Renormalization of topological field theory

International Nuclear Information System (INIS)

Birmingham, D.; Rakowski, M.; Thompson, G.

1988-11-01

One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs

Dimensional crossover and cold-atom realization of topological Mott insulators

Science.gov (United States)

Scheurer, Mathias S.; Rachel, Stephan; Orth, Peter P.

2015-02-01

Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.

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.

Topology of high-dimensional manifolds

Energy Technology Data Exchange (ETDEWEB)

Farrell, F T [State University of New York, Binghamton (United States); Goettshe, L [Abdus Salam ICTP, Trieste (Italy); Lueck, W [Westfaelische Wilhelms-Universitaet Muenster, Muenster (Germany)

2002-08-15

The School on High-Dimensional Manifold Topology took place at the Abdus Salam ICTP, Trieste from 21 May 2001 to 8 June 2001. The focus of the school was on the classification of manifolds and related aspects of K-theory, geometry, and operator theory. The topics covered included: surgery theory, algebraic K- and L-theory, controlled topology, homology manifolds, exotic aspherical manifolds, homeomorphism and diffeomorphism groups, and scalar curvature. The school consisted of 2 weeks of lecture courses and one week of conference. Thwo-part lecture notes volume contains the notes of most of the lecture courses.

Engineering topological phases with a three-dimensional nodal-loop semimetal

Science.gov (United States)

Li, Linhu; Yap, Han Hoe; Araújo, Miguel A. N.; Gong, Jiangbin

2017-12-01

A three-dimensional (3D) nodal-loop semimetal phase is exploited to engineer a number of intriguing phases featuring different peculiar topological surface states. In particular, by introducing various two-dimensional gap terms to a 3D tight-binding model of a nodal-loop semimetal, we obtain a rich variety of topological phases of great interest to ongoing theoretical and experimental studies, including a chiral insulator, degenerate-surface-loop insulator, and second-order topological insulator, as well as a Weyl semimetal with tunable Fermi arc profiles. The unique concept underlying our approach is to engineer topological surface states that inherit their dispersion relations from a gap term. The results provide one rather unified principle for the creation of novel topological phases and can guide the search for new topological materials. Two-terminal transport studies are also carried out to distinguish the engineered topological phases.

Disorder effect in two-dimensional topological insulators

International Nuclear Information System (INIS)

Zhang Xianglin; Feng Shiping; Guo Huaiming

2012-01-01

We conduct a systematic study on the disorder effect in two-dimensional (2D) topological insulators by calculating the Z 2 topological invariant. Starting from the trivial and nontrivial topological phases of the model describing HgTe/CdTe quantum wells (QWs), we introduce three different kinds of disorder into the system, including the fluctuations in the on-site potential, the hopping amplitude and the topological mass. These kinds of disorder commonly exist in HgTe/CdTe QWs grown experimentally. By explicit numerical calculations, we show that all three kinds of disorder have the similar effect: the topological phase in the system is not only robust to them, but also can be brought about by introducing them to the trivial insulator phase. These results make a further confirmation and extendability of the study on the interplay between the disorder and the topological phase.

Pseudogap and Fermi-Surface Topology in the Two-Dimensional Hubbard Model

Science.gov (United States)

Wu, Wei; Scheurer, Mathias S.; Chatterjee, Shubhayu; Sachdev, Subir; Georges, Antoine; Ferrero, Michel

2018-04-01

One of the distinctive features of hole-doped cuprate superconductors is the onset of a "pseudogap" below a temperature T* . Recent experiments suggest that there may be a connection between the existence of the pseudogap and the topology of the Fermi surface. Here, we address this issue by studying the two-dimensional Hubbard model with two distinct numerical methods. We find that the pseudogap only exists when the Fermi surface is holelike and that, for a broad range of parameters, its opening is concomitant with a Fermi-surface topology change from electronlike to holelike. We identify a common link between these observations: The polelike feature of the electronic self-energy associated with the formation of the pseudogap is found to also control the degree of particle-hole asymmetry, and hence the Fermi-surface topology transition. We interpret our results in the framework of an SU(2) gauge theory of fluctuating antiferromagnetism. We show that a mean-field treatment of this theory in a metallic state with U(1) topological order provides an explanation of this polelike feature and a good description of our numerical results. We discuss the relevance of our results to experiments on cuprates.

Identifying Two-Dimensional Z 2 Antiferromagnetic Topological Insulators

Science.gov (United States)

Bègue, F.; Pujol, P.; Ramazashvili, R.

2018-01-01

We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate Néel antiferromagnet, where staggered magnetization breaks the symmetry with respect to both elementary translation and time reversal, but retains their product as a symmetry. In contrast to the so-called Z 2 topological insulators, an exhaustive characterization of antiferromagnetic topological phases with the help of topological invariants has been missing. We analyze a simple model of an antiferromagnetic topological insulator and chart its phase diagram, using a recently proposed criterion for centrosymmetric systems [13]. We then adapt two methods, originally designed for paramagnetic systems, and make antiferromagnetic topological phases manifest. The proposed methods apply far beyond the particular examples treated in this work, and admit straightforward generalization. We illustrate this by two examples of non-centrosymmetric systems, where no simple criteria have been known to identify topological phases. We also present, for some cases, an explicit construction of edge states in an antiferromagnetic topological insulator.

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

Topologically protected states in one-dimensional systems

CERN Document Server

Fefferman, C L; Weinstein, M I

2017-01-01

The authors study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". They then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized "edge states". These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.

Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators

Science.gov (United States)

Pervishko, Anastasiia A.; Yudin, Dmitry; Shelykh, Ivan A.

2018-02-01

Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect within recently proposed Brillouin-Wigner perturbation theory that allows us to map a time-dependent problem into a stationary one. Our analysis reveals that both the gap and the components of the group velocity of the surface states can be tuned in a controllable fashion by adjusting the intensity of the driving field within an experimentally accessible range and demonstrate the effect of light-induced band inversion in the spectrum of the surface states for high enough values of the pump.

(3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Energy Technology Data Exchange (ETDEWEB)

Dittrich, Bianca [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)

2017-05-22

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably. We in particular show that the fusion bases of the (2+1)-dimensional theory lead to a rich set of bases for the (3+1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian. Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.

Topological organization of (low-dimensional) chaos

International Nuclear Information System (INIS)

Tufillaro, N.B.

1992-01-01

Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template describes the primary folding and stretching mechanisms of phase space responsible for the chaotic motion. Topological invariants of the unstable periodic orbits in the closure of the strange set are calculated from the (reconstructed) template. These topological invariants must be consistent with ampersand ny model put forth to describe the time series data, and are useful in invalidating (or gaining confidence in) any model intended to describe the dynamical system generating the time series

Yang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting Bosons

Science.gov (United States)

Yan, Yangqian; Zhou, Qi

2018-06-01

The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.

Topology of Flow Separation on Three-Dimensional Bodies

Science.gov (United States)

Chapman, Gary T.; Yates, Leslie A.

1991-01-01

In recent years there has been extensive research on three-dimensional flow separation. There are two different approaches: the phenomenological approach and a mathematical approach using topology. These two approaches are reviewed briefly and the shortcomings of some of the past works are discussed. A comprehensive approach applicable to incompressible and compressible steady-state flows as well as incompressible unsteady flow is then presented. The approach is similar to earlier topological approaches to separation but is more complete and in some cases adds more emphasis to certain points than in the past. To assist in the classification of various types of flow, nomenclature is introduced to describe the skin-friction portraits on the surface. This method of classification is then demonstrated on several categories of flow to illustrate particular points as well as the diversity of flow separation. The categories include attached, two-dimensional separation and three different types of simple, three-dimensional primary separation, secondary separation, and compound separation. Hypothetical experiments are utilized to illustrate the topological terminology and its role in characterizing these flows. These hypothetical experiments use colored oil injected onto the surface at singular points in the skin-friction portrait. Actual flow-visualization information, if available, is used to corroborate the hypothetical examples.

Three-dimensional fractional topological insulators in coupled Rashba layers

Science.gov (United States)

Volpez, Yanick; Loss, Daniel; Klinovaja, Jelena

2017-08-01

We propose a model of three-dimensional topological insulators consisting of weakly coupled electron- and hole-gas layers with Rashba spin-orbit interaction stacked along a given axis. We show that in the presence of strong electron-electron interactions the system realizes a fractional strong topological insulator, where the rotational symmetry and condensation energy arguments still allow us to treat the problem as quasi-one-dimensional with bosonization techniques. We also show that if Rashba and Dresselhaus spin-orbit interaction terms are equally strong, by doping the system with magnetic impurities, one can bring it into the Weyl semimetal phase.

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

Topological phases of interacting fermions in one-dimensional superconductor - normal metal geometry

Energy Technology Data Exchange (ETDEWEB)

Meidan, Dganit [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universitaet Berlin, 14195 Berlin (Germany); Romito, Alessandro; Brouwer, Piet W. [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)

2015-07-01

One-dimensional superconductors can be in non-trivial topological phases harboring Majorana end-states, which possess non-abelian statistics. It has been recently established that in the presence of interactions the classification of topological superconducting phases can be significantly altered. Specifically, for one-dimensional superconductors possessing a time reversal symmetry (BDI class), interactions reduce the infinitely many non-interacting phases (Z topological index) to eight distinct ones (Z{sub 8} topological index). In this talk I will consider multi-mode superconducting wires in such BDI class when probed by an external contact, and discuss their low temperature and voltage bias transport properties. I will first show that the Andreev reflection component of the scattering matrix of the probing lead provides a topological index, r=-4,.., 4, which distinguish the eight topological phases. The two topologically equivalent phases with r= 4,-4 support emergent many-body end states, which are identified to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-fermi liquid fixed point where a multiple channel Kondo effect develops.

Spontaneous transition to a stochastic state in a four-dimensional Yang-Mills quantum theory

International Nuclear Information System (INIS)

Semikhatov, A.M.

1983-01-01

The quantum expectation values in a four-dimensional Yang-Mills theory are represented in each topological sector as expectation values over the diffusion which develops in the ''fourth'' Euclidean time. The Langevin equations of this diffusion are stochastic duality equations in the A 4 = 0 gauge

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.)

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.

Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus

Directory of Open Access Journals (Sweden)

Zhong Wang

2014-01-01

Full Text Available We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.

Topological higher gauge theory: From BF to BFCG theory

International Nuclear Information System (INIS)

Girelli, F.; Pfeiffer, H.; Popescu, E. M.

2008-01-01

We study generalizations of three- and four-dimensional BF theories in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of Yetter, Mackaay, and Porter. Under certain conditions, we can present their corresponding continuum counterparts in terms of classical Lagrangians. We then explain that two of these models are already familiar from the literature: the ΣΦEA model of three-dimensional gravity coupled to topological matter and also a four-dimensional model of BF theory coupled to topological matter

(d -2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States

Science.gov (United States)

Song, Zhida; Fang, Zhong; Fang, Chen

2017-12-01

We study fourfold rotation-invariant gapped topological systems with time-reversal symmetry in two and three dimensions (d =2 , 3). We show that in both cases nontrivial topology is manifested by the presence of the (d -2 )-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through the explicit construction of microscopic models having robust (d -2 )-dimensional edge states.

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)

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)

Engineering topological edge states in two dimensional magnetic photonic crystal

Science.gov (United States)

Yang, Bing; Wu, Tong; Zhang, Xiangdong

2017-01-01

Based on a perturbative approach, we propose a simple and efficient method to engineer the topological edge states in two dimensional magnetic photonic crystals. The topological edge states in the microstructures can be constructed and varied by altering the parameters of the microstructure according to the field-energy distributions of the Bloch states at the related Bloch wave vectors. The validity of the proposed method has been demonstrated by exact numerical calculations through three concrete examples. Our method makes the topological edge states "designable."

Unruly topologies in two-dimensional quantum gravity

International Nuclear Information System (INIS)

Hartle, J.B.

1985-01-01

A sum over histories formulation of quantum geometry could involve sums over different topologies as well as sums over different metrics. In classical gravity a geometry is a manifold with a metric, but it is difficult to implement a sum over manifolds in quantum gravity. In this difficulty, motivation is found for including in the sum over histories, geometries defined on more general objects than manifolds-unruly topologies. In simplicial two-dimensional quantum gravity a class of simplicial complexes is found to which the gravitational action can be extended, for which sums over the class are straightforwardly defined, and for which a manifold dominates the sum in the classical limit. The situation in higher dimensions is discussed. (author)

Particle-vortex duality in topological insulators and superconductors

Energy Technology Data Exchange (ETDEWEB)

Murugan, Jeff [The Laboratory for Quantum Gravity & Strings, Department of Mathematics and Applied Mathematics, University of Cape Town,Private Bag, Rondebosch, 7700 (South Africa); School of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540 (United States); Nastase, Horatiu [Instituto de Física Teórica, UNESP-Universidade Estadual Paulista,R. Dr. Bento T. Ferraz 271, Bl. II, Sao Paulo 01140-070, SP (Brazil)

2017-05-31

We investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path integral in the standard way, while in three dimensions, it takes the form of “self-duality in odd dimensions'. In this sense, it is closely related to the particle-vortex duality of planar systems. In particular, we use this to elaborate on Son’s conjecture that a three dimensional Dirac fermion that can be thought of as the surface mode of a four dimensional topological insulator is dual to a composite fermion.

Euler numbers of four-dimensional rotating black holes with the Euclidean signature

International Nuclear Information System (INIS)

Ma Zhengze

2003-01-01

For a black hole's spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number to which it is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the spacetime manifolds of black holes. Using this formula, we obtain that the Euler numbers of Kerr and Kerr-Newman black holes are 2. We also obtain that the Euler number of the Kerr-Sen metric in the heterotic string theory with one boost angle nonzero is 2, which is in accordance with its topology

Topology and incompleteness for 2+1-dimensional cosmological spacetimes

Science.gov (United States)

Fajman, David

2017-06-01

We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.

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.

Topologically protected bound states in one-dimensional Floquet acoustic waveguide systems

Science.gov (United States)

Peng, Yu-Gui; Geng, Zhi-Guo; Zhu, Xue-Feng

2018-03-01

Topological manipulation of sound has recently been a hot spot in acoustics due to the fascinating property of defect immune transport. To the best of our knowledge, the studies on one-dimensional (1D) topological acoustic systems hitherto mainly focus on the case of the Su-Schrieffer-Heeger model. Here, we show that topologically protected bound states may also exist in 1D periodically modulated acoustic waveguide systems, viz., 1D Floquet topological insulators. The results show that tuning the coupling strength in a waveguide lattice could trigger topological phase transition, which gives rise to topologically protected interface states as we put together two waveguide lattices featured with different topological phases or winding numbers. However, for the combined lattice, input at the waveguides other than the interfacial ones will excite bulk states. We have further verified the robustness of interface bound states against the variation of coupling strengths between the two distinct waveguide lattices. This work extends the scope of topological acoustics and may promote potential applications for acoustic devices with topological functionalities.

The Topology Optimization of Three-dimensional Cooling Fins by the Internal Element Connectivity Parameterization Method

International Nuclear Information System (INIS)

Yoo, Sung Min; Kim, Yoon Young

2007-01-01

This work is concerned with the topology optimization of three-dimensional cooling fins or heat sinks. Motivated by earlier success of the Internal Element Connectivity Method (I-ECP) method in two dimensional problems, the extension of I-ECP to three-dimensional problems is carried out. The main efforts were made to maintain the numerical trouble-free characteristics of I-ECP for full three-dimensional problems; a serious numerical problem appearing in thermal topology optimization is erroneous temperature undershooting. The effectiveness of the present implementation was checked through the design optimization of three-dimensional fins

Current Harmonics Cancellation in Three-Phase Four-Wire Systems by Using a Four-Branch Star Filtering Topology

DEFF Research Database (Denmark)

Rodriguez, Pedro; Candela, J. I.; Luna, A.

2009-01-01

This paper presents a new solution for filtering current harmonics in three-phase four-wire networks. The original four-branch star (FBS) filter topology presented in this paper is characterized by a particular layout of single-phase inductances and capacitors, without using any transformer......, a specific implementation of a three-phase four-wire hybrid power filter is presented as an illustrative application of the filtering topology. An extensive evaluation using simulation and experimental results from a DSP-based laboratory prototype is conducted in order to verify and validate the good...... only passive components are employed, or as a hybrid filter, when its behavior is improved by integrating a power converter into the filter structure. The paper analyzes the proposed topology, and derives fundamental concepts about the control of the resulting hybrid power filter. From this analysis...

Optical transitions in two-dimensional topological insulators with point defects

Science.gov (United States)

Sablikov, Vladimir A.; Sukhanov, Aleksei A.

2016-12-01

Nontrivial properties of electronic states in topological insulators are inherent not only to the surface and boundary states, but to bound states localized at structure defects as well. We clarify how the unusual properties of the defect-induced bound states are manifested in optical absorption spectra in two-dimensional topological insulators. The calculations are carried out for defects with short-range potential. We find that the defects give rise to the appearance of specific features in the absorption spectrum, which are an inherent property of topological insulators. They have the form of two or three absorption peaks that are due to intracenter transitions between electron-like and hole-like bound states.

Topological origin of edge states in two-dimensional inversion-symmetric insulators and semimetals

NARCIS (Netherlands)

Miert, Guido van|info:eu-repo/dai/nl/413490378; Ortix, Carmine|info:eu-repo/dai/nl/413315304; de Morais Smith, C.|info:eu-repo/dai/nl/304836346

2017-01-01

Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal ($\\mathcal{T}$) and inversion ($\\mathcal{I}$) symmetry. This allows

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

TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions

Science.gov (United States)

2017-01-01

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/ PMID:28749969

Entanglement entropy for (3+1)-dimensional topological order with excitations

Science.gov (United States)

Wen, Xueda; He, Huan; Tiwari, Apoorv; Zheng, Yunqin; Ye, Peng

2018-02-01

Excitations in (3+1)-dimensional [(3+1)D] topologically ordered phases have very rich structures. (3+1)D topological phases support both pointlike and stringlike excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the following question: How do different types of topological excitations contribute to the entanglement entropy or, alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological order? We are mainly interested in (3+1)D topological order that can be realized in Dijkgraaf-Witten (DW) gauge theories, which are labeled by a finite group G and its group 4-cocycle ω ∈H4[G ;U(1 ) ] up to group automorphisms. We find that each topological excitation contributes a universal constant lndi to the entanglement entropy, where di is the quantum dimension that depends on both the structure of the excitation and the data (G ,ω ) . The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory (G ,ω ) . In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles ω from the others.

Charge-spin Transport in Surface-disordered Three-dimensional Topological Insulators

Science.gov (United States)

Peng, Xingyue

As one of the most promising candidates for the building block of the novel spintronic circuit, the topological insulator (TI) has attracted world-wide interest of study. Robust topological order protected by time-reversal symmetry (TRS) makes charge transport and spin generation in TIs significantly different from traditional three-dimensional (3D) or two-dimensional (2D) electronic systems. However, to date, charge transport and spin generation in 3D TIs are still primarily modeled as single-surface phenomena, happening independently on top and bottom surfaces. In this dissertation, I will demonstrate via both experimental findings and theoretical modeling that this "single surface'' theory neither correctly describes a realistic 3D TI-based device nor reveals the amazingly distinct physical picture of spin transport dynamics in 3D TIs. Instead, I present a new viewpoint of the spin transport dynamics where the role of the insulating yet topologically non-trivial bulk of a 3D TI becomes explicit. Within this new theory, many mysterious transport and magneto-transport anomalies can be naturally explained. The 3D TI system turns out to be more similar to its low dimensional sibling--2D TI rather than some other systems sharing the Dirac dispersion, such as graphene. This work not only provides valuable fundamental physical insights on charge-spin transport in 3D TIs, but also offers important guidance to the design of 3D TI-based spintronic devices.

Effect of disorders on topological phases in one-dimensional optical superlattices

International Nuclear Information System (INIS)

Wang Zhizhou; Wu Yidong; Du Huijing; Jing Xili

2016-01-01

In a recent paper, Lang et al. proposed that edge states and topological phases can be observed in one-dimensional optical superlattices. They showed that the topological phases can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions. However, disorders are not considered in their model. To study the effect of disorders on the topological phases, we introduce random potentials to the model for optical superlattcies. Our calculations show that edge states are robust against the disorders. We find the edge states are very sensitive to the number of the sites in the optical superlattice and we propose a simple rule to describe the relationship between the edge states and the number of sites. The density plateaus are also robust against weak disorders provided that the average density is calculated over a long interval. The widths of the plateaus are proportional to the widths of the bulk energy gaps when there are disorders. The disorders can diminish the bulk energy gaps. So the widths of the plateaus decrease with the increase of disorders and the density plateaus disappear when disorders are too strong. The results in our paper can be used to guide the experimental detection of topological phases in one-dimensional systems. (paper)

Extended supersymmetry in four-dimensional Euclidean space

International Nuclear Information System (INIS)

McKeon, D.G.C.; Sherry, T.N.

2000-01-01

Since the generators of the two SU(2) groups which comprise SO(4) are not Hermitian conjugates of each other, the simplest supersymmetry algebra in four-dimensional Euclidean space more closely resembles the N=2 than the N=1 supersymmetry algebra in four-dimensional Minkowski space. An extended supersymmetry algebra in four-dimensional Euclidean space is considered in this paper; its structure resembles that of N=4 supersymmetry in four-dimensional Minkowski space. The relationship of this algebra to the algebra found by dimensionally reducing the N=1 supersymmetry algebra in ten-dimensional Euclidean space to four-dimensional Euclidean space is examined. The dimensional reduction of N=1 super Yang-Mills theory in ten-dimensional Minkowski space to four-dimensional Euclidean space is also considered

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.

Topological Quantum Phase Transitions in Two-Dimensional Hexagonal Lattice Bilayers

Science.gov (United States)

Zhai, Xuechao; Jin, Guojun

2013-09-01

Since the successful fabrication of graphene, two-dimensional hexagonal lattice structures have become a research hotspot in condensed matter physics. In this short review, we theoretically focus on discussing the possible realization of a topological insulator (TI) phase in systems of graphene bilayer (GBL) and boron nitride bilayer (BNBL), whose band structures can be experimentally modulated by an interlayer bias voltage. Under the bias, a band gap can be opened in AB-stacked GBL but is still closed in AA-stacked GBL and significantly reduced in AA- or AB-stacked BNBL. In the presence of spin-orbit couplings (SOCs), further demonstrations indicate whether the topological quantum phase transition can be realized strongly depends on the stacking orders and symmetries of structures. It is observed that a bulk band gap can be first closed and then reopened when the Rashba SOC increases for gated AB-stacked GBL or when the intrinsic SOC increases for gated AA-stacked BNBL. This gives a distinct signal for a topological quantum phase transition, which is further characterized by a jump of the ℤ2 topological invariant. At fixed SOCs, the TI phase can be well switched by the interlayer bias and the phase boundaries are precisely determined. For AA-stacked GBL and AB-stacked BNBL, no strong TI phase exists, regardless of the strength of the intrinsic or Rashba SOCs. At last, a brief overview is given on other two-dimensional hexagonal materials including silicene and molybdenum disulfide bilayers.

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)

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

Science.gov (United States)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas

OpenAIRE

Wang, Pei; Yi, Wei; Xianlong, Gao

2014-01-01

We study the quench dynamics of a one-dimensional ultracold Fermi gas in an optical lattice potential with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of t...

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

Science.gov (United States)

Deng, Yongbo; Korvink, Jan G

2016-05-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

Coherent structures and flow topology of transitional separated-reattached flow over two and three dimensional geometrical shapes

Science.gov (United States)

Diabil, Hayder Azeez; Li, Xin Kai; Abdalla, Ibrahim Elrayah

2017-09-01

Large-scale organized motions (commonly referred to coherent structures) and flow topology of a transitional separated-reattached flow have been visualised and investigated using flow visualisation techniques. Two geometrical shapes including two-dimensional flat plate with rectangular leading edge and three-dimensional square cylinder are chosen to shed a light on the flow topology and present coherent structures of the flow over these shapes. For both geometries and in the early stage of the transition, two-dimensional Kelvin-Helmholtz rolls are formed downstream of the leading edge. They are observed to be twisting around the square cylinder while they stay flat in the case of the two-dimensional flat plate. For both geometrical shapes, the two-dimensional Kelvin-Helmholtz rolls move downstream of the leading edge and they are subjected to distortion to form three-dimensional hairpin structures. The flow topology in the flat plate is different from that in the square cylinder. For the flat plate, there is a merging process by a pairing of the Kelvin-Helmholtz rolls to form a large structure that breaks down directly into many hairpin structures. For the squire cylinder case, the Kelvin-Helmholtz roll evolves topologically to form a hairpin structure. In the squire cylinder case, the reattachment length is much shorter and a forming of the three-dimensional structures is closer to the leading edge than that in the flat plate case.

Long-range string orders and topological quantum phase transitions in the one-dimensional quantum compass model.

Science.gov (United States)

Wang, Hai Tao; Cho, Sam Young

2015-01-14

In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies.

Magnetotransport and induced superconductivity in Bi based three-dimensional topological insulators

International Nuclear Information System (INIS)

Veldhorst, M.; Snelder, M.; Hoek, M.; Molenaar, C.G.; Leusink, D.P.; Golubov, A.A.; Hilgenkamp, H.; Brinkman, A.

2013-01-01

The surface of a three-dimensional (3D) topological insulator is conducting and the topologically nontrivial nature of the surface states is observed in experiments. It is the aim of this paper to review and analyze experimental observations with respect to the magnetotransport in Bi-based 3D topological insulators, as well as the superconducting transport properties of hybrid structures consisting of superconductors and these topological insulators. The helical spin-momentum coupling of the surface state electrons becomes visible in quantum corrections to the conductivity and magnetoresistance oscillations. An analysis will be provided of the reported magnetoresistance, also in the presence of bulk conductivity shunts. Special attention is given to the large and linear magnetoresistance. Superconductivity can be induced in topological superconductors by means of the proximity effect. The induced supercurrents, Josephson effects and current-phase relations will be reviewed. These materials hold great potential in the field of spintronics and the route towards Majorana devices. (copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Magnetotransport and induced superconductivity in Bi based three-dimensional topological insulators

Energy Technology Data Exchange (ETDEWEB)

Veldhorst, M.; Snelder, M.; Hoek, M.; Molenaar, C.G.; Leusink, D.P.; Golubov, A.A.; Hilgenkamp, H.; Brinkman, A. [MESA + Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)

2013-02-15

The surface of a three-dimensional (3D) topological insulator is conducting and the topologically nontrivial nature of the surface states is observed in experiments. It is the aim of this paper to review and analyze experimental observations with respect to the magnetotransport in Bi-based 3D topological insulators, as well as the superconducting transport properties of hybrid structures consisting of superconductors and these topological insulators. The helical spin-momentum coupling of the surface state electrons becomes visible in quantum corrections to the conductivity and magnetoresistance oscillations. An analysis will be provided of the reported magnetoresistance, also in the presence of bulk conductivity shunts. Special attention is given to the large and linear magnetoresistance. Superconductivity can be induced in topological superconductors by means of the proximity effect. The induced supercurrents, Josephson effects and current-phase relations will be reviewed. These materials hold great potential in the field of spintronics and the route towards Majorana devices. (copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Topology and geometry of six-dimensional (1, 0) supergravity black hole horizons

International Nuclear Information System (INIS)

Akyol, M; Papadopoulos, G

2012-01-01

We show that the supersymmetric near horizon black hole geometries of six-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally AdS 3 x Σ 3 , where Σ 3 is a homology 3-sphere, or R 1,1 )xS 4 , where S 4 is a 4-manifold whose geometry depends on the hypermultiplet scalars. In both cases, we find that the tensorini multiplet scalars are constant and the associated 3-form field strengths vanish. We also demonstrate that the AdS 3 x Σ 3 horizons preserve two, four and eight supersymmetries. For horizons with four supersymmetries, Σ 3 is in addition a non-trivial circle fibration over a topological 2-sphere. The near horizon geometries preserving eight supersymmetries are locally isometric to either AdS 3 x S 3 or R 1, 1 x T 4 . Moreover, we show that the R 1,1 xS horizons preserve one, two and four supersymmetries and the geometry of S is Riemann, Kaehler and hyper-Kaehler, respectively. (paper)

Charges and Electromagnetic Radiation as Topological Excitations

Directory of Open Access Journals (Sweden)

Manfried Faber

2017-01-01

Full Text Available We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.

One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology

Directory of Open Access Journals (Sweden)

2016-04-01

Full Text Available There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata

Directory of Open Access Journals (Sweden)

Nicolai Lang, Hans Peter Büchler

2018-01-01

Full Text Available Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.

Topological energy conversion through the bulk or the boundary of driven systems

Science.gov (United States)

Peng, Yang; Refael, Gil

2018-04-01

Combining physical and synthetic dimensions allows a controllable realization and manipulation of high-dimensional topological states. In our work, we introduce two quasiperiodically driven one-dimensional systems which enable tunable topological energy conversion between different driving sources. Using three drives, we realize a four-dimensional quantum Hall state which allows energy conversion between two of the drives within the bulk of the one-dimensional system. With only two drives, we achieve energy conversion between the two at the edge of the chain. Both effects are a manifestation of the effective axion electrodynamics in a three-dimensional time-reversal-invariant topological insulator. Furthermore, we explore the effects of disorder and commensurability of the driving frequencies, and show the phenomena are robust. We propose two experimental platforms, based on semiconductor heterostructures and ultracold atoms in optical lattices, in order to observe the topological energy conversion.

Simulations of four-dimensional simplicial quantum gravity as dynamical triangulation

International Nuclear Information System (INIS)

Agishtein, M.E.; Migdal, A.A.

1992-01-01

In this paper, Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. The authors studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: the authors reached about 5 x 10 4 simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. The authors varied the gravitational constant, and they found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). The authors studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths

Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks

OpenAIRE

Shabani, J.; Kjaergaard, M.; Suominen, H. J.; Kim, Younghyun; Nichele, F.; Pakrouski, K.; Stankevic, T.; Lutchyn, R. M.; Krogstrup, P.; Feidenhans'l, R.; Kraemer, S.; Nayak, C.; Troyer, M.; Marcus, C. M.; Palmstrøm, C. J.

2015-01-01

Progress in the emergent field of topological superconductivity relies on synthesis of new material combinations, combining superconductivity, low density, and spin-orbit coupling (SOC). For example, theory [1-4] indicates that the interface between a one-dimensional (1D) semiconductor (Sm) with strong SOC and a superconductor (S) hosts Majorana modes with nontrivial topological properties [5-8]. Recently, epitaxial growth of Al on InAs nanowires was shown to yield a high quality S-Sm system ...

Interplay between topology and disorder in a two-dimensional semi-Dirac material

OpenAIRE

Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

2017-01-01

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one, and a parabolic dispersion in the orthogonal, direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semi-metal, as it generates a momentum independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three dist...

Vortex line topology during vortex tube reconnection

Science.gov (United States)

McGavin, P.; Pontin, D. I.

2018-05-01

This paper addresses reconnection of vortex tubes, with particular focus on the topology of the vortex lines (field lines of the vorticity). This analysis of vortex line topology reveals key features of the reconnection process, such as the generation of many small flux rings, formed when reconnection occurs in multiple locations in the vortex sheet between the tubes. Consideration of three-dimensional reconnection principles leads to a robust measurement of the reconnection rate, even once instabilities break the symmetry. It also allows us to identify internal reconnection of vortex lines within the individual vortex tubes. Finally, the introduction of a third vortex tube is shown to render the vortex reconnection process fully three-dimensional, leading to a fundamental change in the topological structure of the process. An additional interesting feature is the generation of vorticity null points.

Topology of two-dimensional turbulent flows of dust and gas

Science.gov (United States)

Mitra, Dhrubaditya; Perlekar, Prasad

2018-04-01

We perform direct numerical simulations (DNS) of passive heavy inertial particles (dust) in homogeneous and isotropic two-dimensional turbulent flows (gas) for a range of Stokes number, StDNS confirms that the statistics of topological properties of B are the same in Eulerian and Lagrangian frames only if the Eulerian data are weighed by the dust density. We use this correspondence to study the statistics of topological properties of A in the Lagrangian frame from our Eulerian simulations by calculating density-weighted probability distribution functions. We further find that in the Lagrangian frame, the mean value of the trace of A is negative and its magnitude increases with St approximately as exp(-C /St) with a constant C ≈0.1 . The statistical distribution of different topological structures that appear in the dust flow is different in Eulerian and Lagrangian (density-weighted Eulerian) cases, particularly for St close to unity. In both of these cases, for small St the topological structures have close to zero divergence and are either vortical (elliptic) or strain dominated (hyperbolic, saddle). As St increases, the contribution to negative divergence comes mostly from saddles and the contribution to positive divergence comes from both vortices and saddles. Compared to the Eulerian case, the Lagrangian (density-weighted Eulerian) case has less outward spirals and more converging saddles. Inward spirals are the least probable topological structures in both cases.

