphic curves in K3s and Calabi-Yau 3-folds. 48 refs

Two-dimensional topological photonic systems

Science.gov (United States)

Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng

2017-09-01

The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.

Spintronics Based on Topological Insulators

Science.gov (United States)

Fan, Yabin; Wang, Kang L.

2016-10-01

Spintronics using topological insulators (TIs) as strong spin-orbit coupling (SOC) materials have emerged and shown rapid progress in the past few years. Different from traditional heavy metals, TIs exhibit very strong SOC and nontrivial topological surface states that originate in the bulk band topology order, which can provide very efficient means to manipulate adjacent magnetic materials when passing a charge current through them. In this paper, we review the recent progress in the TI-based magnetic spintronics research field. In particular, we focus on the spin-orbit torque (SOT)-induced magnetization switching in the magnetic TI structures, spin-torque ferromagnetic resonance (ST-FMR) measurements in the TI/ferromagnet structures, spin pumping and spin injection effects in the TI/magnet structures, as well as the electrical detection of the surface spin-polarized current in TIs. Finally, we discuss the challenges and opportunities in the TI-based spintronics field and its potential applications in ultralow power dissipation spintronic memory and logic devices.

Topological nanophononic states by band inversion

Science.gov (United States)

Esmann, Martin; Lamberti, Fabrice Roland; Senellart, Pascale; Favero, Ivan; Krebs, Olivier; Lanco, Loïc; Gomez Carbonell, Carmen; Lemaître, Aristide; Lanzillotti-Kimura, Norberto Daniel

2018-04-01

Nanophononics is essential for the engineering of thermal transport in nanostructured electronic devices, it greatly facilitates the manipulation of mechanical resonators in the quantum regime, and it could unveil a new route in quantum communications using phonons as carriers of information. Acoustic phonons also constitute a versatile platform for the study of fundamental wave dynamics, including Bloch oscillations, Wannier-Stark ladders, and other localization phenomena. Many of the phenomena studied in nanophononics were inspired by their counterparts in optics and electronics. In these fields, the consideration of topological invariants to control wave dynamics has already had a great impact for the generation of robust confined states. Interestingly, the use of topological phases to engineer nanophononic devices remains an unexplored and promising field. Conversely, the use of acoustic phonons could constitute a rich platform to study topological states. Here, we introduce the concept of topological invariants to nanophononics and experimentally implement a nanophononic system supporting a robust topological interface state at 350 GHz. The state is constructed through band inversion, i.e., by concatenating two semiconductor superlattices with inverted spatial mode symmetries. The existence of this state is purely determined by the Zak phases of the constituent superlattices, i.e., the one-dimensional Berry phase. We experimentally evidenced the mode through Raman spectroscopy. The reported robust topological interface states could become part of nanophononic devices requiring resonant structures such as sensors or phonon lasers.

High-Harmonic Generation in Solids with and without Topological Edge States

Science.gov (United States)

Bauer, Dieter; Hansen, Kenneth K.

2018-04-01

High-harmonic generation in the two topological phases of a finite, one-dimensional, periodic structure is investigated using a self-consistent time-dependent density functional theory approach. For harmonic photon energies smaller than the band gap, the harmonic yield is found to differ by up to 14 orders of magnitude for the two topological phases. This giant topological effect is explained by the degree of destructive interference in the harmonic emission of all valence-band (and edge-state) electrons, which strongly depends on whether or not topological edge states are present. The combination of strong-field laser physics with topological condensed matter opens up new possibilities to electronically control strong-field-based light or particle sources or—conversely—to steer by all optical means topological electronics.

Background field quantization in non-covariant gauges: Renormalization and WTST identities

International Nuclear Information System (INIS)

McKeon, G.; Phillips, S.B.; Samant, S.S.; Sherry, T.N.

1986-01-01

Background field quantization of pure YM theories in non-covariant gauges is treated with particular emphasis on renormalization. Gauge fixing terms of the form (1/2α)n . Qsup(a)fsup(ab)n . Qsup(b) are considered where fsup(ab) can assume the forms fsup(ab)sub((i))=-deltasup(ab) (the axial gauge), fsup(ab)sub((ii))=(n . D(A))sup(2ab)/n 4 and fsup(ab)sub((iii))=D 2 (A)sup(ab)/n 2 (the planar gauge). For the cases where fsup(ab) depends explicitly on the background field Asub(μ)sup(a) the ghost sector is enlarged by the addition of appropriate Nielson-Kallosh ghost fields. The BRS identities for these gauge choices are derived and solved. The quantum-corrected versions of both the bare background field gauge transformations and the bare quantum field gauge transformations are obtained from the BRS analysis. It is also shown that, to one loop, all the counter terms are determined by the background field independent part of the theory and this result is used, in cases (ii) and (iii), to derive all the counter terms and to show that Kallosh's theorem is verified. The result is also used to demonstrate the pathological nature of case (i) for αnot=0, in particular the result that Kallosh's theorem is not applicable. The result that the generating functional of Green functions is independent of the background field Asub(μ)sup(a) in the absence of all external sources is generalized to the case of non-covariant gauges. The equality established by Abbott between the 1PI generating functionals GAMMA tilde[A,0] and GAMMAsub(c)[anti Q; A] sub(anti Q=A), where GAMMAsub(c) is a conventional generating functional in an A-dependent gauge, is analysed. We show that the WTST identities satisfied by GAMMAsub(c) reduce, when anti Q is set equal to A, to the naive Ward-identity satisfied by GAMMA tilde[A,0]. (orig.)

Renormalization using the background-field method

International Nuclear Information System (INIS)

Ichinose, S.; Omote, M.

1982-01-01

Renormalization using the background-field method is examined in detail. The subtraction mechanism of subdivergences is described with reference to multi-loop diagrams and one- and two-loop counter-term formulae are explicitly given. The original one-loop counter-term formula of 't Hooft is thereby improved. The present method of renormalization is far easier to manage than the usual one owing to the fact only gauge-invariant quantities are to be considered when worked in an appropriate gauge. Gravity and Yang-Mills theories are studied as examples. (orig.)

Topology Optimization of a High-Temperature Superconducting Field Winding of a Synchronous Machine

DEFF Research Database (Denmark)

Pozzi, Matias; Mijatovic, Nenad; Jensen, Bogi Bech

2013-01-01

This paper presents topology optimization (TO) of the high-temperature superconductor (HTS) field winding of an HTS synchronous machine. The TO problem is defined in order to find the minimum HTS material usage for a given HTS synchronous machine design. Optimization is performed using a modified...... genetic algorithm with local optimization search based on on/off sensitivity analysis. The results show an optimal HTS coil distribution, achieving compact designs with a maximum of approximately 22% of the available space for the field winding occupied with HTS tape. In addition, this paper describes...... potential HTS savings, which could be achieved using multiple power supplies for the excitation of the machine. Using the TO approach combined with two excitation currents, an additional HTS saving of 9.1% can be achieved....

Acoustic topological insulator and robust one-way sound transport

Science.gov (United States)

He, Cheng; Ni, Xu; Ge, Hao; Sun, Xiao-Chen; Chen, Yan-Bin; Lu, Ming-Hui; Liu, Xiao-Ping; Chen, Yan-Feng

2016-12-01

Topological design of materials enables topological symmetries and facilitates unique backscattering-immune wave transport. In airborne acoustics, however, the intrinsic longitudinal nature of sound polarization makes the use of the conventional spin-orbital interaction mechanism impossible for achieving band inversion. The topological gauge flux is then typically introduced with a moving background in theoretical models. Its practical implementation is a serious challenge, though, due to inherent dynamic instabilities and noise. Here we realize the inversion of acoustic energy bands at a double Dirac cone and provide an experimental demonstration of an acoustic topological insulator. By manipulating the hopping interaction of neighbouring ’atoms’ in this new topological material, we successfully demonstrate the acoustic quantum spin Hall effect, characterized by robust pseudospin-dependent one-way edge sound transport. Our results are promising for the exploration of new routes for experimentally studying topological phenomena and related applications, for example, sound-noise reduction.

Topology of plasma equilibria and the current closure condition

International Nuclear Information System (INIS)

Kocic, S.; Mahajan, S.M.; Hazeltine, R.D.

2005-01-01

A virtually complete description of the topology of stationary incompressible Euler flows and the magnetic field satisfying the magnetostatic equation is given by a theorem due to Arnol'd. We apply this theorem to describe the topology of stationary states of plasmas with significant fluid flow, obeying the Hall magnetohydrodynamics model equations. In the context of the integrability (nonchaotic topology) of the magnetic and velocity fields, we discuss the validity of conditions analogous to that of Greene and Johnson, which, in the case of magnetostatic equations, states that the line integral ∫dl/B is the same for each closed magnetic field line on a given magnetic surface. We also show how this property follows from the existence of a continuous volume-preserving symmetry of the magnetic field

Dynamics of Plasma Jets and Bubbles Launched into a Transverse Background Magnetic Field

Science.gov (United States)

Zhang, Yue

2017-10-01

A coaxial magnetized plasma gun has been utilized to launch both plasma jets (open B-field) and plasma bubbles (closed B-field) into a transverse background magnetic field in the HelCat (Helicon-Cathode) linear device at the University of New Mexico. These situations may have bearing on fusion plasmas (e.g. plasma injection for tokamak fueling, ELM pacing, or disruption mitigation) and astrophysical settings (e.g. astrophysical jet stability, coronal mass ejections, etc.). The magnetic Reynolds number of the gun plasma is 100 , so that magnetic advection dominates over magnetic diffusion. The gun plasma ram pressure, ρjetVjet2 >B02 / 2μ0 , the background magnetic pressure, so that the jet or bubble can easily penetrate the background B-field, B0. When the gun axial B-field is weak compared to the gun azimuthal field, a current-driven jet is formed with a global helical magnetic configuration. Applying the transverse background magnetic field, it is observed that the n = 1 kink mode is stabilized, while magnetic probe measurements show contrarily that the safety factor q(a) drops below unity. At the same time, a sheared axial jet velocity is measured. We conclude that the tension force arising from increasing curvature of the background magnetic field induces the measured sheared flow gradient above the theoretical kink-stabilization threshold, resulting in the emergent kink stabilization of the injected plasma jet. In the case of injected bubbles, spheromak-like plasma formation is verified. However, when the spheromak plasma propagates into the transverse background magnetic field, the typical self-closed global symmetry magnetic configuration does not hold any more. In the region where the bubble toroidal field opposed the background B-field, the magneto-Rayleigh-Taylor (MRT) instability has been observed. Details of the experiment setup, diagnostics, experimental results and theoretical analysis will be presented. Supported by the National Science Foundation

Algebraic renormalization of Yang-Mills theory with background field method

International Nuclear Information System (INIS)

Grassi, P.A.