Signatures of Majorana bound states in one-dimensional topological superconductors

International Nuclear Information System (INIS)

Pientka, Falko

2014-01-01

Topological states of matter have fascinated condensed matter physicists for the past three decades. Famous examples include the integer and fractional quantum Hall states exhibiting a spectacular conductance quantization as well as topological insulators in two and three dimensions featuring gapless Dirac fermions at the boundary. Very recently, novel topological phases in superconductors have been subject of intense experimental and theoretical investigation. One-dimensional topological superconductors are particularly intriguing as they host exotic Majorana end states. These are zero-energy bound states with nonabelian exchange statistics potentially useful for topologically protected quantum computing. Recent theoretical and experimental advances have put the realization of Majorana states within reach of current measurement techniques. In this thesis we investigate signatures of Majorana bound states in realistic experiments aiming to improve the theoretical understanding of ongoing experimental efforts and to design novel measurement schemes, which exhibit convincing signatures of Majoranas. In particular we account for nonideal experimental conditions which can lead to qualitatively new features. Possible signatures of Majoranas can be accessed in the Josephson current through a weak link between two topological superconductors although the signatures in the dc Josephson effect are typically obscured by inevitable quasiparticle relaxation in the superconductor. Here we propose a measurement scheme in mesoscopic superconducting rings, where Majorana signatures persist even for infinitely fast relaxation. In a separate project we outline an alternative to the standard Josephson experiment in topological superconductors based on quantum wires. We delineate how Majoranas can be detected, when the Josephson current is induced by noncollinear magnetic fields applied to the two banks of the junction instead of a superconducting phase difference. Another important

New results in topological field theory and Abelian gauge theory

International Nuclear Information System (INIS)

Thompson, G.

1995-10-01

These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs

New results in topological field theory and Abelian gauge theory

Energy Technology Data Exchange (ETDEWEB)

Thompson, G

1995-10-01

These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs.

N = 1 supersymmetric indices and the four-dimensional A-model

Science.gov (United States)

Closset, Cyril; Kim, Heeyeon; Willett, Brian

2017-08-01

We compute the supersymmetric partition function of N = 1 supersymmetric gauge theories with an R-symmetry on M_4\\cong M_{g,p}× {S}^1 , a principal elliptic fiber bundle of degree p over a genus- g Riemann surface, Σ g . Equivalently, we compute the generalized supersymmetric index I_{M}{_{g,p}, with the supersymmetric three-manifold M_{g,p} as the spatial slice. The ordinary N = 1 supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological A-model for the abelianized gauge fields on the base Σ g . This A-model — or A-twisted two-dimensional N = (2 , 2) gauge theory — encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on T 2 inside Σ g × T 2. Being defined by compactification on the torus, the A-model also enjoys natural modular properties, governed by the four-dimensional 't Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.

Topology and isometries of the de Sitter space-time

International Nuclear Information System (INIS)

Mitskevich, N.V.; Senin, Yu.E.

1982-01-01

Spaces with a constant four-dimensional curvature, which are locally isometric to the de Sitter space-time but differing from it in topology are considered. The de Sitter spaces are considered in coordinates fitted at best for introduction of topology for three cross sections: S 3 , S 1 x S 2 , S 1 x S 2 x S 3 . It is shown that the de Sitter space-time covered by the family of layers, each of them is topologically identical, may be covered by another family of topologically identical layers. But layers in these families will have different topology

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.

Interplay between topology and disorder in a two-dimensional semi-Dirac material

Science.gov (United States)

Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

2018-01-01

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes—single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.

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.

Supergravity and the knitting of the Kalb-Ramond two-form in eight-dimensional topological gravity

Energy Technology Data Exchange (ETDEWEB)

Baulieu, Laurent; Bellon, Marc; Tanzini, Alessandro

2003-07-17

Topological Euclidean gravity is built in eight dimensions for manifolds with Spin(7) subset of SO(8) holonomy. In a previous work, we considered the construction of an eight-dimensional topological theory describing the graviton and one graviphoton. Here we solve the question of determining a topological model for the combined system of a metric and a Kalb-Ramond two-form gauge field. We then recover the complete N=1, D=8 supergravity theory in a twisted form. We observe that the generalized self-duality conditions of our model correspond to the octonionic string equations.

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.

All-electric spin modulator based on a two-dimensional topological insulator

Energy Technology Data Exchange (ETDEWEB)

Xiao, Xianbo; Ai, Guoping [School of Computer Science, Jiangxi University of Traditional Chinese Medicine, Nanchang 330004 (China); Liu, Ying; Yang, Shengyuan A., E-mail: shengyuan-yang@sutd.edu.sg [Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372 (Singapore); Liu, Zhengfang [School of Science, East China Jiaotong University, Nanchang 330013 (China); Zhou, Guanghui, E-mail: ghzhou@hunnu.edu.cn [Key Laboratory for Low-Dimensional Structures and Quantum Manipulation (Ministry of Education), and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081 (China)

2016-01-18

We propose and investigate a spin modulator device consisting of two ferromagnetic leads connected by a two-dimensional topological insulator as the channel material. It exploits the unique features of the topological spin-helical edge states, such that the injected carriers with a non-collinear spin-polarization direction would travel through both edges and show interference effect. The conductance of the device can be controlled in a simple and all-electric manner by a side-gate voltage, which effectively rotates the spin-polarization of the carrier. At low voltages, the rotation angle is linear in the gate voltage, and the device can function as a good spin-polarization rotator by replacing the drain electrode with a non-magnetic material.

Coupling effect of topological states and Chern insulators in two-dimensional triangular lattices

Science.gov (United States)

Zhang, Jiayong; Zhao, Bao; Xue, Yang; Zhou, Tong; Yang, Zhongqin

2018-03-01

We investigate topological states of two-dimensional (2D) triangular lattices with multiorbitals. Tight-binding model calculations of a 2D triangular lattice based on px and py orbitals exhibit very interesting doubly degenerate energy points at different positions (Γ and K /K' ) in momentum space, with quadratic non-Dirac and linear Dirac band dispersions, respectively. Counterintuitively, the system shows a global topologically trivial rather than nontrivial state with consideration of spin-orbit coupling due to the "destructive interference effect" between the topological states at the Γ and K /K' points. The topologically nontrivial state can emerge by introducing another set of triangular lattices to the system (bitriangular lattices) due to the breakdown of the interference effect. With first-principles calculations, we predict an intrinsic Chern insulating behavior (quantum anomalous Hall effect) in a family of the 2D triangular lattice metal-organic framework of Co(C21N3H15) (TPyB-Co) from this scheme. Our results provide a different path and theoretical guidance for the search for and design of new 2D topological quantum materials.

Inverse Operation of Four-dimensional Vector Matrix

OpenAIRE

H J Bao; A J Sang; H X Chen

2011-01-01

This is a new series of study to define and prove multidimensional vector matrix mathematics, which includes four-dimensional vector matrix determinant, four-dimensional vector matrix inverse and related properties. There are innovative concepts of multi-dimensional vector matrix mathematics created by authors with numerous applications in engineering, math, video conferencing, 3D TV, and other fields.

Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes

Energy Technology Data Exchange (ETDEWEB)

Olea, Rodrigo [Departamento de Fisica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile)

2005-06-01

In this paper, the connection between the Lorentz-covariant counterterms that regularize the four-dimensional AdS gravity action and topological invariants is explored. It is shown that demanding the spacetime to have a negative constant curvature in the asymptotic region permits the explicit construction of such series of boundary terms. The orthonormal frame is adapted to appropriately describe the boundary geometry and, as a result, the boundary term can be expressed as a functional of the boundary metric, extrinsic curvature and intrinsic curvature. This choice also allows to write down the background-independent Noether charges associated to asymptotic symmetries in standard tensorial formalism. The absence of the Gibbons-Hawking term is a consequence of an action principle based on a boundary condition different than Dirichlet on the metric. This argument makes plausible the idea of regarding this approach as an alternative regularization scheme for AdS gravity in all even dimensions, different than the standard counterterms prescription. As an illustration of the finiteness of the charges and the euclidean action in this framework, the conserved quantities and black hole entropy for four-dimensional Kerr-AdS are computed.

The non-commutative topology of two-dimensional dirty superconductors

Science.gov (United States)

De Nittis, Giuseppe; Schulz-Baldes, Hermann

2018-01-01

Non-commutative analysis tools have successfully been applied to the integer quantum Hall effect, in particular for a proof of the stability of the Hall conductance in an Anderson localization regime and of the bulk-boundary correspondence. In this work, these techniques are implemented to study two-dimensional dirty superconductors described by Bogoliubov-de Gennes Hamiltonians. After a thorough presentation of the basic framework and the topological invariants, Kubo formulas for the thermal, thermoelectric and spin Hall conductance are analyzed together with the corresponding edge currents.

Topology determines force distributions in one-dimensional random spring networks

Science.gov (United States)

Heidemann, Knut M.; Sageman-Furnas, Andrew O.; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F.; Wardetzky, Max

2018-02-01

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N ,z ) . Despite the universal properties of such (N ,z ) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.

Backscattering from width variations in quasi-one-dimensional strips of topological insulators

International Nuclear Information System (INIS)

Takagaki, Y

2012-01-01

Conductance modulations in wide-narrow-wide electron waveguides constructed from a two-dimensional topological insulator are investigated numerically. The conductance exhibits the Fabry-Perot oscillation at the opening of the helical edge states in the narrow segment when the potential offset imposed in the segment is varied. The quantum multiple reflections between the two ends of the narrow segment manifested by the oscillation demonstrate that the topological states are not protected from the scattering caused by an abrupt change in the channel width. The bulk states do not affect the vulnerability against the geometry scattering but they give rise to resonant transmission in an unconventional fashion.

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.

A series of three-dimensional lanthanide coordination polymers with rutile and unprecedented rutile-related topologies.

Science.gov (United States)

Qin, Chao; Wang, Xin-Long; Wang, En-Bo; Su, Zhong-Min

2005-10-03

The complexes of formulas Ln(pydc)(Hpydc) (Ln = Sm (1), Eu (2), Gd (3); H2pydc = pyridine-2,5-dicarboxylic acid) and Ln(pydc)(bc)(H2O) (Ln = Sm (4), Gd (5); Hbc = benzenecarboxylic acid) have been synthesized under hydrothermal conditions and characterized by elemental analysis, IR, TG analysis, and single-crystal X-ray diffraction. Compounds 1-3 are isomorphous and crystallize in the orthorhombic system, space group Pbcn. Their final three-dimensional racemic frameworks can be considered as being constructed by helix-linked scalelike sheets. Compounds 4 and 5 are isostructural and crystallize in the monoclinic system, space group P2(1)/c. pydc ligands bridge dinuclear lanthanide centers to form the three-dimensional frameworks featuring hexagonal channels along the a-axis that are occupied by one-end-coordinated bc ligands. From the topological point of view, the five three-dimensional nets are binodal with six- and three-connected nodes, the former of which exhibit a rutile-related (4.6(2))(2)(4(2).6(9).8(4)) topology that is unprecedented within coordination frames, and the latter two species display a distorted rutile (4.6(2))(2)(4(2).6(10).8(3)) topology. Furthermore, the luminescent properties of 2 were studied.

Topological phases in frustrated synthetic ladders with an odd number of legs

Science.gov (United States)

Barbarino, Simone; Dalmonte, Marcello; Fazio, Rosario; Santoro, Giuseppe E.

2018-01-01

The realization of the Hofstadter model in a strongly anisotropic ladder geometry has now become possible in one-dimensional optical lattices with a synthetic dimension. In this work, we show how the Hofstadter Hamiltonian in such ladder configurations hosts a topological phase of matter which is radically different from its two-dimensional counterpart. This topological phase stems directly from the hybrid nature of the ladder geometry and is protected by a properly defined inversion symmetry. We start our analysis by considering the paradigmatic case of a three-leg ladder which supports a topological phase exhibiting the typical features of topological states in one dimension: robust fermionic edge modes, a degenerate entanglement spectrum, and a nonzero Zak phase; then, we generalize our findings—addressable in the state-of-the-art cold-atom experiments—to ladders with a higher number of legs.

A Four-Dimensional Approach

African Journals Online (AJOL)

... of East Asian Students in English-speaking Countries: A Four-Dimensional ... country's language greatly shapes all aspects of the student's international education ... Taking this ecological approach will help clearly define the role that home ...

Super integrable four-dimensional autonomous mappings

International Nuclear Information System (INIS)

Capel, H W; Sahadevan, R; Rajakumar, S

2007-01-01

A systematic investigation of the complete integrability of a fourth-order autonomous difference equation of the type w(n + 4) = w(n)F(w(n + 1), w(n + 2), w(n + 3)) is presented. We identify seven distinct families of four-dimensional mappings which are super integrable and have three (independent) integrals via a duality relation as introduced in a recent paper by Quispel, Capel and Roberts (2005 J. Phys. A: Math. Gen. 38 3965-80). It is observed that these seven families can be related to the four-dimensional symplectic mappings with two integrals including all the four-dimensional periodic reductions of the integrable double-discrete modified Korteweg-deVries and sine-Gordon equations treated in an earlier paper by two of us (Capel and Sahadevan 2001 Physica A 289 86-106)

A Three-dimensional Topological Model of Ternary Phase Diagram

International Nuclear Information System (INIS)

Mu, Yingxue; Bao, Hong

2017-01-01

In order to obtain a visualization of the complex internal structure of ternary phase diagram, the paper realized a three-dimensional topology model of ternary phase diagram with the designed data structure and improved algorithm, under the guidance of relevant theories of computer graphics. The purpose of the model is mainly to analyze the relationship between each phase region of a ternary phase diagram. The model not only obtain isothermal section graph at any temperature, but also extract a particular phase region in which users are interested. (paper)

Statistical Mechanics of the Geometric Control of Flow Topology in Two-Dimensional Turbulence

Science.gov (United States)

Nadiga, Balasubramanya; Loxley, Peter

2013-04-01

We apply the principle of maximum entropy to two dimensional turbulence in a new fashion to predict the effect of geometry on flow topology. We consider two prototypical regimes of turbulence that lead to frequently observed self-organized coherent structures. Our theory predicts bistable behavior that exhibits hysteresis and large abrupt changes in flow topology in one regime; the other regime is predicted to exhibit monstable behavior with a continuous change of flow topology. The predictions are confirmed in fully nonlinear numerical simulations of the two-dimensional Navier-Stokes equation. These results suggest an explanation of the low frequency regime transitions that have been observed in the non-equilibrium setting of this problem. Following further development in the non-equilibrium context, we expect that insights developed in this problem should be useful in developing a better understanding of the phenomenon of low frequency regime transitions that is a pervasive feature of the weather and climate systems. Familiar occurrences of this phenomenon---wherein extreme and abrupt qualitative changes occur, seemingly randomly, after very long periods of apparent stability---include blocking in the extra-tropical winter atmosphere, the bimodality of the Kuroshio extension system, the Dansgaard-Oeschger events, and the glacial-interglacial transitions.

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

Particle creation and destruction of quantum coherence by topological change

International Nuclear Information System (INIS)

Lavrelashvili, G.V.; Rubakov, V.A.; Tinyakov, P.G.

1988-01-01

The possibility is considered that changes of spatial topology occur as tunneling events in quantum gravity. Creation of scalar and spinor particles during these tunneling transitions is studied. The relevant formalism based on the euclidean Schroedinger equation and coherent state representation is developed. This formalism is illustrated in a two-dimensional example. It is argued that the particle creation during the topological changes induces the loss of quantum coherence. The particle creation is calculated in the case of O(4)-invariant background euclidean four-dimensional metrics. This calculation is used for estimating the loss of quantum coherence. An upper limit on the rate of the topological changes, A -17 M 4 Pl , is derived from the observation of K 0 -anti K 0 oscillations. (orig.)

Low-dimensional morphospace of topological motifs in human fMRI brain networks

Directory of Open Access Journals (Sweden)

Sarah E. Morgan

2018-06-01

Full Text Available We present a low-dimensional morphospace of fMRI brain networks, where axes are defined in a data-driven manner based on the network motifs. The morphospace allows us to identify the key variations in healthy fMRI networks in terms of their underlying motifs, and we observe that two principal components (PCs can account for 97% of the motif variability. The first PC of the motif distribution is correlated with efficiency and inversely correlated with transitivity. Hence this axis approximately conforms to the well-known economical small-world trade-off between integration and segregation in brain networks. Finally, we show that the economical clustering generative model proposed by Vértes et al. (2012 can approximately reproduce the motif morphospace of the real fMRI brain networks, in contrast to other generative models. Overall, the motif morphospace provides a powerful way to visualize the relationships between network properties and to investigate generative or constraining factors in the formation of complex human brain functional networks. Motifs have been described as the building blocks of complex networks. Meanwhile, a morphospace allows networks to be placed in a common space and can reveal the relationships between different network properties and elucidate the driving forces behind network topology. We combine the concepts of motifs and morphospaces to create the first motif morphospace of fMRI brain networks. Crucially, the morphospace axes are defined by the motifs, in a data-driven manner. We observe strong correlations between the networks’ positions in morphospace and their global topological properties, suggesting that motif morphospaces are a powerful way to capture the topology of networks in a low-dimensional space and to compare generative models of brain networks. Motif morphospaces could also be used to study other complex networks’ topologies.

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...

Pair creation, motion, and annihilation of topological defects in two-dimensional nematic liquid crystals

Science.gov (United States)

Cortese, Dario; Eggers, Jens; Liverpool, Tanniemola B.

2018-02-01

We present a framework for the study of disclinations in two-dimensional active nematic liquid crystals and topological defects in general. The order tensor formalism is used to calculate exact multiparticle solutions of the linearized static equations inside a planar uniformly aligned state so that the total charge has to vanish. Topological charge conservation then requires that there is always an equal number of q =1 /2 and q =-1 /2 charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.

Four-dimensional hilbert curves for R-trees

DEFF Research Database (Denmark)

Haverkort, Herman; Walderveen, Freek van

2011-01-01

Two-dimensional R-trees are a class of spatial index structures in which objects are arranged to enable fast window queries: report all objects that intersect a given query window. One of the most successful methods of arranging the objects in the index structure is based on sorting the objects...... according to the positions of their centers along a two-dimensional Hilbert space-filling curve. Alternatively, one may use the coordinates of the objects' bounding boxes to represent each object by a four-dimensional point, and sort these points along a four-dimensional Hilbert-type curve. In experiments...

Photonic topological boundary pumping as a probe of 4D quantum Hall physics.

Science.gov (United States)

Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P; Kraus, Yaacov E; Rechtsman, Mikael C

2018-01-03

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

Photonic topological boundary pumping as a probe of 4D quantum Hall physics

Science.gov (United States)

Zilberberg, Oded; Huang, Sheng; Guglielmon, Jonathan; Wang, Mohan; Chen, Kevin P.; Kraus, Yaacov E.; Rechtsman, Mikael C.

2018-01-01

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals

KAUST Repository

Mei, Jun

2016-09-02

We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Î

Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals

KAUST Repository

Mei, Jun; Chen, Zeguo; Wu, Ying

2016-01-01

We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Î

Four-dimensional strings: Phenomenology and model building

International Nuclear Information System (INIS)

Quiros, M.

1989-01-01

In these lectures we will review some of the last developments in string theories leading to the construction of realistic four-dimensional string models. Special attention will be paid to world-sheet and space-time supersymmetry, modular invariance and model building for supersymmetric and (tachyon-free) nonsupersymmetric ten and four-dimensional models. (orig.)

Derivation of the Time-Reversal Anomaly for (2 +1 )-Dimensional Topological Phases

Science.gov (United States)

Tachikawa, Yuji; Yonekura, Kazuya

2017-09-01

We prove an explicit formula conjectured recently by Wang and Levin for the anomaly of time-reversal symmetry in (2 +1 )-dimensional fermionic topological quantum field theories. The crucial step is to determine the cross-cap state in terms of the modular S matrix and T2 eigenvalues, generalizing the recent analysis by Barkeshli et al. in the bosonic case.

Two-dimensional ferroelectric topological insulators in functionalized atomically thin bismuth layers

Science.gov (United States)

Kou, Liangzhi; Fu, Huixia; Ma, Yandong; Yan, Binghai; Liao, Ting; Du, Aijun; Chen, Changfeng

2018-02-01

We introduce a class of two-dimensional (2D) materials that possess coexisting ferroelectric and topologically insulating orders. Such ferroelectric topological insulators (FETIs) occur in noncentrosymmetric atomic layer structures with strong spin-orbit coupling (SOC). We showcase a prototype 2D FETI in an atomically thin bismuth layer functionalized by C H2OH , which exhibits a large ferroelectric polarization that is switchable by a ligand molecule rotation mechanism and a strong SOC that drives a band inversion leading to the topologically insulating state. An external electric field that switches the ferroelectric polarization also tunes the spin texture in the underlying atomic lattice. Moreover, the functionalized bismuth layer exhibits an additional quantum order driven by the valley splitting at the K and K' points in the Brillouin zone stemming from the symmetry breaking and strong SOC in the system, resulting in a remarkable state of matter with the simultaneous presence of the quantum spin Hall and quantum valley Hall effect. These phenomena are predicted to exist in other similarly constructed 2D FETIs, thereby offering a unique quantum material platform for discovering novel physics and exploring innovative applications.

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

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas with spin–orbit coupling

International Nuclear Information System (INIS)

Wang, Pei; Yi, Wei; Xianlong, Gao

2015-01-01

We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems. (paper)

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas with spin-orbit coupling

Science.gov (United States)

Wang, Pei; Yi, Wei; Xianlong, Gao

2015-01-01

We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.

Topology of Event Horizon

OpenAIRE

Siino, Masaru

1997-01-01

The topologies of event horizons are investigated. Considering the existence of the endpoint of the event horizon, it cannot be differentiable. Then there are the new possibilities of the topology of the event horizon though they are excluded in smooth event horizons. The relation between the topology of the event horizon and the endpoint of it is revealed. A torus event horizon is caused by two-dimensional endpoints. One-dimensional endpoints provide the coalescence of spherical event horizo...

Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

DEFF Research Database (Denmark)

Brøns, Morten; Hartnack, Johan Nicolai

1998-01-01

Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of non-linear coordinate c...

Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

DEFF Research Database (Denmark)

Brøns, Morten; Hartnack, Johan Nicolai

1999-01-01

Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate ch...

Four Mixed-Ligand Zn(II Three-Dimensional Metal-Organic Frameworks: Synthesis, Structural Diversity, and Photoluminescent Property

Directory of Open Access Journals (Sweden)

Chih-Chieh Wang

2017-11-01

Full Text Available Assemblies of four three-dimensional (3D mixed-ligand coordination polymers (CPs having formulas, {[Zn2(bdc2(4-bpdh]·C2H5OH·2H2O}n (1, [Zn(bdc(4-bpdh]n (2, {[Zn2(bdc2(4-bpdh2]·(4-bpdh}n (3, and {[Zn(bdc(4-bpdh]·C2H5OH}n (4 (bdc2− = dianion of 1,4-benzenedicarboxylic acid, 4-bpdh = 2,5-bis(4-pyridyl-3,4-diaza-2,4-hexadiene have been synthesized and structurally characterized by single-crystal X-ray diffraction method. Structural determination reveals that the coordination numbers (geometry of Zn(II ions in 1, 2, 3, and 4 are five (distorted square-pyramidal (SP, six (distorted octahedral (Oh, five (trigonal-bipyramidal (TBP, and four (tetrahedral (Td, respectively, and are bridged by 4-bpdh with bis-monodentate coordination mode and bdc2− ligands with bis-bidentate in 1, chelating/bidentate in 2, bis-monodentate and bis-bidentate in 3, and bis-monodentate in 4, to generate two-fold interpenetrating 3D cube-like metal-organic framework (MOF with pcu topology, non-interpenetrating 3D MOF, two-fold interpenetrating 3D rectangular-box-like MOF with pcu topology and five-fold interpenetrating diamondoid-like MOF with dia topology, respectively. These different intriguing architectures indicate that the coordination numbers and geometries of Zn(II ions, coordination modes of bdc2− ligand, and guest molecules play important roles in the construction of MOFs and the formation of the structural topologies and interpenetrations. Thermal stabilities, and photoluminescence study of 1–4 were also studied in detail. The complexes exhibit ligands based photoluminescence properties at room temperature.

Cooling as a method of finding topological dislocations in lattice models

International Nuclear Information System (INIS)

Gomberoff, K.

1989-01-01

It is well known that the O(3) two-dimensional model has configurations with topological charge Q=1 and action S/sub min/=6.69. Since the exponent characterizing the renormalization-group behavior of this model is 4π such configurations invalidate the standard scaling behavior of the topological susceptibility. The analog exponent for the four-dimensional lattice SU(2) gauge model is 10.77. If there would exist configurations with Q=1 and S<10.77 in this model, they would invalidate the standard scaling behavior of its topological susceptibility. Kremer et al. have calculated the action of different configurations during cooling runs. They report that they do not find any configuration with S<12.7 and Q=1. I show that in the O(3) two-dimensional model cooling runs fail to uncover the well-known configurations with S<8. We conclude that the cooling method is not effective in uncovering the smallest action configurations in the Q=1 sector

Topological Insulator Nanowires and Nanoribbons

KAUST Repository

Kong, Desheng

2010-01-13

Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi2Se3 material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi2Se5 nanomaterials with a variety of morphologies. The synthesis of Bi 2Se5 nanowires and nanoribbons employs Au-catalyzed vapor-liquid-solid (VLS) mechanism. Nanowires, which exhibit rough surfaces, are formed by stacking nanoplatelets along the axial direction of the wires. Nanoribbons are grown along [1120] direction with a rectangular cross-section and have diverse morphologies, including quasi-one-dimensional, sheetlike, zigzag and sawtooth shapes. Scanning tunneling microscopy (STM) studies on nanoribbons show atomically smooth surfaces with ∼ 1 nm step edges, indicating single Se-Bi-Se-Bi-Se quintuple layers. STM measurements reveal a honeycomb atomic lattice, suggesting that the STM tip couples not only to the top Se atomic layer, but also to the Bi atomic layer underneath, which opens up the possibility to investigate the contribution of different atomic orbitais to the topological surface states. Transport measurements of a single nanoribbon device (four terminal resistance and Hall resistance) show great promise for nanoribbons as candidates to study topological surface states. © 2010 American Chemical Society.

Exploring 4D quantum Hall physics with a 2D topological charge pump.

Science.gov (United States)

Lohse, Michael; Schweizer, Christian; Price, Hannah M; Zilberberg, Oded; Bloch, Immanuel

2018-01-03

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant-the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

Exploring 4D quantum Hall physics with a 2D topological charge pump

Science.gov (United States)

Lohse, Michael; Schweizer, Christian; Price, Hannah M.; Zilberberg, Oded; Bloch, Immanuel

2018-01-01

The discovery of topological states of matter has greatly improved our understanding of phase transitions in physical systems. Instead of being described by local order parameters, topological phases are described by global topological invariants and are therefore robust against perturbations. A prominent example is the two-dimensional (2D) integer quantum Hall effect: it is characterized by the first Chern number, which manifests in the quantized Hall response that is induced by an external electric field. Generalizing the quantum Hall effect to four-dimensional (4D) systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number. Here we report the observation of a bulk response with intrinsic 4D topology and demonstrate its quantization by measuring the associated second Chern number. By implementing a 2D topological charge pump using ultracold bosonic atoms in an angled optical superlattice, we realize a dynamical version of the 4D integer quantum Hall effect. Using a small cloud of atoms as a local probe, we fully characterize the nonlinear response of the system via in situ imaging and site-resolved band mapping. Our findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.

Topological Quantization of Instantons in SU(2) Yang–Mills Theory

International Nuclear Information System (INIS)

Wo-Jun, Zhong; Yi-Shi, Duan

2008-01-01

By decomposing SU(2) gauge potential in four-dimensional Euclidean SU(2) Yang–Mills theory in a new way, we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree. It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang–Mills theory. (general)

Massive supermultiplets in four-dimensional superstring theory

International Nuclear Information System (INIS)

Feng Wanzhe; Lüst, Dieter; Schlotterer, Oliver

2012-01-01

We extend the discussion of Feng et al. (2011) on massive Regge excitations on the first mass level of four-dimensional superstring theory. For the lightest massive modes of the open string sector, universal supermultiplets common to all four-dimensional compactifications with N=1,2 and N=4 spacetime supersymmetry are constructed respectively - both their vertex operators and their supersymmetry variations. Massive spinor helicity methods shed light on the interplay between individual polarization states.

Global Anomaly Detection in Two-Dimensional Symmetry-Protected Topological Phases

Science.gov (United States)

Bultinck, Nick; Vanhove, Robijn; Haegeman, Jutho; Verstraete, Frank

2018-04-01

Edge theories of symmetry-protected topological phases are well known to possess global symmetry anomalies. In this Letter we focus on two-dimensional bosonic phases protected by an on-site symmetry and analyze the corresponding edge anomalies in more detail. Physical interpretations of the anomaly in terms of an obstruction to orbifolding and constructing symmetry-preserving boundaries are connected to the cohomology classification of symmetry-protected phases in two dimensions. Using the tensor network and matrix product state formalism we numerically illustrate our arguments and discuss computational detection schemes to identify symmetry-protected order in a ground state wave function.

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...

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.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

Science.gov (United States)

Ahn, Junyeong; Yang, Bohm-Jung

2017-04-01

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

The universe as a topological defect in a higher-dimensional Einstein-Yang-Mills theory

International Nuclear Information System (INIS)

Nakamura, A.; Shiraishi, K.

1989-04-01

An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein-Yang-Mills (EYM) theory. We start with D-dimensional EYM theory in our present analysis. A compactification leads to a D-2 dimensional effective action of Abelian gauge-Higgs theory. We find a 'vortex' solution in the effective theory. Our universe appears to be confined in a center of a 'vortex', which has D-4 large dimensions. In this paper we show an example with SU (2) symmetry in the original EYM theory, and the resulting solution is found to be equivalent to the 'instanton-induced compactification'. The cosmological implication is also mentioned. (author)

The Cardy limit of the topologically twisted index and black strings in AdS{sub 5}

Energy Technology Data Exchange (ETDEWEB)

Hosseini, Seyed Morteza; Nedelin, Anton; Zaffaroni, Alberto [Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN, Sezione di Milano-Bicocca,I-20126 Milano (Italy)

2017-04-04

We evaluate the topologically twisted index of a general four-dimensional N=1 gauge theory in the “high-temperature' limit. The index is the partition function for N=1 theories on S{sup 2}×T{sup 2}, with a partial topological twist along S{sup 2}, in the presence of background magnetic fluxes and fugacities for the global symmetries. We show that the logarithm of the index is proportional to the conformal anomaly coefficient of the two-dimensional N=(0,2) SCFTs obtained from the compactification on S{sup 2}. We also present a universal formula for extracting the index from the four-dimensional conformal anomaly coefficient and its derivatives. We give examples based on theories whose holographic duals are black strings in type IIB backgrounds AdS{sub 5}×SE{sub 5}, where SE{sub 5} are five-dimensional Sasaki-Einstein spaces.

The Topology of Three-Dimensional Symmetric Tensor Fields

Science.gov (United States)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

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.)

Thermoelectric power and topological transitions in quasi-two-dimensional electronic systems

International Nuclear Information System (INIS)

Blanter, Ya.M.; Pantsulaya, A.V.; Varlamov, A.A.

1991-05-01

Electron-impurity relaxation time and the thermoelectric power (TEP) of quasi-two-dimensional electron gas are calculated. Two cases are discussed: the isotropic spectrum and the electronic topological transition (ETT) of the ''neck-breaking'' type. Methods of thermal diagramatic technique are used for the calculation. It is found that the TEP in the vicinity of the ETT greatly exceeds its background value. The results of experimental investigations of the TEP in the metal-oxide-semiconductor structures are compared with the predictions of the proposed theory. (author). 17 refs, 5 figs

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.

Two-dimensional Topology of the Sloan Digital Sky Survey

Science.gov (United States)

Hoyle, Fiona; Vogeley, Michael S.; Gott, J. Richard, III; Blanton, Michael; Tegmark, Max; Weinberg, David H.; Bahcall, N.; Brinkmann, J.; York, D.

2002-12-01

We present the topology of a volume-limited sample of 11,884 galaxies, selected from an apparent magnitude limited sample of over 100,000 galaxies observed as part of the Sloan Digital Sky Survey (SDSS). The data currently cover three main regions on the sky: one in the Galactic north and one in the south, both at zero degrees declination, and one area in the north at higher declination. Each of these areas covers a wide range of survey longitude but a narrow range of survey latitude, allowing the two-dimensional genus to be measured. The genus curves of the SDSS subsamples are similar, after appropriately normalizing these measurements for the different areas. We sum the genus curves from the three areas to obtain the total genus curve of the SDSS. The total curve has a shape similar to the genus curve derived from mock catalogs drawn from the Hubble volume ΛCDM simulation and is similar to that of a Gaussian random field. Likewise, comparison with the genus of the Two-Degree Field Galaxy Redshift Survey, after normalization for the difference in area, reveals remarkable similarity in the topology of these samples. We test for the effects of galaxy-type segregation by splitting the SDSS data into thirds, based on the u*-r* colors of the galaxies, and measure the genus of the reddest and bluest subsamples. This red/blue split in u*-r* is essentially a split by morphology, as explained by Strateva and coworkers. We find that the genus curve for the reddest galaxies exhibits a ``meatball'' shift of the topology-reflecting the concentration of red galaxies in high-density regions-compared to the bluest galaxies and the full sample, in agreement with predictions from simulations.

Fracton topological order from nearest-neighbor two-spin interactions and dualities

Science.gov (United States)

Slagle, Kevin; Kim, Yong Baek

2017-10-01

Fracton topological order describes a remarkable phase of matter, which can be characterized by fracton excitations with constrained dynamics and a ground-state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions, which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order [Vijay, Haah, and Fu, Phys. Rev. B 94, 235157 (2016), 10.1103/PhysRevB.94.235157] but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of six sites. The model is constructed from two orthogonal stacks of Z2 topologically ordered Kitaev honeycomb layers [Kitaev, Ann. Phys. 321, 2 (2006), 10.1016/j.aop.2005.10.005], which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D Z2 topological order. We also find dual descriptions of four quantum phase transitions in our model, all of which appear to be discontinuous first-order transitions.

Topological BF field theory description of topological insulators

International Nuclear Information System (INIS)

Cho, Gil Young; Moore, Joel E.

2011-01-01

Research highlights: → We show that a BF theory is the effective theory of 2D and 3D topological insulators. → The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. → The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. → Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a π flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.

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.)

A No-Go theorem for the nonabelian topological mass mechanism in four dimensions

International Nuclear Information System (INIS)

Henneaux, M.; Sorella, S.P.

1997-07-01

We prove that there is no power-counting renormalizable nonabelian generalization of the Abelian topological mass mechanism in four dimensions. The argument is based on the technique of consistent deformations of the master equation developed by G. Barnich and one of the authors. Recent attempts involving extra fields are also commented upon. (author)

Topology optimization for coated structures

DEFF Research Database (Denmark)

Clausen, Anders; Andreassen, Erik; Sigmund, Ole

2015-01-01

This paper presents new results within the design of three-dimensional (3D) coated structures using topology optimization.The work is an extension of a recently published two-dimensional (2D) method for including coatedstructures into the minimum compliance topology optimization problem. The high...... level of control over key parameters demonstrated for the 2D model can likewise be achieved in 3D. The effectiveness of the approach isdemonstrated with numerical examples, which for the 3D problems have been solved using a parallel topology optimization implementation based on the PETSc toolkit....

Non-Abelian string and particle braiding in topological order: Modular SL (3 ,Z ) representation and (3 +1 ) -dimensional twisted gauge theory

Science.gov (United States)

Wang, Juven C.; Wen, Xiao-Gang

2015-01-01

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.

Fine topology and locally Minkowskian manifolds

Science.gov (United States)

Agrawal, Gunjan; Sinha, Soami Pyari

2018-05-01

Fine topology is one of the several well-known topologies of physical and mathematical relevance. In the present paper, it is obtained that the nonempty open sets of different dimensional Minkowski spaces with the fine topology are not homeomorphic. This leads to the introduction of a new class of manifolds. It turns out that the technique developed here is also applicable to some other topologies, namely, the s-topology, space topology, f-topology, and A-topology.

Topological superconductor in quasi-one-dimensional Tl2 -xMo6Se6

Science.gov (United States)

Huang, Shin-Ming; Hsu, Chuang-Han; Xu, Su-Yang; Lee, Chi-Cheng; Shiau, Shiue-Yuan; Lin, Hsin; Bansil, Arun

2018-01-01

We propose that the quasi-one-dimensional molybdenum selenide compound Tl2 -xMo6Se6 is a time-reversal-invariant topological superconductor induced by intersublattice pairing, even in the absence of spin-orbit coupling (SOC). No noticeable change in superconductivity is observed in Tl-deficient (0 ≤x ≤0.1 ) compounds. At weak SOC, the superconductor prefers the triplet d vector lying perpendicular to the chain direction and two-dimensional E2 u symmetry, which is driven to a nematic order by spontaneous rotation symmetry breaking. The locking energy of the d vector is estimated to be weak and hence the proof of its direction would rely on tunneling or phase-sensitive measurements.

Commutative curvature operators over four-dimensional generalized symmetric

Directory of Open Access Journals (Sweden)

Ali Haji-Badali

2014-12-01

Full Text Available Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

Effect of static charge fluctuations on the conduction along the edge of two-dimensional topological insulator

Science.gov (United States)

Vayrynen, Jukka; Goldstein, Moshe; Glazman, Leonid

2013-03-01

Static charge disorder may create electron puddles in the bulk of a material which nominally is in the insulating state. A single puddle - quantum dot - coupled to the helical edge of a two-dimensional topological insulator enhances the electron backscattering within the edge. The backscattering rate increases with the electron dwelling time in the dot. While remaining inelastic, the backscattering off a dot may be far more effective than the proposed earlier inelastic processes involving a local scatterer with no internal structure. We find the temperature dependence of the dot-induced correction to the universal conductance of the edge. In addition to the single-dot effect, we calculate the classical temperature-independent conductance correction caused by a weakly conducting bulk. We use our theory to assess the effect of static charge fluctuations in a heterostructure on the edge electron transport in a two-dimensional topological insulator. The work at Yale University is supported by NSF DMR Grant No. 1206612 and the Simons Foundation.

Topological aspects of classical and quantum (2+1)-dimensional gravity

International Nuclear Information System (INIS)

Soda, Jiro.

1990-03-01

In order to understand (3+1)-dimensional gravity, (2+1)-dimensional gravity is studied as a toy model. Our emphasis is on its topological aspects, because (2+1)-dimensional gravity without matter fields has no local dynamical degrees of freedom. Starting from a review of the canonical ADM formalism and York's formalism for the initial value problem, we will solve the evolution equations of (2+1)-dimensional gravity with a cosmological constant in the case of g=0 and g=1, where g is the genus of Riemann surface. The dynamics of it is understood as the geodesic motion in the moduli space. This remarkable fact is the same with the case of (2+1)-dimensional pure gravity and seen more apparently from the action level. Indeed we will show the phase space reduction of (2+1)-dimensional gravity in the case of g=1. For g ≥ 2, unfortunately we are not able to explicitly perform the phase space reduction of (2+1)-dimensional gravity due to the complexity of the Hamiltonian constraint equation. Based on this result, we will attempt to incorporate matter fields into (2+1)-dimensional pure gravity. The linearization and mini-superspace methods are used for this purpose. By using the linearization method, we conclude that the transverse-traceless part of the energy-momentum tensor affects the geodesic motion. In the case of the Einstein-Maxwell theory, we observe that the Wilson lines interact with the geometry to bend the geodesic motion. We analyze the mini-superspace model of (2+1)-dimensional gravity with the matter fields in the case of g=0 and g=1. For g=0, a wormhole solution is found but for g=1 we can not find an analogous solution. Quantum gravity is also considered and we succeed to perform the phase space reduction of (2+1)-dimensional gravity in the case of g=1 at the quantum level. From this analysis we argue that the conformal rotation is not necessary in the sense that the Euclidean quantum gravity is inappropriate for the full gravity. (author)

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...

Unmanned Aerial System Four-Dimensional Gunnery Training Device Development

Science.gov (United States)

2017-10-01

Aerial System (UAS) Four-Dimensional Gunnery Training Device: Training Effectiveness Assessment (James & Miller, in press). 31 Technical ...Research Product 2018-05 Unmanned Aerial System Four-Dimensional Gunnery Training Device Development David R. James...for the Department of the Army by Northrop Grumman Corporation. Technical review by Thomas Rhett Graves, Ph.D., U.S. Army Research Institute

Edge states of a three-dimensional topological insulator

International Nuclear Information System (INIS)

Deb, Oindrila; Sen, Diptiman; Soori, Abhiram

2014-01-01

We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi 2 Se 3 to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states. (paper)

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.

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

Science.gov (United States)

Eden, Burkhard; Smirnov, Vladimir A.

2016-10-01

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

Energy Technology Data Exchange (ETDEWEB)

Eden, Burkhard [Institut für Mathematik und Physik, Humboldt-Universität zu Berlin,Zum großen Windkanal 6, 12489 Berlin (Germany); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics, Moscow State University,119992 Moscow (Russian Federation)

2016-10-21

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

Lattice classification of the four-dimensional heterotic strings

International Nuclear Information System (INIS)

Balog, J.; Forgacs, P.; Vecsernyes, P.; Horvath, Z.

1987-06-01

A lattice slicing procedure is proposed which leads to the classification of all four-dimensional chiral heterotic strings based on Conway and Sloane's 22-dimensional self-dual Euclidean lattices. By reversing this procedure it is possible to construct all these theories. (author)

Band structure of a three-dimensional topological insulator quantum wire in the presence of a magnetic field.

Science.gov (United States)

Liu, Zhe; Jiang, Liwei; Zheng, Yisong

2016-07-13

By means of a numerical diagonalization approach, we calculate the electronic structure of a three-dimensional topological insulator (3DTI) quantum wire (QW) in the presence of a magnetic field. The QW can be viewed as a 3DTI film with lateral surfaces, when its rectangular cross section has a large aspect ratio. Our calculation indicates that nonchiral edge states emerge because of the confined states at the lateral surfaces. These states completely cover the valence band region among the Landau levels, which reasonably account for the absence of the [Formula: see text] quantum Hall effect in the relevant experimental works. In an ultrathin 3DTI film, inversion between the electron-type and hole-type bands occurs, which leads to the so-called pseudo-spin Hall effect. In a 3DTI QW with a square cross section, a tilting magnetic field can establish well-defined Landau levels in all four surfaces. In such a case, the quantum Hall edge states are localized at the square corners, characterized by the linearly crossing one-dimensional band profile. And they can be shifted between the adjacent corners by simply rotating the magnetic field.

Topological states in a two-dimensional metal alloy in Si surface: BiAg/Si(111)-4 ×4 surface

Science.gov (United States)

Zhang, Xiaoming; Cui, Bin; Zhao, Mingwen; Liu, Feng

2018-02-01

A bridging topological state with a conventional semiconductor platform offers an attractive route towards future spintronics and quantum device applications. Here, based on first-principles and tight-binding calculations, we demonstrate the existence of topological states hosted by a two-dimensional (2D) metal alloy in a Si surface, the BiAg/Si(111)-4 ×4 surface, which has already been synthesized experimentally. It exhibits a topological insulating state with an energy gap of 71 meV (˜819 K ) above the Fermi level and a topological metallic state with quasiquantized conductance below the Fermi level. The underlying mechanism leading to the formation of such nontrivial states is revealed by analysis of the "charge-transfer" and "orbital-filtering" effect of the Si substrate. A minimal effective tight-binding model is employed to reveal the formation mechanism of the topological states. Our finding opens opportunities to detect topological states and measure its quantized conductance in a large family of 2D surface metal alloys, which have been or are to be grown on semiconductor substrates.

Search for Majorana fermions in topological superconductors.

Energy Technology Data Exchange (ETDEWEB)

Pan, Wei [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shi, Xiaoyan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hawkins, Samuel D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Klem, John Frederick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2014-10-01

The goal of this project is to search for Majorana fermions (a new quantum particle) in a topological superconductor (a new quantum matter achieved in a topological insulator proximitized by an s-wave superconductor). Majorana fermions (MFs) are electron-like particles that are their own anti-particles. MFs are shown to obey non-Abelian statistics and, thus, can be harnessed to make a fault-resistant topological quantum computer. With the arrival of topological insulators, novel schemes to create MFs have been proposed in hybrid systems by combining a topological insulator with a conventional superconductor. In this LDRD project, we will follow the theoretical proposals to search for MFs in one-dimensional (1D) topological superconductors. 1D topological superconductor will be created inside of a quantum point contact (with the metal pinch-off gates made of conventional s-wave superconductors such as niobium) in a two-dimensional topological insulator (such as inverted type-II InAs/GaSb heterostructure).

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.

Renormalization of period doubling in symmetric four-dimensional volume-preserving maps

International Nuclear Information System (INIS)

Mao, J.; Greene, J.M.

1987-01-01

We have determined three maps (truncated at quadratic terms) that are fixed under the renormalization operator of pitchfork period doubling in symmetric four-dimensional volume-preserving maps. Each of these contains the previously known two-dimensional area-preserving map that is fixed under the period-doubling operator. One of these three fixed maps consists of two uncoupled two-dimensional (nonlinear) area-preserving fixed maps. The other two contain also the two-dimensional area-preserving fixed map coupled (in general) with a linear two-dimensional map. The renormalization calculation recovers all numerical results for the pitchfork period doubling in the symmetric four-dimensional volume-preserving maps, reported by Mao and Helleman [Phys. Rev. A 35, 1847 (1987)]. For a large class of nonsymmetric four-dimensional volume-preserving maps, we found that the fixed maps are the same as those for the symmetric maps

Four-dimensional Hall mechanics as a particle on CP3

International Nuclear Information System (INIS)

Bellucci, Stefano; Casteill, Pierre-Yves; Nersessian, Armen

2003-01-01

In order to establish an explicit connection between four-dimensional Hall effect on S 4 and six-dimensional Hall effect on CP 3 , we perform the Hamiltonian reduction of a particle moving on CP 3 in a constant magnetic field to the four-dimensional Hall mechanics (i.e., a-bar particle on S 4 in a SU(2) instanton field). This reduction corresponds to fixing the isospin of the latter system

Twistors and four-dimensional conformal field theory

International Nuclear Information System (INIS)

Singer, M.A.

1990-01-01

This is a report (with technical details omitted) on work concerned with generalizations to four dimensions of two-dimensional Conformed Field Theory. Accounts of this and related material are contained elsewhere. The Hilbert space of the four-dimensional theory has a natural interpretation in terms of massless spinor fields on real Minkowski space. From the twistor point of view this follows from the boundary CR-manifold P being precisely the space of light rays in real compactified Minkowski space. All the amplitudes can therefore be regarded as defined on Hilbert spaces built from Lorentzian spinor fields. Thus the twistor picture provides a kind of halfway house between the Lorentzian and Euclidean field theories. (author)

Visualizing nD Point Clouds as Topological Landscape Profiles to Guide Local Data Analysis

Energy Technology Data Exchange (ETDEWEB)

Oesterling, Patrick [Univ. of Leipzig (Germany). Computer Science Dept.; Heine, Christian [Univ. of Leipzig (Germany). Computer Science Dept.; Federal Inst. of Technology (ETH), Zurich (Switzerland). Dept. of Computer Science; Weber, Gunther H. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Scheuermann, Gerik [Univ. of Leipzig (Germany). Computer Science Dept.

2012-05-04

Analyzing high-dimensional point clouds is a classical challenge in visual analytics. Traditional techniques, such as projections or axis-based techniques, suffer from projection artifacts, occlusion, and visual complexity.We propose to split data analysis into two parts to address these shortcomings. First, a structural overview phase abstracts data by its density distribution. This phase performs topological analysis to support accurate and non-overlapping presentation of the high-dimensional cluster structure as a topological landscape profile. Utilizing a landscape metaphor, it presents clusters and their nesting as hills whose height, width, and shape reflect cluster coherence, size, and stability, respectively. A second local analysis phase utilizes this global structural knowledge to select individual clusters or point sets for further, localized data analysis. Focusing on structural entities significantly reduces visual clutter in established geometric visualizations and permits a clearer, more thorough data analysis. In conclusion, this analysis complements the global topological perspective and enables the user to study subspaces or geometric properties, such as shape.

Topologically massive supergravity

Directory of Open Access Journals (Sweden)

S. Deser

1983-01-01

Full Text Available The locally supersymmetric extension of three-dimensional topologically massive gravity is constructed. Its fermionic part is the sum of the (dynamically trivial Rarita-Schwinger action and a gauge-invariant topological term, of second derivative order, analogous to the gravitational one. It is ghost free and represents a single massive spin 3/2 excitation. The fermion-gravity coupling is minimal and the invariance is under the usual supergravity transformations. The system's energy, as well as that of the original topological gravity, is therefore positive.

Four new topological indices based on the molecular path code.

Science.gov (United States)

Balaban, Alexandru T; Beteringhe, Adrian; Constantinescu, Titus; Filip, Petru A; Ivanciuc, Ovidiu

2007-01-01

The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots: Path-count index: P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.

Pure spinor formalism as an N = 2 topological string

International Nuclear Information System (INIS)

Berkovits, Nathan

2005-01-01

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted c-circumflex = 3 N = 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincare covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action

Spinors and supersymmetry in four-dimensional Euclidean space

International Nuclear Information System (INIS)

McKeon, D.G.C.; Sherry, T.N.

2001-01-01

Spinors in four-dimensional Euclidean space are treated using the decomposition of the Euclidean space SO(4) symmetry group into SU(2)xSU(2). Both 2- and 4-spinor representations of this SO(4) symmetry group are shown to differ significantly from the corresponding spinor representations of the SO(3, 1) symmetry group in Minkowski space. The simplest self conjugate supersymmetry algebra allowed in four-dimensional Euclidean space is demonstrated to be an N=2 supersymmetry algebra which resembles the N=2 supersymmetry algebra in four-dimensional Minkowski space. The differences between the two supersymmetry algebras gives rise to different representations; in particular an analysis of the Clifford algebra structure shows that the momentum invariant is bounded above by the central charges in 4dE, while in 4dM the central charges bound the momentum invariant from below. Dimensional reduction of the N=1 SUSY algebra in six-dimensional Minkowski space (6dM) to 4dE reproduces our SUSY algebra in 4dE. This dimensional reduction can be used to introduce additional generators into the SUSY algebra in 4dE. Well known interpolating maps are used to relate the N=2 SUSY algebra in 4dE derived in this paper to the N=2 SUSY algebra in 4dM. The nature of the spinors in 4dE allows us to write an axially gauge invariant model which is shown to be both Hermitian and anomaly-free. No equivalent model exists in 4dM. Useful formulae in 4dE are collected together in two appendixes

A short course in computational geometry and topology

CERN Document Server

Edelsbrunner, Herbert

2014-01-01

With the aim to bring the subject of Computational Geometry and Topology closer to the scientific audience, this book is written in thirteen ready-to-teach sections organized in four parts: tessellations, complexes, homology, persistence. To speak to the non-specialist, detailed formalisms are often avoided in favor of lively 2- and 3-dimensional illustrations. The book is warmly recommended to everybody who loves geometry and the fascinating world of shapes.

Predicting a new phase (T'') of two-dimensional transition metal di-chalcogenides and strain-controlled topological phase transition

Science.gov (United States)

Ma, Fengxian; Gao, Guoping; Jiao, Yalong; Gu, Yuantong; Bilic, Ante; Zhang, Haijun; Chen, Zhongfang; Du, Aijun

2016-02-01

Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices.Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological

Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals.

Science.gov (United States)

Xu, Lin; Wang, Hai-Xiao; Xu, Ya-Dong; Chen, Huan-Yang; Jiang, Jian-Hua

2016-08-08

A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C6 point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.

Scalar-tensor approach to the construction of theory of topological transformations

International Nuclear Information System (INIS)

Konstantinov, M.Yu.

1985-01-01

Problem of construction of the classical gravitational theory, which solutions in the explicit form contain description of topological transformations, is under study. With this object in view, the scalar-tensor formalism is considered based on a representation of some subclass of space-like hypersurfaces as surfaces of a smooth function level in four-dimensional manifolds. Solutions of the theory along with the Lorentz space-time structure and space-like surface topology define some reference system, but the type of topological transformations is not dependent on the reference system option. All these facts prove the above approach correctness. Two variants of the scalar-tensor theory of topological transformations are considered as an example; one of them is reduced to the Einstein gravitational theory in the regular space region and another represents a nontrivial modification of the Brans-Dikker theory

Optical conductivity of three and two dimensional topological nodal-line semimetals

Science.gov (United States)

Barati, Shahin; Abedinpour, Saeed H.

2017-10-01

The peculiar shape of the Fermi surface of topological nodal-line semimetals at low carrier concentrations results in their unusual optical and transport properties. We analytically investigate the linear optical responses of three- and two-dimensional nodal-line semimetals using the Kubo formula. The optical conductivity of a three-dimensional nodal-line semimetal is anisotropic. Along the axial direction (i.e., the direction perpendicular to the nodal-ring plane), the Drude weight has a linear dependence on the chemical potential at both low and high carrier dopings. For the radial direction (i.e., the direction parallel to the nodal-ring plane), this dependence changes from linear into quadratic in the transition from low into high carrier concentration. The interband contribution into optical conductivity is also anisotropic. In particular, at large frequencies, it saturates to a constant value for the axial direction and linearly increases with frequency along the radial direction. In two-dimensional nodal-line semimetals, no interband optical transition could be induced and the only contribution to the optical conductivity arises from the intraband excitations. The corresponding Drude weight is independent of the carrier density at low carrier concentrations and linearly increases with chemical potential at high carrier doping.

Measurement of the quantum capacitance from two-dimensional surface state of a topological insulator at room temperature

Energy Technology Data Exchange (ETDEWEB)

Choi, Hyunwoo, E-mail: chw0089@gmail.com [Department of Electrical and Computer Engineering, University of Seoul, Seoul 02504 (Korea, Republic of); Kim, Tae Geun, E-mail: tgkim1@korea.ac.kr [School of Electrical Engineering, Korea University, Seoul 02841 (Korea, Republic of); Shin, Changhwan, E-mail: cshin@uos.ac.kr [Department of Electrical and Computer Engineering, University of Seoul, Seoul 02504 (Korea, Republic of)

2017-06-15

Highlights: • The quantum capacitance in topological insulator (TI) at room temperature is directly revealed. • The physical origin of quantum capacitance, the two dimensional surface state of TI, is experimentally validated. • Theoretically calculated results of ideal quantum capacitance can well predict the experimental data. - Abstract: A topological insulator (TI) is a new kind of material that exhibits unique electronic properties owing to its topological surface state (TSS). Previous studies focused on the transport properties of the TSS, since it can be used as the active channel layer in metal-oxide-semiconductor field-effect transistors (MOSFETs). However, a TI with a negative quantum capacitance (QC) effect can be used in the gate stack of MOSFETs, thereby facilitating the creation of ultra-low power electronics. Therefore, it is important to study the physics behind the QC in TIs in the absence of any external magnetic field, at room temperature. We fabricated a simple capacitor structure using a TI (TI-capacitor: Au-TI-SiO{sub 2}-Si), which shows clear evidence of QC at room temperature. In the capacitance-voltage (C-V) measurement, the total capacitance of the TI-capacitor increases in the accumulation regime, since QC is the dominant capacitive component in the series capacitor model (i.e., C{sub T}{sup −1} = C{sub Q}{sup −1} + C{sub SiO2}{sup −1}). Based on the QC model of the two-dimensional electron systems, we quantitatively calculated the QC, and observed that the simulated C-V curve theoretically supports the conclusion that the QC of the TI-capacitor is originated from electron–electron interaction in the two-dimensional surface state of the TI.

Algebraic definition of topological W gravity

International Nuclear Information System (INIS)

Hosono, S.

1992-01-01

In this paper, the authors propose a definition of the topological W gravity using some properties of the principal three-dimensional subalgebra of a simple Lie algebra due to Kostant. In the authors' definition, structures of the two-dimensional topological gravity are naturally embedded in the extended theories. In accordance with the definition, the authors will present some explicit calculations for the W 3 gravity

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.)

Topological mirror superconductivity.

Science.gov (United States)

Zhang, Fan; Kane, C L; Mele, E J

2013-08-02

We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z(2) index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.

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.

Multiple topological phase transitions in a gyromagnetic photonic crystal

KAUST Repository

Chen, Zeguo

2017-04-19

We present the design of a tunable two-dimensional photonic crystal that exhibits multiple topological phases, including a conventional insulator phase, a quantum spin Hall phase, and a quantum anomalous Hall phase under different combinations of geometric parameters and external magnetic fields. Our photonic crystal enables a platform to study the topology evolution attributed to the interplay between crystalline symmetry and time-reversal symmetry. A four-band tight-binding model unambiguously reveals that the topological property is associated with the pseudospin orientations and that it is characterized by the spin Chern number. The emerging quantum anomalous Hall phase features a single helical edge state that is locked by a specific pseudospin. Simulation results demonstrate that the propagation of such a single helical edge state is robust against magnetic impurities. Potential applications, such as spin splitters, are described.

Algebraic topology of spin glasses

International Nuclear Information System (INIS)

Koma, Tohru

2011-01-01

We study the topology of frustration in d-dimensional Ising spin glasses with d ≥ 2 with nearest-neighbor interactions. We prove the following. For any given spin configuration, the domain walls on the unfrustration network are all transverse to a frustrated loop on the unfrustration network, where a domain wall is defined to be a connected element of the collection of all the (d - 1)-cells which are dual to the bonds having an unfavorable energy, and the unfrustration network is the collection of all the unfrustrated plaquettes. These domain walls are topologically nontrivial because they are all related to the global frustration of a loop on the unfrustration network. Taking account of the thermal stability for the domain walls, we can explain the numerical results that three- or higher-dimensional systems exhibit a spin glass phase, whereas two-dimensional ones do not. Namely, in two dimensions, the thermal fluctuations of the topologically nontrivial domain walls destroy the order of the frozen spins on the unfrustration network, whereas they do not in three or higher dimensions. This may be interpreted as a global topological effect of the frustrations.

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

Four-dimensional optical manipulation of colloidal particles

DEFF Research Database (Denmark)

Rodrigo, P.J.; Daria, V.R.; Glückstad, J.

2005-01-01

We transform a TEM00 laser mode into multiple counterpropagating optical traps to achieve four-dimensional simultaneous manipulation of multiple particles. Efficient synthesis and dynamic control of the counterpropagating-beam traps is carried out via the generalized phase contrast method......, and a spatial polarization-encoding scheme. Our experiments genuinely demonstrate real-time, interactive particle-position control for forming arbitrary volumetric constellations and complex three-dimensional trajectories of multiple particles. This opens up doors for cross-disciplinary cutting-edge research...

Metadynamics surfing on topology barriers: the CP{sup N−1} case

Energy Technology Data Exchange (ETDEWEB)

Laio, A. [SISSA,Via Bonomea 265, I-34136, Trieste (Italy); Martinelli, G. [SISSA,Via Bonomea 265, I-34136, Trieste (Italy); INFN - Sezione di Roma La Sapienza,Piazzale Aldo Moro 5, 00185 Roma (Italy); Sanfilippo, F. [School of Physics and Astronomy, University of Southampton,Southampton SO17 1BJ (United Kingdom)

2016-07-18

As one approaches the continuum limit, QCD systems, investigated via numerical simulations, remain trapped in sectors of field space with fixed topological charge. As a consequence the numerical studies of physical quantities may give biased results. The same is true in the case of two dimensional CP{sup N−1} models. In this paper we show that metadynamics, when used to simulate CP{sup N−1}, allows to address efficiently this problem. By studying CP{sup 20} we show that we are able to reconstruct the free energy of the topological charge F(Q) and compute the topological susceptibility as a function of the coupling and of the volume. This is a very important physical quantity in studies of the dynamics of the θ vacuum and of the axion. This method can in principle be extended to QCD applications.

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.

Optical cryptography topology based on a three-dimensional particle-like distribution and diffractive imaging.

Science.gov (United States)

Chen, Wen; Chen, Xudong

2011-05-09

In recent years, coherent diffractive imaging has been considered as a promising alternative for information retrieval instead of conventional interference methods. Coherent diffractive imaging using the X-ray light source has opened up a new research perspective for the measurement of non-crystalline and biological specimens, and can achieve unprecedentedly high resolutions. In this paper, we show how a three-dimensional (3D) particle-like distribution and coherent diffractive imaging can be applied for a study of optical cryptography. An optical multiple-random-phase-mask encoding approach is used, and the plaintext is considered as a series of particles distributed in a 3D space. A topology concept is also introduced into the proposed optical cryptosystem. During image decryption, a retrieval algorithm is developed to extract the plaintext from the ciphertexts. In addition, security and advantages of the proposed optical cryptography topology are also analyzed. © 2011 Optical Society of America

Aharonov–Bohm interference in topological insulator nanoribbons

KAUST Repository

Peng, Hailin

2009-12-13

Topological insulators represent unusual phases of quantum matter with an insulating bulk gap and gapless edges or surface states. The two-dimensional topological insulator phase was predicted in HgTe quantum wells and confirmed by transport measurements. Recently, Bi2 Se3 and related materials have been proposed as three-dimensional topological insulators with a single Dirac cone on the surface, protected by time-reversal symmetry. The topological surface states have been observed by angle-resolved photoemission spectroscopy experiments. However, few transport measurements in this context have been reported, presumably owing to the predominance of bulk carriers from crystal defects or thermal excitations. Here we show unambiguous transport evidence of topological surface states through periodic quantum interference effects in layered single-crystalline Bi2 Se3 nanoribbons, which have larger surface-to-volume ratios than bulk materials and can therefore manifest surface effects. Pronounced Aharonov-Bohm oscillations in the magnetoresistance clearly demonstrate the coherent propagation of two-dimensional electrons around the perimeter of the nanoribbon surface, as expected from the topological nature of the surface states. The dominance of the primary h/e oscillation, where h is Plancks constant and e is the electron charge, and its temperature dependence demonstrate the robustness of these states. Our results suggest that topological insulator nanoribbons afford promising materials for future spintronic devices at room temperature.

Observational modeling of topological spaces

International Nuclear Information System (INIS)

Molaei, M.R.

2009-01-01

In this paper a model for a multi-dimensional observer by using of the fuzzy theory is presented. Relative form of Tychonoff theorem is proved. The notion of topological entropy is extended. The persistence of relative topological entropy under relative conjugate relation is proved.

Supertwistor orbifolds: gauge theory amplitudes and topological strings

International Nuclear Information System (INIS)

Park, Jaemo; Rey, Soojong

2004-01-01

Witten established correspondence between multiparton amplitudes in four-dimensional maximally supersymmetric gauge theory and topological string theory on supertwistor space CP 3verticalbar4 . We extend Witten's correspondence to gauge theories with lower supersymmetries, product gauge groups, and fermions and scalars in complex representations. Such gauge theories arise in high-energy limit of the Standard Model of strong and electroweak interactions. We construct such theories by orbifolding prescription. Much like gauge and string theories, such prescription is applicable equally well to topological string theories on supertwistor space. We work out several examples of orbifolds of CP 3verticalbar4 that are dual to N=2,1,0 quiver gauge theories. We study gauged sigma model describing topological B-model on the superorbifolds, and explore mirror pairs with particular attention to the parity symmetry. We check the orbifold construction by studying multiparton amplitudes in these theories with particular attention to those involving fermions in bifundamental representations and interactions involving U(1) subgroups. (author)

Four-dimensional conversion for spiritual leadership development: A ...

African Journals Online (AJOL)

The process of a four-dimensional conversion and/or transformation strives in helping the leadership of an organisation, especially such as the church, with practical ways that may lead to the development of an effective leadership by observing the four important aspects of human spirituality as elaborated on in the article.

Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states

Science.gov (United States)

He, Pan; Zhang, Steven S.-L.; Zhu, Dapeng; Liu, Yang; Wang, Yi; Yu, Jiawei; Vignale, Giovanni; Yang, Hyunsoo

2018-05-01

Surface states of three-dimensional topological insulators exhibit the phenomenon of spin-momentum locking, whereby the orientation of an electron spin is determined by its momentum. Probing the spin texture of these states is of critical importance for the realization of topological insulator devices, but the main technique currently available is spin- and angle-resolved photoemission spectroscopy. Here we reveal a close link between the spin texture and a new kind of magnetoresistance, which depends on the relative orientation of the current with respect to the magnetic field as well as the crystallographic axes, and scales linearly with both the applied electric and magnetic fields. This bilinear magnetoelectric resistance can be used to map the spin texture of topological surface states by simple transport measurements. For a prototypical Bi2Se3 single layer, we can map both the in-plane and out-of-plane components of the spin texture (the latter arising from hexagonal warping). Theoretical calculations suggest that the bilinear magnetoelectric resistance originates from conversion of a non-equilibrium spin current into a charge current under application of the external magnetic field.

Topological anisotropy of stone-wales waves in graphenic fragments.

Science.gov (United States)

Ori, Ottorino; Cataldo, Franco; Putz, Mihai V

2011-01-01

Stone-Wales operators interchange four adjacent hexagons with two pentagon-heptagon 5|7 pairs that, graphically, may be iteratively propagated in the graphene layer, originating a new interesting structural defect called here Stone-Wales wave. By minimization, the Wiener index topological invariant evidences a marked anisotropy of the Stone-Wales defects that, topologically, are in fact preferably generated and propagated along the diagonal of the graphenic fragments, including carbon nanotubes and graphene nanoribbons. This peculiar edge-effect is shown in this paper having a predominant topological origin, leaving to future experimental investigations the task of verifying the occurrence in nature of wave-like defects similar to the ones proposed here. Graph-theoretical tools used in this paper for the generation and the propagation of the Stone-Wales defects waves are applicable to investigate isomeric modifications of chemical structures with various dimensionality like fullerenes, nanotubes, graphenic layers, schwarzites, zeolites.

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.

Topological mapping and navigation in indoor environment with invisible barcode

International Nuclear Information System (INIS)

Huh, Jin Wook; Chung, Woong Sik; Chung, Wan Kyun

2006-01-01

This paper addresses the localization and navigation problem using invisible two dimensional barcodes on the floor. Compared with other methods using natural/artificial landmark, the proposed localization method has great advantages in cost and appearance, since the location of the robot is perfectly known using the barcode information after the mapping is finished. We also propose a navigation algorithm which uses the topological structure. For the topological information, we define nodes and edges which are suitable for indoor navigation, especially for large area having multiple rooms, many walls and many static obstacles. The proposed algorithm also has an advantage that errors occurred in each node are mutually independent and can be compensated exactly after some navigation using barcode. Simulation and experimental results were performed to verify the algorithm in the barcode environment, and the result showed an excellent performance. After mapping, it is also possible to solve the kidnapped case and generate paths using topological information

Topological and magnetic properties of the QCD vacuum probed by overlap fermions

International Nuclear Information System (INIS)

Braguta, V.V.; Buividovich, P.V.; Polikarpov, M.I.