1996-01-01

In this paper the renormalizability of Yang-Mills theory in the background gauge fixing is studied. By means of Ward identities of background gauge invariance and Slavnov-Taylor identities, in a regularization-independent way, the stability of the model under radiative corrections is proved and its renormalizability is verified. In particular, it is shown that the splitting between background and quantum field is stable under radiative corrections and this splitting does not introduce any new anomalies. (orig.)

Self-organization of topological defects for a triangular-lattice magnetic dots array subject to a perpendicular magnetic field

Directory of Open Access Journals (Sweden)

R.S. Khymyn

2014-09-01

Full Text Available The regular array of magnetic particles (magnetic dots of the form of a two-dimensional triangular lattice in the presence of external magnetic field demonstrates complicated magnetic structures. The magnetic symmetry of the ground state for such a system is lower than that for the underlying lattice. Long range dipole-dipole interaction leads to a specific antiferromagnetic order in small fields, whereas a set of linear topological defects appears with the growth of the magnetic field. Self-organization of such defects determines the magnetization process for a system within a wide range of external magnetic fields.

Geometrical protection of topological magnetic solitons in microprocessed chiral magnets

Science.gov (United States)

Mito, Masaki; Ohsumi, Hiroyuki; Tsuruta, Kazuki; Kotani, Yoshinori; Nakamura, Tetsuya; Togawa, Yoshihiko; Shinozaki, Misako; Kato, Yusuke; Kishine, Jun-ichiro; Ohe, Jun-ichiro; Kousaka, Yusuke; Akimitsu, Jun; Inoue, Katsuya

2018-01-01

A chiral soliton lattice stabilized in a monoaxial chiral magnet CrNb3S6 is a magnetic superlattice consisting of magnetic kinks with a ferromagnetic background. The magnetic kinks are considered to be topological magnetic solitons (TMSs). Changes in the TMS number yield discretized responses in magnetization and electrical conductivity, and this effect is more prominent in smaller crystals. We demonstrate that, in microprocessed CrNb3S6 crystals, TMSs are geometrically protected through element-selected micromagnetometry using soft x-ray magnetic circular dichroism (MCD). A series of x-ray MCD data is supported by mean-field and micromagnetic analyses. By designing the microcrystal geometry, TMS numbers can be successfully changed and fixed over a wide range of magnetic fields.

Emergent Momentum-Space Skyrmion Texture on the Surface of Topological Insulators

Science.gov (United States)

Mohanta, Narayan; Kampf, Arno P.; Kopp, Thilo

The quantum anomalous Hall effect has been theoretically predicted and experimentally verified in magnetic topological insulators. In addition, the surface states of these materials exhibit a hedgehog-like ``spin'' texture in momentum space. Here, we apply the previously formulated low-energy model for Bi2Se3, a parent compound for magnetic topological insulators, to a slab geometry in which an exchange field acts only within one of the surface layers. In this sample set up, the hedgehog transforms into a skyrmion texture beyond a critical exchange field. This critical field marks a transition between two topologically distinct phases. The topological phase transition takes place without energy gap closing at the Fermi level and leaves the transverse Hall conductance unchanged and quantized to e2 / 2 h . The momentum-space skyrmion texture persists in a finite field range. It may find its realization in hybrid heterostructures with an interface between a three-dimensional topological insulator and a ferromagnetic insulator. The work was supported by the Deutsche Forschungsgemeinschaft through TRR 80.

Filters in topology optimization

DEFF Research Database (Denmark)

Bourdin, Blaise

1999-01-01

In this article, a modified (``filtered'') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field using a convolution operator. In this setting...... it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ``filtering'' technique is also shown to cope with two important numerical problems in topology optimization...

Topology in Condensed Matter

CERN Document Server

Monastyrsky, M I

2006-01-01

This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

An introduction to topological Yang-Mills theory

International Nuclear Information System (INIS)

Baal, P. van; Rijksuniversiteit Utrecht

1990-01-01

In these lecture notes I give a ''historical'' introduction to topological gauge theories. My main aim is to clearly explain the origin of the Hamiltonian which forms the basis of Witten's construction of topological gauge theory. I show how this Hamiltonian arises from Witten's formulation of Morse theory as applied by Floer to the infinite dimensional space of gauge connections, with the Chern-Simons functional as the appriopriate Morse function(al). I therefore discuss the De Rham cohomology, Hodge theory, Morse theory, Floer homology, Witten's construction of the Lagrangian for topological gauge theory, the subsequent BRST formulation of topological quantum field theory and finally Witten's construction of the Donaldson polynomials. (author)

Topological transport in Dirac nodal-line semimetals

Science.gov (United States)

Rui, W. B.; Zhao, Y. X.; Schnyder, Andreas P.

2018-04-01

Topological nodal-line semimetals are characterized by one-dimensional Dirac nodal rings that are protected by the combined symmetry of inversion P and time-reversal T . The stability of these Dirac rings is guaranteed by a quantized ±π Berry phase and their low-energy physics is described by a one-parameter family of (2+1)-dimensional quantum field theories exhibiting the parity anomaly. Here we study the Berry-phase supported topological transport of P T -invariant nodal-line semimetals. We find that small inversion breaking allows for an electric-field-induced anomalous transverse current, whose universal component originates from the parity anomaly. Due to this Hall-like current, carriers at opposite sides of the Dirac nodal ring flow to opposite surfaces when an electric field is applied. To detect the topological currents, we propose a dumbbell device, which uses surface states to filter charges based on their momenta. Suggestions for experiments and device applications are discussed.

Irrational Charge from Topological Order

Science.gov (United States)

Moessner, R.; Sondhi, S. L.

2010-10-01

Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic charge plays this role, these quasiparticles are also characterized by their intrinsic charge. We show that one can take advantage of the topological order fairly generally to produce periodic Hamiltonians which endow the quasiparticles with continuously variable, generically irrational, intrinsic charges. Examples include various topologically ordered lattice models, the three-dimensional resonating valence bond liquid on bipartite lattices as well as water and spin ice. By contrast, the gauge charges of the quasiparticles retain their quantized values.

Tensorial spacetime geometries and background-independent quantum field theory

International Nuclear Information System (INIS)

Raetzel, Dennis

2012-01-01

Famously, Einstein read off the geometry of spacetime from Maxwell's equations. Today, we take this geometry that serious that our fundamental theory of matter, the standard model of particle physics, is based on it. However, it seems that there is a gap in our understanding if it comes to the physics outside of the solar system. Independent surveys show that we need concepts like dark matter and dark energy to make our models fit with the observations. But these concepts do not fit in the standard model of particle physics. To overcome this problem, at least, we have to be open to matter fields with kinematics and dynamics beyond the standard model. But these matter fields might then very well correspond to different spacetime geometries. This is the basis of this thesis: it studies the underlying spacetime geometries and ventures into the quantization of those matter fields independently of any background geometry. In the first part of this thesis, conditions are identified that a general tensorial geometry must fulfill to serve as a viable spacetime structure. Kinematics of massless and massive point particles on such geometries are introduced and the physical implications are investigated. Additionally, field equations for massive matter fields are constructed like for example a modified Dirac equation. In the second part, a background independent formulation of quantum field theory, the general boundary formulation, is reviewed. The general boundary formulation is then applied to the Unruh effect as a testing ground and first attempts are made to quantize massive matter fields on tensorial spacetimes.

Topological strings from quantum mechanics

International Nuclear Information System (INIS)

Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki

2014-12-01

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P 2 , local P 1 x P 1 and local F 1 . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.

SO(N) reformulated link invariants from topological strings

International Nuclear Information System (INIS)

Borhade, Pravina; Ramadevi, P.

2005-01-01

Large N duality conjecture between U(N) Chern-Simons gauge theory on S 3 and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the conjectured form for the expectation value of the topological operators in A-model string theory led to a reformulation of link invariants in U(N) Chern-Simons theory giving new polynomial invariants whose integer coefficients could be given a topological meaning. We show that the A-model topological operator involving SO(N) holonomy leads to a reformulation of link invariants in SO(N) Chern-Simons theory. Surprisingly, the SO(N) reformulated invariants also has a similar form with integer coefficients. The topological meaning of the integer coefficients needs to be explored from the duality conjecture relating SO(N) Chern-Simons theory to A-model closed string theory on orientifold of the resolved conifold background

Prequantum classical statistical field theory: background field as a source of everything?

International Nuclear Information System (INIS)

Khrennikov, Andrei

2011-01-01

Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's 'double solution' approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special 'prequantum fields': the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the 'photonic field' (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of 'vacuum fluctuations') might play the role of a source of such pulses, i.e., the source of everything.

The holographic RG flow in a field theory on a curved background

International Nuclear Information System (INIS)

Cardoso, Gabriel Lopes; Luest, Dieter

2002-01-01

As shown by Freedman, Gubser, Pilch and Warner, the RG flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term can be described in terms of a supersymmetric domain wall solution in five-dimensional N=8 gauged supergravity. The FGPW flow is an example of a holographic RG flow in a field theory on a flat background. Here we put the field theory studied by Freedman, Gubser, Pilch and Warner on a curved AdS 4 background, and we construct the supersymmetric domain wall solution which describes the RG flow in this field theory. This solution is a curved (non-Ricci flat) domain wall solution. This example demonstrates that holographic RG flows in supersymmetric field theories on a curved AdS 4 background can be described in terms of curved supersymmetric domain wall solutions. (author)

Topological insulating phases of non-Abelian anyonic chains

Energy Technology Data Exchange (ETDEWEB)

DeGottardi, Wade

2014-08-01

Boundary conformal field theory is brought to bear on the study of topological insulating phases of non- Abelian anyonic chains. These phases display protected anyonic end modes. We consider spin-1/2 su(2)t chains at any level k, focusing on the most prominent examples: the case k = 2 describes Ising anyons (equivalent to Majorana fermions) and k = 3 corresponds to Fibonacci anyons. The method we develop is quite general and rests on a deep connection between boundary conformal field theory and topological symmetry. This method tightly constrains the nature of the topological insulating phases of these chains for general k. Emergent anyons which arise at domain walls are shown to have the same braiding properties as the physical quasiparticles. This suggests a "solid-stat.e" topological quantum computation scheme in which emergent anyons are braided by tuning the couplings of non-Abelian quasiparticles in a fixed network.

Non-perturbative effects and the refined topological string

Energy Technology Data Exchange (ETDEWEB)

Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematiques; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics

2013-06-15

The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P{sup 1} x P{sup 1}, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.

Particles with changeable topology in nematic colloids

International Nuclear Information System (INIS)

Ravnik, Miha; Čopar, Simon; Žumer, Slobodan

2015-01-01

We show that nematic colloids can serve as a highly variable and controllable platform for studying inclusions with changeable topology and their effects on the surrounding ordering fields. We explore morphing of toroidal and knotted colloidal particles into effective spheres, distinctively changing their Euler characteristic and affecting the surrounding nematic field, including topological defect structures. With toroidal particles, the inner nematic defect eventually transitions from a wide loop to a point defect (a small loop). Trefoil particles become linked with two knotted defect loops, mutually forming a three component link, that upon tightening transform into a two-component particle-defect loop link. For more detailed topological analysis, Pontryagin-Thom surfaces are calculated and visualised, indicating an interesting cascade of defect rewirings caused by the shape morphing of the knotted particles. (paper)

Flow downstream of the heliospheric terminal shock: Magnetic field line topology and solar cycle imprint

Science.gov (United States)

Nerney, Steven; Suess, S. T.; Schmahl, E. J.

1995-01-01

The topology of the magnetic field in the heliosheath is illustrated using plots of the field lines. It is shown that the Archimedean spiral inside the terminal shock is rotated back in the heliosheath into nested spirals that are advected in the direction of the interstellar wind. The 22-year solar magnetic cycle is imprinted onto these field lines in the form of unipolar magnetic envelopes surrounded by volumes of strongly mixed polarity. Each envelope is defined by the changing tilt of the heliospheric current sheet, which is in turn defined by the boundary of unipolar high-latitude regions on the Sun that shrink to the pole at solar maximum and expand to the equator at solar minimum. The detailed shape of the envelopes is regulated by the solar wind velocity structure in the heliosheath.

Higher dimensional quantum Hall effect as A-class topological insulator

Energy Technology Data Exchange (ETDEWEB)

Hasebe, Kazuki, E-mail: khasebe@stanford.edu

2014-09-15

We perform a detail study of higher dimensional quantum Hall effects and A-class topological insulators with emphasis on their relations to non-commutative geometry. There are two different formulations of non-commutative geometry for higher dimensional fuzzy spheres: the ordinary commutator formulation and quantum Nambu bracket formulation. Corresponding to these formulations, we introduce two kinds of monopole gauge fields: non-abelian gauge field and antisymmetric tensor gauge field, which respectively realize the non-commutative geometry of fuzzy sphere in the lowest Landau level. We establish connection between the two types of monopole gauge fields through Chern–Simons term, and derive explicit form of tensor monopole gauge fields with higher string-like singularity. The connection between two types of monopole is applied to generalize the concept of flux attachment in quantum Hall effect to A-class topological insulator. We propose tensor type Chern–Simons theory as the effective field theory for membranes in A-class topological insulators. Membranes turn out to be fractionally charged objects and the phase entanglement mediated by tensor gauge field transforms the membrane statistics to be anyonic. The index theorem supports the dimensional hierarchy of A-class topological insulator. Analogies to D-brane physics of string theory are discussed too.

Lectures on the Topological Vertex

CERN Document Server

Mariño, M

2008-01-01

In this lectures, I will summarize the approach to Gromov–Witten invariants on toric Calabi–Yau threefolds based on large N dualities. Since the large N duality/topological vertex approach computes Gromov–Witten invariants in terms of Chern–Simons knot and link invariants, Sect. 2 is devoted to a review of these. Section 3 reviews topological strings and Gromov–Witten invariants, and gives some information about the open string case. Section 4 introduces the class of geometries we will deal with, namely toric (noncompact) Calabi–Yau manifolds, and we present a useful graphical way to represent these manifolds which constitutes the geometric core of the theory of the topological vertex. Finally, in Sect. 5, we define the vertex and present some explicit formulae for it and some simple applications. A brief Appendix contains useful information about symmetric polynomials. It has not been possible to present all the relevant background and physical derivations in this set of lectures. However, these...

Topological protection of multiparticle dissipative transport

Science.gov (United States)

Loehr, Johannes; Loenne, Michael; Ernst, Adrian; de Las Heras, Daniel; Fischer, Thomas M.

2016-06-01

Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.

Topology Optimisation for Coupled Convection Problems

DEFF Research Database (Denmark)

Alexandersen, Joe

This thesis deals with topology optimisation for coupled convection problems. The aim is to extend and apply topology optimisation to steady-state conjugate heat transfer problems, where the heat conduction equation governs the heat transfer in a solid and is coupled to thermal transport...... in a surrounding uid, governed by a convection-diffusion equation, where the convective velocity field is found from solving the isothermal incompressible steady-state Navier-Stokes equations. Topology optimisation is also applied to steady-state natural convection problems. The modelling is done using stabilised...... finite elements, the formulation and implementation of which was done partly during a special course as prepatory work for this thesis. The formulation is extended with a Brinkman friction term in order to facilitate the topology optimisation of fluid flow and convective cooling problems. The derived...

Open membranes in a constant C-field background and noncommutative boundary strings

International Nuclear Information System (INIS)

Kawamoto, Shoichi; Sasakura, Naoki

2000-01-01

We investigate the dynamics of open membrane boundaries in a constant C-field background. We follow the analysis for open strings in a B-field background, and take some approximations. We find that open membrane boundaries do show noncommutativity in this case by explicit calculations. Membrane boundaries are one dimensional strings, so we face a new type of noncommutativity, that is, noncommutative strings. (author)

Topological mechanics: from metamaterials to active matter

Science.gov (United States)

Vitelli, Vincenzo

2015-03-01

Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable acoustic response, which originate in the geometry of their unit cell. At the heart of such unusual behavior is often a mechanism: a motion that does not significantly stretch or compress the links between constituent elements. When activated by motors or external fields, these soft motions become the building blocks of robots and smart materials. In this talk, we discuss topological mechanisms that possess two key properties: (i) their existence cannot be traced to a local imbalance between degrees of freedom and constraints (ii) they are robust against a wide range of structural deformations or changes in material parameters. The continuum elasticity of these mechanical structures is captured by non-linear field theories with a topological boundary term similar to topological insulators and quantum Hall systems. We present several applications of these concepts to the design and experimental realization of 2D and 3D topological structures based on linkages, origami, buckling meta-materials and lastly active media that break time-reversal symmetry.

Topological insulators/superconductors: Potential future electronic materials

International Nuclear Information System (INIS)

Hor, Y. S.

2014-01-01

A new material called topological insulator has been discovered and becomes one of the fastest growing field in condensed matter physics. Topological insulator is a new quantum phase of matter which has Dirac-like conductivity on its surface, but bulk insulator through its interior. It is considered a challenging problem for the surface transport measurements because of dominant internal conductance due to imperfections of the existing crystals of topological insulators. By a proper method, the internal bulk conduction can be suppressed in a topological insulator, and permit the detection of the surface currents which is necessary for future fault-tolerant quantum computing applications. Doped topological insulators have depicted a large variety of bulk physical properties ranging from magnetic to superconducting behaviors. By chemical doping, a TI can change into a bulk superconductor. Nb x Bi 2 Se 3 is shown to be a superconductor with T c ∼ 3.2 K, which could be a potential candidate for a topological superconductor

Magnetic field topology of the cool, active, short-period binary system σ2 Coronae Borealis

Science.gov (United States)

Rosén, L.; Kochukhov, O.; Alecian, E.; Neiner, C.; Morin, J.; Wade, G. A.; BinaMIcS Collaboration

2018-06-01

Aims: The goal of this work is to study the cool, active binary star σ2 CrB, focussing on its magnetic field. The two F9-G0 components of this system are tidally locked and in a close orbit, increasing the chance of interaction between their magnetospheres. Methods: We used Stokes IV data from the twin spectropolarimeters Narval at the TBL and ESPaDOnS at the CFHT. The least-squares deconvolution multi-line technique was used to increase the signal-to-noise ratio of the data. We then applied a new binary Zeeman-Doppler imaging code to reconstruct simultaneously the magnetic topology and brightness distribution of both components of σ2 CrB. This analysis was carried out for two observational epochs in 2014 and 2017. Results: A previously unconfirmed magnetic field of the primary star has been securely detected. At the same time, the polarisation signatures of the secondary appear to have a systematically larger amplitude than that of the primary. This corresponds to a stronger magnetic field, for which the magnetic energy of the secondary exceeds that of the primary by a factor of 3.3-5.7. While the magnetic energy is similar for the secondary star in the two epochs, the magnetic energy is about twice as high in 2017 for the primary. The magnetic field topology of the two stars in the earlier epoch (2014) is very different. The fractions of energy in the dipole and quadrupole components of the secondary are similar and thereafter decrease with increasing harmonic angular degree ℓ. At the same time, for the primary the fraction of energy in the dipole component is low and the maximum energy contribution comes from ℓ = 4. However, in the 2017 epoch both stars have similar field topologies and a systematically decreasing energy with increasing ℓ. In the earlier epoch, the magnetic field at the visible pole appears to be of opposite polarity for the primary and secondary, suggesting linked magnetospheres. The apparent rotational periods of both σ2 Cr

Anisotropic effects of background fields on Born-Infeld electromagnetic waves

International Nuclear Information System (INIS)

Aiello, Matias; Bengochea, Gabriel R.; Ferraro, Rafael

2007-01-01

We show exact solutions of the Born-Infeld theory for electromagnetic plane waves propagating in the presence of static background fields. The non-linear character of the Born-Infeld equations generates an interaction between the background and the wave that changes the speed of propagation and adds a longitudinal component to the wave. As a consequence, in a magnetic background the ray direction differs from the propagation direction-a behavior resembling the one of a wave in an anisotropic medium. This feature could open up a way to experimental tests of the Born-Infeld theory

Anisotropic effects of background fields on Born-Infeld electromagnetic waves

Energy Technology Data Exchange (ETDEWEB)

Aiello, Matias [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina) and Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)]. E-mail: aiello@iafe.uba.ar; Bengochea, Gabriel R. [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina) and Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)]. E-mail: gabriel@iafe.uba.ar; Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina) and Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)]. E-mail: ferraro@iafe.uba.ar

2007-01-22

We show exact solutions of the Born-Infeld theory for electromagnetic plane waves propagating in the presence of static background fields. The non-linear character of the Born-Infeld equations generates an interaction between the background and the wave that changes the speed of propagation and adds a longitudinal component to the wave. As a consequence, in a magnetic background the ray direction differs from the propagation direction-a behavior resembling the one of a wave in an anisotropic medium. This feature could open up a way to experimental tests of the Born-Infeld theory.

The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time

International Nuclear Information System (INIS)

Marek-Crnjac, L.

2006-01-01

In the present work we show the connections between the topology of four-manifolds, conformal field theory, the mathematical probability theory and Cantorian space-time. In all these different mathematical fields, we find as the main connection the appearance of the golden mean

Topological orbifold models and quantum cohomology rings

International Nuclear Information System (INIS)

Zaslow, E.

1993-01-01

We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of CP 1 by the dihedral group D 4 , how to compute the complete ring of observables. Through this procedure, we compute all the rings from dihedral CP 1 orbifolds. We then consider CP 2 /D 4 , and show how the techniques of topological-anti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds. (orig.)