2013-02-01

We study some of the local CP-odd and magnetic properties of the non-Abelian vacuum with use of overlap fermions within the quenched lattice gauge theory. Among these properties are the following: inhomogeneous spatial distribution of the topological charge density (chirality for massless fermions) in SU(2) gluodynamics (for uncooled gauge configurations the chirality is localized on low-dimensional defects with d=2.3, while a sequence of cooling steps gives rise to four-dimensional instantons and hence a four-dimensional structure of the chirality distribution); finite local fluctuations of the chirality growing with the strength of an external magnetic field; magnetization and susceptibility of the QCD vacuum in SU(3) theory; magnetic catalysis of the chiral symmetry breaking, and the electric conductivity of the QCD vacuum in strong magnetic fields.

Topological and magnetic properties of the QCD vacuum probed by overlap fermions

Energy Technology Data Exchange (ETDEWEB)

Braguta, V.V. [Institut Fiziki Vysokikh Ehnergij, Protvino (Russian Federation); Institute of Theoretical and Experimental Physics, Moscow (Russian Federation); Buividovich, P.V. [Univ. Regensburg (Germany). ITP; Kalaydzhyan, T. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Polikarpov, M.I. [Institute of Theoretical and Experimental Physics, Moscow (Russian Federation)

2013-02-15

We study some of the local CP-odd and magnetic properties of the non-Abelian vacuum with use of overlap fermions within the quenched lattice gauge theory. Among these properties are the following: inhomogeneous spatial distribution of the topological charge density (chirality for massless fermions) in SU(2) gluodynamics (for uncooled gauge configurations the chirality is localized on low-dimensional defects with d=2.3, while a sequence of cooling steps gives rise to four-dimensional instantons and hence a four-dimensional structure of the chirality distribution); finite local fluctuations of the chirality growing with the strength of an external magnetic field; magnetization and susceptibility of the QCD vacuum in SU(3) theory; magnetic catalysis of the chiral symmetry breaking, and the electric conductivity of the QCD vacuum in strong magnetic fields.

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.)

Observation of a phononic quadrupole topological insulator

Science.gov (United States)

Serra-Garcia, Marc; Peri, Valerio; Süsstrunk, Roman; Bilal, Osama R.; Larsen, Tom; Villanueva, Luis Guillermo; Huber, Sebastian D.

2018-03-01

The modern theory of charge polarization in solids is based on a generalization of Berry’s phase. The possibility of the quantization of this phase arising from parallel transport in momentum space is essential to our understanding of systems with topological band structures. Although based on the concept of charge polarization, this same theory can also be used to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. The theory of this quantized polarization has recently been extended from the dipole moment to higher multipole moments. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states. However, such a state of matter has not previously been observed experimentally. Here we report measurements of a phononic quadrupole topological insulator. We experimentally characterize the bulk, edge and corner physics of a mechanical metamaterial (a material with tailored mechanical properties) and find the predicted gapped edge and in-gap corner states. We corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases that are predicted by the quadrupole theory. These topological corner states are an important stepping stone to the experimental realization of topologically protected wave guides in higher dimensions, and thereby open up a new path for the design of metamaterials.

Topological probability and connection strength induced activity in complex neural networks

International Nuclear Information System (INIS)

Du-Qu, Wei; Bo, Zhang; Dong-Yuan, Qiu; Xiao-Shu, Luo

2010-01-01

Recent experimental evidence suggests that some brain activities can be assigned to small-world networks. In this work, we investigate how the topological probability p and connection strength C affect the activities of discrete neural networks with small-world (SW) connections. Network elements are described by two-dimensional map neurons (2DMNs) with the values of parameters at which no activity occurs. It is found that when the value of p is smaller or larger, there are no active neurons in the network, no matter what the value of connection strength is; for a given appropriate connection strength, there is an intermediate range of topological probability where the activity of 2DMN network is induced and enhanced. On the other hand, for a given intermediate topological probability level, there exists an optimal value of connection strength such that the frequency of activity reaches its maximum. The possible mechanism behind the action of topological probability and connection strength is addressed based on the bifurcation method. Furthermore, the effects of noise and transmission delay on the activity of neural network are also studied. (general)

Sensitivity of quantum walks to a boundary of two-dimensional lattices: approaches based on the CGMV method and topological phases

International Nuclear Information System (INIS)

Endo, Takako; Konno, Norio; Obuse, Hideaki; Segawa, Etsuo

2017-01-01

In this paper, we treat quantum walks in a two-dimensional lattice with cutting edges along a straight boundary introduced by Asboth and Edge (2015 Phys. Rev . A 91 022324) in order to study one-dimensional edge states originating from topological phases of matter and to obtain collateral evidence of how a quantum walker reacts to the boundary. Firstly, we connect this model to the CMV matrix, which provides a 5-term recursion relation of the Laurent polynomial associated with spectral measure on the unit circle. Secondly, we explicitly derive the spectra of bulk and edge states of the quantum walk with the boundary using spectral analysis of the CMV matrix. Thirdly, while topological numbers of the model studied so far are well-defined only when gaps in the bulk spectrum exist, we find a new topological number defined only when there are no gaps in the bulk spectrum. We confirm that the existence of the spectrum for edge states derived from the CMV matrix is consistent with the prediction from a bulk-edge correspondence using topological numbers calculated in the cases where gaps in the bulk spectrum do or do not exist. Finally, we show how the edge states contribute to the asymptotic behavior of the quantum walk through limit theorems of the finding probability. Conversely, we also propose a differential equation using this limit distribution whose solution is the underlying edge state. (paper)

Topological 2-dimensional quantum mechanics

International Nuclear Information System (INIS)

Dasnieres de Veigy, A.; Ouvry, S.

1992-12-01

A Chern-Simons Lagrangian is defined for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. Exact N-body eigenstates are proposed and a perturbative algorithm is set up. The case where some particles are fixed on a lattice, is discussed, and curved manifolds are considered. (author) 14 refs

Uniform topology on EQ-algebras

Directory of Open Access Journals (Sweden)

Yang Jiang

2017-04-01

Full Text Available In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, , and then the part induce a uniform topology in E. We prove that the pair (E, is a topological EQ-algebra, and some properties of (E, are investigated. In particular, we show that (E, is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.

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)

ALGEBRAIC TOPOLOGY

Indian Academy of Sciences (India)

tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).

Comment on non-renormalization theorem in the four dimensional superstrings

International Nuclear Information System (INIS)

Soda, Jiro; Nakazawa, Naohito; Sakai, Kenji; Ojima, Shuichi.

1987-10-01

We discuss non-renormalization theorem in the context of the four dimensional superstrings. We explicitly demonstrate that the graviton 3-point one-loop amplitude does not vanish in contrast to the ten dimensional superstring theories. (author)

Exploring photonic topological insulator states in a circuit-QED lattice

Science.gov (United States)

Li, Jing-Ling; Shan, Chuan-Jia; Zhao, Feng

2018-04-01

We propose a simple protocol to explore the topological properties of photonic integer quantum Hall states in a one-dimensional circiut-QED lattice. By periodically modulating the on-site photonic energies in such a lattice, we demonstrate that this one-dimensional lattice model can be mapped into a two-dimensional integer quantum Hall insulator model. Based on the lattice-based cavity input-output theory, we show that both the photonic topological protected edge states and topological invariants can be clearly measured from the final steady state of the resonator lattice after taking into account cavity dissipation. Interestingly, we also find that the measurement signals associated with the above topological features are quite unambitious even in five coupled dissipative resonators. Our work opens up a new prospect of exploring topological states with a small-size dissipative quantum artificial lattice, which is quite attractive to the current quantum optics community.

Hawking radiation from four-dimensional Schwarzschild black holes in M theory

International Nuclear Information System (INIS)

Das, S.R.; Mathur, S.D.; Ramadevi, P.

1999-01-01

Recently a method has been developed for relating four dimensional Schwarzschild black holes in M theory to near-extremal black holes in string theory with four charges, using suitably defined open-quotes boostsclose quotes and T dualities. We show that this method can be extended to obtain the emission rate of low energy massless scalars for the four dimensional Schwarzschild hole from the microscopic picture of radiation from the near extremal hole. copyright 1999 The American Physical Society

Aharonov–Bohm interference in topological insulator nanoribbons

KAUST Repository

Peng, Hailin; Lai, Keji; Kong, Desheng; Meister, Stefan; Chen, Yulin; Qi, Xiao-Liang; Zhang, Shou-Cheng; Shen, Zhi-Xun; Cui, Yi

2009-01-01

Topological insulators represent unusual phases of quantum matter with an insulating bulk gap and gapless edges or surface states. The two-dimensional topological insulator phase was predicted in HgTe quantum wells and confirmed by transport

Dynamical topological invariant after a quantum quench

Science.gov (United States)

Yang, Chao; Li, Linhu; Chen, Shu

2018-02-01

We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.

Reconstructing Topological Graphs and Continua

OpenAIRE

Gartside, Paul; Pitz, Max F.; Suabedissen, Rolf

2015-01-01

The deck of a topological space $X$ is the set $\\mathcal{D}(X)=\\{[X \\setminus \\{x\\}] \\colon x \\in X\\}$, where $[Z]$ denotes the homeomorphism class of $Z$. A space $X$ is topologically reconstructible if whenever $\\mathcal{D}(X)=\\mathcal{D}(Y)$ then $X$ is homeomorphic to $Y$. It is shown that all metrizable compact connected spaces are reconstructible. It follows that all finite graphs, when viewed as a 1-dimensional cell-complex, are reconstructible in the topological sense, and more genera...

Clapeyron equation and phase equilibrium properties in higher dimensional charged topological dilaton AdS black holes with a nonlinear source

Energy Technology Data Exchange (ETDEWEB)

Li, Huai-Fan; Zhao, Hui-Hua; Zhang, Li-Chun; Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China)

2017-05-15

Using Maxwell's equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black hole with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in the P-v diagrams. The two-phase equilibrium curves in the P-T diagrams are plotted, and we take the first order approximation of volume v in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for a higher dimensional charged topological black hole with a nonlinear source. The latent heat of an isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems. (orig.)

Topological amplitudes in string theory

International Nuclear Information System (INIS)

Antoniadis, I.; Taylor, T.R.

1993-07-01

We show that certain type II string amplitudes at genus g are given by the topological partition F g discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional effective action of the form Σ g F g W 2g , where W is the chiral superfield of N = 2 supergravitational multiplet. The holomorphic anomaly of F g is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings. (author). 22 refs, 2 figs

Three dimensional nonlinear magnetic AdS solutions through topological defects

International Nuclear Information System (INIS)

Hendi, S.H.; Panah, B.E.; Momennia, M.; Panahiyan, S.

2015-01-01

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known Born-Infeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appears too. (orig.)

Generalized Modular Transformations in (3+1D Topologically Ordered Phases and Triple Linking Invariant of Loop Braiding

Directory of Open Access Journals (Sweden)

Shenghan Jiang

2014-09-01

Full Text Available In topologically ordered quantum states of matter in (2+1D (spacetime dimensions, the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property that is directly related to global transformations of the ground-state wave functions on a torus (the modular transformations. On the other hand, there are theoretical descriptions of various topologically ordered states in (3+1D, which exhibit both pointlike and looplike excitations, but systematic understanding of the fundamental physical distinctions between phases, and how these distinctions are connected to quantum statistics of excitations, is still lacking. One main result of this work is that the three-dimensional generalization of modular transformations, when applied to topologically ordered ground states, is directly related to a certain braiding process of looplike excitations. This specific braiding surprisingly involves three loops simultaneously, and can distinguish different topologically ordered states. Our second main result is the identification of the three-loop braiding as a process in which the worldsheets of the three loops have a nontrivial triple linking number, which is a topological invariant characterizing closed two-dimensional surfaces in four dimensions. In this work, we consider realizations of topological order in (3+1D using cohomological gauge theory in which the loops have Abelian statistics and explicitly demonstrate our results on examples with Z_{2}×Z_{2} topological order.

Feasibility of four-dimensional preoperative simulation for elbow debridement arthroplasty.

Science.gov (United States)

Yamamoto, Michiro; Murakami, Yukimi; Iwatsuki, Katsuyuki; Kurimoto, Shigeru; Hirata, Hitoshi

2016-04-02

Recent advances in imaging modalities have enabled three-dimensional preoperative simulation. A four-dimensional preoperative simulation system would be useful for debridement arthroplasty of primary degenerative elbow osteoarthritis because it would be able to detect the impingement lesions. We developed a four-dimensional simulation system by adding the anatomical axis to the three-dimensional computed tomography scan data of the affected arm in one position. Eleven patients with primary degenerative elbow osteoarthritis were included. A "two rings" method was used to calculate the flexion-extension axis of the elbow by converting the surface of the trochlea and capitellum into two rings. A four-dimensional simulation movie was created and showed the optimal range of motion and the impingement area requiring excision. To evaluate the reliability of the flexion-extension axis, interobserver and intraobserver reliabilities regarding the assessment of bony overlap volumes were calculated twice for each patient by two authors. Patients were treated by open or arthroscopic debridement arthroplasties. Pre- and postoperative examinations included elbow range of motion measurement, and completion of the patient-rated questionnaire Hand20, Japanese Orthopaedic Association-Japan Elbow Society Elbow Function Score, and the Mayo Elbow Performance Score. Measurement of the bony overlap volume showed an intraobserver intraclass correlation coefficient of 0.93 and 0.90, and an interobserver intraclass correlation coefficient of 0.94. The mean elbow flexion-extension arc significantly improved from 101° to 125°. The mean Hand20 score significantly improved from 52 to 22. The mean Japanese Orthopaedic Association-Japan Elbow Society Elbow Function Score significantly improved from 67 to 88. The mean Mayo Elbow Performance Score significantly improved from 71 to 91 at the final follow-up evaluation. We showed that four-dimensional, preoperative simulation can be generated by

Four-dimensional computed tomography angiographic evaluation of cranial dural arteriovenous fistula before and after embolization.

Science.gov (United States)

Tian, Bing; Xu, Bing; Lu, Jianping; Liu, Qi; Wang, Li; Wang, Minjie

2015-06-01

This study aimed to evaluate the usefulness of four-dimensional CTA before and after embolization treatment with ONYX-18 in eleven patients with cranial dural arteriovenous fistulas, and to compare the results with those of the reference standard DSA. Eleven patients with cranial dural arteriovenous fistulas detected on DSA underwent transarterial embolization with ONYX-18. Four-dimensional CTA was performed an average of 2 days before and 4 days after DSA. Four-dimensional CTA and DSA images were reviewed by two neuroradiologists for identification of feeding arteries and drainage veins and for determining treatment effects. Interobserver and intermodality agreement between four-dimensional CTA and DSA were assessed. Forty-two feeding arteries were identified for 14 fistulas in the 11 patients. Of these, 36 (85.71%) were detected on four-dimensional CTA. After transarterial embolization, one patient got partly embolized, and the fistulas in the remaining 10 patients were completely occluded. The interobserver agreement for four-dimensional CTA and intermodality agreement between four-dimensional CTA and DSA were excellent (κ=1) for shunt location, identification of drainage veins, and fistula occlusion after treatment. Four-dimensional CTA images are highly accurate when compared with DSA images both before and after transarterial embolization treatment. Four-dimensional CTA can be used for diagnosis as well as follow-up of cranial dural arteriovenous fistulas in clinical settings. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Fall Foliage Topology Seminars

CERN Document Server

1990-01-01

This book demonstrates the lively interaction between algebraic topology, very low dimensional topology and combinatorial group theory. Many of the ideas presented are still in their infancy, and it is hoped that the work here will spur others to new and exciting developments. Among the many techniques disussed are the use of obstruction groups to distinguish certain exact sequences and several graph theoretic techniques with applications to the theory of groups.

Chiral topological insulator of magnons

Science.gov (United States)

Li, Bo; Kovalev, Alexey A.

2018-05-01

We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to opening of the gap. Finally, we show that by changing certain parameters, the system can be tuned between the chiral topological insulator, three-dimensional magnon anomalous Hall, and Weyl magnon phases.

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

Energy Technology Data Exchange (ETDEWEB)

Troisi, Antonio [Universita degli Studi di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Salerno (Italy)

2017-03-15

Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f(R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R) = f{sub 0}R{sup n} the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions. (orig.)

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

Oscillator potential for the four-dimensional Hall effect

International Nuclear Information System (INIS)

Mardoyan, Levon; Nersessian, Armen

2005-01-01

We suggest an exactly solvable model of an oscillator on a four-dimensional sphere interacting with an SU(2) Yang monopole. We show that the properties of the model essentially depend on the monopole charge

Identification of Architectural Functions in A Four-Dimensional Space

Directory of Open Access Journals (Sweden)

Firza Utama

2012-06-01

Full Text Available This research has explored the possibilities and concept of architectural space in a virtual environment. The virtual environment exists as a different concept, and challenges the constraints of the physical world. One of the possibilities in a virtual environment is that it is able to extend the spatial dimension higher than the physical three-dimension. To take the advantage of this possibility, this research has applied some geometrical four-dimensional (4D methods to define virtual architectural space. The spatial characteristics of 4D space is established by analyzing the four-dimensional structure that can be comprehended by human participant for its spatial quality, and by developing a system to control the fourth axis of movement. Multiple three-dimensional spaces that fluidly change their volume have been defined as one of the possibilities of virtual architecturalspace concept in order to enrich our understanding of virtual spatial experience.

Topological Equivalence of Objects. Teacher's Guide for Use with Stretching and Bending. Working Paper No. 18a.

Science.gov (United States)

Shah, Sair Ali

The notions of topological equivalence for one-, two-, and three-dimensional figures, as well as for graphs and networks, are developed for classroom use with children between the ages of three and ten. Properties of open and closed curves are also examined. This manual, addressed to the teacher, describes several activities related to each…

Kaluza-Klein cosmology from five-dimensional Lovelock-Cartan theory

Science.gov (United States)

Castillo-Felisola, Oscar; Corral, Cristóbal; del Pino, Simón; Ramírez, Francisca

2016-12-01

We study the Kaluza-Klein dimensional reduction of the Lovelock-Cartan theory in five-dimensional spacetime, with a compact dimension of S1 topology. We find cosmological solutions of the Friedmann-Robertson-Walker class in the reduced spacetime. The torsion and the fields arising from the dimensional reduction induce a nonvanishing energy-momentum tensor in four dimensions. We find solutions describing expanding, contracting, and bouncing universes. The model shows a dynamical compactification of the extra dimension in some regions of the parameter space.

Topological terms induced by finite temperature and density fluctuations

International Nuclear Information System (INIS)

Niemi, A.J.; Department of Physics, The Ohio State University, Columbus, Ohio 43210)

1986-01-01

In (3+1)-dimensional finite-temperature and -density SU(2) gauge theories with left-handed fermions, the three-dimensional Chern-Simons term (topological mass) can be induced by radiative corrections. This result is derived by use of a family's index theorem which also implies that in many other quantum field theories various additional lower-dimensional topological terms can be induced. In the high-temperature limit these terms dominate the partition function, which suggests applications to early-Universe cosmology

Lectures on controlled topology: Mapping cylinder neighborhoods

Energy Technology Data Exchange (ETDEWEB)

Quinn, F [Department of Mathematics, Virginia Tech, Blacksburg, VA (United States)

2002-08-15

The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional Topology, Trieste, Italy 2001. (author)

Lectures on controlled topology: Mapping cylinder neighborhoods

International Nuclear Information System (INIS)

Quinn, F.

2002-01-01

The existence theorem for mapping cylinder neighborhoods is discussed as a prototypical example of controlled topology and its applications. The first of a projected series developed from lectures at the Summer School on High-Dimensional Topology, Trieste, Italy 2001. (author)

Duality in twisted N=4 supersymmetric gauge theories in four dimensions

CERN Document Server

Labastida, J.M.F.; Lozano, Carlos

1999-01-01

We consider a twisted version of the four-dimensional N=4 supersymmetric Yang-Mills theory with gauge groups SU(2) and SO(3), and bare masses for two of its chiral multiplets, thereby breaking N=4 down to N=2. Using the wall-crossing technique introduced by Moore and Witten within the u-plane approach to twisted topological field theories, we compute the partition function and all the topological correlation functions for the case of simply-connected spin four-manifolds of simple type. By including 't Hooft fluxes, we analyse the properties of the resulting formulae under duality transformations. The partition function transforms in the same way as the one first presented by Vafa and Witten for another twist of the N=4 supersymmetric theory in their strong coupling test of S-duality. Both partition functions coincide on K3. The topological correlation functions turn out to transform covariantly under duality, following a simple pattern which seems to be inherent in a general type of topological quantum field ...

Manipulating topological-insulator properties using quantum confinement

International Nuclear Information System (INIS)

Kotulla, M; Zülicke, U

2017-01-01

Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators are insulating in the bulk but have conductive surface or edge states. Topological materials show various unusual physical properties and are surmised to enable the creation of exotic Majorana-fermion quasiparticles. How the signatures of topological behavior evolve when the system size is reduced is interesting from both a fundamental and an application-oriented point of view, as such understanding may form the basis for tailoring systems to be in specific topological phases. This work considers the specific case of quantum-well confinement defining two-dimensional layers. Based on the effective-Hamiltonian description of bulk topological insulators, and using a harmonic-oscillator potential as an example for a softer-than-hard-wall confinement, we have studied the interplay of band inversion and size quantization. Our model system provides a useful platform for systematic study of the transition between the normal and topological phases, including the development of band inversion and the formation of massless-Dirac-fermion surface states. The effects of bare size quantization, two-dimensional-subband mixing, and electron–hole asymmetry are disentangled and their respective physical consequences elucidated. (paper)

Four-dimensional Printing of Liquid Crystal Elastomers.

Science.gov (United States)

Ambulo, Cedric P; Burroughs, Julia J; Boothby, Jennifer M; Kim, Hyun; Shankar, M Ravi; Ware, Taylor H

2017-10-25

Three-dimensional structures capable of reversible changes in shape, i.e., four-dimensional-printed structures, may enable new generations of soft robotics, implantable medical devices, and consumer products. Here, thermally responsive liquid crystal elastomers (LCEs) are direct-write printed into 3D structures with a controlled molecular order. Molecular order is locally programmed by controlling the print path used to build the 3D object, and this order controls the stimulus response. Each aligned LCE filament undergoes 40% reversible contraction along the print direction on heating. By printing objects with controlled geometry and stimulus response, magnified shape transformations, for example, volumetric contractions or rapid, repetitive snap-through transitions, are realized.

Four-dimensional optical coherence tomography imaging of total liquid ventilated rats

Science.gov (United States)

Kirsten, Lars; Schnabel, Christian; Gaertner, Maria; Koch, Edmund

2013-06-01

Optical coherence tomography (OCT) can be utilized for the spatially and temporally resolved visualization of alveolar tissue and its dynamics in rodent models, which allows the investigation of lung dynamics on the microscopic scale of single alveoli. The findings could provide experimental input data for numerical simulations of lung tissue mechanics and could support the development of protective ventilation strategies. Real four-dimensional OCT imaging permits the acquisition of several OCT stacks within one single ventilation cycle. Thus, the entire four-dimensional information is directly obtained. Compared to conventional virtual four-dimensional OCT imaging, where the image acquisition is extended over many ventilation cycles and is triggered on pressure levels, real four-dimensional OCT is less vulnerable against motion artifacts and non-reproducible movement of the lung tissue over subsequent ventilation cycles, which widely reduces image artifacts. However, OCT imaging of alveolar tissue is affected by refraction and total internal reflection at air-tissue interfaces. Thus, only the first alveolar layer beneath the pleura is visible. To circumvent this effect, total liquid ventilation can be carried out to match the refractive indices of lung tissue and the breathing medium, which improves the visibility of the alveolar structure, the image quality and the penetration depth and provides the real structure of the alveolar tissue. In this study, a combination of four-dimensional OCT imaging with total liquid ventilation allowed the visualization of the alveolar structure in rat lung tissue benefiting from the improved depth range beneath the pleura and from the high spatial and temporal resolution.

Topological excitations and Monte-Carlo simulation of the Abelian-Higgs model

International Nuclear Information System (INIS)

Ranft, J.

1981-01-01

The phase structure and topological excitations, in particular the magnetic monopole current density, are investigated in a Monte-Carlo simulation of the lattice version of the four-dimensional Abelian-Higgs model. The monopole current density is found to be large in the confinement phase and rapidly decreasing in the Coulomb and Higgs phases. This result supports the view that confinement is neglected with the condensation of monopole-antimonopole pairs

Spin-polarized currents in the tunnel contact of a normal conductor and a two-dimensional topological insulator

International Nuclear Information System (INIS)

Sukhanov, A. A.; Sablikov, V. A.

2013-01-01

The spin filtering of electrons tunneling from the edge states of a two-dimensional topological insulator into a normal conductor under a magnetic field (external or induced due to proximity to a magnetic insulator) is studied. Calculations are performed for a tunnel contact of finite length between the topological insulator and an electronic multimode quantum strip. It is shown that the flow of tunneling electrons is split in the strip, so that spin-polarized currents arise in its left and right branches. These currents can be effectively controlled by the contact voltage and the chemical potential of the system. The presence of a magnetic field, which splits the spin subbands of the electron spectrum in the strip, gives rise to switching of the spin current between the strip branches

Topology Optimization of Thermal Heat Sinks

DEFF Research Database (Denmark)

Klaas Haertel, Jan Hendrik; Engelbrecht, Kurt; Lazarov, Boyan Stefanov

2015-01-01

In this paper, topology optimization is applied to optimize the cooling performance of thermal heat sinks. The coupled two-dimensional thermofluid model of a heat sink cooled with forced convection and a density-based topology optimization including density filtering and projection are implemented...... in COMSOL Multiphysics. The optimization objective is to minimize the heat sink’s temperature for a prescribed pressure drop and fixed heat generation. To conduct the optimization, COMSOL’s Optimization Module with GCMMA as the optimization method is used. The implementation of this topology optimization...... approach in COMSOL Multiphysics is described in this paper and results for optimized two-dimensional heat sinks are presented. Furthermore, parameter studies regarding the effect of the prescribed pressure drop of the system on Reynolds number and realized heat sink temperature are presented and discussed....

Topological Phase Transition in Layered GaS and GaSe

KAUST Repository

Zhu, Zhiyong; Cheng, Yingchun; Schwingenschlö gl, Udo

2012-01-01

By fully relativistic first principles calculations, we predict that appropriate strain engineering of layered GaX (X=S, Se) leads to a new class of three-dimensional topological insulators with an excitation gap of up to 135 meV. Our results provide a new perspective on the formation of three-dimensional topological insulators. Band inversion can be induced by strain only, without considering any spin-orbit coupling. The latter, however, is indispensable for the formation of local band gaps at the crossing points of the inverted bands. Our study indicates that three-dimensional topological insulators can also be realized in materials which comprise light elements only.

Topological Phase Transition in Layered GaS and GaSe

KAUST Repository

Zhu, Zhiyong

2012-06-29

By fully relativistic first principles calculations, we predict that appropriate strain engineering of layered GaX (X=S, Se) leads to a new class of three-dimensional topological insulators with an excitation gap of up to 135 meV. Our results provide a new perspective on the formation of three-dimensional topological insulators. Band inversion can be induced by strain only, without considering any spin-orbit coupling. The latter, however, is indispensable for the formation of local band gaps at the crossing points of the inverted bands. Our study indicates that three-dimensional topological insulators can also be realized in materials which comprise light elements only.

Common time in a four-dimensional symmetry framework

International Nuclear Information System (INIS)

Hsu, J.P.; Sherry, T.N.

1980-01-01

Following the ideas of Poincare, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, we analyze clock systems and light propagation within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporating common time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of reference. A further consequence is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds an two-way speeds of light signals is considered in detail

Topological Field Theory of Time-Reversal Invariant Insulators

Energy Technology Data Exchange (ETDEWEB)

Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.

2010-03-19

We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.

Statistical Entropy of Four-Dimensional Extremal Black Holes

International Nuclear Information System (INIS)

Maldacena, J.M.; Strominger, A.

1996-01-01

String theory is used to count microstates of four-dimensional extremal black holes in compactifications with N=4 and N=8 supersymmetry. The result agrees for large charges with the Bekenstein-Hawking entropy. copyright 1996 The American Physical Society

Spin-orbit torque-driven magnetization switching in 2D-topological insulator heterostructure

Science.gov (United States)

Soleimani, Maryam; Jalili, Seifollah; Mahfouzi, Farzad; Kioussis, Nicholas

2017-02-01

Charge pumping and spin-orbit torque (SOT) are two reciprocal phenomena widely studied in ferromagnet (FM)/topological insulator (TI) heterostructures. However, the SOT and its corresponding switching phase diagram for a FM island in proximity to a two-dimensional topological insulator (2DTI) has not been explored yet. We have addressed these features, using the recently developed adiabatic expansion of time-dependent nonequilibrium Green's function (NEGF) in the presence of both precessing magnetization and bias voltage. We have calculated the angular and spatial dependence of different components of the SOT on the FM island. We determined the switching phase diagram of the FM for different orientations of the easy axis. The results can be used as a guideline for the future experiments on such systems.

Parafermionic wires at the interface of chiral topological states

Science.gov (United States)

Santos, Luiz; Hughes, Taylor

We discuss a scenario where local interactions form one-dimensional gapped interfaces between a pair of distinct chiral two-dimensional topological states such that each gapped region terminates at a domain wall separating the chiral gapless edge states of these phases. We show that this type of T-junction supports point-like fractionalized excitations obeying parafermion statistics, thus implying that the one-dimensional gapped interface forms an effective topological parafermionic wire possessing a non-trivial ground state degeneracy. The physical properties of the anyon condensate that gives rise to the gapped interface are investigated. Remarkably, this condensate causes the gapped interface to behave as a type of anyon ``Andreev reflector'' in the bulk, whereby anyons from one phase, upon hitting the interface, can be transformed into a combination of reflected anyons and outgoing anyons from the other phase. Thus, we conclude that while different topological orders can be connected via gapped interfaces, the interfaces are themselves topological.

A simple proof of the recent generalizations of Hawking's black hole topology theorem

Energy Technology Data Exchange (ETDEWEB)

Racz, Istvan [RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)], E-mail: iracz@sunserv.kfki.hu

2008-08-21

A key result in four-dimensional black hole physics, since the early 1970s, is Hawking's topology theorem assertion that the cross-sections of an 'apparent horizon', separating the black hole region from the rest of the spacetime, are topologically 2-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus-dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently, Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalized to the case of black holes in higher dimensions. Our aim here is to give a simple self-contained proof of these generalizations, which also makes their range of applicability transparent. (fast track communication)

Topological and trivial magnetic oscillations in nodal loop semimetals

Science.gov (United States)

Oroszlány, László; Dóra, Balázs; Cserti, József; Cortijo, Alberto

2018-05-01

Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals host coexisting topological and trivial magnetic oscillations. These originate from mapping the topological properties of the extremal Fermi surface cross sections onto the physics of two dimensional semi-Dirac systems, stemming from merging two massless Dirac cones. By tuning the chemical potential and the direction of magnetic field, a sharp transition is identified from purely trivial oscillations, arising from the Landau levels of a normal two dimensional (2D) electron gas, to a phase where oscillations of topological and trivial origin coexist, originating from 2D massless Dirac and semi-Dirac points, respectively. These could in principle be directly identified in current experiments.

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

Topology Discovery Using Cisco Discovery Protocol

OpenAIRE

Rodriguez, Sergio R.

2009-01-01

In this paper we address the problem of discovering network topology in proprietary networks. Namely, we investigate topology discovery in Cisco-based networks. Cisco devices run Cisco Discovery Protocol (CDP) which holds information about these devices. We first compare properties of topologies that can be obtained from networks deploying CDP versus Spanning Tree Protocol (STP) and Management Information Base (MIB) Forwarding Database (FDB). Then we describe a method of discovering topology ...

The topology of large-scale structure. V - Two-dimensional topology of sky maps

Science.gov (United States)

Gott, J. R., III; Mao, Shude; Park, Changbom; Lahav, Ofer

1992-01-01

A 2D algorithm is applied to observed sky maps and numerical simulations. It is found that when topology is studied on smoothing scales larger than the correlation length, the topology is approximately in agreement with the random phase formula for the 2D genus-threshold density relation, G2(nu) varies as nu(e) exp-nu-squared/2. Some samples show small 'meatball shifts' similar to those seen in corresponding 3D observational samples and similar to those produced by biasing in cold dark matter simulations. The observational results are thus consistent with the standard model in which the structure in the universe today has grown from small fluctuations caused by random quantum noise in the early universe.

Variability of four-dimensional computed tomography patient models

NARCIS (Netherlands)

Sonke, Jan-Jakob; Lebesque, Joos; van Herk, Marcel

2008-01-01

PURPOSE: To quantify the interfractional variability in lung tumor trajectory and mean position during the course of radiation therapy. METHODS AND MATERIALS: Repeat four-dimensional (4D) cone-beam computed tomography (CBCT) scans (median, nine scans/patient) routinely acquired during the course of

Shifts of integration variable within four- and N-dimensional Feynman integrals

International Nuclear Information System (INIS)

Elias, V.; McKeon, G.; Mann, R.B.