Electrically controlled band gap and topological phase transition in two-dimensional multilayer germanane

International Nuclear Information System (INIS)

Qi, Jingshan; Li, Xiao; Qian, Xiaofeng

2016-01-01

Electrically controlled band gap and topological electronic states are important for the next-generation topological quantum devices. In this letter, we study the electric field control of band gap and topological phase transitions in multilayer germanane. We find that although the monolayer and multilayer germananes are normal insulators, a vertical electric field can significantly reduce the band gap of multilayer germananes owing to the giant Stark effect. The decrease of band gap eventually leads to band inversion, transforming them into topological insulators with nontrivial Z_2 invariant. The electrically controlled topological phase transition in multilayer germananes provides a potential route to manipulate topologically protected edge states and design topological quantum devices. This strategy should be generally applicable to a broad range of materials, including other two-dimensional materials and ultrathin films with controlled growth.

Propagation of optical vortices with fractional topological charge in free space

Science.gov (United States)

Ali, Tamelia; Kreminska, Liubov; Golovin, Andrii B.; Crouse, David T.

2014-10-01

The behavior of the optical vortices with fractional topological charges in the far-field is assessed through numerical modeling and confirmed by experimental results. The generation of fractional topological charge variations of the phase within a Gaussian beam was achieved by using a liquid crystal spatial light modulator (LCoS SLM). It is shown that a laser beam carrying an optical vortex with a fractional topological charge evolves into a beam with a topological charge of integer value, specifically an integer value closer to the fractional number in the far field. A potential application of this work is for data transmission within optical telecommunication systems.

CFT and topological recursion

CERN Document Server

Kostov, Ivan

2010-01-01

We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT approach and the topological recursion, and show their equivalence. The CFT approach reformulates the problem in terms of a conformal field theory on a Riemann surface, while the topological recursion is based on a recurrence equation for the observables representing symplectic invariants on the complex curve. The two approaches lead to two different graph expansions, one of which can be obtained as a partial resummation of the other.

Topology

CERN Document Server

Hocking, John G

1988-01-01

""As textbook and reference work, this is a valuable addition to the topological literature."" - Mathematical ReviewsDesigned as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.There are four set-theoretic chapters, followed by four primarily algebraic chapters. Chapter I covers the fundamentals of topological and metrical spaces, mappings, compactness, product spaces, the Tychonoff t

Topological hierarchy matters — topological matters with superlattices of defects

International Nuclear Information System (INIS)

He Jing; Kou Su-Peng

2016-01-01

Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states. In this paper, we review the defects effect in these topological states and study new types of topological matters — topological hierarchy matters. We find that both topological defects (quantized vortices) and non topological defects (vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects. These topological mid-gap states have nontrivial topological properties, including the nonzero Chern number and the gapless edge states. Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters. (topical review)

Detecting topology in a nearly flat hyperbolic universe

OpenAIRE

Weeks, Jeffrey R.

2002-01-01

Cosmic microwave background data shows the observable universe to be nearly flat, but leaves open the question of whether it is simply or multiply connected. Several authors have investigated whether the topology of a multiply connect hyperbolic universe would be detectable when 0.9 < Omega < 1. However, the possibility of detecting a given topology varies depending on the location of the observer within the space. Recent studies have assumed the observer sits at a favorable location. The pre...

Universe as a topological defect

International Nuclear Information System (INIS)

Anabalon, Andres; Willison, Steven; Zanelli, Jorge

2008-01-01

Four-dimensional Einstein's general relativity is shown to arise from a gauge theory for the conformal group, SO(4,2). The theory is constructed from a topological dimensional reduction of the six-dimensional Euler density integrated over a manifold with a four-dimensional topological defect. The resulting action is a four-dimensional theory defined by a gauged Wess-Zumino-Witten term. An ansatz is found which reduces the full set of field equations to those of Einstein's general relativity. When the same ansatz is replaced in the action, the gauged WZW term reduces to the Einstein-Hilbert action. Furthermore, the unique coupling constant in the action can be shown to take integer values if the fields are allowed to be analytically continued to complex values

Magnetic Monopoles, Center Vortices and Topology of Gauge Fields

OpenAIRE

Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Schafke, A.

1999-01-01

The topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills Theory. For this purpose the continuum analog of the maximum center gauge is constructed.

Magnetic monopoles, center vortices and topology of gauge fields

International Nuclear Information System (INIS)

Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Schaefke, A.

2000-01-01

The topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills Theory. For this purpose the continuum analog of the maximum center gauge is constructed

Duo gating on a 3D topological insulator - independent tuning of both topological surface states

Science.gov (United States)

Li, Chuan; de Ronde, Bob; Snelder, Marieke; Stehno, Martin; Huang, Yingkai; Golden, Mark; Brinkman, Alexander; ICE Team; IOP Collaboration

ABSTRACT: Topological insulators are associated with a trove of exciting physics, such as the ability to host robust anyons, Majorana Bound States, which can be used for quantum computation. For future Majorana devices it is desirable to have the Fermi energy tuned as close as possible to the Dirac point of the topological surface state. Based on previous work on gating BSTS, we report the experimental progress towards gate-tuning of the top and bottom topological surface states of BiSbTeSe2 crystal flakes. When the Fermi level is moved across the Dirac point conduction is shown to change from electron dominated transport to hole dominated transport independently for either surface. In the high magnetic field, one can tune the system precisely between the different landau levels of both surfaces, thus a full gating map of the possible landau levels combination is established. In addition, we provide a simple capacitance model to explain the general hysteresis behaviors in topological insulator systems.

Vacuum background fields in QCD as a source of confinement

International Nuclear Information System (INIS)

Simonov, Yu.A.

1987-01-01

Large distance behaviour of quark and gluon Green functions is studied in vacuum background fields. Periodic and bounded stochastic fields do not ensure confinement. New stochastic vacuum configurations are suggested, which generate a superlocalization regime, i.e. a large distance decay of Green functions faster than the exponential one. This latter regime corresponds to the confinement

Topological Rényi entropy after a quantum quench.

Science.gov (United States)

Halász, Gábor B; Hamma, Alioscia

2013-04-26

We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Rényi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Rényi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.

Extending the radial diffusion model of Falthammar to non-dipole background field

Energy Technology Data Exchange (ETDEWEB)

Cunningham, Gregory Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-05-26

A model for radial diffusion caused by electromagnetic disturbances was published by Falthammar (1965) using a two-parameter model of the disturbance perturbing a background dipole magnetic field. Schulz and Lanzerotti (1974) extended this model by recognizing the two parameter perturbation as the leading (non--dipole) terms of the Mead Williams magnetic field model. They emphasized that the magnetic perturbation in such a model induces an electric ield that can be calculated from the motion of field lines on which the particles are ‘frozen’. Roederer and Zhang (2014) describe how the field lines on which the particles are frozen can be calculated by tracing the unperturbed field lines from the minimum-B location to the ionospheric footpoint, and then tracing the perturbed field (which shares the same ionospheric footpoint due to the frozen -in condition) from the ionospheric footpoint back to a perturbed minimum B location. The instantaneous change n Roederer L*, dL*/dt, can then be computed as the product (dL*/dphi)*(dphi/dt). dL*/Dphi is linearly dependent on the perturbation parameters (to first order) and is obtained by computing the drift across L*-labeled perturbed field lines, while dphi/dt is related to the bounce-averaged gradient-curvature drift velocity. The advantage of assuming a dipole background magnetic field, as in these previous studies, is that the instantaneous dL*/dt can be computed analytically (with some approximations), as can the DLL that results from integrating dL*/dt over time and computing the expected value of (dL*)^2. The approach can also be applied to complex background magnetic field models like T89 or TS04, on top of which the small perturbations are added, but an analytical solution is not possible and so a numerical solution must be implemented. In this talk, I discuss our progress in implementing a numerical solution to the calculation of DL*L* using arbitrary background field models with simple electromagnetic

Riemann, topology, and physics

CERN Document Server

Monastyrsky, Michael I

2008-01-01

This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...

Algebraic topology a primer

CERN Document Server

Deo, Satya

2018-01-01

This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...

Surface representations of two- and three-dimensional fluid flow topology

Science.gov (United States)

Helman, James L.; Hesselink, Lambertus

1990-01-01

We discuss our work using critical point analysis to generate representations of the vector field topology of numerical flow data sets. Critical points are located and characterized in a two-dimensional domain, which may be either a two-dimensional flow field or the tangential velocity field near a three-dimensional body. Tangent curves are then integrated out along the principal directions of certain classes of critical points. The points and curves are linked to form a skeleton representing the two-dimensional vector field topology. When generated from the tangential velocity field near a body in a three-dimensional flow, the skeleton includes the critical points and curves which provide a basis for analyzing the three-dimensional structure of the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations to generate surfaces representing the topology of the associated flow separations.

The inception of pulsed discharges in air: simulations in background fields above and below breakdown

Science.gov (United States)

Sun, Anbang; Teunissen, Jannis; Ebert, Ute

2014-11-01

We investigate discharge inception in air, in uniform background electric fields above and below the breakdown threshold. We perform 3D particle simulations that include a natural level of background ionization in the form of positive and \\text{O}2- ions. In background fields below breakdown, we use a strongly ionized seed of electrons and positive ions to enhance the field locally. In the region of enhanced field, we observe the growth of positive streamers, as in previous simulations with 2D plasma fluid models. The inclusion of background ionization has little effect in this case. When the background field is above the breakdown threshold, the situation is very different. Electrons can then detach from \\text{O}2- and start ionization avalanches in the whole volume. These avalanches together create one extended discharge, in contrast to the ‘double-headed’ streamers found in many fluid simulations.

Quintic quasi-topological gravity

Energy Technology Data Exchange (ETDEWEB)

Cisterna, Adolfo [Vicerrectoría académica, Universidad Central de Chile,Toesca 1783 Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile,Casilla 567, Valdivia (Chile); Guajardo, Luis; Hassaïne, Mokhtar [Instituto de Matemática y Física, Universidad de Talca,Casilla 747, Talca (Chile); Oliva, Julio [Departamento de Física, Universidad de Concepción,Casilla, 160-C, Concepción (Chile)

2017-04-11

We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R{sup 5} terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff’s Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler’s polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in https://arxiv.org/abs/1003.4773, the general geometric structure of these Lagrangians remains an open problem.

Conservation laws and stress-energy-momentum tensors for systems with background fields

Energy Technology Data Exchange (ETDEWEB)

Gratus, Jonathan, E-mail: j.gratus@lancaster.ac.uk [Lancaster University, Lancaster LA1 4YB (United Kingdom); The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD (United Kingdom); Obukhov, Yuri N., E-mail: yo@thp.uni-koeln.de [Institute for Theoretical Physics, University of Cologne, 50923 Koeln (Germany); Tucker, Robin W., E-mail: r.tucker@lancaster.ac.uk [Lancaster University, Lancaster LA1 4YB (United Kingdom); The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD (United Kingdom)

2012-10-15

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.

RELATIONSHIP BETWEEN CHROMOSPHERIC EVAPORATION AND MAGNETIC FIELD TOPOLOGY IN AN M-CLASS SOLAR FLARE

Energy Technology Data Exchange (ETDEWEB)

Sadykov, Viacheslav M; Kosovichev, Alexander G [Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102 (United States); Sharykin, Ivan N; Zimovets, Ivan V [Space Research Institute (IKI) of Russian Academy of Sciences, Moscow 117997 (Russian Federation); Dominguez, Santiago Vargas [Universidad Nacional de Colombia, Sede Bogotá, Observatorio Astronómico, Carrera 45 # 26-85, Bogotá (Colombia)

2016-09-01

Chromospheric evaporation is observed as Doppler blueshift during solar flares. It plays a key role in the dynamics and energetics of solar flares; however, its mechanism is still unknown. In this paper, we present a detailed analysis of spatially resolved multi-wavelength observations of chromospheric evaporation during an M 1.0-class solar flare (SOL2014-06-12T21:12) using data from NASA’s Interface Region Imaging Spectrograph and HMI/ SDO (the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory), and high-resolution observations from VIS/NST (the Visible Imaging Spectrometer at the New Solar Telescope). The results show that the averaged over the flare region Fe xxi blueshift of the hot (10{sup 7} K) evaporating plasma is delayed relative to the C ii redshift of the relatively cold (10{sup 4} K) chromospheric plasma by about one minute. The spatial distribution of the delays is not uniform across the region and can be as long as two minutes in several zones. Using vector magnetograms from HMI, we reconstruct the magnetic field topology and the quasi-separatrix layer, and find that the blueshift delay regions as well as the H α flare ribbons are connected to the region of the magnetic polarity inversion line (PIL) and an expanding flux rope via a system of low-lying loop arcades with a height of ≲4.5 Mm. As a result, the chromospheric evaporation may be driven by the energy release in the vicinity of PIL, and has the observed properties due to a local magnetic field topology.

Nontrivial topological states on a Möbius band

NARCIS (Netherlands)

Beugeling, W.; Quelle, A.; Morais Smith, C.

2014-01-01

In the field of topological insulators, the topological properties of quantum states in samples with simple geometries, such as a cylinder or a ribbon, have been classified and understood during the past decade. Here we extend these studies to a Möbius band and argue that its lack of orientability

Topological insulators Dirac equation in condensed matter

CERN Document Server

Shen, Shun-Qing

2017-01-01

This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already b...

Surfaces and slabs of fractional topological insulator heterostructures

Science.gov (United States)

Sahoo, Sharmistha; Sirota, Alexander; Cho, Gil Young; Teo, Jeffrey C. Y.

2017-10-01

Fractional topological insulators (FTIs) are electronic topological phases in (3 +1 ) dimensions enriched by time reversal (TR) and charge U (1 ) conservation symmetries. We focus on the simplest series of fermionic FTIs, whose bulk quasiparticles consist of deconfined partons that carry fractional electric charges in integral units of e*=e /(2 n +1 ) and couple to a discrete Z2 n +1 gauge theory. We propose massive symmetry preserving or breaking FTI surface states. Combining the long-ranged entangled bulk with these topological surface states, we deduce the novel topological order of quasi-(2 +1 ) -dimensional FTI slabs as well as their corresponding edge conformal field theories.

The consistency assessment of topological relations in cartographic generalization

Science.gov (United States)

Zheng, Chunyan; Guo, Qingsheng; Du, Xiaochu

2006-10-01

The field of research in the generalization assessment has been less studied than the generalization process itself, and it is very important to keep topological relation consistency for meeting generalization quality. This paper proposes a methodology to assess the quality of generalized map from topological relations consistency. Taking roads (including railway) and residential areas for examples, from the viewpoint of the spatial cognition, some issues about topological consistency in different map scales are analyzed. The statistic information about the inconsistent topological relations can be obtained by comparing the two matrices: one is the matrix for the topological relations in the generalized map; the other is the theoretical matrix for the topological relations that should be maintained after generalization. Based on the fuzzy set theory and the classification of map object types, the consistency evaluation model of topological relations is established. The paper proves the feasibility of the method through the example about how to evaluate the local topological relations between simple roads and residential area finally.

Fermi arc mediated entropy transport in topological semimetals

Science.gov (United States)

McCormick, Timothy M.; Watzman, Sarah J.; Heremans, Joseph P.; Trivedi, Nandini

2018-05-01

The low-energy excitations of topological Weyl semimetals are composed of linearly dispersing Weyl fermions that act as monopoles of Berry curvature in the bulk momentum space. Furthermore, on the surface there exist topologically protected Fermi arcs at the projections of these Weyl points. We propose a pathway for entropy transport involving Fermi arcs on one surface connecting to Fermi arcs on the other surface via the bulk Weyl monopoles. We present results for the temperature and magnetic field dependence of the magnetothermal conductance of this conveyor belt channel. The circulating currents result in a net entropy transport without any net charge transport. We provide results for the Fermi arc mediated magnetothermal conductivity in the low-field semiclassical limit as well as in the high-field ultraquantum limit, where only chiral Landau levels are involved. Our work provides a proposed signature of Fermi arc mediated magnetothermal transport and sets the stage for utilizing and manipulating the topological Fermi arcs in thermal applications.

Interface currents in topological superconductor–ferromagnet heterostructures

International Nuclear Information System (INIS)

Brydon, P M R; Timm, Carsten; Schnyder, Andreas P

2013-01-01

We propose the existence of a substantial charge current parallel to the interface between a noncentrosymmetric superconductor and a metallic ferromagnet. Our analysis focuses upon two complementary orbital-angular-momentum pairing states of the superconductor, exemplifying topologically nontrivial states which are gapped and gapless in the bulk, respectively. Utilizing a quasiclassical scattering theory, we derive an expression for the interface current in terms of Andreev reflection coefficients. Performing a systematic study of the current, we find stark qualitative differences between the gapped and gapless superconductors, which reflect the very different underlying topological properties. For the fully gapped superconductor, there is a sharp drop in the zero-temperature current as the system is tuned from a topologically nontrivial to a trivial phase. We explain this in terms of the sudden disappearance of the contribution to the current from the subgap edge states at the topological transition. The current in the gapless superconductor is characterized by a dramatic enhancement at low temperatures, and exhibits a singular dependence on the exchange-field strength in the ferromagnetic metal at zero temperature. This is caused by the energy shift of the strongly spin-polarized nondegenerate zero-energy flat bands due to their coupling to the exchange field. We argue that the interface current provides a novel test of the topology of the superconductor, and discuss prospects for the experimental verification of our predictions. (paper)

Cavity quantum chromodynamics in the presence of a classical background field

International Nuclear Information System (INIS)

Gavin, E.J.O.; Viollier, R.D.

1988-01-01

The QCD (quantum chromodynamics) Lagrange density is constructed in which the gluon field has a classical part, using the background field gauge. The conserved currents deriving from the symmetries of this theory are given and used to define boundary conditions on the field operators on the surface of a spherical, static cavity. The field operators are expanded in terms of a complete set of cavity modes that satisfy the boundary conditions and the field equations in the Dirac picture. 13 refs

Topology and shape optimization of induced-charge electro-osmotic micropumps

DEFF Research Database (Denmark)

Gregersen, Misha Marie; Okkels, Fridolin; Bazant, M. Z.

2009-01-01

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 topology and shape of the dielectric solid. In particular, we extend existing...... conventional electrokinetic models with an artificial design field to describe the transition from the liquid electrolyte to the solid dielectric. Using this design field, we have succeeded in applying the method of topology optimization to find system geometries with non-trivial topologies that maximize...... the net induced electro-osmotic flow rate through the electrolytic capacitor in the direction parallel to the capacitor plates. Once found, the performance of the topology-optimized geometries has been validated by transferring them to conventional electrokinetic models not relying on the artificial...

Higgs boson decay into two photons in an electromagnetic background field

DEFF Research Database (Denmark)

Nielsen, N. K.

2014-01-01

The amplitude for Higgs boson decay into two photons in a homogeneous and time-independent magnetic field is investigated by proper-time regularization in a gauge-invariant manner and is found to be singular at large field values. The singularity is caused by the component of the charged vector...... boson field that is tachyonic in a strong magnetic field. Also, tools for the computation of the amplitude in a more general electromagnetic background are developed....

Topological matter, integrable models and fusion rings

International Nuclear Information System (INIS)

Nemeschansky, D.; Warner, N.P.

1992-01-01

We show how topological G k /G k models can be embedded into the topological matter models that are obtained by perturbing the twisted N = 2 supersymmetric, hermitian symmetric, coset models. In particular, this leads to an embedding of the fusion ring of G as a sub-ring of the perturbed, chiral primary ring. The perturbation of the twisted N = 2 model that leads to the fusion ring is also shown to lead to an integrable N = 2 supersymmetric field theory when the untwisted N = 2 superconformal field theory is perturbed by the same operator and its hermitian conjugate. (orig.)

Renormalization of gauge theories in the background-field approach arXiv

CERN Document Server

Barvinsky, Andrei O.; Herrero-Valea, Mario; Sibiryakov, Sergey M.; Steinwachs, Christian F.

Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.

Gauge symmetries, topology, and quantisation

International Nuclear Information System (INIS)

Balachandran, A.P.

1994-01-01

The following two loosely connected sets of topics are reviewed in these lecture notes: (1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. (2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under (1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern-Simons action using the preceding ideas. Under (2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin-statistics theorem

Topological sigma B model in 4-dimensions

International Nuclear Information System (INIS)

Jun, Hyun-Keun; Park, Jae-Suk

2008-01-01

We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on complex structure of X, while is independent of Kaehler metric of X. The theory is also a 4-dimensional topological field theory in the sense that the theory is independent of variation of Riemannian metric of the source 4-manifold M, potentially leading to new smooth invariant of 4-manifolds. We argue that the theory also comes with a topological family parametrized by the extended moduli space of complex structures.

Comparison of different lattice definitions of the topological charge

International Nuclear Information System (INIS)

Cichy, Krzysztof; Ottnad, Konstantin; Bonn Univ.; Bonn Univ.; Urbach, Carsten; Zimmermann, Falk; Bonn Univ.; Wenger, Urs

2014-11-01

We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac operator, spectral projectors, spectral flow of the Hermitian Wilson-Dirac operator and field theoretic with different kinds of smoothing of gauge fields (HYP and APE smearings, gradient flow, cooling). We also show some results on the topological susceptibility.

On a quantized scalar field in the de Sitter and Nariai universes

International Nuclear Information System (INIS)

Nariai, Hidekazu.

1984-08-01

After canonical quantization of a massive or massless scalar field in the de Sitter and Nariai universes (both of which satisfy the same Einstein equations with a non-vanishing cosmological constant, Rsub(μν)=Agsub(μν), but their topological structures differ from each other), the uniquely obtained 4-dimensional commutation functions in both universes are comparatively studied with due emphasis on their topological structures, as well as the difference of couplings to the background universe. (author)

Higgsless superconductivity from topological defects in compact BF terms

Directory of Open Access Journals (Sweden)

M. Cristina Diamantini

2015-02-01

Full Text Available 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.