1983-01-01

We resolve inconsistencies between integration in four dimensions, where shifts of integration variable may lead to surface terms, and dimensional regularization, where no surface terms accompany such shifts, by showing that surface terms arise only for discrete values of the dimension parameter. General formulas for variable-of-integration shifts within N-dimensional Feynman integrals are presented, and the VVA triangle anomaly is interpreted as a manifestation of surface terms occurring in exactly four dimensions

Lectures on 2d gauge theories. Topological aspects and path integral techniques

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1993-10-01

In these lectures are discussed two classes of two-dimensional field theories which are not obviously topological, but which nevertheless exhibit an intriguing equivalence with certain topological theories. These classes are two-dimensional Yang-Mills theory and the so-called G/G gauged Wess-Zumino-Witten model. The aim is to exhibit and extract the topological information contained in these theories and to present a technique which allows to calculate directly their partition functions and topological correlation functions on arbitrary closed surfaces. 34 refs

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.

D-branes and coherent topological charge structure in QCD

Science.gov (United States)

Thacker, Hank

2006-12-01

Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, co- herent, locally 3-dimensional sheets of topological charge embedded in 4D space, with opposite sign sheets interleaved. Studies of localization properties of Dirac eigenmodes have also shown evidence for the delocalization of low-lying modes on effectively 3-dimensional surfaces. In this talk, I review some theoretical ideas which suggest the possibility of 3-dimensionally coherent topological charge structure in 4-dimensional gauge theory and provide a possible interpretation of the observed structure. I begin with Luscher's "Wilson bag" integral over the 3-index Chern- Simons tensor. The analogy with a Wilson loop as a charged world line in 2-dimensional CP N-1 sigma models suggests that the Wilson bag surface represents the world volume of a physical membrane. The large-N chiral Lagrangian arguments of Witten also indicate the existence of multiple "k-vacuum" states with discontinuous transitions between k-vacua at θ = odd multi- ples of π. The domain walls between these vacua have the properties of a Wilson bag surface. Finally, I review the AdS/CFT duality view of θ dependence in QCD. The dual realtionship be- tween topological charge in gauge theory and Ramond-Ramond charge in type IIA string theory suggests that the coherent topological charge sheets observed on the lattice are the holographic image of wrapped D6 branes.

The coupling of Poisson sigma models to topological backgrounds

Energy Technology Data Exchange (ETDEWEB)

Rosa, Dario [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of)

2016-12-13

We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.

Homological Order in Three and Four dimensions: Wilson Algebra, Entanglement Entropy and Twist Defects

Science.gov (United States)

Roy, Abhishek; Chen, Xiao; Teo, Jeffrey

2013-03-01

We investigate homological orders in two, three and four dimensions by studying Zk toric code models on simplicial, cellular or in general differential complexes. The ground state degeneracy is obtained from Wilson loop and surface operators, and the homological intersection form. We compute these for a series of closed 3 and 4 dimensional manifolds and study the projective representations of mapping class groups (modular transformations). Braiding statistics between point and string excitations in (3+1)-dimensions or between dual string excitations in (4+1)-dimensions are topologically determined by the higher dimensional linking number, and can be understood by an effective topological field theory. An algorithm for calculating entanglemnent entropy of any bipartition of closed manifolds is presented, and its topological signature is completely characterized homologically. Extrinsic twist defects (or disclinations) are studied in 2,3 and 4 dimensions and are shown to carry exotic fusion and braiding properties. Simons Fellowship

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

Energy Technology Data Exchange (ETDEWEB)

Baskan, O.; Clercx, H. J. H [Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Speetjens, M. F. M. [Energy Technology Laboratory, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Metcalfe, G. [Commonwealth Scientific and Industrial Research Organisation, Melbourne, Victoria 3190 (Australia); Swinburne University of Technology, Department of Mechanical Engineering, Hawthorn VIC 3122 (Australia)

2015-10-15

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

Science.gov (United States)

Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

2015-10-01

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

Topological dynamics of vortex-line networks in hexagonal manganites

Science.gov (United States)

Xue, Fei; Wang, Nan; Wang, Xueyun; Ji, Yanzhou; Cheong, Sang-Wook; Chen, Long-Qing

2018-01-01

The two-dimensional X Y model is the first well-studied system with topological point defects. On the other hand, although topological line defects are common in three-dimensional systems, the evolution mechanism of line defects is not fully understood. The six domains in hexagonal manganites converge to vortex lines in three dimensions. Using phase-field simulations, we predicted that during the domain coarsening process, the vortex-line network undergoes three types of basic topological changes, i.e., vortex-line loop shrinking, coalescence, and splitting. It is shown that the vortex-antivortex annihilation controls the scaling dynamics.

Effect of strong disorder on three-dimensional chiral topological insulators: Phase diagrams, maps of the bulk invariant, and existence of topological extended bulk states

Science.gov (United States)

Song, Juntao; Fine, Carolyn; Prodan, Emil

2014-11-01

The effect of strong disorder on chiral-symmetric three-dimensional lattice models is investigated via analytical and numerical methods. The phase diagrams of the models are computed using the noncommutative winding number, as functions of disorder strength and model's parameters. The localized/delocalized characteristic of the quantum states is probed with level statistics analysis. Our study reconfirms the accurate quantization of the noncommutative winding number in the presence of strong disorder, and its effectiveness as a numerical tool. Extended bulk states are detected above and below the Fermi level, which are observed to undergo the so-called "levitation and pair annihilation" process when the system is driven through a topological transition. This suggests that the bulk invariant is carried by these extended states, in stark contrast with the one-dimensional case where the extended states are completely absent and the bulk invariant is carried by the localized states.

Rendering the Topological Spines

Energy Technology Data Exchange (ETDEWEB)

Nieves-Rivera, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-05-05

Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.

Abe homotopy classification of topological excitations under the topological influence of vortices

International Nuclear Information System (INIS)

Kobayashi, Shingo; Kobayashi, Michikazu; Kawaguchi, Yuki; Nitta, Muneto; Ueda, Masahito

2012-01-01

Topological excitations are usually classified by the nth homotopy group π n . However, for topological excitations that coexist with vortices, there are cases in which an element of π n cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of π n corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of π 1 on π n . In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group κ n . The nth Abe homotopy group κ n is defined as a semi-direct product of π 1 and π n . In this framework, the action of π 1 on π n is understood as originating from noncommutativity between π 1 and π n . We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is S n /K, where S n is an n-dimensional sphere and K is a discrete subgroup of SO(n+1). We show that the influence of vortices on a topological excitation exists only if n is even and K includes a nontrivial element of O(n)/SO(n).

Four-dimensional computed tomography angiographic evaluation of cranial dural arteriovenous fistula before and after embolization

International Nuclear Information System (INIS)

Tian, Bing; Xu, Bing; Lu, Jianping; Liu, Qi; Wang, Li; Wang, Minjie

2015-01-01

Highlights: • 4D CTA showed excellent agreement with DSA with regard to identification of feeding arteries and drainage veins. • The most important finding was 4D CTA in determining the impact of DAVF treatment with transarterial embolization. • 4D CTA provides images similar to those obtained with DSA both before and after treatment. - Abstract: Purpose: This study aimed to evaluate the usefulness of four-dimensional CTA before and after embolization treatment with ONYX-18 in eleven patients with cranial dural arteriovenous fistulas, and to compare the results with those of the reference standard DSA. Patients and Methods: Eleven patients with cranial dural arteriovenous fistulas detected on DSA underwent transarterial embolization with ONYX-18. Four-dimensional CTA was performed an average of 2 days before and 4 days after DSA. Four-dimensional CTA and DSA images were reviewed by two neuroradiologists for identification of feeding arteries and drainage veins and for determining treatment effects. Interobserver and intermodality agreement between four-dimensional CTA and DSA were assessed. Results: Forty-two feeding arteries were identified for 14 fistulas in the 11 patients. Of these, 36 (85.71%) were detected on four-dimensional CTA. After transarterial embolization, one patient got partly embolized, and the fistulas in the remaining 10 patients were completely occluded. The interobserver agreement for four-dimensional CTA and intermodality agreement between four-dimensional CTA and DSA were excellent (κ = 1) for shunt location, identification of drainage veins, and fistula occlusion after treatment. Conclusion: Four-dimensional CTA images are highly accurate when compared with DSA images both before and after transarterial embolization treatment. Four-dimensional CTA can be used for diagnosis as well as follow-up of cranial dural arteriovenous fistulas in clinical settings

Topological excitations in semiconductor heterostructures

International Nuclear Information System (INIS)

Koushik, R.; Mukerjee, Subroto; Ghosh, Arindam; Baenninger, Matthias; Narayan, Vijay; Pepper, Michael; Farrer, Ian; Ritchie, David A.

2013-01-01

Topological defects play an important role in the melting phenomena in two-dimensions. In this work, we report experimental observation of topological defect induced melting in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. The phenomenon is characterised by measurement of conductivity which goes to zero in a Berezinskii-Kosterlitz-Thouless like transition. Further evidence is provided via low-frequency conductivity noise measurements

Monolayer group-III monochalcogenides by oxygen functionalization: a promising class of two-dimensional topological insulators

Science.gov (United States)

Zhou, Si; Liu, Cheng-Cheng; Zhao, Jijun; Yao, Yugui

2018-03-01

Monolayer group-III monochalcogenides (MX, M = Ga, In; X = S, Se, Te), an emerging category of two-dimensional (2D) semiconductors, hold great promise for electronics, optoelectronics and catalysts. By first-principles calculations, we show that the phonon dispersion and Raman spectra, as well as the electronic and topological properties of monolayer MX can be tuned by oxygen functionalization. Chemisorption of oxygen atoms on one side or both sides of the MX sheet narrows or even closes the band gap, enlarges work function, and significantly reduces the carrier effective mass. More excitingly, InS, InSe, and InTe monolayers with double-side oxygen functionalization are 2D topological insulators with sizeable bulk gap up to 0.21 eV. Their low-energy bands near the Fermi level are dominated by the px and py orbitals of atoms, allowing band engineering via in-plane strains. Our studies provide viable strategy for realizing quantum spin Hall effect in monolayer group-III monochalcogenides at room temperature, and utilizing these novel 2D materials for high-speed and dissipationless transport devices.

Topological vector spaces and their applications

CERN Document Server

Bogachev, V I

2017-01-01

This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Four-dimensional maps of the human somatosensory system.

Science.gov (United States)

Avanzini, Pietro; Abdollahi, Rouhollah O; Sartori, Ivana; Caruana, Fausto; Pelliccia, Veronica; Casaceli, Giuseppe; Mai, Roberto; Lo Russo, Giorgio; Rizzolatti, Giacomo; Orban, Guy A

2016-03-29

A fine-grained description of the spatiotemporal dynamics of human brain activity is a major goal of neuroscientific research. Limitations in spatial and temporal resolution of available noninvasive recording and imaging techniques have hindered so far the acquisition of precise, comprehensive four-dimensional maps of human neural activity. The present study combines anatomical and functional data from intracerebral recordings of nearly 100 patients, to generate highly resolved four-dimensional maps of human cortical processing of nonpainful somatosensory stimuli. These maps indicate that the human somatosensory system devoted to the hand encompasses a widespread network covering more than 10% of the cortical surface of both hemispheres. This network includes phasic components, centered on primary somatosensory cortex and neighboring motor, premotor, and inferior parietal regions, and tonic components, centered on opercular and insular areas, and involving human parietal rostroventral area and ventral medial-superior-temporal area. The technique described opens new avenues for investigating the neural basis of all levels of cortical processing in humans.

Two Topologically Distinct Dirac-Line Semimetal Phases and Topological Phase Transitions in Rhombohedrally Stacked Honeycomb Lattices

Science.gov (United States)

Hyart, T.; Ojajärvi, R.; Heikkilä, T. T.

2018-04-01

Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model.

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

Four Dimensional Trace Space Measurement

Energy Technology Data Exchange (ETDEWEB)

Hernandez, M.

2005-02-10

Future high energy colliders and FELs (Free Electron Lasers) such as the proposed LCLS (Linac Coherent Light Source) at SLAC require high brightness electron beams. In general a high brightness electron beam will contain a large number of electrons that occupy a short longitudinal duration, can be focused to a small transverse area while having small transverse divergences. Therefore the beam must have a high peak current and occupy small areas in transverse phase space and so have small transverse emittances. Additionally the beam should propagate at high energy and have a low energy spread to reduce chromatic effects. The requirements of the LCLS for example are pulses which contain 10{sup 10} electrons in a temporal duration of 10 ps FWHM with projected normalized transverse emittances of 1{pi} mm mrad[1]. Currently the most promising method of producing such a beam is the RF photoinjector. The GTF (Gun Test Facility) at SLAC was constructed to produce and characterize laser and electron beams which fulfill the LCLS requirements. Emittance measurements of the electron beam at the GTF contain evidence of strong coupling between the transverse dimensions of the beam. This thesis explores the effects of this coupling on the determination of the projected emittances of the electron beam. In the presence of such a coupling the projected normalized emittance is no longer a conserved quantity. The conserved quantity is the normalized full four dimensional phase space occupied by the beam. A method to determine the presence and evaluate the strength of the coupling in emittance measurements made in the laboratory is developed. A method to calculate the four dimensional volume the beam occupies in phase space using quantities available in the laboratory environment is also developed. Results of measurements made of the electron beam at the GTF that demonstrate these concepts are presented and discussed.

Emergent Topological Phenomena in Thin Films of Pyrochlore Iridates

Science.gov (United States)

Yang, Bohm-Jung; Nagaosa, Naoto

2014-06-01

Because of the recent development of thin film and artificial superstructure growth techniques, it is possible to control the dimensionality of the system, smoothly between two and three dimensions. In this Letter we unveil the dimensional crossover of emergent topological phenomena in correlated topological materials. In particular, by focusing on the thin film of pyrochlore iridate antiferromagnets grown along the [111] direction, we demonstrate that the thin film can have a giant anomalous Hall conductance, proportional to the thickness of the film, even though there is no Hall effect in 3D bulk material. Moreover, in the case of ultrathin films, a quantized anomalous Hall conductance can be observed, despite the fact that the system is an antiferromagnet. In addition, we uncover the emergence of a new topological phase, the nontrivial topological properties of which are hidden in the bulk insulator and manifest only in thin films. This shows that the thin film of correlated topological materials is a new platform to search for unexplored novel topological phenomena.

Ripple-modulated electronic structure of a 3D topological insulator.

Science.gov (United States)

Okada, Yoshinori; Zhou, Wenwen; Walkup, D; Dhital, Chetan; Wilson, Stephen D; Madhavan, V

2012-01-01

Three-dimensional topological insulators host linearly dispersing states with unique properties and a strong potential for applications. An important ingredient in realizing some of the more exotic states in topological insulators is the ability to manipulate local electronic properties. Direct analogy to the Dirac material graphene suggests that a possible avenue for controlling local properties is via a controlled structural deformation such as the formation of ripples. However, the influence of such ripples on topological insulators is yet to be explored. Here we use scanning tunnelling microscopy to determine the effects of one-dimensional buckling on the electronic properties of Bi(2)Te(3.) By tracking spatial variations of the interference patterns generated by the Dirac electrons we show that buckling imposes a periodic potential, which locally modulates the surface-state dispersion. This suggests that forming one- and two-dimensional ripples is a viable method for creating nanoscale potential landscapes that can be used to control the properties of Dirac electrons in topological insulators.

Four-dimensional reconstruction of cultural heritage sites based on photogrammetry and clustering

Science.gov (United States)

Voulodimos, Athanasios; Doulamis, Nikolaos; Fritsch, Dieter; Makantasis, Konstantinos; Doulamis, Anastasios; Klein, Michael

2017-01-01

A system designed and developed for the three-dimensional (3-D) reconstruction of cultural heritage (CH) assets is presented. Two basic approaches are presented. The first one, resulting in an "approximate" 3-D model, uses images retrieved in online multimedia collections; it employs a clustering-based technique to perform content-based filtering and eliminate outliers that significantly reduce the performance of 3-D reconstruction frameworks. The second one is based on input image data acquired through terrestrial laser scanning, as well as close range and airborne photogrammetry; it follows a sophisticated multistep strategy, which leads to a "precise" 3-D model. Furthermore, the concept of change history maps is proposed to address the computational limitations involved in four-dimensional (4-D) modeling, i.e., capturing 3-D models of a CH landmark or site at different time instances. The system also comprises a presentation viewer, which manages the display of the multifaceted CH content collected and created. The described methods have been successfully applied and evaluated in challenging real-world scenarios, including the 4-D reconstruction of the historic Market Square of the German city of Calw in the context of the 4-D-CH-World EU project.

Spacetime representation of topological phononics

Science.gov (United States)

Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

2018-05-01

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

Extending topological surgery to natural processes and dynamical systems.

Directory of Open Access Journals (Sweden)

Stathis Antoniou

Full Text Available Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromosomal crossover, DNA recombination and when cosmic magnetic lines reconnect, while 2-dimensional surgery happens in the formation of tornadoes, in the phenomenon of Falaco solitons, in drop coalescence and in the cell mitosis. Inspired by such phenomena, we introduce new theoretical concepts which enhance topological surgery with the observed forces and dynamics. To do this, we first extend the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on arcs or surfaces but are 2-dimensional or 3-dimensional, we fill in the interior space by defining the notion of solid topological surgery. We further introduce the notion of embedded surgery in S3 for modeling phenomena which involve more intrinsically the ambient space, such as the appearance of knotting in DNA and phenomena where the causes and effect of the process lies beyond the initial manifold, such as the formation of black holes. Finally, we connect these new theoretical concepts with a dynamical system and we present it as a model for both 2-dimensional 0-surgery and natural phenomena exhibiting a 'hole drilling' behavior. We hope that through this study, topology and dynamics of many natural phenomena, as well as topological surgery itself, will be better understood.

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.

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

Explorations in topology map coloring, surfaces and knots

CERN Document Server

Gay, David

2013-01-01

Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigation

One-way quantum computation with four-dimensional photonic qudits

International Nuclear Information System (INIS)

Joo, Jaewoo; Knight, Peter L.; O'Brien, Jeremy L.; Rudolph, Terry

2007-01-01

We consider the possibility of performing linear optical quantum computations making use of extra photonic degrees of freedom. In particular, we focus on the case where we use photons as quadbits, four-dimensional photonic qudits. The basic 2-quadbit cluster state is a hyperentangled state across polarization and two spatial mode degrees of freedom. We examine the nondeterministic methods whereby such states can be created from single photons and/or Bell pairs and then give some mechanisms for performing higher-dimensional fusion gates

Topological Material-Based Spin Devices

Science.gov (United States)

Zhang, Minhao; Wang, Xuefeng

Three-dimensional topological insulators have insulating bulk and gapless helical surface states. One of the most fascinating properties of the metallic surface states is the spin-momentum helical locking. The giant current-driven torques on the magnetic layer have been discovered in TI/ferromagnet bilayers originating from the spin-momentum helical locking, enabling the efficient magnetization switching with a low current density. We demonstrated the current-direction dependent on-off state in TIs-based spin valve devices for memory and logic applications. Further, we demonstrated the Bi2Se3 system will go from a topologically nontrivial state to a topologically trivial state when Bi atoms are replaced by lighter In atoms. Here, topologically trivial metal (BixIny)2 Se3 with high mobility also facilitates the realization of its application in multifunctional spintronic devices.

Topology of classical vacuum space-time

International Nuclear Information System (INIS)

Cho, Y.M.

2007-04-01

We present a topological classification of classical vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology π 3 (S 3 ) = π 3 (S 2 ). Viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group, we construct all possible vacuum gravitational connections which give a vanishing curvature tensor. With this we show that the vacuum connection has the knot topology, the same topology which describes the multiple vacua of SU(2) gauge theory. We discuss the physical implications of our result in quantum gravity. (author)

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

Topological supersymmetric structure of hadron cross sections

International Nuclear Information System (INIS)

Gauron, P.; Nicolescu, B.; Ouvry, S.

1980-12-01

Recently a way of fully implementing unitarity in the framework of a Dual Topological Unitarization theory, including not only mesons but also baryons, was found. This theory consists in the topological description of hadron interactions involving confined quarks in terms of two 2-dimensional surfaces (a closed 'quantum' surface and a bounded 'classical' surface). We show that this description directly leads, at the zeroth order of the topological expansion, to certain relations between hadron cross-sections, in nice agreement with experimental data. A new topological suppression mechanism is shown to play an important dynamical role. We also point out a new topological supersymmetry property, which leads to realistic experimental consequences. A possible topological origin of the rho and ω universality relations emerges as a by-product of our study

A novel four-dimensional analytical approach for analysis of complex samples.

Science.gov (United States)

Stephan, Susanne; Jakob, Cornelia; Hippler, Jörg; Schmitz, Oliver J

2016-05-01

A two-dimensional LC (2D-LC) method, based on the work of Erni and Frei in 1978, was developed and coupled to an ion mobility-high-resolution mass spectrometer (IM-MS), which enabled the separation of complex samples in four dimensions (2D-LC, ion mobility spectrometry (IMS), and mass spectrometry (MS)). This approach works as a continuous multiheart-cutting LC system, using a long modulation time of 4 min, which allows the complete transfer of most of the first - dimension peaks to the second - dimension column without fractionation, in comparison to comprehensive two-dimensional liquid chromatography. Hence, each compound delivers only one peak in the second dimension, which simplifies the data handling even when ion mobility spectrometry as a third and mass spectrometry as a fourth dimension are introduced. The analysis of a plant extract from Ginkgo biloba shows the separation power of this four-dimensional separation method with a calculated total peak capacity of more than 8700. Furthermore, the advantage of ion mobility for characterizing unknown compounds by their collision cross section (CCS) and accurate mass in a non-target approach is shown for different matrices like plant extracts and coffee. Graphical abstract Principle of the four-dimensional separation.

Influence of topology in a quantum ring

International Nuclear Information System (INIS)

Netto, A.L. Silva; Chesman, C.; Furtado, C.

2008-01-01

In this Letter we study the quantum rings in the presence of a topological defect. We use geometric theory of defects to describe one and two-dimensional quantum rings in the presence of a single screw dislocation. In addition we consider some potential in a two dimensional ring and calculate their energy spectrum. It is shown that the energy spectrum depend on the parabolic way on the burgers vectors of the screw dislocation. We also show that the presence of a topological defect introduces a new contribution for the Aharonov-Bohm effect in the quantum ring

New four-dimensional symmetry

International Nuclear Information System (INIS)

Hsu, J.P.

1976-01-01

A new picture of nature is proposed in which there are only two fundamental universal constants anti e (identical with e/c) and dirac constant (identical with dirac constant/c). The theory is developed within the framework of a new four-dimensional symmetry which is constructed on the basis of the Poincare--Einstein principle of relativity for the laws of physics and the Newtonian concept of time. One obtains a new space--light transformation law, a velocity-addition law, and so on. In this symmetry scheme, the speed of light is constant and is completely relative. The new theory is logically self-consistent, and it moreover is in agreement with all previously established experimental facts, such as the ''lifetime dilatation'' of unstable particles, the Michelson--Morley experiment, etc. There is a difference relative to the usual theory, though, in that our theory predicts a new law for the Doppler frequency shift, which can be tested experimentally by measuring the second-order frequency shift

Topological Insulator Nanowires and Nanoribbons

KAUST Repository

Kong, Desheng; Randel, Jason C.; Peng, Hailin; Cha, Judy J.; Meister, Stefan; Lai, Keji; Chen, Yulin; Shen, Zhi-Xun; Manoharan, Hari C.; Cui, Yi

2010-01-01

Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi2Se3 material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive

An Invitation to the Mathematics of Topological Quantum Computation

International Nuclear Information System (INIS)

Rowell, E C

2016-01-01

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematician's perspective on some of the advantages and challenges of this model, highlighting some recent advances. We then give a short description of how we might extend the theory to three-dimensional materials. (paper)

The topology of galaxy clustering.

Science.gov (United States)

Coles, P.; Plionis, M.

The authors discuss an objective method for quantifying the topology of the galaxy distribution using only projected galaxy counts. The method is a useful complement to fully three-dimensional studies of topology based on the genus by virtue of the enormous projected data sets available. Applying the method to the Lick counts they find no evidence for large-scale non-gaussian behaviour, whereas the small-scale distribution is strongly non-gaussian, with a shift in the meatball direction.

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.

Four-dimensional anti-de Sitter toroidal black holes from a three-dimensional perspective: Full complexity

International Nuclear Information System (INIS)

Zanchin, Vilson T.; Kleber, Antares; Lemos, Jose P.S.

2002-01-01

The dimensional reduction of black hole solutions in four-dimensional (4D) general relativity is performed and new 3D black hole solutions are obtained. Considering a 4D spacetime with one spacelike Killing vector, it is possible to split the Einstein-Hilbert-Maxwell action with a cosmological term in terms of 3D quantities. Definitions of quasilocal mass and charges in 3D spacetimes are reviewed. The analysis is then particularized to the toroidal charged rotating anti-de Sitter black hole. The reinterpretation of the fields and charges in terms of a three-dimensional point of view is given in each case, and the causal structure analyzed

The second law in four-dimensional Einstein–Gauss–Bonnet gravity

International Nuclear Information System (INIS)

Chatterjee, Saugata; Parikh, Maulik

2014-01-01

The topological contribution of a Gauss–Bonnet term in four dimensions to black hole entropy opens up the possibility of a violation of the second law of thermodynamics in black hole mergers. We show, however, that the second law is not violated in the regime where Einstein–Gauss–Bonnet holds as an effective theory and black holes can be treated thermodynamically. For mergers of anti-de Sitter (AdS) black holes, the second law appears to be violated even in Einstein gravity; we argue, however, that the second law holds when gravitational potential energy is taken into account. (paper)

Ultra high speed optical transmission using subcarrier-multiplexed four-dimensional LDPC-coded modulation.

Science.gov (United States)

Batshon, Hussam G; Djordjevic, Ivan; Schmidt, Ted

2010-09-13

We propose a subcarrier-multiplexed four-dimensional LDPC bit-interleaved coded modulation scheme that is capable of achieving beyond 480 Gb/s single-channel transmission rate over optical channels. Subcarrier-multiplexed four-dimensional LDPC coded modulation scheme outperforms the corresponding dual polarization schemes by up to 4.6 dB in OSNR at BER 10(-8).

Real-space mapping of topological invariants using artificial neural networks

Science.gov (United States)

Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

2018-03-01

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

Current-induced switching of magnetic molecules on topological insulator surfaces

Science.gov (United States)

Locane, Elina; Brouwer, Piet W.

2017-03-01

Electrical currents at the surface or edge of a topological insulator are intrinsically spin polarized. We show that such surface or edge currents can be used to switch the orientation of a molecular magnet weakly coupled to the surface or edge of a topological insulator. For the edge of a two-dimensional topological insulator as well as for the surface of a three-dimensional topological insulator the application of a well-chosen surface or edge current can lead to a complete polarization of the molecule if the molecule's magnetic anisotropy axis is appropriately aligned with the current direction. For a generic orientation of the molecule a nonzero but incomplete polarization is obtained. We calculate the probability distribution of the magnetic states and the switching rates as a function of the applied current.

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)

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.

On the topology of untrapped surfaces

Energy Technology Data Exchange (ETDEWEB)

Racz, Istvan, E-mail: iracz@rmki.kfki.h [RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)

2009-03-07

Recently a simple proof of the generalizations of Hawking's black hole topology theorem and its application to topological black holes for higher dimensional (n >= 4) spacetimes was given by Racz I (2008 Class. Quantum Grav. 25 162001). By applying the associated new line of argument it is proven here that strictly stable untrapped surfaces possess exactly the same topological properties as strictly stable marginally outer trapped surfaces (MOTSs) are known to. In addition, a quasi-local notion of outwards and inwards pointing spacelike directions-applicable to untrapped and marginally trapped surfaces-is also introduced.

Lateral topological crystalline insulator heterostructure

Science.gov (United States)

Sun, Qilong; Dai, Ying; Niu, Chengwang; Ma, Yandong; Wei, Wei; Yu, Lin; Huang, Baibiao

2017-06-01

The emergence of lateral heterostructures fabricated by two-dimensional building blocks brings many exciting realms in material science and device physics. Enriching available nanomaterials for creating such heterostructures and enabling the underlying new physics is highly coveted for the integration of next-generation devices. Here, we report a breakthrough in lateral heterostructure based on the monolayer square transition-metal dichalcogenides MX2 (M  =  W, X  =  S/Se) modules. Our results reveal that the MX2 lateral heterostructure (1S-MX2 LHS) can possess excellent thermal and dynamical stability. Remarkably, the highly desired two-dimensional topological crystalline insulator phase is confirmed by the calculated mirror Chern number {{n}\\text{M}}=-1 . A nontrivial band gap of 65 meV is obtained with SOC, indicating the potential for room-temperature observation and applications. The topologically protected edge states emerge at the edges of two different nanoribbons between the bulk band gap, which is consistent with the mirror Chern number. In addition, a strain-induced topological phase transition in 1S-MX2 LHS is also revealed, endowing the potential utilities in electronics and spintronics. Our predictions not only introduce new member and vitality into the studies of lateral heterostructures, but also highlight the promise of lateral heterostructure as appealing topological crystalline insulator platforms with excellent stability for future devices.

Weakly interacting topological insulators: Quantum criticality and the renormalization group approach

Science.gov (United States)

Chen, Wei

2018-03-01

For D -dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D - or (D +1 ) -dimensional integration over a certain curvature function that is expressed in terms of single-particle Green's functions. Based on the divergence of curvature function at the topological phase transition, we demonstrate how a renormalization group approach circumvents these integrations and reduces the necessary calculation to that for the Green's function alone, rendering a numerically efficient tool to identify topological phase transitions in a large parameter space. The method further unveils a number of statistical aspects related to the quantum criticality in weakly interacting topological insulators, including correlation function, critical exponents, and scaling laws, that can be used to characterize the topological phase transitions driven by either interacting or noninteracting parameters. We use 1D class BDI and 2D class A Dirac models with electron-electron and electron-phonon interactions to demonstrate these principles and find that interactions may change the critical exponents of the topological insulators.

Valley polarized quantum Hall effect and topological insulator phase transitions in silicene

KAUST Repository

Tahir, M.

2013-01-25

The electronic properties of silicene are distinct from both the conventional two dimensional electron gas and the famous graphene due to strong spin orbit interaction and the buckled structure. Silicene has the potential to overcome limitations encountered for graphene, in particular the zero band gap and weak spin orbit interaction. We demonstrate a valley polarized quantum Hall effect and topological insulator phase transitions. We use the Kubo formalism to discuss the Hall conductivity and address the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that the combination of an electric field with intrinsic spin orbit interaction leads to quantum phase transitions at the charge neutrality point, providing a tool to experimentally tune the topological state. Silicene constitutes a model system for exploring the spin and valley physics not accessible in graphene due to the small spin orbit interaction.

Topological properties of function spaces $C_k(X,2)$ over zero-dimensional metric spaces $X$

OpenAIRE

Gabriyelyan, S.

2015-01-01

Let $X$ be a zero-dimensional metric space and $X'$ its derived set. We prove the following assertions: (1) the space $C_k(X,2)$ is an Ascoli space iff $C_k(X,2)$ is $k_\\mathbb{R}$-space iff either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (2) $C_k(X,2)$ is a $k$-space iff either $X$ is a topological sum of a Polish locally compact space and a discrete space or $X$ is not locally compact but $X'$ is compact, (3) $C_k(X,2)$ is a sequential space iff $X$ is a Pol...

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.

Topology of Fermi surfaces and anomaly inflows

Energy Technology Data Exchange (ETDEWEB)

Adem, Alejandro; Camarena, Omar Antolín [Department of Mathematics, University of British Columbia,1984 Mathematics Road, Vancouver, V6T 1Z2 (Canada); Semenoff, Gordon W. [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver, V6T 1Z1 (Canada); Sheinbaum, Daniel [Department of Mathematics, University of British Columbia,1984 Mathematics Road, Vancouver, V6T 1Z2 (Canada)

2016-11-14

We derive a rigorous classification of topologically stable Fermi surfaces of non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations. For systems on an infinite crystal it is shown that there can only be topologically unstable Fermi surfaces. For systems on a half-space and with a gapped bulk, our derivation naturally yields a K-theory classification. Given the d−1-dimensional surface Brillouin zone X{sub s} of a d-dimensional half-space, our result implies that different classes of globally stable Fermi surfaces belong in K{sup −1}(X{sub s}) for systems with only discrete translation-invariance. This result has a chiral anomaly inflow interpretation, as it reduces to the spectral flow for d=2. Through equivariant homotopy methods we extend these results for symmetry classes AI, AII, C and D and discuss their corresponding anomaly inflow interpretation.

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

Topological magnetoelectric pump in three dimensions

Science.gov (United States)

Fukui, Takahiro; Fujiwara, Takanori

2017-11-01

We study the topological pump for a lattice fermion model mainly in three spatial dimensions. We first calculate the U(1) current density for the Dirac model defined in continuous space-time to review the known results as well as to introduce some technical details convenient for the calculations of the lattice model. We next investigate the U(1) current density for a lattice fermion model, a variant of the Wilson-Dirac model. The model we introduce is defined on a lattice in space but in continuous time, which is suited for the study of the topological pump. For such a model, we derive the conserved U(1) current density and calculate it directly for the (1 +1 )-dimensional system as well as (3 +1 )-dimensional system in the limit of the small lattice constant. We find that the current includes a nontrivial lattice effect characterized by the Chern number, and therefore the pumped particle number is quantized by the topological reason. Finally, we study the topological temporal pump in 3 +1 dimensions by numerical calculations. We discuss the relationship between the second Chern number and the first Chern number, the bulk-edge correspondence, and the generalized Streda formula which enables us to compute the second Chern number using the spectral asymmetry.