Scalar field vacuum expectation value induced by gravitational wave background

Science.gov (United States)

Jones, Preston; McDougall, Patrick; Ragsdale, Michael; Singleton, Douglas

2018-06-01

We show that a massless scalar field in a gravitational wave background can develop a non-zero vacuum expectation value. We draw comparisons to the generation of a non-zero vacuum expectation value for a scalar field in the Higgs mechanism and with the dynamical Casimir vacuum. We propose that this vacuum expectation value, generated by a gravitational wave, can be connected with particle production from gravitational waves and may have consequences for the early Universe where scalar fields are thought to play an important role.

Descriptive Topology in Selected Topics of Functional Analysis

CERN Document Server

Kakol, J; Pellicer, Manuel Lopez

2011-01-01

"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Frechet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical set

A topological introduction to nonlinear analysis

CERN Document Server

Brown, Robert F

2014-01-01

This third edition of A Topological Introduction to Nonlinear Analysis is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. For this third edition, several new chapters present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply...

Experimental investigation of coaxial-gun-formed plasmas injected into a background transverse magnetic field or plasma

Science.gov (United States)

Zhang, Yue; Fisher, Dustin M.; Gilmore, Mark; Hsu, Scott C.; Lynn, Alan G.

2018-05-01

Injection of coaxial-gun-formed magnetized plasmas into a background transverse vacuum magnetic field or into a background magnetized plasma has been studied in the helicon-cathode (HelCat) linear plasma device at the University of New Mexico [M. Gilmore et al., J. Plasma Phys. 81, 345810104 (2015)]. A magnetized plasma jet launched into a background transverse magnetic field shows emergent kink stabilization of the jet due to the formation of a sheared flow in the jet above the kink stabilization threshold 0.1kVA [Y. Zhang et al., Phys. Plasmas 24, 110702 (2017)]. Injection of a spheromak-like plasma into a transverse background magnetic field led to the observation of finger-like structures on the side with a stronger magnetic field null between the spheromak and the background field. The finger-like structures are consistent with magneto-Rayleigh-Taylor instability. Jets or spheromaks launched into a background, low-β magnetized plasma show similar behavior as above, respectively, in both cases.

Induced topological pressure for topological dynamical systems

International Nuclear Information System (INIS)

Xing, Zhitao; Chen, Ercai

2015-01-01

In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure

Developing Topological Insulator Fiber Based Photon Pairs Source for Ultrafast Optoelectronic Applications

Science.gov (United States)

2016-04-01

of a thin layer of topological insulator Bi2Se3 with the transmission of T = 50%. We apply magnetic field B=3 tesla normal to the sample and parallel...nonlinear induced by magnetic field in the Topological Insulator Bi2Se3 and Molybdenum Disulfide MoS2. The nonlinear effect is pulse broadening...Topological Insulator Q- Switched Erbium-Doped Fiber Laser”, IEEE J. Sel. Top. Quant. Electron., 20, 0900508 (2014). [2]. Shuqing Chen et al, “Stable Q

Topological insulator infrared pseudo-bolometer with polarization sensitivity

Energy Technology Data Exchange (ETDEWEB)

Sharma, Peter Anand

2017-10-25

Topological insulators can be utilized in a new type of infrared photodetector that is intrinsically sensitive to the polarization of incident light and static magnetic fields. The detector isolates single topological insulator surfaces and allows light collection and exposure to static magnetic fields. The wavelength range of interest is between 750 nm and about 100 microns. This detector eliminates the need for external polarization selective optics. Polarization sensitive infrared photodetectors are useful for optoelectronics applications, such as light detection in environments with low visibility in the visible wavelength regime.

Introductory lectures on fibre bundles and topology for physicists

Energy Technology Data Exchange (ETDEWEB)

Thomas, G.H.

1978-05-01

These lectures may provide useful background material for understanding gauge theories, particularly the nonperturbative effects such as instantons and monopoles. The mathematical language of topology and fibre bundles is introduced.

Introductory lectures on fibre bundles and topology for physicists

International Nuclear Information System (INIS)

Thomas, G.H.

1978-05-01

These lectures may provide useful background material for understanding gauge theories, particularly the nonperturbative effects such as instantons and monopoles. The mathematical language of topology and fibre bundles is introduced

Simulating cosmic microwave background maps in multiconnected spaces

International Nuclear Information System (INIS)

Riazuelo, Alain; Uzan, Jean-Philippe; Lehoucq, Roland; Weeks, Jeffrey

2004-01-01

This paper describes the computation of cosmic microwave background (CMB) anisotropies in a universe with multiconnected spatial sections and focuses on the implementation of the topology in standard CMB computer codes. The key ingredient is the computation of the eigenmodes of the Laplacian with boundary conditions compatible with multiconnected space topology. The correlators of the coefficients of the decomposition of the temperature fluctuation in spherical harmonics are computed and examples are given for spatially flat spaces and one family of spherical spaces, namely, the lens spaces. Under the hypothesis of Gaussian initial conditions, these correlators encode all the topological information of the CMB and suffice to simulate CMB maps

Superconducting Coset Topological Fluids in Josephson Junction Arrays

CERN Document Server

Diamantini, M C; Trugenberger, C A; Sodano, Pasquale; Trugenberger, Carlo A.

2006-01-01

We show that the superconducting ground state of planar Josephson junction arrays is a P- and T-invariant coset topological quantum fluid whose topological order is characterized by the degeneracy 2 on the torus. This new mechanism for planar superconductivity is the P- and T-invariant analogue of Laughlin's quantum Hall fluids. The T=0 insulator-superconductor quantum transition is a quantum critical point characterized by gauge fields and deconfined degrees of freedom. Experiments on toroidal Josephson junction arrays could provide the first direct evidence for topological order and superconducting quantum fluids.

HgTe based topological insulators

International Nuclear Information System (INIS)

Bruene, Christoph

2014-01-01

This PhD thesis summarizes the discovery of topological insulators and highlights the developments on their experimental observations. The work focuses on HgTe. The thesis is structured as follows: - The first chapter of this thesis will give a brief overview on discoveries in the field of topological insulators. It focuses on works relevant to experimental results presented in the following chapters. This includes a short outline of the early predictions and a summary of important results concerning 2-dimensional topological insulators while the final section discusses observations concerning 3-dimensional topological insulators. - The discovery of the quantum spin Hall effect in HgTe marked the first experimental observation of a topological insulator. Chapter 2 focuses on HgTe quantum wells and the quantum spin Hall effect. The growth of high quality HgTe quantum wells was one of the major goals for this work. In a final set of experiments the spin polarization of the edge channels was investigated. Here, we could make use of the advantage that HgTe quantum well structures exhibit a large Rashba spin orbit splitting. - HgTe as a 3-dimensional topological insulator is presented in chapter 3. - Chapters 4-6 serve as in depth overviews of selected works: Chapter 4 presents a detailed overview on the all electrical detection of the spin Hall effect in HgTe quantum wells. The detection of the spin polarization of the quantum spin Hall effect is shown in chapter 5 and chapter 6 gives a detailed overview on the quantum Hall effect originating from the topological surface state in strained bulk HgTe.

Topological defects in the second-class phase transformations

International Nuclear Information System (INIS)

Dobrowolski, T.

2002-06-01

The dynamics of systems during second-class phase transformations are presented.in a frame of quantum fields theory. It is shown that solutions of non-linear field equations generate some topological defects what result in symmetry breaking and field phase transformations

Topological instability of a semi-bounded magnetic fluid drop under influence of magnetic and ultrasound fields

Energy Technology Data Exchange (ETDEWEB)

Bashtovoi, V., E-mail: bashv@rambler.ru [Belarussian National Technical University, 65 Nezavisimosti Ave., Minsk 220013 (Belarus); Reks, A. [Belarussian National Technical University, 65 Nezavisimosti Ave., Minsk 220013 (Belarus); Baev, A. [Institute of Applied Physics of NAS of Belarus, 16 Akademicheskaya str., Minsk 220072 (Belarus); Mansoor, Al-Jhaish Taha Malik [Belarussian National Technical University, 65 Nezavisimosti Ave., Minsk 220013 (Belarus)

2017-06-01

Theoretical and experimental results on deformation and disintegration on parts (topological instability) of semi-bounded magnetic fluid drop placed on horizontal plate in the presence of gravity and vertical external uniform magnetic field, and the influence of acoustic wave on these processes, as well as an experimental results of acoustic fountain on free surface of magnetic fluid are presented. The role of individual mechanisms leading to disintegration is analyzed, and analytical relationships and experimental dependences for critical parameters are established.

Topological photonic orbital-angular-momentum switch

Science.gov (United States)

Luo, Xi-Wang; Zhang, Chuanwei; Guo, Guang-Can; Zhou, Zheng-Wei

2018-04-01

The large number of available orbital-angular-momentum (OAM) states of photons provides a unique resource for many important applications in quantum information and optical communications. However, conventional OAM switching devices usually rely on precise parameter control and are limited by slow switching rate and low efficiency. Here we propose a robust, fast, and efficient photonic OAM switch device based on a topological process, where photons are adiabatically pumped to a target OAM state on demand. Such topological OAM pumping can be realized through manipulating photons in a few degenerate main cavities and involves only a limited number of optical elements. A large change of OAM at ˜10q can be realized with only q degenerate main cavities and at most 5 q pumping cycles. The topological photonic OAM switch may become a powerful device for broad applications in many different fields and motivate a topological design of conventional optical devices.

Perspectives in Analysis, Geometry, and Topology

CERN Document Server

Itenberg, I V; Passare, Mikael

2012-01-01

The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Design principles for HgTe based topological insulator devices

Science.gov (United States)

Sengupta, Parijat; Kubis, Tillmann; Tan, Yaohua; Povolotskyi, Michael; Klimeck, Gerhard

2013-07-01

The topological insulator properties of CdTe/HgTe/CdTe quantum wells are theoretically studied. The CdTe/HgTe/CdTe quantum well behaves as a topological insulator beyond a critical well width dimension. It is shown that if the barrier (CdTe) and well-region (HgTe) are altered by replacing them with the alloy CdxHg1-xTe of various stoichiometries, the critical width can be changed. The critical quantum well width is shown to depend on temperature, applied stress, growth directions, and external electric fields. Based on these results, a novel device concept is proposed that allows to switch between a normal semiconducting and topological insulator state through application of moderate external electric fields.

Open string in the constant B-field background

International Nuclear Information System (INIS)

Jing Jian; Long Zhengwen

2005-01-01

A new method is proposed to quantize open strings in this paper. To illustrate our method, we analyze free open string as well as open string in the D-brane background with a nonvanishing B-field, respectively. The Poisson brackets among Fourier components are obtained firstly then we get the Poisson brackets among open string's coordinates. The noncommutativity of coordinates along the D-brane is reproduced. Some ambiguities in the previous discussions can be avoided

Topology Optimization for Additive Manufacturing

DEFF Research Database (Denmark)

Clausen, Anders

This PhD thesis deals with the combination of topology optimization and additive man-ufacturing (AM, also known as 3D-printing). In addition to my own works, the thesis contains a broader review and assessment of the literature within the field. The thesis first presents a classification...... of the various AM technologies, a review of relevant manufacturing materials, the properties of these materials in the additively manufactured part, as well as manufacturing constraints with a potential for design optimization. Subsequently, specific topology optimization formulations relevant for the most im...... for scalable manufacturing. In relation to interface problems it is shown how a flexible void area may be included into a standard minimum compliance problem by employing an additional design variable field and a sensitivity filter. Furthermore, it is shown how the design of coated structures may be modeled...

Compact solar UV burst triggered in a magnetic field with a fan-spine topology

Science.gov (United States)

Chitta, L. P.; Peter, H.; Young, P. R.; Huang, Y.-M.

2017-09-01

Context. Solar ultraviolet (UV) bursts are small-scale features that exhibit intermittent brightenings that are thought to be due to magnetic reconnection. They are observed abundantly in the chromosphere and transition region, in particular in active regions. Aims: We investigate in detail a UV burst related to a magnetic feature that is advected by the moat flow from a sunspot towards a pore. The moving feature is parasitic in that its magnetic polarity is opposite to that of the spot and the pore. This comparably simple photospheric magnetic field distribution allows for an unambiguous interpretation of the magnetic geometry leading to the onset of the observed UV burst. Methods: We used UV spectroscopic and slit-jaw observations from the Interface Region Imaging Spectrograph (IRIS) to identify and study chromospheric and transition region spectral signatures of said UV burst. To investigate the magnetic topology surrounding the UV burst, we used a two-hour-long time sequence of simultaneous line-of-sight magnetograms from the Helioseismic and Magnetic Imager (HMI) and performed data-driven 3D magnetic field extrapolations by means of a magnetofrictional relaxation technique. We can connect UV burst signatures to the overlying extreme UV (EUV) coronal loops observed by the Atmospheric Imaging Assembly (AIA). Results: The UV burst shows a variety of extremely broad line profiles indicating plasma flows in excess of ±200 km s-1 at times. The whole structure is divided into two spatially distinct zones of predominantly up- and downflows. The magnetic field extrapolations show a persistent fan-spine magnetic topology at the UV burst. The associated 3D magnetic null point exists at a height of about 500 km above the photosphere and evolves co-spatially with the observed UV burst. The EUV emission at the footpoints of coronal loops is correlated with the evolution of the underlying UV burst. Conclusions: The magnetic field around the null point is sheared by

Factorising the 3D topologically twisted index

Science.gov (United States)

Cabo-Bizet, Alejandro

2017-04-01

We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on {S}_2 times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on {S}_2 times halves of {S}_1 , second as TTCSM on {S}_2 times {S}_1 — with a puncture, — and third as TTCSM on {S}_2× {S}_1 . In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.

Topology in Molecular Biology

CERN Document Server

Monastyrsky, Michail Ilych

2007-01-01

The book presents a class of new results in molecular biology for which topological methods and ideas are important. These include: the large-scale conformation properties of DNA; computational methods (Monte Carlo) allowing the simulation of large-scale properties of DNA; the tangle model of DNA recombination and other applications of Knot theory; dynamics of supercoiled DNA and biocatalitic properties of DNA; the structure of proteins; and other very recent problems in molecular biology. The text also provides a short course of modern topology intended for the broad audience of biologists and physicists. The authors are renowned specialists in their fields and some of the new results presented here are documented for the first time in monographic form.

Acoustic design by topology optimization

DEFF Research Database (Denmark)

Dühring, Maria Bayard; Jensen, Jakob Søndergaard; Sigmund, Ole

2008-01-01

To bring down noise levels in human surroundings is an important issue and a method to reduce noise by means of topology optimization is presented here. The acoustic field is modeled by Helmholtz equation and the topology optimization method is based on continuous material interpolation functions...... in the density and bulk modulus. The objective function is the squared sound pressure amplitude. First, room acoustic problems are considered and it is shown that the sound level can be reduced in a certain part of the room by an optimized distribution of reflecting material in a design domain along the ceiling...

General topology

CERN Document Server

Willard, Stephen

2004-01-01

Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: ""continuous topology,"" represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and ""geometric topology,"" covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340

Gravity Model for Topological Features on a Cylindrical Manifold

Directory of Open Access Journals (Sweden)

Bayak I.

2008-04-01

Full Text Available A model aimed at understanding quantum gravity in terms of Birkho’s approach is discussed. The geometry of this model is constructed by using a winding map of Minkowski space into a R3 S1 -cylinder. The basic field of this model is a field of unit vectors defined through the velocity field of a flow wrapping the cylinder. The degeneration of some parts of the flow into circles (topological features results in in- homogeneities and gives rise to a scalar field, analogous to the gravitational field. The geometry and dynamics of this field are briefly discussed. We treat the intersections be- tween the topological features and the observer’s 3-space as matter particles and argue that these entities are likely to possess some quantum properties.

Some geometry and topology

International Nuclear Information System (INIS)

Marmo, G.; Morandi, G.

1995-01-01

In this lecture some mathematical problems that arise when one deals with low-dimensional field theories, such as homotopy and topological invariants, differential calculus on Lie groups and coset spaces, fiber spaces and parallel transport, differential calculus on fiber bundles, sequences on principal bundles and Chern-Simons terms are discussed

Exact Foldy-Wouthuysen transformation for gravitational waves and magnetic field background

International Nuclear Information System (INIS)

Goncalves, Bruno; Obukhov, Yuri N.; Shapiro, Ilya L.

2007-01-01

We consider an exact Foldy-Wouthuysen transformation for the Dirac spinor field on the combined background of a gravitational wave and constant uniform magnetic field. By taking the classical limit of the spinor field Hamiltonian, we arrive at the equations of motion for the nonrelativistic spinning particle. Two different kinds of gravitational fields are considered and in both cases the effect of the gravitational wave on the spinor field and on the corresponding spinning particle may be enforced by a sufficiently strong magnetic field. This result can be relevant for astrophysical applications and, in principle, useful for creating the gravitational wave detectors based on atomic physics and precise interferometry

Vacuum fluctuations of the supersymmetric field in curved background

International Nuclear Information System (INIS)

Bilić, Neven; Domazet, Silvije; Guberina, Branko

2012-01-01

We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants.

Vacuum fluctuations of the supersymmetric field in curved background

Energy Technology Data Exchange (ETDEWEB)

Bilic, Neven, E-mail: bilic@thphys.irb.hr [Rudjer Boskovic Institute, POB 180, HR-10002 Zagreb (Croatia); Domazet, Silvije, E-mail: sdomazet@irb.hr [Rudjer Boskovic Institute, POB 180, HR-10002 Zagreb (Croatia); Guberina, Branko, E-mail: guberina@thphys.irb.hr [Rudjer Boskovic Institute, POB 180, HR-10002 Zagreb (Croatia)

2012-01-16

We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants.

Cosmic microwave background polarization signals from tangled magnetic fields.

Science.gov (United States)

Seshadri, T R; Subramanian, K

2001-09-03

Tangled, primordial cosmic magnetic fields create small rotational velocity perturbations on the last scattering surface of the cosmic microwave background radiation. For fields which redshift to a present value of B0 = 3 x 10(-9) G, these vector modes are shown to generate polarization anisotropies of order 0.1-4 microK on small angular scales (500

Topological Nematic States and Non-Abelian Lattice Dislocations

Directory of Open Access Journals (Sweden)

Maissam Barkeshli

2012-08-01

Full Text Available An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number N, which can be mapped to an N-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.

Topological Nematic States and Non-Abelian Lattice Dislocations

Science.gov (United States)

Barkeshli, Maissam; Qi, Xiao-Liang

2012-07-01

An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number N, which can be mapped to an N-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.

Impact of stochastic primordial magnetic fields on the scalar contribution to cosmic microwave background anisotropies

International Nuclear Information System (INIS)

Finelli, Fabio; Paci, Francesco; Paoletti, Daniela

2008-01-01

We study the impact of a stochastic background of primordial magnetic fields on the scalar contribution of cosmic microwave background (CMB) anisotropies and on the matter power spectrum. We give the correct initial conditions for cosmological perturbations and the exact expressions for the energy density and Lorentz force associated to the stochastic background of primordial magnetic fields, given a power-law for their spectra cut at a damping scale. The dependence of the CMB temperature and polarization spectra on the relevant parameters of the primordial magnetic fields is illustrated.

ORGANIZATION OF GRAPHIC INFORMATION FOR VIEWING THE MULTILAYER VLSI TOPOLOGY

Directory of Open Access Journals (Sweden)

V. I. Romanov

2016-01-01

Full Text Available One of the possible ways to reorganize of graphical information describing the set of topology layers of modern VLSI. The method is directed on the use in the conditions of the bounded size of video card memory. An additional effect, providing high performance of forming multi- image layout a multi-layer topology of modern VLSI, is achieved by preloading the required texture by means of auxiliary background process.

THE COSMIC INFRARED BACKGROUND EXPERIMENT (CIBER): THE WIDE-FIELD IMAGERS

Energy Technology Data Exchange (ETDEWEB)

Bock, J.; Battle, J. [Jet Propulsion Laboratory (JPL), National Aeronautics and Space Administration (NASA), Pasadena, CA 91109 (United States); Sullivan, I. [Department of Physics, University of Washington, Seattle, WA 98195 (United States); Arai, T.; Matsumoto, T.; Matsuura, S.; Tsumura, K. [Department of Space Astronomy and Astrophysics, Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), Sagamihara, Kanagawa 252-5210 (Japan); Cooray, A.; Mitchell-Wynne, K.; Smidt, J. [Center for Cosmology, University of California, Irvine, CA 92697 (United States); Hristov, V.; Lam, A. C.; Levenson, L. R.; Mason, P. [Department of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125 (United States); Keating, B.; Renbarger, T. [Department of Physics, University of California, San Diego, San Diego, CA 92093 (United States); Kim, M. G. [Department of Physics and Astronomy, Seoul National University, Seoul 151-742 (Korea, Republic of); Lee, D. H. [Institute of Astronomy and Astrophysics, Academia Sinica, National Taiwan University, Taipei 10617, Taiwan (China); Nam, U. W. [Korea Astronomy and Space Science Institute (KASI), Daejeon 305-348 (Korea, Republic of); Suzuki, K. [Instrument Development Group of Technical Center, Nagoya University, Nagoya, Aichi 464-8602 (Japan); and others

2013-08-15

We have developed and characterized an imaging instrument to measure the spatial properties of the diffuse near-infrared extragalactic background light (EBL) in a search for fluctuations from z > 6 galaxies during the epoch of reionization. The instrument is part of the Cosmic Infrared Background Experiment (CIBER), designed to observe the EBL above Earth's atmosphere during a suborbital sounding rocket flight. The imaging instrument incorporates a 2 Degree-Sign Multiplication-Sign 2 Degree-Sign field of view to measure fluctuations over the predicted peak of the spatial power spectrum at 10 arcmin, and 7'' Multiplication-Sign 7'' pixels, to remove lower redshift galaxies to a depth sufficient to reduce the low-redshift galaxy clustering foreground below instrumental sensitivity. The imaging instrument employs two cameras with {Delta}{lambda}/{lambda} {approx} 0.5 bandpasses centered at 1.1 {mu}m and 1.6 {mu}m to spectrally discriminate reionization extragalactic background fluctuations from local foreground fluctuations. CIBER operates at wavelengths where the electromagnetic spectrum of the reionization extragalactic background is thought to peak, and complements fluctuation measurements by AKARI and Spitzer at longer wavelengths. We have characterized the instrument in the laboratory, including measurements of the sensitivity, flat-field response, stray light performance, and noise properties. Several modifications were made to the instrument following a first flight in 2009 February. The instrument performed to specifications in three subsequent flights, and the scientific data are now being analyzed.