Proximity effects in topological insulator heterostructures

International Nuclear Information System (INIS)

Li Xiao-Guang; Wu Guang-Fen; Zhang Gu-Feng; Culcer Dimitrie; Zhang Zhen-Yu; Chen Hua

2013-01-01

Topological insulators (TIs) are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to Tl-based heterostructures, in which conventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent studies on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insulator or other topologically trivial systems. Using first-principles approaches, we have realized the tunability of the vertical location of the topological helical state via intriguing dual-proximity effects. To further elucidate the control parameters of this effect, we have used the graphene-based heterostructures as prototypical systems to reveal a more complete phase diagram. On the application side of the topological helical states, we have presented a catalysis example, where the topological helical state plays an essential role in facilitating surface reactions by serving as an effective electron bath. These discoveries lay the foundation for accurate manipulation of the real space properties of the topological helical state in TI-based heterostructures and pave the way for realization of the salient functionality of topological insulators in future device applications. (topical review - low-dimensional nanostructures and devices)

Topology of Neutral Hydrogen within the Small Magellanic Cloud

Science.gov (United States)

Chepurnov, A.; Gordon, J.; Lazarian, A.; Stanimirovic, S.

2008-12-01

In this paper, genus statistics have been applied to an H I column density map of the Small Magellanic Cloud in order to study its topology. To learn how topology changes with the scale of the system, we provide topology studies for column density maps at varying resolutions. To evaluate the statistical error of the genus, we randomly reassign the phases of the Fourier modes while keeping the amplitudes. We find that at the smallest scales studied (40 pc meatball" topology) in four cases and positive (a "swiss cheese" topology) in two cases. In four regions, there is no statistically significant topology shift at large scales.

Two-Loop Master Integrals for $\\gamma^{*} \\to 3$ Jets the Non-Planar Topologies

CERN Document Server

Gehrmann, T

2001-01-01

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper, we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in $\\e=(4-d)/2$, where $d$ is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies.

Quantum oscillation evidence for a topological semimetal phase in ZrSnTe

Science.gov (United States)

Hu, Jin; Zhu, Yanglin; Gui, Xin; Graf, David; Tang, Zhijie; Xie, Weiwei; Mao, Zhiqiang

2018-04-01

The layered WHM-type (W =Zr /Hf /La , H =Si /Ge /Sn /Sb , M =S /Se /Te ) materials represent a large family of topological semimetals, which provides an excellent platform to study the evolution of topological semimetal state with the fine tuning of spin-orbit coupling and structural dimensionality for various combinations of W , H , and M elements. In this work, through high field de Haas-van Alphen (dHvA) quantum oscillation studies, we have found evidence for the predicted topological nontrivial bands in ZrSnTe. Furthermore, from the angular dependence of quantum oscillation frequency, we have revealed the three-dimensional Fermi surface topologies of this layered material owing to strong interlayer coupling.

Energy analysis of four dimensional extended hyperbolic Scarf I plus three dimensional separable trigonometric noncentral potentials using SUSY QM approach

International Nuclear Information System (INIS)

Suparmi, A.; Cari, C.; Deta, U. A.; Handhika, J.

2016-01-01

The non-relativistic energies and wave functions of extended hyperbolic Scarf I plus separable non-central shape invariant potential in four dimensions are investigated using Supersymmetric Quantum Mechanics (SUSY QM) Approach. The three dimensional separable non-central shape invariant angular potential consists of trigonometric Scarf II, Manning Rosen and Poschl-Teller potentials. The four dimensional Schrodinger equation with separable shape invariant non-central potential is reduced into four one dimensional Schrodinger equations through variable separation method. By using SUSY QM, the non-relativistic energies and radial wave functions are obtained from radial Schrodinger equation, the orbital quantum numbers and angular wave functions are obtained from angular Schrodinger equations. The extended potential means there is perturbation terms in potential and cause the decrease in energy spectra of Scarf I potential. (paper)

Study of Topological Distributions of Inclusive Three- and Four-jet Events at the LHC

Science.gov (United States)

Gupta, Ruchi; CMS Collaboration

2016-04-01

A study of inclusive topological distributions of three- and four-jet events has been conducted by the CMS Collaboration at the LHC with a data sample corresponding to an integrated luminosity of 5.1 fb-1 at a centre of mass energy of 7 TeV. Kinematic and angular distributions in inclusive multijet final states serve as a natural probe of quantum chromodynamics and can reveal its inner dynamics. Comparisons are carried out with the data and predictions of leading order calculations and parton shower generators. The compared data results are corrected for detector effects and can be directly compared with other models or next-to-leading order theoretical predictions.

From bosonic topological transition to symmetric fermion mass generation

Science.gov (United States)

You, Yi-Zhuang; He, Yin-Chen; Vishwanath, Ashvin; Xu, Cenke

2018-03-01

A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal SO (4 ) symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors (Nf=4 ). Within a systematic renormalization group analysis, we identify the critical point with the desired O (4 ) emergent symmetry and all expected deformations. By lowering the microscopic symmetry, we recover the previous Nf=2 noncompact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU (2 ) quantum chromodynamics-Higgs theory with Nf=4 flavors of SU (2 ) fundamental fermions and one SU (2 ) fundamental Higgs boson. This provides a consistency check on both theories.

Exotic Lifshitz transitions in topological materials

Science.gov (United States)

Volovik, G. E.

2018-01-01

Topological Lifshitz transitions involve many types of topological structures in momentum and frequency-momentum spaces, such as Fermi surfaces, Dirac lines, Dirac and Weyl points, etc., each of which has its own stability-supporting topological invariant ( N_1, N_2, N_3, {\\tilde N}_3, etc.). The topology of the shape of Fermi surfaces and Dirac lines and the interconnection of objects of different dimensionalities produce a variety of Lifshitz transition classes. Lifshitz transitions have important implications for many areas of physics. To give examples, transition-related singularities can increase the superconducting transition temperature; Lifshitz transitions are the possible origin of the small masses of elementary particles in our Universe, and a black hole horizon serves as the surface of the Lifshitz transition between vacua with type-I and type-II Weyl points.

Exploring topological phases with quantum walks

International Nuclear Information System (INIS)

Kitagawa, Takuya; Rudner, Mark S.; Berg, Erez; Demler, Eugene

2010-01-01

The quantum walk was originally proposed as a quantum-mechanical analog of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete-time quantum walks provide a versatile platform for studying topological phases, which are currently the subject of intense theoretical and experimental investigations. In particular, we demonstrate that recent experimental realizations of quantum walks with cold atoms, photons, and ions simulate a nontrivial one-dimensional topological phase. With simple modifications, the quantum walk can be engineered to realize all of the topological phases, which have been classified in one and two dimensions. We further discuss the existence of robust edge modes at phase boundaries, which provide experimental signatures for the nontrivial topological character of the system.

Nonrenormalizable quantum field models in four-dimensional space-time

International Nuclear Information System (INIS)

Raczka, R.

1978-01-01

The construction of no-cutoff Euclidean Green's functions for nonrenormalizable interactions L/sub I/(phi) = lambda∫ddelta (epsilon): expepsilonphi: in four-dimensional space-time is carried out. It is shown that all axioms for the generating functional of the Euclidean Green's function are satisfied except perhaps SO(4) invariance

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.

Topological patterns of mesh textures in serpentinites

Science.gov (United States)

Miyazawa, M.; Suzuki, A.; Shimizu, H.; Okamoto, A.; Hiraoka, Y.; Obayashi, I.; Tsuji, T.; Ito, T.

2017-12-01

Serpentinization is a hydration process that forms serpentine minerals and magnetite within the oceanic lithosphere. Microfractures crosscut these minerals during the reactions, and the structures look like mesh textures. It has been known that the patterns of microfractures and the system evolutions are affected by the hydration reaction and fluid transport in fractures and within matrices. This study aims at quantifying the topological patterns of the mesh textures and understanding possible conditions of fluid transport and reaction during serpentinization in the oceanic lithosphere. Two-dimensional simulation by the distinct element method (DEM) generates fracture patterns due to serpentinization. The microfracture patterns are evaluated by persistent homology, which measures features of connected components of a topological space and encodes multi-scale topological features in the persistence diagrams. The persistence diagrams of the different mesh textures are evaluated by principal component analysis to bring out the strong patterns of persistence diagrams. This approach help extract feature values of fracture patterns from high-dimensional and complex datasets.

Four-dimensional Hooke's law can encompass linear elasticity and inertia

International Nuclear Information System (INIS)

Antoci, S.; Mihich, L.

1999-01-01

The question is examined whether the formally straightforward extension of Hooke's time-honoured stress-strain relation to the four dimensions of special and of general relativity can make physical sense. The four-dimensional Hooke law is found able to account for the inertia of matter; in the flat-space, slow-motion approximation the field equations for the displacement four-vector field ξ i can encompass both linear elasticity and inertia. In this limit one just recovers the equations of motion of the classical theory of elasticity

A covariant form of the Maxwell's equations in four-dimensional spaces with an arbitrary signature

International Nuclear Information System (INIS)

Lukac, I.

1991-01-01

The concept of duality in the four-dimensional spaces with the arbitrary constant metric is strictly mathematically formulated. A covariant model for covariant and contravariant bivectors in this space based on three four-dimensional vectors is proposed. 14 refs

Quantum walk with a four-dimensional coin

International Nuclear Information System (INIS)

Hamilton, Craig S; Gabris, Aurel; Jex, Igor; Barnett, Stephen M

2011-01-01

We examine the physical implementation of a discrete time quantum walk with a four-dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay loop, with time being our position space. The quantum coin is implemented using the internal states of the photon: the polarization and two of the orbital angular momentum states. We demonstrate how to implement this physically and what components would be needed. We then illustrate some of the results that could be obtained by performing the experiment.

Topology Optimization of Lightweight Lattice Structural Composites Inspired by Cuttlefish Bone

Science.gov (United States)

Hu, Zhong; Gadipudi, Varun Kumar; Salem, David R.

2018-03-01

Lattice structural composites are of great interest to various industries where lightweight multifunctionality is important, especially aerospace. However, strong coupling among the composition, microstructure, porous topology, and fabrication of such materials impedes conventional trial-and-error experimental development. In this work, a discontinuous carbon fiber reinforced polymer matrix composite was adopted for structural design. A reliable and robust design approach for developing lightweight multifunctional lattice structural composites was proposed, inspired by biomimetics and based on topology optimization. Three-dimensional periodic lattice blocks were initially designed, inspired by the cuttlefish bone microstructure. The topologies of the three-dimensional periodic blocks were further optimized by computer modeling, and the mechanical properties of the topology optimized lightweight lattice structures were characterized by computer modeling. The lattice structures with optimal performance were identified.

Intrinsic nonadiabatic topological torque in magnetic skyrmions and vortices

KAUST Repository

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

2017-01-01

We propose that topological spin currents flowing in topologically nontrivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic nonadiabatic torque of the form Tt∼[(∂xm×∂ym)·m]∂ym. We show that this torque, which is absent in one-dimensional domain walls and/or nontopological textures, is responsible for the enhanced nonadiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be crucial, especially to determine their robustness against defects and pinning centers.

Intrinsic nonadiabatic topological torque in magnetic skyrmions and vortices

KAUST Repository

Akosa, Collins Ashu

2017-03-01

We propose that topological spin currents flowing in topologically nontrivial magnetic textures, such as magnetic skyrmions and vortices, produce an intrinsic nonadiabatic torque of the form Tt∼[(∂xm×∂ym)·m]∂ym. We show that this torque, which is absent in one-dimensional domain walls and/or nontopological textures, is responsible for the enhanced nonadiabaticity parameter observed in magnetic vortices compared to one-dimensional textures. The impact of this torque on the motion of magnetic skyrmions is expected to be crucial, especially to determine their robustness against defects and pinning centers.

Four-Dimensional Ultrafast Electron Microscopy: Insights into an Emerging Technique

KAUST Repository

Adhikari, Aniruddha; Eliason, Jeffrey K.; Sun, Jingya; Bose, Riya; Flannigan, David J.; Mohammed, Omar F.

2016-01-01

Four-dimensional ultrafast electron microscopy (4D-UEM) is a novel analytical technique that aims to fulfill the long-held dream of researchers to investigate materials at extremely short spatial and temporal resolutions by integrating the excellent

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.

Higher-order topological insulators and superconductors protected by inversion symmetry

Science.gov (United States)

Khalaf, Eslam

2018-05-01

We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that propagate along one-dimensional curves (hinges) or are localized at some points (corners) on the surface. We provide a complete classification of inversion-protected higher-order topological insulators and superconductors in any spatial dimension for the 10 symmetry classes by means of a layer construction. We discuss possible physical realizations of such states starting with a time-reversal-invariant topological insulator (class AII) in three dimensions or a time-reversal-invariant topological superconductor (class DIII) in two or three dimensions. The former exhibits one-dimensional chiral or helical modes propagating along opposite edges, whereas the latter hosts Majorana zero modes localized to two opposite corners. Being protected by inversion, such states are not pinned to a specific pair of edges or corners, thus offering the possibility of controlling their location by applying inversion-symmetric perturbations such as magnetic field.

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

Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: Crossover between bulk and surface transport

KAUST Repository

Ghosh, Sumit; Manchon, Aurelien

2018-01-01

Current-driven spin-orbit torques are investigated in a heterostructure composed of a ferromagnet deposited on top of a three-dimensional topological insulator using the linear response formalism. We develop a tight-binding model of the heterostructure adopting a minimal interfacial hybridization scheme that promotes induced magnetic exchange on the topological surface states, as well as induced Rashba-like spin-orbit coupling in the ferromagnet. Therefore our model accounts for the spin Hall effect from bulk states together with inverse spin galvanic and magnetoelectric effects at the interface on equal footing. By varying the transport energy across the band structure, we uncover a crossover from surface-dominated to bulk-dominated transport regimes. We show that the spin density profile and the nature of the spin-orbit torques differ substantially in both regimes. Our results, which compare favorably with experimental observations, demonstrate that the large dampinglike torque reported recently is more likely attributed to the Berry curvature of interfacial states, while spin Hall torque remains small even in the bulk-dominated regime.

Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: Crossover between bulk and surface transport

KAUST Repository

Ghosh, Sumit

2018-04-02

Current-driven spin-orbit torques are investigated in a heterostructure composed of a ferromagnet deposited on top of a three-dimensional topological insulator using the linear response formalism. We develop a tight-binding model of the heterostructure adopting a minimal interfacial hybridization scheme that promotes induced magnetic exchange on the topological surface states, as well as induced Rashba-like spin-orbit coupling in the ferromagnet. Therefore our model accounts for the spin Hall effect from bulk states together with inverse spin galvanic and magnetoelectric effects at the interface on equal footing. By varying the transport energy across the band structure, we uncover a crossover from surface-dominated to bulk-dominated transport regimes. We show that the spin density profile and the nature of the spin-orbit torques differ substantially in both regimes. Our results, which compare favorably with experimental observations, demonstrate that the large dampinglike torque reported recently is more likely attributed to the Berry curvature of interfacial states, while spin Hall torque remains small even in the bulk-dominated regime.

Topological Crystalline Superconductivity in Locally Noncentrosymmetric Multilayer Superconductors.

Science.gov (United States)

Yoshida, Tomohiro; Sigrist, Manfred; Yanase, Youichi

2015-07-10

Topological crystalline superconductivity in locally noncentrosymmetric multilayer superconductors (SCs) is proposed. We study the odd-parity pair-density wave (PDW) state induced by the spin-singlet pairing interaction through the spin-orbit coupling. It is shown that the PDW state is a topological crystalline SC protected by a mirror symmetry, although it is topologically trivial according to the classification based on the standard topological periodic table. The topological property of the mirror subsectors is intuitively explained by adiabatically changing the Bogoliubov-de Gennes Hamiltonian. A subsector of the bilayer PDW state reduces to the two-dimensional noncentrosymmetric SC, while a subsector of the trilayer PDW state is topologically equivalent to the spinless p-wave SC. Chiral Majorana edge modes in trilayers can be realized without Cooper pairs in the spin-triplet channel and chemical potential tuning.

Topology optimization of Channel flow problems

DEFF Research Database (Denmark)

Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.

2005-01-01

function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical......This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low to moderate Reynolds numbers. This makes the flow problem non-linear and hence a non-trivial extension of the work of [Borrvall&Petersson 2002......]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...

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

Charged rotating black holes in four-dimensional gauged and ungauged supergravities

International Nuclear Information System (INIS)

Chong, Z.-W.; Cvetic, M.; Lue, H.; Pope, C.N.

2005-01-01

We study four-dimensional non-extremal charged rotating black holes in ungauged and gauged supergravity. In the ungauged case, we obtain rotating black holes with four independent charges, as solutions of N=2 supergravity coupled to three Abelian vector multiplets. This is done by reducing the theory along the time direction to three dimensions, where it has an O(4,4) global symmetry. Applied to the reduction of the uncharged Kerr metric, O(1,1) 4 is a subject of O(4,4) transformations generate new solutions that correspond, after lifting back to four dimensions, to the introduction of four independent electromagnetic charges. In the case where these charges are set pairwise equal, we then generalise the four-dimensional rotating black holes to solutions of gauged N=4 supergravity, with mass, angular momentum and two independent electromagnetic charges. The dilaton and axion fields are non-constant. We also find generalisations of the gauged and ungauged solutions to include the NUT parameter, and for the ungauged solutions, the acceleration parameter too. The solutions in gauged supergravity provide new gravitational backgrounds for a further study of the AdS 4 /CFT 3 correspondence at non-zero temperature

Operator algebras and topology

International Nuclear Information System (INIS)

Schick, T.

2002-01-01

These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)

Naked singularities in four-dimensional string backgrounds

International Nuclear Information System (INIS)

Mohammedi, N.

1993-04-01

It is shown that gauged nonlinear sigma models can be always deformed by terms proportional to the field strength of the gauge fields (nonminimal gauging). These deformations can be interpreted as perturbations, by marginal operators, of conformal coset models. When applied to the SL(2, R)xSU(2)/U(1)xU(1)) WZWN model, a large class of four-dimensional curved spacetime backgrounds are obtained. In particular, a naked singularity may form at a time when the volume of the universe is different from zero. (orig.)

Macroscopic Floquet topological crystalline steel and superconductor pump

Science.gov (United States)

Rossi, Anna M. E. B.; Bugase, Jonas; Fischer, Thomas M.

2017-08-01

The transport of a macroscopic steel sphere and a superconducting sphere on top of two-dimensional periodic magnetic patterns is studied experimentally and compared with the theory and with experiments on topological transport of magnetic colloids. Transport of the steel and superconducting sphere is achieved by moving an external permanent magnet on a closed loop around the two-dimensional crystal. The transport is topological, i.e., the spheres are transported by a primitive unit vector of the lattice when the external magnet loop winds around specific directions. We experimentally determine the set of directions the loops must enclose for nontrivial transport of the spheres into various directions. We show that the loops can be used to sort steel and superconducting spheres. We show that the topological transport is robust with respect to the scale of the system and therefore speculate on its down scalability to the molecular scale.

Finite-temperature symmetry restoration in the four-dimensional Φ4 model with four components

International Nuclear Information System (INIS)

Jansen, K.

1990-01-01

The finite-temperature symmetry restoration in the four-dimensional φ 4 theory with four components and with an infinite self-coupling is studied by means of Monte Carlo simulations on lattices with time extensions L t =4,5,6 and space extensions 12 3 -28 3 . The numerical calculations are done by means of the Wolff cluster algorithm which is very efficient for simulations near a phase transition. The numerical results are in good agreement with an improved one-loop expansion and with the 1/N-expansion, indicating that in the electroweak theory the symmetry restoration temperature T sr is about 350 GeV. (orig.)

Topological orders in rigid states

International Nuclear Information System (INIS)

Wen, X.G.

1990-01-01

The authors study a new kind of ordering topological order in rigid states (the states with no local gapless excitations). This paper concentrates on characterization of the different topological orders. As an example the authors discuss in detail chiral spin states of 2+1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. The authors show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. The authors also discuss the symmetry properties of the degenerate ground states of chiral spin states. The authors find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90 degrees rotation

Network topology mapper

Science.gov (United States)

Quist, Daniel A [Los Alamos, NM; Gavrilov, Eugene M [Los Alamos, NM; Fisk, Michael E [Jemez, NM

2008-01-15

A method enables the topology of an acyclic fully propagated network to be discovered. A list of switches that comprise the network is formed and the MAC address cache for each one of the switches is determined. For each pair of switches, from the MAC address caches the remaining switches that see the pair of switches are located. For each pair of switches the remaining switches are determined that see one of the pair of switches on a first port and the second one of the pair of switches on a second port. A list of insiders is formed for every pair of switches. It is determined whether the insider for each pair of switches is a graph edge and adjacent ones of the graph edges are determined. A symmetric adjacency matrix is formed from the graph edges to represent the topology of the data link network.

Electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES)

Energy Technology Data Exchange (ETDEWEB)

Wu, Yun [Iowa State Univ., Ames, IA (United States)

2016-12-17

The discovery of quantum Hall e ect has motivated the use of topology instead of broken symmetry to classify the states of matter. Quantum spin Hall e ect has been proposed to have a separation of spin currents as an analogue of the charge currents separation in quantum Hall e ect, leading us to the era of topological insulators. Three-dimensional analogue of the Dirac state in graphene has brought us the three-dimensional Dirac states. Materials with three-dimensional Dirac states could potentially be the parent compounds for Weyl semimetals and topological insulators when time-reversal or space inversion symmetry is broken. In addition to the single Dirac point linking the two dispersion cones in the Dirac/Weyl semimetals, Dirac points can form a line in the momentum space, resulting in a topological node line semimetal. These fascinating novel topological quantum materials could provide us platforms for studying the relativistic physics in condensed matter systems and potentially lead to design of new electronic devices that run faster and consume less power than traditional, silicon based transistors. In this thesis, we present the electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES).

Stable de Sitter vacua in four-dimensional supergravity originating from five dimensions

International Nuclear Information System (INIS)

Oegetbil, O.

2008-01-01

The five-dimensional stable de Sitter ground states in N=2 supergravity obtained by gauging SO(1,1) symmetry of the real symmetric scalar manifold (in particular, a generic Jordan family manifold of the vector multiplets) simultaneously with a subgroup R s of the R-symmetry group descend to four-dimensional de Sitter ground states under certain conditions. First, the holomorphic section in four dimensions has to be chosen carefully by using the symplectic freedom in four dimensions; second, a group contraction is necessary to bring the potential into a desired form. Under these conditions, stable de Sitter vacua can be obtained in dimensionally reduced theories (from 5D to 4D) if the semidirect product of SO(1,1) with R (1,1) together with a simultaneous R s is gauged. We review the stable de Sitter vacua in four dimensions found in earlier literature for N=2 Yang-Mills Einstein supergravity with the SO(2,1)xR s gauge group in a symplectic basis that comes naturally after dimensional reduction. Although this particular gauge group does not descend directly from five dimensions, we show that its contraction does. Hence, two different theories overlap in certain limits. Examples of stable de Sitter vacua are given for the cases: (i) R s =U(1) R , (ii) R s =SU(2) R , and (iii) N=2 Yang-Mills/Einstein supergravity theory coupled to a universal hypermultiplet. We conclude with a discussion regarding the extension of our results to supergravity theories with more general homogeneous scalar manifolds.

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...

Strain effects in topological insulators: Topological order and the emergence of switchable topological interface states in Sb2Te3/Bi2Te3 heterojunctions

Science.gov (United States)

Aramberri, H.; Muñoz, M. C.

2017-05-01

We investigate the effects of strain on the topological order of the Bi2Se3 family of topological insulators by ab initio first-principles methods. Strain can induce a topological phase transition and we present the phase diagram for the 3D topological insulators, Bi2Te3 , Sb2Te3 , Bi2Se3 , and Sb2Se3 , under combined uniaxial and biaxial strain. Their phase diagram is universal and shows metallic and insulating phases, both topologically trivial and nontrivial. In particular, uniaxial tension can drive the four compounds into a topologically trivial insulating phase. We propose a Sb2Te3/Bi2Te3 heterojunction in which a strain-induced topological interface state arises in the common gap of this normal insulator-topological insulator heterojunction. Unexpectedly, the interface state is confined in the topologically trivial subsystem and is physically protected from ambient impurities. It can be switched on or off by means of uniaxial strain and therefore Sb2Te3 /Bi2Te3 heterojunctions provide a topological system which hosts tunable robust helical interface states with promising spintronic applications.

Topology vs. Anderson localization: non-perturbative solutions in one dimension

OpenAIRE

Altland, Alexander; Bagrets, Dmitry; Kamenev, Alex

2014-01-01

We present an analytic theory of quantum criticality in quasi one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters $(g,\\chi)$ representing localization and topological properties, respectively. Certain critical values of $\\chi$ (half-integer for $\\Bbb{Z}$ classes, or zero for $\\Bbb{Z}_2$ classes) define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated t...

Topology Optimization of Nanophotonic Devices

DEFF Research Database (Denmark)

Yang, Lirong

This thesis explores the various aspects of utilizing topology optimization in designing nanophotonic devices. Either frequency-domain or time-domain methods is used in combination with the optimization algorithms, depending on various aims of the designing problems. The frequency-domain methods...... lengthscale and flexible pulse delay are addressed to demonstrate time-domain based topology optimization’s potential in designing complicated photonic structures with specifications on the time characteristics of pulses....

Supergravity duals of supersymmetric four dimensional gauge theories

Energy Technology Data Exchange (ETDEWEB)

Bigazzi, F [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Cotrone, A L [Centre de Physique Theorique, Ecole Polytechnique, Palaiseau Cedex (France); [INFN, Rome (Italy); Petrini, M [Centre de Physique Theorique, Ecole Polytechnique, Palaiseau (France); Zaffaroni, A [Universita di Milano-Bicocca and INFN, Milan (Italy)

2002-03-01

This article contains an overview of some recent attempts of understanding supergravity and string duals of four dimensional gauge theories using the AdS/CFT correspondence. We discuss the general philosophy underlying the various ways to realize Super Yang-Mills theories in terms of systems of branes. We then review some of the existing duals for N=2 and N=1 theories. We also discuss differences and similarities with realistic theories. (author)

Higher (odd dimensional quantum Hall effect and extended dimensional hierarchy

Directory of Open Access Journals (Sweden)

Kazuki Hasebe

2017-07-01

Full Text Available We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1 monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.

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

Geometry and topology of wild translation surfaces

OpenAIRE

Randecker, Anja

2016-01-01

A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.

Supersymmetric black holes with lens-space topology.

Science.gov (United States)

Kunduri, Hari K; Lucietti, James

2014-11-21

We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional supergravity. It is regular on and outside an event horizon of lens-space topology L(2,1). It is the first example of an asymptotically flat black hole with lens-space topology. The solution is characterized by a charge, two angular momenta, and a magnetic flux through a noncontractible disk region ending on the horizon, with one constraint relating these.

Trivial topological phase of CaAgP and the topological nodal-line transition in CaAg (P1 -xA sx)

Science.gov (United States)

Xu, N.; Qian, Y. T.; Wu, Q. S.; Autès, G.; Matt, C. E.; Lv, B. Q.; Yao, M. Y.; Strocov, V. N.; Pomjakushina, E.; Conder, K.; Plumb, N. C.; Radovic, M.; Yazyev, O. V.; Qian, T.; Ding, H.; Mesot, J.; Shi, M.

2018-04-01

By performing angle-resolved photoemission spectroscopy and first-principles calculations, we address the topological phase of CaAgP and investigate the topological phase transition in CaAg (P1 -xA sx) . We reveal that in CaAgP, the bulk band gap and surface states with a large bandwidth are topologically trivial, in agreement with hybrid density functional theory calculations. The calculations also indicate that application of "negative" hydrostatic pressure can transform trivial semiconducting CaAgP into an ideal topological nodal-line semimetal phase. The topological transition can be realized by partial isovalent P/As substitution at x =0.38 .

A computational study of the topology of vortex breakdown

Science.gov (United States)

Spall, Robert E.; Gatski, Thomas B.

1991-01-01

A fully three-dimensional numerical simulation of vortex breakdown using the unsteady, incompressible Navier-Stokes equations has been performed. Solutions to four distinct types of breakdown are identified and compared with experimental results. The computed solutions include weak helical, double helix, spiral, and bubble-type breakdowns. The topological structure of the various breakdowns as well as their interrelationship are studied. The data reveal that the asymmetric modes of breakdown may be subject to additional breakdowns as the vortex core evolves in the streamwise direction. The solutions also show that the freestream axial velocity distribution has a significant effect on the position and type of vortex breakdown.

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...

Nematic order on the surface of a three-dimensional topological insulator

Science.gov (United States)

Lundgren, Rex; Yerzhakov, Hennadii; Maciejko, Joseph

2017-12-01

We study the spontaneous breaking of rotational symmetry in the helical surface state of three-dimensional topological insulators due to strong electron-electron interactions, focusing on time-reversal invariant nematic order. Owing to the strongly spin-orbit coupled nature of the surface state, the nematic order parameter is linear in the electron momentum and necessarily involves the electron spin, in contrast with spin-degenerate nematic Fermi liquids. For a chemical potential at the Dirac point (zero doping), we find a first-order phase transition at zero temperature between isotropic and nematic Dirac semimetals. This extends to a thermal phase transition that changes from first to second order at a finite-temperature tricritical point. At finite doping, we find a transition between isotropic and nematic helical Fermi liquids that is second order even at zero temperature. Focusing on finite doping, we discuss various observable consequences of nematic order, such as anisotropies in transport and the spin susceptibility, the partial breakdown of spin-momentum locking, collective modes and induced spin fluctuations, and non-Fermi-liquid behavior at the quantum critical point and in the nematic phase.

Machine Learning Topological Invariants with Neural Networks

Science.gov (United States)

Zhang, Pengfei; Shen, Huitao; Zhai, Hui

2018-02-01

In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.

World-volume effective theory for higher-dimensional black holes.

Science.gov (United States)

Emparan, Roberto; Harmark, Troels; Niarchos, Vasilis; Obers, Niels A

2009-05-15

We argue that the main feature behind novel properties of higher-dimensional black holes, compared to four-dimensional ones, is that their horizons can have two characteristic lengths of very different size. We develop a long-distance world-volume effective theory that captures the black hole dynamics at scales much larger than the short scale. In this limit the black hole is regarded as a blackfold: a black brane (possibly boosted locally) whose world volume spans a curved submanifold of the spacetime. This approach reveals black objects with novel horizon geometries and topologies more complex than the black ring, but more generally it provides a new organizing framework for the dynamics of higher-dimensional black holes.

Emergence of the scale-invariant proportion in a flock from the metric-topological interaction.

Science.gov (United States)

Niizato, Takayuki; Murakami, Hisashi; Gunji, Yukio-Pegio

2014-05-01

Recently, it has become possible to more precisely analyze flocking behavior. Such research has prompted a reconsideration of the notion of neighborhoods in the theoretical model. Flocking based on topological distance is one such result. In a topological flocking model, a bird does not interact with its neighbors on the basis of a fixed-size neighborhood (i.e., on the basis of metric distance), but instead interacts with its nearest seven neighbors. Cavagna et al., moreover, found a new phenomenon in flocks that can be explained by neither metric distance nor topological distance: they found that correlated domains in a flock were larger than the metric and topological distance and that these domains were proportional to the total flock size. However, the role of scale-free correlation is still unclear. In a previous study, we constructed a metric-topological interaction model on three-dimensional spaces and showed that this model exhibited scale-free correlation. In this study, we found that scale-free correlation in a two-dimensional flock was more robust than in a three-dimensional flock for the threshold parameter. Furthermore, we also found a qualitative difference in behavior from using the fluctuation coherence, which we observed on three-dimensional flocking behavior. Our study suggests that two-dimensional flocks try to maintain a balance between the flock size and flock mobility by breaking into several smaller flocks. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Topology optimization of vibration and wave propagation problems

DEFF Research Database (Denmark)

Jensen, Jakob Søndergaard

2007-01-01

The method of topology optimization is a versatile method to determine optimal material layouts in mechanical structures. The method relies on, in principle, unlimited design freedom that can be used to design materials, structures and devices with significantly improved performance and sometimes...... novel functionality. This paper addresses basic issues in simulation and topology design of vibration and wave propagation problems. Steady-state and transient wave propagation problems are addressed and application examples for both cases are presented....

A New Method of Chinese Address Extraction Based on Address Tree Model

Directory of Open Access Journals (Sweden)

KANG Mengjun

2015-01-01

Full Text Available Address is a spatial location encoding method of individual geographical area. In China, address planning is relatively backward due to the rapid development of the city, resulting in the presence of large number of non-standard address. The space constrain relationship of standard address model is analyzed in this paper and a new method of standard address extraction based on the tree model is proposed, which regards topological relationship as consistent criteria of space constraints. With this method, standard address can be extracted and errors can be excluded from non-standard address. Results indicate that higher math rate can be obtained with this method.

The role of topology in materials

CERN Document Server

Saxena, Avadh

2018-01-01

This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foa...