Topological Derivatives in Shape Optimization

CERN Document Server

Novotny, Antonio André

2013-01-01

The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intende...

Topological Hall and spin Hall effects in disordered skyrmionic textures

KAUST Repository

Ndiaye, Papa Birame; Akosa, Collins Ashu; Manchon, Aurelien

2017-01-01

We carry out a thorough study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy-band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real-space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and find that the adiabatic approximation still holds for large skyrmions as well as for nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that the topological Hall effect is highly sensitive to momentum scattering.

Localized topological states in Bragg multihelicoidal fibers with twist defects

Science.gov (United States)

Alexeyev, C. N.; Lapin, B. P.; Milione, G.; Yavorsky, M. A.

2016-06-01

We have studied the influence of a twist defect in multihelicoidal Bragg fibers on the emerging of localized defect modes. We have shown that if such a fiber is excited with a Gaussian beam this leads to the appearance of a defect-localized topological state, whose topological charge coincides with the order of rotational symmetry of the fiber's refractive index. We have shown that this effect has a pronounced crossover behavior. We have also formulated a principle of creating the systems that can nestle defect-localized topologically charged modes. According to this principle, such systems have to possess topological activity, that is, the ability to change the topological charge of the incoming field, and operate in the Bragg regime.

Topological Hall and spin Hall effects in disordered skyrmionic textures

KAUST Repository

Ndiaye, Papa Birame

2017-02-24

We carry out a thorough study of the topological Hall and topological spin Hall effects in disordered skyrmionic systems: the dimensionless (spin) Hall angles are evaluated across the energy-band structure in the multiprobe Landauer-Büttiker formalism and their link to the effective magnetic field emerging from the real-space topology of the spin texture is highlighted. We discuss these results for an optimal skyrmion size and for various sizes of the sample and find that the adiabatic approximation still holds for large skyrmions as well as for nanoskyrmions. Finally, we test the robustness of the topological signals against disorder strength and show that the topological Hall effect is highly sensitive to momentum scattering.

Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow

International Nuclear Information System (INIS)

Ni, Xu; He, Cheng; Sun, Xiao-Chen; Liu, Xiao-ping; Lu, Ming-Hui; Chen, Yan-Feng; Feng, Liang

2015-01-01

Recent explorations of topology in physical systems have led to a new paradigm of condensed matters characterized by topologically protected states and phase transition, for example, topologically protected photonic crystals enabled by magneto-optical effects. However, in other wave systems such as acoustics, topological states cannot be simply reproduced due to the absence of similar magnetics-related sound–matter interactions in naturally available materials. Here, we propose an acoustic topological structure by creating an effective gauge magnetic field for sound using circularly flowing air in the designed acoustic ring resonators. The created gauge magnetic field breaks the time-reversal symmetry, and therefore topological properties can be designed to be nontrivial with non-zero Chern numbers and thus to enable a topological sonic crystal, in which the topologically protected acoustic edge-state transport is observed, featuring robust one-way propagation characteristics against a variety of topological defects and impurities. Our results open a new venue to non-magnetic topological structures and promise a unique approach to effective manipulation of acoustic interfacial transport at will. (paper)

Cosmic microwave background observables of small field models of inflation

International Nuclear Information System (INIS)

Ben-Dayan, Ido; Brustein, Ram

2010-01-01

We construct a class of single small field models of inflation that can predict, contrary to popular wisdom, an observable gravitational wave signal in the cosmic microwave background anisotropies. The spectral index, its running, the tensor to scalar ratio and the number of e-folds can cover all the parameter space currently allowed by cosmological observations. A unique feature of models in this class is their ability to predict a negative spectral index running in accordance with recent cosmic microwave background observations. We discuss the new class of models from an effective field theory perspective and show that if the dimensionless trilinear coupling is small, as required for consistency, then the observed spectral index running implies a high scale of inflation and hence an observable gravitational wave signal. All the models share a distinct prediction of higher power at smaller scales, making them easy targets for detection

SATA Stochastic Algebraic Topology and Applications

Science.gov (United States)

2017-01-23

discretized loops with topological constraints [8]. (10) Applications of critical point theory to statistical inference problems...comparison, which provides background material. 1: Statistics of random functions From a mathematical standpoint, our basic setup here starts... applications , leads to a need for statistical analysis, the first step of which requires asymptotic distribution results for estimators. The first such

Quantum and classical contributions to linear magnetoresistance in topological insulator thin films

International Nuclear Information System (INIS)

Singh, Sourabh; Gopal, R. K.; Sarkar, Jit; Mitra, Chiranjib

2016-01-01

Three dimensional topological insulators possess backscattering immune relativistic Dirac fermions on their surface due to nontrivial topology of the bulk band structure. Both metallic and bulk insulating topological insulators exhibit weak-antilocalization in the low magnetic field and linear like magnetoresistance in higher fields. We explore the linear magnetoresistance in bulk insulating topological insulator Bi 2-x Sb x Te 3-y Se y thin films grown by pulsed laser deposition technique. Thin films of Bi 2-x Sb x Te 3-y Se y were found to be insulating in nature, which conclusively establishes the origin of linear magnetoresistance from surface Dirac states. The films were thoroughly characterized for their crystallinity and composition and then subjected to transport measurements. We present a careful analysis taking into considerations all the existing models of linear magnetoresistance. We comprehend that the competition between classical and quantum contributions to magnetoresistance results in linear magnetoresistance in high fields. We observe that the cross-over field decreases with increasing temperature and the physical argument for this behavior is explained.

Grassmannian topological Kazama-Suzuki models and cohomology

International Nuclear Information System (INIS)

Blau, M.; Hussain, F.; Thompson, G.

1995-10-01

We investigate in detail the topological gauged Wess-Zumino-Witten models describing topological Kazama-Suzuki models based on complex Grassmannians. We show that there is a topological sector in which the ring of observables (constructed from the Grassmann odd scalars of the theory) coincides with the classical cohomology ring of the Grassmanian for all values of the level k. We also analyze the general ring structure of bosonic correlation functions, uncovering a whole hierarchy of level-rank relations (including the standard level-rank duality) among models based on different Grassmannians. Using the previously established localization of the topological Kazama-Suzuki model to an Abelian topological field theory, we reduce the correlators to finite-dimensional purely algebraic expressions. As an application, these are evaluated explicitly for the CP(2) model at level k and shown for all k to coincide with the cohomological intersection numbers of the two-plane Grassmannian G(2,K + 2), thus realizing the level-rank duality between this model and the G(2, k + 2) model at level one. (author). 28 refs

Differential and symplectic topology of knots and curves

CERN Document Server

Tabachnikov, S

1999-01-01

This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory (""quantum"" knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is

Energy spectrum of tearing mode turbulence in sheared background field

Science.gov (United States)

Hu, Di; Bhattacharjee, Amitava; Huang, Yi-Min

2018-06-01

The energy spectrum of tearing mode turbulence in a sheared background magnetic field is studied in this work. We consider the scenario where the nonlinear interaction of overlapping large-scale modes excites a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction on the large-scale field. The turbulence we discuss here differs from traditional MHD turbulence mainly in two aspects. One is the existence of many linearly stable small-scale modes which cause an effective damping during the energy cascade. The other is the scale-independent anisotropy induced by the large-scale modes tilting the sheared background field, as opposed to the scale-dependent anisotropy frequently encountered in traditional critically balanced turbulence theories. Due to these two differences, the energy spectrum deviates from a simple power law and takes the form of a power law multiplied by an exponential falloff. Numerical simulations are carried out using visco-resistive MHD equations to verify our theoretical predictions, and a reasonable agreement is found between the numerical results and our model.

Combining Topological Hardware and Topological Software: Color-Code Quantum Computing with Topological Superconductor Networks

Science.gov (United States)

Litinski, Daniel; Kesselring, Markus S.; Eisert, Jens; von Oppen, Felix

2017-07-01

We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall-superconductor hybrids.

Combining Topological Hardware and Topological Software: Color-Code Quantum Computing with Topological Superconductor Networks

Directory of Open Access Journals (Sweden)

Daniel Litinski

2017-09-01

Full Text Available We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall–superconductor hybrids.

Length scale and manufacturability in density-based topology optimization

DEFF Research Database (Denmark)

Lazarov, Boyan Stefanov; Wang, Fengwen; Sigmund, Ole

2016-01-01

Since its original introduction in structural design, density-based topology optimization has been applied to a number of other fields such as microelectromechanical systems, photonics, acoustics and fluid mechanics. The methodology has been well accepted in industrial design processes where it can...... provide competitive designs in terms of cost, materials and functionality under a wide set of constraints. However, the optimized topologies are often considered as conceptual due to loosely defined topologies and the need of postprocessing. Subsequent amendments can affect the optimized design...

Geometric Model of Topological Insulators from the Maxwell Algebra

Science.gov (United States)

Palumbo, Giandomenico

I propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincare' algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, I derive a relativistic version of the Wen-Zee term and I show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space. This work is part of the DITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).

The dispersionless Lax equations and topological minimal models

International Nuclear Information System (INIS)

Krichever, I.

1992-01-01

It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the tree level partition functions, of A n topological minimal models are found. The Virasoro constraints for the analogue of the τ-function of the dispersionless Lax equation corresponding to these models are proved. (orig.)

Factorising the 3D topologically twisted index

Energy Technology Data Exchange (ETDEWEB)

Cabo-Bizet, Alejandro [Instituto de Astronomía y Física del Espacio (CONICET-UBA),Ciudad Universitaria, C.P. 1428, Buenos Aires (Argentina)

2017-04-20

We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on S{sub 2} times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on S{sub 2} times halves of S{sub 1}, second as TTCSM on S{sub 2} times S{sub 1} — with a puncture, — and third as TTCSM on S{sub 2}×S{sub 1}. In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.

Combinatorial-topological framework for the analysis of global dynamics

Science.gov (United States)

Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł

2012-12-01

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.

Combinatorial-topological framework for the analysis of global dynamics.

Science.gov (United States)

Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł

2012-12-01

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications.

Three-dimensional topological insulators and bosonization

Energy Technology Data Exchange (ETDEWEB)