Electrical and proximity-magnetic effects induced quantum Goos–Hänchen shift on the surface of topological insulator

Energy Technology Data Exchange (ETDEWEB)

Kuai, Jian [School of Physics and Electronics, Yancheng Teachers College, Yancheng, 224002 Jiangsu (China); Da, H.X., E-mail: haixia8779@163.com [Electrical and Computer Engineering Department, National University of Singapore, 4 Engineering Drive 3, 117576 (Singapore)

2014-03-15

We use scattering matrix method to theoretically demonstrate that the quantum Goos–Hänchen shift of the surface on three-dimensional topological insulator coated by ferromagnetic strips is sensitive to the magnitude of ferromagnetic magnetization. The dependence of quantum Goos–Hänchen shift on magnetization and gate bias is investigated by performing station phase approach. It is found that quantum Goos–Hänchen shift is positive and large under the magnetic barrier but may be positive as well as negative values under the gate bias. Furthermore, the position of quantum Goos–Hänchen peak can also be modulated by the combination of gate bias and proximity magnetic effects. Our results indicate that topological insulators are another candidates to support quantum Goos–Hänchen shift. - Highlights: • Quantum Goos–Hänchen shift of the surface on three-dimensional topological insulators is first investigated. • The magnetization affects quantum Goos–Hänchen shift of the surface on three-dimensional topological insulators. • Quantum Goos–Hänchen shift of the surface on three-dimensional topological insulators can be manipulated by the gate voltages.

Topological identification of the first uninodal 8-connected lsz MOF built from 2,2'-difluorobiphenyl-4,4'-dicarboxylate pillars and cadmium(II)-triazolate layers.

Science.gov (United States)

Zhang, Yuchi; Wu, Yuanhua; He, Xin; Ma, Junhan; Shen, Xuan; Zhu, Dunru

2018-03-01

Using polynuclear metal clusters as nodes, many high-symmetry high-connectivity nets, like 8-connnected bcu and 12-connected fcu, have been attained in metal-organic frameworks (MOFs). However, construction of low-symmetry high-connected MOFs with a novel topology still remains a big challenge. For example, a uninodal 8-connected lsz network, observed in inorganic ZrSiO 4 , has not been topologically identified in MOFs. Using 2,2'-difluorobiphenyl-4,4'-dicarboxylic acid (H 2 L) as a new linker and 1,2,4-triazole (Htrz) as a coligand, a novel three-dimensional Cd II -MOF, namely poly[tetrakis(μ 4 -2,2'-difluorobiphenyl-4,4'-dicarboxylato-κ 5 O 1 ,O 1' :O 1' :O 4 :O 4' )tetrakis(N,N-dimethylformamide-κO)tetrakis(μ 3 -1,2,4-triazolato-κ 3 N 1 :N 2 :N 4 )hexacadmium(II)], [Cd 6 (C 14 H 6 F 2 O 4 ) 4 (C 2 H 2 N 3 ) 4 (C 3 H 7 NO) 4 ] n , (I), has been prepared. Single-crystal structure analysis indicates that six different Cd II ions co-exist in (I) and each Cd II ion displays a distorted [CdO 4 N 2 ] octahedral geometry with four equatorial O atoms and two axial N atoms. Three Cd II ions are connected by four carboxylate groups and four trz - ligands to form a linear trinuclear [Cd 3 (COO) 4 (trz) 4 ] cluster, as do the other three Cd II ions. Two Cd 3 clusters are linked by trz - ligands in a μ 1,2,4 -bridging mode to produce a two-dimensional Cd II -triazolate layer with (6,3) topology in the ab plane. These two-dimensional layers are further pillared by the L 2- ligands along the c axis to generate a complicated three-dimensional framework. Topologically, regarding the Cd 3 cluster as an 8-connected node, the whole architecture of (I) is a uninodal 8-connected lsz framework with the Schläfli symbol (4 22 ·6 6 ). Complex (I) was further characterized by elemental analysis, IR spectroscopy, powder X-ray diffraction, thermogravimetric analysis and a photoluminescence study. MOF (I) has a high thermal and water stability.

Topological Oxide Insulator in Cubic Perovskite Structure

Science.gov (United States)

Jin, Hosub; Rhim, Sonny H.; Im, Jino; Freeman, Arthur J.

2013-01-01

The emergence of topologically protected conducting states with the chiral spin texture is the most prominent feature at the surface of topological insulators. On the application side, large band gap and high resistivity to distinguish surface from bulk degrees of freedom should be guaranteed for the full usage of the surface states. Here, we suggest that the oxide cubic perovskite YBiO3, more than just an oxide, defines itself as a new three-dimensional topological insulator exhibiting both a large bulk band gap and a high resistivity. Based on first-principles calculations varying the spin-orbit coupling strength, the non-trivial band topology of YBiO3 is investigated, where the spin-orbit coupling of the Bi 6p orbital plays a crucial role. Taking the exquisite synthesis techniques in oxide electronics into account, YBiO3 can also be used to provide various interface configurations hosting exotic topological phenomena combined with other quantum phases. PMID:23575973

Weak antilocalization in a three-dimensional topological insulator based on a high-mobility HgTe film

Science.gov (United States)

Savchenko, M. L.; Kozlov, D. A.; Kvon, Z. D.; Mikhailov, N. N.; Dvoretsky, S. A.

2016-09-01

The anomalous magnetoresistance (AMR) caused by the weak antilocalization effects in a three-dimensional topological insulator based on a strained mercury telluride film is experimentally studied. It is demonstrated that the obtained results are in a good agreement with the universal theory of Zduniak, Dyakonov, and Knap. It is found that the AMR in the bulk band gap is far below that expected for the system of Dirac fermions. Such a discrepancy can assumingly be related to a nonzero effective mass of Dirac fermions. The filling of energy bands in the bulk is accompanied by a pronounced increase in the AMR. This is a signature of the weak coupling between the surface and bulk charge carriers.

Quantum transport in new two-dimensional heterostructures: Thin films of topological insulators, phosphorene

Science.gov (United States)

Majidi, Leyla; Zare, Moslem; Asgari, Reza

2018-06-01

The unusual features of the charge and spin transport characteristics are investigated in new two-dimensional heterostructures. Intraband specular Andreev reflection is realized in a topological insulator thin film normal/superconducting junction in the presence of a gate electric field. Perfect specular electron-hole conversion is shown for different excitation energy values in a wide experimentally available range of the electric field and also for all angles of incidence when the excitation energy has a particular value. It is further demonstrated that the transmission probabilities of the incoming electrons from different spin subbands to the monolayer phosphorene ferromagnetic/normal/ferromagnetic (F/N/F) hybrid structure have different behavior with the angle of incidence and perfect transmission occurs at defined angles of incidence to the proposed structure with different length of the N region, and different alignments of magnetization vectors. Moreover, the sign change of the spin-current density is demonstrated by tuning the chemical potential and exchange field of the F region.

Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow.

Science.gov (United States)

Ohkitani, Koji; Al Sulti, Fayeza

2010-06-01

A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

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

Quantum spin Hall effect in IV-VI topological crystalline insulators

Science.gov (United States)

Safaei, S.; Galicka, M.; Kacman, P.; Buczko, R.

2015-06-01

We envision that the quantum spin Hall effect should be observed in (111)-oriented thin films of SnSe and SnTe topological crystalline insulators. Using a tight-binding approach supported by first-principles calculations of the band structures, we demonstrate that in these films the energy gaps in the two-dimensional band spectrum depend in an oscillatory fashion on the layer thickness. These results as well as the calculated topological invariant indexes and edge state spin polarizations show that for films ˜20-40 monolayers thick a two-dimensional topological insulator phase appears. In this range of thicknesses in both SnSe and SnTe, (111)-oriented films edge states with Dirac cones with opposite spin polarization in their two branches are obtained. While in the SnTe layers a single Dirac cone appears at the projection of the {\\boldsymbol{}}\\bar{Γ } point of the two-dimensional Brillouin zone, in the SnSe (111)-oriented layers three Dirac cones at {\\boldsymbol{}}\\bar{M} points projections are predicted.

Registration-based Reconstruction of Four-dimensional Cone Beam Computed Tomography

DEFF Research Database (Denmark)

Christoffersen, Christian; Hansen, David Christoffer; Poulsen, Per Rugaard

2013-01-01

We present a new method for reconstruction of four-dimensional (4D) cone beam computed tomography from an undersampled set of X-ray projections. The novelty of the proposed method lies in utilizing optical flow based registration to facilitate that each temporal phase is reconstructed from the full...

Topological photonic crystals with zero Berry curvature

Science.gov (United States)

Liu, Feng; Deng, Hai-Yao; Wakabayashi, Katsunori

2018-02-01

Topological photonic crystals are designed based on the concept of Zak's phase rather than the topological invariants such as the Chern number and spin Chern number, which rely on the existence of a nonvanishing Berry curvature. Our photonic crystals (PCs) are made of pure dielectrics and sit on a square lattice obeying the C4 v point-group symmetry. Two varieties of PCs are considered: one closely resembles the electronic two-dimensional Su-Schrieffer-Heeger model, and the other continues as an extension of this analogy. In both cases, the topological transitions are induced by adjusting the lattice constants. Topological edge modes (TEMs) are shown to exist within the nontrivial photonic band gaps on the termination of those PCs. The high efficiency of these TEMs transferring electromagnetic energy against several types of disorders has been demonstrated using the finite-element method.

Quantum anomalous Hall effect and topological phase transition in two-dimensional antiferromagnetic Chern insulator NiOsCl6

Science.gov (United States)

Yang, Wei-Wei; Li, Lei; Zhao, Jing-Sheng; Liu, Xiao-Xiong; Deng, Jian-Bo; Tao, Xiao-Ma; Hu, Xian-Ru

2018-05-01

By doing calculations based on density functional theory, we predict that the two-dimensional anti-ferromagnetic (AFM) NiOsCl6 as a Chern insulator can realize the quantum anomalous Hall (QAH) effect. We investigate the magnetocrystalline anisotropy energies in different magnetic configurations and the Néel AFM configuration is proved to be ground state. When considering spin–orbit coupling (SOC), this layered material with spins perpendicular to the plane shows properties as a Chern insulator characterized by an inversion band structure and a nonzero Chern number. The nontrivial band gap is 37 meV and the Chern number C  =  ‑1, which are induced by a strong SOC and AFM order. With strong SOC, the NiOsCl6 system performs a continuous topological phase transition from the Chern insulator to the trivial insulator upon the increasing Coulomb repulsion U. The critical U c is indicated as 0.23 eV, at which the system is in a metallic phase with . Upon increasing U, the E g reduces linearly with C  =  ‑1 for 0    U c . At last we analysis the QAH properties and this continuous topological phase transition theoretically in a two-band model. This AFM Chern insulator NiOsCl6 proposes not only a promising way to realize the QAH effect, but also a new material to study the continuous topological phase transition.

Magneto-photoconductivity of three dimensional topological insulator bismuth telluride

Science.gov (United States)

Cao, Bingchen; Eginligil, Mustafa; Yu, Ting

2018-03-01

Magnetic field dependence of the photocurrent in a 3D topological insulator is studied. Among the 3D topological insulators bismuth telluride has unique hexagonal warping and spin texture which has been studied by photoemission, scanning tunnelling microscopy and transport. Here, we report on low temperature magneto-photoconductivity, up to 7 T, of two metallic bismuth telluride topological insulator samples with 68 and 110 nm thicknesses excited by 2.33 eV photon energy along the magnetic field perpendicular to the sample plane. At 4 K, both samples exhibit negative magneto-photoconductance below 4 T, which is as a result of weak-antilocalization of Dirac fermions similar to the previous observations in electrical transport. However the thinner sample shows positive magneto-photoconductance above 4 T. This can be attributed to the coupling of surface states. On the other hand, the thicker sample shows no positive magneto-photoconductance up to 7 T since there is only one surface state at play. By fitting the magneto-photoconductivity data of the thicker sample to the localization formula, we obtain weak antilocalization behaviour at 4, 10, and 20 K, as expected; however, weak localization behaviour at 30 K, which is a sign of surface states masked by bulk states. Also, from the temperature dependence of phase coherence length bulk carrier-carrier interaction is identified separately from the surface states. Therefore, it is possible to distinguish surface states by magneto-photoconductivity at low temperature, even in metallic samples.

Signatures of topological superconductivity

Energy Technology Data Exchange (ETDEWEB)

Peng, Yang

2017-07-19

The prediction and experimental discovery of topological insulators brought the importance of topology in condensed matter physics into the limelight. Topology hence acts as a new dimension along which more and more new states of matter start to emerge. One of these topological states of matter, namely topological superconductors, comes into the focus because of their gapless excitations. These gapless excitations, especially in one dimensional topological superconductors, are Majorana zero modes localized at the ends of the superconductor and exhibit exotic nonabelian statistics, which can be potentially applied to fault-tolerant quantum computation. Given their highly interesting physical properties and potential applications to quantum computation, both theorists and experimentalists spend great efforts to realize topological supercondoctors and to detect Majoranas. In two projects within this thesis, we investigate the properties of Majorana zero modes in realistic materials which are absent in simple theoretical models. We find that the superconducting proximity effect, an essential ingredient in all existing platforms for topological superconductors, plays a significant role in determining the localization property of the Majoranas. Strong proximity coupling between the normal system and the superconducting substrate can lead to strongly localized Majoranas, which can explain the observation in a recent experiment. Motivated by experiments in Molenkamp's group, we also look at realistic quantum spin Hall Josephson junctions, in which charge puddles acting as magnetic impurities are coupled to the helical edge states. We find that with this setup, the junction generically realizes an exotic 8π periodic Josephson effect, which is absent in a pristine Josephson junction. In another two projects, we propose more pronounced signatures of Majoranas that are accessible with current experimental techniques. The first one is a transport measurement, which uses

Topological Order in Silicon Photonics

Science.gov (United States)

2017-02-07

photonic edge states and quantum emitters [ S. Barik , H. Miyake, W. DeGottardi, E. Waks and M. Hafezi, New J. Phys., 18, 11301 (2016) ]. Entanglement... Barik , H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi “Two-Dimensionally Confined Topological Edge States in Photonic Crystals”, New J. Phys., 18

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

DEFF Research Database (Denmark)

Bauer, Dieter; Hansen, Kenneth Christian Klochmann

2018-01-01

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...

Topology Optimization of Sub-Wavelength Antennas

DEFF Research Database (Denmark)

Erentok, Aycan; Sigmund, Ole

2011-01-01

We propose a topology optimization strategy for the systematic design of a three-dimensional (3D), conductor-based sub-wavelength antenna. The post-processed finite-element (FE) models of the optimized structure are shown to be self-resonant, efficient and exhibit distorted omnidirectional...

Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

Directory of Open Access Journals (Sweden)

Hongling Ye

2015-01-01

Full Text Available The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM design variable fields. The composite exponential function (CEF is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

The theory of critical phenomena in two-dimensional systems

International Nuclear Information System (INIS)

Olvera de la C, M.

1981-01-01

An exposition of the theory of critical phenomena in two-dimensional physical systems is presented. The first six chapters deal with the mean field theory of critical phenomena, scale invariance of the thermodynamic functions, Kadanoff's spin block construction, Wilson's renormalization group treatment of critical phenomena in configuration space, and the two-dimensional Ising model on a triangular lattice. The second part of this work is made of four chapters devoted to the application of the ideas expounded in the first part to the discussion of critical phenomena in superfluid films, two-dimensional crystals and the two-dimensional XY model of magnetic systems. Chapters seven to ten are devoted to the following subjects: analysis of long range order in one, two, and three-dimensional physical systems. Topological defects in the XY model, in superfluid films and in two-dimensional crystals. The Thouless-Kosterlitz iterated mean field theory of the dipole gas. The renormalization group treatment of the XY model, superfluid films and two-dimensional crystal. (author)

Efficient Reanalysis Procedures in Structural Topology Optimization

DEFF Research Database (Denmark)

Amir, Oded

This thesis examines efficient solution procedures for the structural analysis problem within topology optimization. The research is motivated by the observation that when the nested approach to structural optimization is applied, most of the computational effort is invested in repeated solutions...... on approximate reanalysis. For cases where memory limitations require the utilization of iterative equation solvers, we suggest efficient procedures based on alternative termination criteria for such solvers. These approaches are tested on two- and three-dimensional topology optimization problems including...

Four-branch Star Hybrid Power Filter for Three-phase Four-wire Systems

DEFF Research Database (Denmark)

Blaabjerg, Frede; Teodorescu, Remus; Rodriguez, Pedro

2008-01-01

and derives fundamental concepts about the control of the resulting hybrid power filter. From this analysis, a specifc implementation of a three-phase four-wire hybrid power filter is presented as an illustrative application of the filtering topology. An extensive evaluation using simulation and experimental......This paper presents a new concept for filtering current harmonics in three-phase four-wire networks. The four-branch star (FBS) filtering topology presented in this work is characterized by a particular layout consisting of single-phase inductances and capacitors. Via this layout, a power filter...

Thermoelectric properties of 3D topological insulator: Direct observation of topological surface and its gap opened states

Science.gov (United States)

Matsushita, Stephane Yu; Huynh, Khuong Kim; Yoshino, Harukazu; Tu, Ngoc Han; Tanabe, Yoichi; Tanigaki, Katsumi

2017-10-01

We report thermoelectric (TE) properties of topological surface Dirac states (TSDS) in three-dimensional topological insulators (3D-TIs) purely isolated from the bulk by employing single-crystal B i2 -xS bxT e3 -yS ey films epitaxially grown in the ultrathin limit. Two intrinsic nontrivial topological surface states, a metallic TSDS (m-TSDS) and a gap-opened semiconducting topological state (g-TSDS), are successfully observed by electrical transport, and important TE parameters [electrical conductivity (σ), thermal conductivity (κ), and thermopower (S )] are accurately determined. Pure m-TSDS gives S =-44 μ V K-1 , which is an order of magnitude higher than those of the conventional metals and the value is enhanced to -212 μ V K-1 for g-TSDS. It is clearly shown that the semiclassical Boltzmann transport equation (SBTE) in the framework of constant relaxation time (τ) most frequently used for conventional analysis cannot be valid in 3D-TIs and strong energy dependent relaxation time τ(E ) beyond the Born approximation is essential for making intrinsic interpretations. Although σ is protected on the m-TSDS, κ is greatly influenced by the disorder on the topological surface, giving a dissimilar effect between topologically protected electronic conduction and phonon transport.

Moyal Deformations of Gravity via SU ( N ) Gauge Theories, Branes and Topological Chern-Simons Matrix Models

CERN Document Server

Castro \\C

2003-01-01

Moyal noncommutative star-product deformations of higher dimensional gravitational Einstein-Hilbert actions via lower-dimensional SU(\\infty) gauge theories are constructed explicitly based on the holographic reduction principle. New reparametrization invariant p-brane actions and their Moyal star product deformations follows. It is conjectured that topological Chern-Simons brane actions associated with higher-dimensional "knots" have a one-to-one correspondence with topological Chern-Simons Matrix models in the large N limit. The corresponding large N limit of Topological BF Matrix models leads to Kalb-Ramond couplings of antisymmetric-tensor fields to p-branes. The former Chern-Simons branes display higher-spin W_\\infty symmetries which are very relevant in the study of W_\\infty Gravity, the Quantum Hall effect and its higher-dimensional generalizations. We conclude by arguing why this interplay between condensed matter models, higher-dimensional extensions of the Quantum Hall effect, Chern-Simons Matrix mod...

Electrically controlled crossing of energy levels in quantum dots in two-dimensional topological insulators

Energy Technology Data Exchange (ETDEWEB)

Sukhanov, Aleksei A.

2017-05-15

We study the energy spectra of bound states in quantum dots (QDs) formed by an electrostatic potential in two-dimensional topological insulator (TI) and their transformation with changes in QD depth and radius. It is found that, unlike a trivial insulator, the energy difference between the levels of the ground state and first excited state can decrease with decreasing the radius and increasing the depth of the QD so that these levels intersect under some critical condition. The crossing of the levels results in unusual features of optical properties caused by intraceneter electron transitions. In particular, it leads to significant changes of light absorption due to electron transitions between such levels and to the transient electroluminescence induced by electrical tuning of QD and TI parameters. In the case of magnetic TIs, the polarization direction of the absorbed or emitted circularly polarized light is changed due to the level crossing.

Electrically controlled crossing of energy levels in quantum dots in two-dimensional topological insulators

Science.gov (United States)

Sukhanov, Aleksei A.

2017-05-01

We study the energy spectra of bound states in quantum dots (QDs) formed by an electrostatic potential in two-dimensional topological insulator (TI) and their transformation with changes in QD depth and radius. It is found that, unlike a trivial insulator, the energy difference between the levels of the ground state and first excited state can decrease with decreasing the radius and increasing the depth of the QD so that these levels intersect under some critical condition. The crossing of the levels results in unusual features of optical properties caused by intraceneter electron transitions. In particular, it leads to significant changes of light absorption due to electron transitions between such levels and to the transient electroluminescence induced by electrical tuning of QD and TI parameters. In the case of magnetic TIs, the polarization direction of the absorbed or emitted circularly polarized light is changed due to the level crossing.

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

Four-dimensional computed tomographic analysis of esophageal mobility during normal respiration

NARCIS (Netherlands)

Dieleman, Edith M. T.; Senan, Suresh; Vincent, Andrew; Lagerwaard, Frank J.; Slotman, Ben J.; van Sörnsen de Koste, John R.

2007-01-01

BACKGROUND: Chemo-radiotherapy for thoracic tumors can result in high-grade radiation esophagitis. Treatment planning to reduce esophageal irradiation requires organ motion to be accounted for. In this study, esophageal mobility was assessed using four-dimensional computed tomography (4DCT). METHODS

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).

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.

Irreversible Markov chains in spin models: Topological excitations

Science.gov (United States)

Lei, Ze; Krauth, Werner

2018-01-01

We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads to slow decay of vortex-antivortex correlations while spin waves decorrelate very quickly. Using a Fréchet description of the maximum vortex-antivortex distance, we quantify the contributions of topological excitations to the equilibrium correlations, and show that they vary from a dynamical critical exponent z∼ 2 at the critical temperature to z∼ 0 in the limit of zero temperature. We confirm the event-chain algorithm's fast relaxation (corresponding to z = 0) of spin waves in the harmonic approximation to the XY model. Mixing times (describing the approach towards equilibrium from the least favorable initial state) however remain much larger than equilibrium correlation times at low temperatures. We also describe the respective influence of topological monopole-antimonopole excitations and of spin waves on the event-chain dynamics in the three-dimensional Heisenberg model.

Hall conductance and topological invariant for open systems.

Science.gov (United States)

Shen, H Z; Wang, W; Yi, X X

2014-09-24

The Hall conductivity given by the Kubo formula is a linear response of quantum transverse transport to a weak electric field. It has been intensively studied for quantum systems without decoherence, but it is barely explored for systems subject to decoherence. In this paper, we develop a formulism to deal with this issue for topological insulators. The Hall conductance of a topological insulator coupled to an environment is derived, the derivation is based on a linear response theory developed for open systems in this paper. As an application, the Hall conductance of a two-band topological insulator and a two-dimensional lattice is presented and discussed.

Superconducting proximity effect in topological materials

Science.gov (United States)

Reeg, Christopher R.

In recent years, there has been a renewed interest in the proximity effect due to its role in the realization of topological superconductivity. In this dissertation, we discuss several results that have been obtained in the field of proximity-induced superconductivity and relate the results to the search for Majorana fermions. First, we show that repulsive electron-electron interactions can induce a non-Majorana zero-energy bound state at the interface between a conventional superconductor and a normal metal. We show that this state is very sensitive to disorder, owing to its lack of topological protection. Second, we show that Rashba spin-orbit coupling, which is one of the key ingredients in engineering a topological superconductor, induces triplet pairing in the proximity effect. When the spin-orbit coupling is strong (i.e., when the characteristic energy scale for spin-orbit coupling is comparable to the Fermi energy), the induced singlet and triplet pairing amplitudes can be comparable in magnitude. Finally, we discuss how the size of the proximity-induced gap, which appears in a low-dimensional material coupled to a superconductor, evolves as the thickness of the (quasi-)low-dimensional material is increased. We show that the induced gap can be comparable to the bulk energy gap of the underlying superconductor in materials that are much thicker than the Fermi wavelength, even in the presence of an interfacial barrier and strong Fermi surface mismatch. This result has important experimental consequences for topological superconductivity, as a sizable gap is required to isolate and detect the Majorana modes.

Electrically tunable robust edge states in graphene-based topological photonic crystal slabs

Science.gov (United States)

Song, Zidong; Liu, HongJun; Huang, Nan; Wang, ZhaoLu

2018-03-01

Topological photonic crystals are optical structures supporting topologically protected unidirectional edge states that exhibit robustness against defects. Here, we propose a graphene-based all-dielectric photonic crystal slab structure that supports two-dimensionally confined topological edge states. These topological edge states can be confined in the out-of-plane direction by two parallel graphene sheets. In the structure, the excitation frequency range of topological edge states can be dynamically and continuously tuned by varying bias voltage across the two parallel graphene sheets. Utilizing this kind of architecture, we construct Z-shaped channels to realize topological edge transmission with diffrerent frequencies. The proposal provides a new degree of freedom to dynamically control topological edge states and potential applications for robust integrated photonic devices and optical communication systems.

Density character of subgroups of topological groups

OpenAIRE

Leiderman, Arkady; Morris, Sidney A.; Tkachenko, Mikhail G.

2015-01-01

A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie groups which consists of projective limits of finite-dimensional Lie groups and proved that it contains all compact groups, locally compact abelian groups and connected locally compact groups and is closed under products and closed subgroups. A topological group...

Spherical and planar three-dimensional anti-de Sitter black holes

International Nuclear Information System (INIS)

Zanchin, Vilson T; Miranda, Alex S

2004-01-01

The technique of dimensional reduction was used in a recent paper (Zanchin V T, Kleber A and Lemos J P S 2002 Phys. Rev. D 66 064022) where a three-dimensional (3D) Einstein-Maxwell-dilaton theory was built from the usual four-dimensional (4D) Einstein-Maxwell-Hilbert action for general relativity. Starting from a class of 4D toroidal black holes in asymptotically anti-de Sitter (AdS) spacetimes several 3D black holes were obtained and studied in such a context. In the present work we choose a particular case of the 3D action which presents Maxwell field, dilaton field and an extra scalar field, besides gravity field and a negative cosmological constant, and obtain new 3D static black hole solutions whose horizons may have spherical or planar topology. We show that there is a 3D static spherically symmetric solution analogous to the 4D Reissner-Nordstroem-AdS black hole, and obtain other new 3D black holes with planar topology. From the static spherical solutions, new rotating 3D black holes are also obtained and analysed in some detail

Bosonisation of four dimensional real fermionic string models and asymmetric orbifolds

International Nuclear Information System (INIS)

Bailin, D.; Dunbar, D.C.; Love, A.

1990-01-01

Models of four dimensional strings based on internal world-sheet fermions are bosonised and the partition functions are compared with the partition functions of asymmetric Z 2 M orbifold models. Selection rules and couplings are also compared between the two formations. (orig.)

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

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...

Magnetic susceptibility in the edged topological disordered nanoscopic cylinder

International Nuclear Information System (INIS)

Faizabadi, Edris; Omidi, Mahboubeh

2011-01-01

The effects of edged topological disorder on magnetic susceptibility are investigated in a nanoscopic cylinder threaded by a magnetic flux. Persistent current versus even or odd number of electrons shows different signs in ordered and disordered cylinders and also in short or long ones. In addition, temperature-averaged susceptibility has only diamagnetic signs in strong regimes and it is associated with paramagnetic signs in ordered and weak disordered ones. Besides, in an edged topological disordered cylinder, the temperature-averaged susceptibility decreases by raising the temperature somewhat and then increasing initiates and finally at high temperature tends to zero as the ordered one. - Research highlights: → Magnetic susceptibility in one-dimensional topological disordered quantum ring. → Edged topological disorder effect on magnetic susceptibility in nanoscopic cylinder. → Edged topological disorder effect on temperature-averaged susceptibility in cylinder.

Topological phase transition of Dirac superconductors in the presence of pseudo-scalar pairings

Science.gov (United States)

Salehi, Morteza; Jafari, S. A.

2018-06-01

Motivated by recent developments in the field of topological superconductors, we show that there is a topological phase transition (TPT) for three dimensional Dirac superconductors (3DDS) in the presence of pseudo-scalar superconducting order parameter which leads to the appearance of a two dimensional Majorana sea (2DMS) on its surface. The perfect Andreev-Klein transmission, resonant peak with robust character in the differential conductance and 4π periodic Josephson current are experimental signatures of 2DMS.

Stochastic quantization and topological theories

International Nuclear Information System (INIS)

Fainberg, V.Y.; Subbotin, A.V.; Kuznetsov, A.N.

1992-01-01

In the last two years topological quantum field theories (TQFT) have attached much attention. This paper reports that from the very beginning it was realized that due to a peculiar BRST-like symmetry these models admitted so-called Nicolai mapping: the Nicolai variables, in terms of which actions of the theories become gaussian, are nothing but (anti-) selfduality conditions or their generalizations. This fact became a starting point in the quest of possible stochastic interpretation to topological field theories. The reasons behind were quite simple and included, in particular, the well-known relations between stochastic processes and supersymmetry. The main goal would have been achieved, if it were possible to construct stochastic processes governed by Langevin or Fokker-Planck equations in a real Euclidean time leading to TQFT's path integrals (equivalently: to reformulate TQFTs as non-equilibrium phase dynamics of stochastic processes). Further on, if it would appear that these processes correspond to the stochastic quantization of theories of some definite kind, one could expect (d + 1)-dimensional TQFTs to share some common properties with d-dimensional ones

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...

Observation of symmetry-protected topological band with ultracold fermions

Science.gov (United States)

Song, Bo; Zhang, Long; He, Chengdong; Poon, Ting Fung Jeffrey; Hajiyev, Elnur; Zhang, Shanchao; Liu, Xiong-Jun; Jo, Gyu-Boong

2018-01-01

Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal invariant topological insulator, a symmetry-protected topological (SPT) phase in the symplectic class of the Altland-Zirnbauer classification. We report the observation for ultracold atoms of a noninteracting SPT band in a one-dimensional optical lattice and study quench dynamics between topologically distinct regimes. The observed SPT band can be protected by a magnetic group and a nonlocal chiral symmetry, with the band topology being measured via Bloch states at symmetric momenta. The topology also resides in far-from-equilibrium spin dynamics, which are predicted and observed in experiment to exhibit qualitatively distinct behaviors in quenching to trivial and nontrivial regimes, revealing two fundamental types of spin-relaxation dynamics related to bulk topology. This work opens the way to expanding the scope of SPT physics with ultracold atoms and studying nonequilibrium quantum dynamics in these exotic systems. PMID:29492457

Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2

KAUST Repository

Zhang, Qingyun

2015-02-11

Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the (M) over bar points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.

Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2

KAUST Repository

Zhang, Qingyun; Cheng, Yingchun; Schwingenschlö gl, Udo

2015-01-01

Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS2 and TlSbS2 under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS2 and TlSbS2 when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the (M) over bar points are anisotropic with large out-of-plane component. TlBiS2 shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.

Decision-making for supplying energy projects: A four-dimensional model

International Nuclear Information System (INIS)

Smith Stegen, Karen; Palovic, Martin

2014-01-01

Highlights: • Extant pipeline evaluation models offer insufficient supplier analysis tools. • We offer a four-dimensional decision-making tool to augment extant models. • Model employs four filters to help decision makers eliminate unsuitable suppliers. • Aids in prioritization of best courses of action for overcoming obstacles. • Case study of Nabucco pipeline shows Azerbaijan would have been best supply option. - Abstract: Importing states and regions employ myriad strategies to enhance energy security, from stockpiling to diversification to efficiency programs. As has occurred in recent years, importers can seek diversification by initiating pipeline and liquefied natural gas projects, meaning they may also have to select suppliers. However, most extant pipeline evaluation models erroneously assume suppliers are known and thus neglect supplier selection. We propose a decision-making tool to augment these older models: a systematic and replicable four-dimensional model to help policymakers and managers identify suitable suppliers and prioritize the best courses of action for overcoming obstacles. The first three dimensions—timeframe, supply availability and infrastructure constraints—filter out unsuitable suppliers. The fourth dimension then assesses the political, geopolitical and commercial stability of the remaining candidates. To demonstrate the model in practice, we assess the original Nabucco pipeline proposal, which was designed to transport gas from the Caspian and Middle East regions to Europe

Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

Science.gov (United States)

Yin, Chuanhao; Jiang, Hui; Li, Linhu; Lü, Rong; Chen, Shu

2018-05-01

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems are integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number ν of a non-Hermitian system is equal to half of the summation of two winding numbers ν1 and ν2 associated with two exceptional points, respectively. The winding numbers ν1 and ν2 represent the times of the real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers. We further find that the difference of ν1 and ν2 is related to the second winding number or energy vorticity. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number ν1 and ν2.

Quadratic stabilisability of multi-agent systems under switching topologies

Science.gov (United States)

Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long

2014-12-01

This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.

Cohomological rigidity of manifolds defined by 3-dimensional polytopes

Science.gov (United States)

Buchstaber, V. M.; Erokhovets, N. Yu.; Masuda, M.; Panov, T. E.; Park, S.

2017-04-01

A family of closed manifolds is said to be cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. Cohomological rigidity is established here for large families of 3-dimensional and 6-dimensional manifolds defined by 3-dimensional polytopes. The class \\mathscr{P} of 3-dimensional combinatorial simple polytopes P different from tetrahedra and without facets forming 3- and 4-belts is studied. This class includes mathematical fullerenes, that is, simple 3- polytopes with only 5-gonal and 6-gonal facets. By a theorem of Pogorelov, any polytope in \\mathscr{P} admits in Lobachevsky 3-space a right-angled realisation which is unique up to isometry. Our families of smooth manifolds are associated with polytopes in the class \\mathscr{P}. The first family consists of 3-dimensional small covers of polytopes in \\mathscr{P}, or equivalently, hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes in \\mathscr{P}. Our main result is that both families are cohomologically rigid, that is, two manifolds M and M' from either family are diffeomorphic if and only if their cohomology rings are isomorphic. It is also proved that if M and M' are diffeomorphic, then their corresponding polytopes P and P' are combinatorially equivalent. These results are intertwined with classical subjects in geometry and topology such as the combinatorics of 3-polytopes, the Four Colour Theorem, aspherical manifolds, a diffeomorphism classification of 6-manifolds, and invariance of Pontryagin classes. The proofs use techniques of toric topology. Bibliography: 69 titles.

Baryons and baryonic matter in four-fermion interaction models

International Nuclear Information System (INIS)

Urlichs, K.

2007-01-01

In this work we discuss baryons and baryonic matter in simple four-fermion interaction theories, the Gross-Neveu model and the Nambu-Jona-Lasinio model in 1+1 and 2+1 space-time dimensions. These models are designed as toy models for dynamical symmetry breaking in strong interaction physics. Pointlike interactions (''four-fermion'' interactions) between quarks replace the full gluon mediated interaction of quantum chromodynamics. We consider the limit of a large number of fermion flavors, where a mean field approach becomes exact. This method is formulated in the language of relativistic many particle theory and is equivalent to the Hartree-Fock approximation. In 1+1 dimensions, we generalize known results on the ground state to the case where chiral symmetry is broken explicitly by a bare mass term. For the Gross-Neveu model, we derive an exact self-consistent solution for the finite density ground state, consisting of a one-dimensional array of equally spaced potential wells, a baryon crystal. For the Nambu- Jona-Lasinio model we apply the derivative expansion technique to calculate the total energy in powers of derivatives of the mean field. In a picture akin to the Skyrme model of nuclear physics, the baryon emerges as a topological soliton. The solution for both the single baryon and dense baryonic matter is given in a systematic expansion in powers of the pion mass. The solution of the Hartree-Fock problem is more complicated in 2+1 dimensions. In the massless Gross-Neveu model we derive an exact self-consistent solution by extending the baryon crystal of the 1+1 dimensional model, maintaining translational invariance in one spatial direction. This one-dimensional configuration is energetically degenerate to the translationally invariant solution, a hint in favor of a possible translational symmetry breakdown by more general geometrical structures. In the Nambu-Jona-Lasinio model, topological soliton configurations induce a finite baryon number. In contrast

Baryons and baryonic matter in four-fermion interaction models

Energy Technology Data Exchange (ETDEWEB)

Urlichs, K.

2007-02-23

In this work we discuss baryons and baryonic matter in simple four-fermion interaction theories, the Gross-Neveu model and the Nambu-Jona-Lasinio model in 1+1 and 2+1 space-time dimensions. These models are designed as toy models for dynamical symmetry breaking in strong interaction physics. Pointlike interactions (''four-fermion'' interactions) between quarks replace the full gluon mediated interaction of quantum chromodynamics. We consider the limit of a large number of fermion flavors, where a mean field approach becomes exact. This method is formulated in the language of relativistic many particle theory and is equivalent to the Hartree-Fock approximation. In 1+1 dimensions, we generalize known results on the ground state to the case where chiral symmetry is broken explicitly by a bare mass term. For the Gross-Neveu model, we derive an exact self-consistent solution for the finite density ground state, consisting of a one-dimensional array of equally spaced potential wells, a baryon crystal. For the Nambu- Jona-Lasinio model we apply the derivative expansion technique to calculate the total energy in powers of derivatives of the mean field. In a picture akin to the Skyrme model of nuclear physics, the baryon emerges as a topological soliton. The solution for both the single baryon and dense baryonic matter is given in a systematic expansion in powers of the pion mass. The solution of the Hartree-Fock problem is more complicated in 2+1 dimensions. In the massless Gross-Neveu model we derive an exact self-consistent solution by extending the baryon crystal of the 1+1 dimensional model, maintaining translational invariance in one spatial direction. This one-dimensional configuration is energetically degenerate to the translationally invariant solution, a hint in favor of a possible translational symmetry breakdown by more general geometrical structures. In the Nambu-Jona-Lasinio model, topological soliton configurations induce a finite baryon

Dichromatic State Sum Models for Four-Manifolds from Pivotal Functors

Science.gov (United States)

Bärenz, Manuel; Barrett, John

2017-11-01

A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant. A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models. Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed.

Three-dimensional Majorana fermions in chiral superconductors.

Science.gov (United States)

Kozii, Vladyslav; Venderbos, Jörn W F; Fu, Liang

2016-12-01

Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs 4 Sb 12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.

Impact of network topology on self-organized criticality

Science.gov (United States)

Hoffmann, Heiko

2018-02-01

The general mechanisms behind self-organized criticality (SOC) are still unknown. Several microscopic and mean-field theory approaches have been suggested, but they do not explain the dependence of the exponents on the underlying network topology of the SOC system. Here, we first report the phenomena that in the Bak-Tang-Wiesenfeld (BTW) model, sites inside an avalanche area largely return to their original state after the passing of an avalanche, forming, effectively, critically arranged clusters of sites. Then, we hypothesize that SOC relies on the formation process of these clusters, and present a model of such formation. For low-dimensional networks, we show theoretically and in simulation that the exponent of the cluster-size distribution is proportional to the ratio of the fractal dimension of the cluster boundary and the dimensionality of the network. For the BTW model, in our simulations, the exponent of the avalanche-area distribution matched approximately our prediction based on this ratio for two-dimensional networks, but deviated for higher dimensions. We hypothesize a transition from cluster formation to the mean-field theory process with increasing dimensionality. This work sheds light onto the mechanisms behind SOC, particularly, the impact of the network topology.

Topology and graph theory applied to cortical anatomy may help explain working memory capacity for three or four simultaneous items.

Science.gov (United States)

Glassman, Robert B

2003-04-15

Cognitive experimentation suggests that at any single instant only three or four items ("chunks") are simultaneously prominent as a working memory (WM) trace, if we disregard the rehearsal component of WM. The reason for small WM capacity may concern combinatorial manageability. How might the neural representations of these few coactive chunks occupy a spatially distributed set of areas of the sheet-like cortex, while providing both order and flexibility to associate items in WM? Each attribute of each simultaneously active WM item must have broad access to the representational facilities of the cortical sheet, comprising tens of thousands of modular "cortical columns." The two hypothesized neural levels of WM during any moment of cognition comprise (a) "binding" together of many distributed attribute representations within each respective WM chunk, and (b) combinatorial play among three or four WM chunk-representations. Anatomical and functional evidence of cortical unity through its depth suggests that cortex may be viewed as essentially planar in its distribution of activations. Thus, a moment's WM is hypothesized here to reside in myriad activated cortical planar "patches," each subdivided into up to four amoeboid "subpatches." Two different lines of topological reasoning suggest orderly associations of such representations. (1) The four-color principle of map topology, and the related K(4) is planar theorem of graph theory, imply that if a small cortical area is dynamically subdivided into no more than four, discretely bounded planar subareas, then each such segment has ample free access to each of the others. (2) A hypothetical alternative to such associative adjacency of simultaneously active cortical representations of chunk-attributes is associative overlap, whereby, in dense cortical neuropil, activated subpatches behave like Venn diagrams of intersecting sets. As the number of Venn-like coactive subpatches within a patch increases, maintaining ad hoc

A topological multilayer model of the human body.

Science.gov (United States)

Barbeito, Antonio; Painho, Marco; Cabral, Pedro; O'Neill, João

2015-11-04

Geographical information systems deal with spatial databases in which topological models are described with alphanumeric information. Its graphical interfaces implement the multilayer concept and provide powerful interaction tools. In this study, we apply these concepts to the human body creating a representation that would allow an interactive, precise, and detailed anatomical study. A vector surface component of the human body is built using a three-dimensional (3-D) reconstruction methodology. This multilayer concept is implemented by associating raster components with the corresponding vector surfaces, which include neighbourhood topology enabling spatial analysis. A root mean square error of 0.18 mm validated the three-dimensional reconstruction technique of internal anatomical structures. The expansion of the identification and the development of a neighbourhood analysis function are the new tools provided in this model.

Using maximum topology matching to explore differences in species distribution models

Science.gov (United States)

Poco, Jorge; Doraiswamy, Harish; Talbert, Marian; Morisette, Jeffrey; Silva, Claudio

2015-01-01

Species distribution models (SDM) are used to help understand what drives the distribution of various plant and animal species. These models are typically high dimensional scalar functions, where the dimensions of the domain correspond to predictor variables of the model algorithm. Understanding and exploring the differences between models help ecologists understand areas where their data or understanding of the system is incomplete and will help guide further investigation in these regions. These differences can also indicate an important source of model to model uncertainty. However, it is cumbersome and often impractical to perform this analysis using existing tools, which allows for manual exploration of the models usually as 1-dimensional curves. In this paper, we propose a topology-based framework to help ecologists explore the differences in various SDMs directly in the high dimensional domain. In order to accomplish this, we introduce the concept of maximum topology matching that computes a locality-aware correspondence between similar extrema of two scalar functions. The matching is then used to compute the similarity between two functions. We also design a visualization interface that allows ecologists to explore SDMs using their topological features and to study the differences between pairs of models found using maximum topological matching. We demonstrate the utility of the proposed framework through several use cases using different data sets and report the feedback obtained from ecologists.

Quantum theory of string in the four-dimensional space-time

International Nuclear Information System (INIS)

Pron'ko, G.P.

1986-01-01

The Lorentz invariant quantum theory of string is constructed in four-dimensional space-time. Unlike the traditional approach whose result was breaking of Lorentz invariance, our method is based on the usage of other variables for description of string configurations. The method of an auxiliary spectral problem for periodic potentials is the main tool in construction of these new variables

The scalar curvature problem on the four dimensional half sphere

CERN Document Server

Ben-Ayed, M; El-Mehdi, K

2003-01-01

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature for some metric conformal to the standard one. Our proof involves the study of critical points at infinity of the associated variational problem.

Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission.

Science.gov (United States)

Djordjevic, Ivan; Batshon, Hussam G; Xu, Lei; Wang, Ting

2011-01-17

We propose a four-dimensional (4D) coded multiband-OFDM scheme suitable for beyond 1.4 Tb/s serial optical transport. The proposed scheme organizes the N-dimensional (ND) signal constellation points in the form of signal matrix; employs 2D-inverse FFT and 2D-FFT to perform modulation and demodulation, respectively; and exploits both orthogonal polarizations. This scheme can fully exploit advantages of OFDM to deal with chromatic dispersion, PMD and PDL effects; and multidimensional signal constellations to improve OSNR sensitivity of conventional optical OFDM. The improvement of 4D-OFDM over corresponding polarization-multiplexed QAM (with the same number of constellation points) ranges from 1.79 dB for 16 signal constellation point-four-dimensional-OFDM (16-4D-OFDM) up to 4.53 dB for 128-4D-OFDM.

Lower dimensional gravity

International Nuclear Information System (INIS)

Brown, J.D.

1988-01-01

This book addresses the subject of gravity theories in two and three spacetime dimensions. The prevailing philosophy is that lower dimensional models of gravity provide a useful arena for developing new ideas and insights, which are applicable to four dimensional gravity. The first chapter consists of a comprehensive introduction to both two and three dimensional gravity, including a discussion of their basic structures. In the second chapter, the asymptotic structure of three dimensional Einstein gravity with a negative cosmological constant is analyzed. The third chapter contains a treatment of the effects of matter sources in classical two dimensional gravity. The fourth chapter gives a complete analysis of particle pair creation by electric and gravitational fields in two dimensions, and the resulting effect on the cosmological constant

Once more about the topologically massive gauge theory

International Nuclear Information System (INIS)

Kogan, Ya.I.

1989-01-01

The general properties of the three-dimensional gauge theory with the topological mass is discussed namely the long-range interaction of the Aharonov-Bohm type. It is argued that Chern-Simons gauge theories must be considered as the infrared limit of the topologically massive theories. The analogy between the Landau problem of a charged particle in a magnetic field and quantization of this gauge theory is considered, as well as the quantization condition for the Abelian Chern-Simons term. 38 refs.; 5 figs

Energy Management Dynamic Control Topology In MANET

Science.gov (United States)

Madhusudan, G.; Kumar, TNR

2017-08-01

Topology management via per-node transmission power adjustment has been shown effective in extending network lifetime. The existing algorithms constructs static topologies which fail to take the residual energy of network nodes, and cannot balance energy consumption efficiently. To address this problem, a Light Weighted Distributed Topology Control algorithm EMDCT(Energy Management Dynamic Control Topology ) is proposed in this paper. Based on the link metric of the network, both the energy consumption rate level and residual energy levels at the two end nodes are considered. EMDCT generates a Dynamic Topology that changes with the variation of node energy without the aid of location information, each node determines its transmission power according to local network information, which reduces the overhead complexity of EMDCT greatly. The experiment results show that EMDCT preserves network connectivity and manitains minimum-cost property of the network also it can extend network lifetime more remarkably.

Time-Space Topology Optimization

DEFF Research Database (Denmark)

Jensen, Jakob Søndergaard

2008-01-01

A method for space-time topology optimization is outlined. The space-time optimization strategy produces structures with optimized material distributions that vary in space and in time. The method is demonstrated for one-dimensional wave propagation in an elastic bar that has a time-dependent Young......’s modulus and is subjected to a transient load. In the example an optimized dynamic structure is demonstrated that compresses a propagating Gauss pulse....

Energy and angular-momentum non-conservation in four-dimensional gauge theories

International Nuclear Information System (INIS)

Manohar, A.

1985-01-01

We study energy and angular-momentum non-conservation on four-dimensional chiral gauge theories using Landau levels. These effects are physical manifestations of the usual gauge anomaly, and enable us to understand in a semi-classical approximation why anomaly cancellation is required for a consistent field theory. (orig.)

Nanoscale electron transport at the surface of a topological insulator

Science.gov (United States)

Bauer, Sebastian; Bobisch, Christian A.

2016-04-01

The use of three-dimensional topological insulators for disruptive technologies critically depends on the dissipationless transport of electrons at the surface, because of the suppression of backscattering at defects. However, in real devices, defects are unavoidable and scattering at angles other than 180° is allowed for such materials. Until now, this has been studied indirectly by bulk measurements and by the analysis of the local density of states in close vicinity to defect sites. Here, we directly measure the nanoscale voltage drop caused by the scattering at step edges, which occurs if a lateral current flows along a three-dimensional topological insulator. The experiments were performed using scanning tunnelling potentiometry for thin Bi2Se3 films. So far, the observed voltage drops are small because of large contributions of the bulk to the electronic transport. However, for the use of ideal topological insulating thin films in devices, these contributions would play a significant role.

On the four-dimensional character of micro-physical phenomena

International Nuclear Information System (INIS)

Rietdijk, C.W.

1984-01-01

It is proved that retroactive effects exist in Nature. This emphasizes the fact that micro-processes constitute integrated wholes so much that it is no longer far-fetched to posit the hypothesis that events, that is, action, rather than objects, constitute the proper stuff of the (four-dimensional) Universe. Mind here, too, that retroactivity implies that the future and future parts of events 'exist already'. Then, distances between (e.g., alternative) events A and B have to be measured by the quantity of 'occurring' or action that is needed in order to transform event A into event B. The action metric so introduced appears to be in a position to solve the nonlocality paradoxes of quantum mechanics such as wave-particle 'duality' and the EPR paradox. In this connection, the Minkowski metric corresponds to a macro scheme which cannot be 'interpolated' to within a micro-process, i.e., to within action quanta, without producing serious metrical distortions. Generally, metric is considered to be a property of events, it having no existence independent of them as a 'pre-existing scheme'. Planck's elementary quantities of action h are seen as real entities in the four-dimensional world, i.e., as the 'atoms of occurring'. By intersecting (dilated) series of them with a now-hyperplane we in an imaginable way get the wave patterns satisfying the relevant wave equation. (Auth.)

Influence of magnetic disorders on quantum anomalous Hall effect in magnetic topological insulator films beyond the two-dimensional limit

Science.gov (United States)

Xing, Yanxia; Xu, Fuming; Cheung, King Tai; Sun, Qing-feng; Wang, Jian; Yao, Yugui

2018-04-01

Quantum anomalous Hall effect (QAHE) has been experimentally realized in magnetic topological insulator (MTI) thin films fabricated on magnetically doped {({{Bi}},{{Sb}})}2{{{Te}}}3. In an MTI thin film with the magnetic easy axis along the normal direction (z-direction), orientations of magnetic dopants are randomly distributed around the magnetic easy axis, acting as magnetic disorders. With the aid of the non-equilibrium Green's function and Landauer–Büttiker formalism, we numerically study the influence of magnetic disorders on QAHE in an MTI thin film modeled by a three-dimensional tight-binding Hamiltonian. It is found that, due to the existence of gapless side surface states, QAHE is protected even in the presence of magnetic disorders as long as the z-component of magnetic moment of all magnetic dopants are positive. More importantly, such magnetic disorders also suppress the dissipation of the chiral edge states and enhance the quality of QAHE in MTI films. In addition, the effect of magnetic disorders depends very much on the film thickness, and the optimal influence is achieved at certain thickness. These findings are new features for QAHE in three-dimensional systems, not present in two-dimensional systems.

Optical Coherence Tomography for Retinal Surgery: Perioperative Analysis to Real-Time Four-Dimensional Image-Guided Surgery.

Science.gov (United States)

Carrasco-Zevallos, Oscar M; Keller, Brenton; Viehland, Christian; Shen, Liangbo; Seider, Michael I; Izatt, Joseph A; Toth, Cynthia A

2016-07-01

Magnification of the surgical field using the operating microscope facilitated profound innovations in retinal surgery in the 1970s, such as pars plana vitrectomy. Although surgical instrumentation and illumination techniques are continually developing, the operating microscope for vitreoretinal procedures has remained essentially unchanged and currently limits the surgeon's depth perception and assessment of subtle microanatomy. Optical coherence tomography (OCT) has revolutionized clinical management of retinal pathology, and its introduction into the operating suite may have a similar impact on surgical visualization and treatment. In this article, we review the evolution of OCT for retinal surgery, from perioperative analysis to live volumetric (four-dimensional, 4D) image-guided surgery. We begin by briefly addressing the benefits and limitations of the operating microscope, the progression of OCT technology, and OCT applications in clinical/perioperative retinal imaging. Next, we review intraoperative OCT (iOCT) applications using handheld probes during surgical pauses, two-dimensional (2D) microscope-integrated OCT (MIOCT) of live surgery, and volumetric MIOCT of live surgery. The iOCT discussion focuses on technological advancements, applications during human retinal surgery, translational difficulties and limitations, and future directions.

Acquiring a four-dimensional computed tomography dataset using an external respiratory signal

International Nuclear Information System (INIS)

Vedam, S S; Keall, P J; Kini, V R; Mostafavi, H; Shukla, H P; Mohan, R

2003-01-01

Four-dimensional (4D) methods strive to achieve highly conformal radiotherapy, particularly for lung and breast tumours, in the presence of respiratory-induced motion of tumours and normal tissues. Four-dimensional radiotherapy accounts for respiratory motion during imaging, planning and radiation delivery, and requires a 4D CT image in which the internal anatomy motion as a function of the respiratory cycle can be quantified. The aims of our research were (a) to develop a method to acquire 4D CT images from a spiral CT scan using an external respiratory signal and (b) to examine the potential utility of 4D CT imaging. A commercially available respiratory motion monitoring system provided an 'external' tracking signal of the patient's breathing. Simultaneous recording of a TTL 'X-Ray ON' signal from the CT scanner indicated the start time of CT image acquisition, thus facilitating time stamping of all subsequent images. An over-sampled spiral CT scan was acquired using a pitch of 0.5 and scanner rotation time of 1.5 s. Each image from such a scan was sorted into an image bin that corresponded with the phase of the respiratory cycle in which the image was acquired. The complete set of such image bins accumulated over a respiratory cycle constitutes a 4D CT dataset. Four-dimensional CT datasets of a mechanical oscillator phantom and a patient undergoing lung radiotherapy were acquired. Motion artefacts were significantly reduced in the images in the 4D CT dataset compared to the three-dimensional (3D) images, for which respiratory motion was not accounted. Accounting for respiratory motion using 4D CT imaging is feasible and yields images with less distortion than 3D images. 4D images also contain respiratory motion information not available in a 3D CT image

Ring-array processor distribution topology for optical interconnects

Science.gov (United States)

Li, Yao; Ha, Berlin; Wang, Ting; Wang, Sunyu; Katz, A.; Lu, X. J.; Kanterakis, E.

1992-01-01

The existing linear and rectangular processor distribution topologies for optical interconnects, although promising in many respects, cannot solve problems such as clock skews, the lack of supporting elements for efficient optical implementation, etc. The use of a ring-array processor distribution topology, however, can overcome these problems. Here, a study of the ring-array topology is conducted with an aim of implementing various fast clock rate, high-performance, compact optical networks for digital electronic multiprocessor computers. Practical design issues are addressed. Some proof-of-principle experimental results are included.

Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties

Directory of Open Access Journals (Sweden)

Qinghai Zhao

2015-01-01

Full Text Available A robust topology optimization (RTO approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.

No-go theorems for R symmetries in four-dimensional GUTs

CERN Document Server

Fallbacher, Maximilian; Vaudrevange, Patrick K S

2011-01-01

We prove that it is impossible to construct a grand unified model, based on a simple gauge group, in four dimensions that leads to the exact MSSM, nor to a singlet extension, and possesses an unbroken R symmetry. This implies that no MSSM model with either a Z_{M>=3}^R or U(1)_R symmetry can be completed by a four-dimensional GUT in the ultraviolet. However, our no-go theorem does not apply to GUT models with extra dimensions. We also show that it is impossible to construct a 4D GUT that leads to the MSSM plus an additional anomaly-free symmetry that forbids the mu term.

The nature of the topological intuition

OpenAIRE

Sultanova L. B.

2016-01-01

The article is devoted to the nature of the topological intuition and disclosure of the specifics of topological heuristics in the framework of philosophical theory of knowledge. As we know, intuition is a one of the support categories of the theory of knowledge, the driving force of scientific research. Great importance is mathematical intuition for the solution of non-standard problems, for which there is no algorithm for such a solution. In such cases, the mathematician addresses the so-ca...

Embedding of attitude determination in n-dimensional spaces

Science.gov (United States)

Bar-Itzhack, Itzhack Y.; Markley, F. Landis

1988-01-01

The problem of attitude determination in n-dimensional spaces is addressed. The proper parameters are found, and it is shown that not all three-dimensional methods have useful extensions to higher dimensions. It is demonstrated that Rodriguez parameters are conveniently extendable to other dimensions. An algorithm for using these parameters in the general n-dimensional case is developed and tested with a four-dimensional example. The correct mathematical description of angular velocities is addressed, showing that angular velocity in n dimensions cannot be represented by a vector but rather by a tensor of the second rank. Only in three dimensions can the angular velocity be described by a vector.

Four dimensional sigma model coupled to the metric tensor field

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1980-02-01

We discuss the four dimensional nonlinear sigma model with an internal O(n) invariance coupled to the metric tensor field satisfying Einstein equations. We derive a bound on the coupling constant between the sigma field and the metric tensor using the theory of harmonic maps. A special attention is paid to Einstein spaces and some new explicit solutions of the model are constructed. (author)

Magnetoconductance in InN/GaN quantum wells in topological insulator phase

Science.gov (United States)

Bardyszewski, W.; Rodak, D.; Łepkowski, S. P.

2017-04-01

We present a theoretical study of the magnetic-field effect on the electronic properties of the two-dimensional, hypothetical topological insulator based on the InN/GaN quantum well system. Using the effective two-dimensional Hamiltonian, we have modelled magneto-transport in mesoscopic, symmetric samples of such materials. It turns out that, as in the case of the other two-dimensional topological insulators, the magnetoconductance in such samples is quantized due to the presence of helical edge states for magnetic fields below a certain critical value and for fairly small disorder strength. However, in our case the helical edge transport is much more prone to the disorder than, for example, in the case of topological insulators based on the HgTe/CdTe quantum wells. At low enough level of disorder and for the Fermi energy located in the energy gap of an infinite planar quantum well, we may expect an interesting phenomenon of non-monotonic dependence of the conductance on the magnetic field caused by the complicated interplay of couplings between the heavy hole, light hole and conduction subbands.

Trees and spatial topology change in CDT

DEFF Research Database (Denmark)

Ambjorn, Jan; Budd, Timothy George

2013-01-01

Generalized causal dynamical triangulations (generalized CDT) is a model of two-dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur. We solve the model at the discretized level using bijections between quadrangulations and trees. In the continuum...

Weak antilocalization effect and noncentrosymmetric superconductivity in a topologically nontrivial semimetal LuPdBi

KAUST Repository

Xu, Guizhou; Wang, Wenhong; Zhang, Xiaoming; Du, Yin; Liu, Enke; Wang, Shouguo; Wu, Guangheng; Liu, Zhongyuan; Zhang, Xixiang

2014-01-01

A large number of half-Heusler compounds have been recently proposed as three-dimensional (3D) topological insulators (TIs) with tunable physical properties. However, no transport measurements associated with the topological surface states have been observed in these half-Heusler candidates due to the dominating contribution from bulk electrical conductance. Here we show that, by reducing the mobility of bulk carriers, a two-dimensional (2D) weak antilocalization (WAL) effect, one of the hallmarks of topological surface states, was experimentally revealed from the tilted magnetic field dependence of magnetoconductance in a topologically nontrivial semimetal LuPdBi. Besides the observation of a 2D WAL effect, a superconducting transition was revealed at T c ∼ 1.7â.K in the same bulk LuPdBi. Quantitative analysis within the framework of a generalized BCS theory leads to the conclusion that the noncentrosymmetric superconductivity of LuPdBi is fully gapped with a possibly unconventional pairing character. The co-existence of superconductivity and the transport signature of topological surface states in the same bulk alloy suggests that LuPdBi represents a very promising candidate as a topological superconductor.

Weak antilocalization effect and noncentrosymmetric superconductivity in a topologically nontrivial semimetal LuPdBi

KAUST Repository

Xu, Guizhou

2014-07-21

A large number of half-Heusler compounds have been recently proposed as three-dimensional (3D) topological insulators (TIs) with tunable physical properties. However, no transport measurements associated with the topological surface states have been observed in these half-Heusler candidates due to the dominating contribution from bulk electrical conductance. Here we show that, by reducing the mobility of bulk carriers, a two-dimensional (2D) weak antilocalization (WAL) effect, one of the hallmarks of topological surface states, was experimentally revealed from the tilted magnetic field dependence of magnetoconductance in a topologically nontrivial semimetal LuPdBi. Besides the observation of a 2D WAL effect, a superconducting transition was revealed at T c ∼ 1.7â.K in the same bulk LuPdBi. Quantitative analysis within the framework of a generalized BCS theory leads to the conclusion that the noncentrosymmetric superconductivity of LuPdBi is fully gapped with a possibly unconventional pairing character. The co-existence of superconductivity and the transport signature of topological surface states in the same bulk alloy suggests that LuPdBi represents a very promising candidate as a topological superconductor.

Haunted Kaluza universe with four-dimensional Lorentzian flat, Kerr, and Taub-NUT slices

International Nuclear Information System (INIS)

Ivanov, Rossen I.; Prodanov, Emil M.

2005-01-01

The duality between the original Kaluza's theory and Klein's subsequent modification is duality between slicing and threading decomposition of the five-dimensional spacetime. The field equations of the original Kaluza's theory lead to the interpretation of the four-dimensional Lorentzian Kerr and Taub-NUT solutions as resulting from static electric and magnetic charges and dipoles in the presence of ghost matter and constant dilaton, which models Newton's constant

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.

Topological Superconductivity on the Surface of Fe-Based Superconductors.

Science.gov (United States)

Xu, Gang; Lian, Biao; Tang, Peizhe; Qi, Xiao-Liang; Zhang, Shou-Cheng

2016-07-22

As one of the simplest systems for realizing Majorana fermions, the topological superconductor plays an important role in both condensed matter physics and quantum computations. Based on ab initio calculations and the analysis of an effective 8-band model with superconducting pairing, we demonstrate that the three-dimensional extended s-wave Fe-based superconductors such as Fe_{1+y}Se_{0.5}Te_{0.5} have a metallic topologically nontrivial band structure, and exhibit a normal-topological-normal superconductivity phase transition on the (001) surface by tuning the bulk carrier doping level. In the topological superconductivity (TSC) phase, a Majorana zero mode is trapped at the end of a magnetic vortex line. We further show that the surface TSC phase only exists up to a certain bulk pairing gap, and there is a normal-topological phase transition driven by the temperature, which has not been discussed before. These results pave an effective way to realize the TSC and Majorana fermions in a large class of superconductors.

Bifurcation structures and transient chaos in a four-dimensional Chua model

Energy Technology Data Exchange (ETDEWEB)

Hoff, Anderson, E-mail: hoffande@gmail.com; Silva, Denilson T. da; Manchein, Cesar, E-mail: cesar.manchein@udesc.br; Albuquerque, Holokx A., E-mail: holokx.albuquerque@udesc.br

2014-01-10

A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic diagrams and regarding numerical continuation method, the bifurcation curves are obtained. Combining both methods the bifurcation structures of the model were obtained with the possibility to describe the shrimp-shaped domains and their endoskeletons. We study the effect of a parameter that controls the dimension of the system leading the model to present transient chaos with its corresponding basin of attraction being riddled.

Nanometric holograms based on a topological insulator material.

Science.gov (United States)

Yue, Zengji; Xue, Gaolei; Liu, Juan; Wang, Yongtian; Gu, Min

2017-05-18

Holography has extremely extensive applications in conventional optical instruments spanning optical microscopy and imaging, three-dimensional displays and metrology. To integrate holography with modern low-dimensional electronic devices, holograms need to be thinned to a nanometric scale. However, to keep a pronounced phase shift modulation, the thickness of holograms has been generally limited to the optical wavelength scale, which hinders their integration with ultrathin electronic devices. Here, we break this limit and achieve 60 nm holograms using a topological insulator material. We discover that nanometric topological insulator thin films act as an intrinsic optical resonant cavity due to the unequal refractive indices in their metallic surfaces and bulk. The resonant cavity leads to enhancement of phase shifts and thus the holographic imaging. Our work paves a way towards integrating holography with flat electronic devices for optical imaging, data storage and information security.

Gauge-invariant factorization and canonical quantization of topologically massive gauge theories in any dimension

International Nuclear Information System (INIS)

Bertrand, Bruno; Govaerts, Jan

2007-01-01

Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the (2+1)-dimensional Maxwell-Chern-Simons and (3+1)-dimensional Cremmer-Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However, through an appropriate canonical transformation, a gauge-invariant factorization of phase space into two orthogonal sectors is feasible. The first of these sectors includes canonically conjugate gauge-invariant variables with free massive excitations. The second sector, which decouples from the total Hamiltonian, is equivalent to the phase-space description of the associated non-dynamical pure TFT. Within canonical quantization, a likewise factorization of quantum states thus arises for the full spectrum of TMGT in any dimension. This new factorization scheme also enables a definition of the usual projection from TMGT onto topological quantum field theories in a most natural and transparent way. None of these results rely on any gauge-fixing procedure whatsoever

Topological Magnon Bands in a Kagome Lattice Ferromagnet.

Science.gov (United States)

Chisnell, R; Helton, J S; Freedman, D E; Singh, D K; Bewley, R I; Nocera, D G; Lee, Y S

2015-10-02

There is great interest in finding materials possessing quasiparticles with topological properties. Such materials may have novel excitations that exist on their boundaries which are protected against disorder. We report experimental evidence that magnons in an insulating kagome ferromagnet can have a topological band structure. Our neutron scattering measurements further reveal that one of the bands is flat due to the unique geometry of the kagome lattice. Spin wave calculations show that the measured band structure follows from a simple Heisenberg Hamiltonian with a Dzyaloshinkii-Moriya interaction. This serves as the first realization of an effectively two-dimensional topological magnon insulator--a new class of magnetic material that should display both a magnon Hall effect and protected chiral edge modes.

String propagation in an exact four-dimensional black hole background

International Nuclear Information System (INIS)

Mahapatra, S.

1997-01-01

We study string propagation in an exact, stringy, four-dimensional dyonic black hole background. The exact solutions in terms of elliptic functions describing string configurations in the J=0 limit are obtained by solving the string equations of motion and constraints. By using the covariant formalism, we also investigate the propagation of physical perturbations along the string in the given curved background. copyright 1997 The American Physical Society

Gauge constructs and immersions of four-dimensional spacetimes in (4 + k)-dimensional flat spaces: algebraic evaluation of gravity fields

International Nuclear Information System (INIS)

Edelen, Dominic G B

2003-01-01

Local action of the fundamental group SO(a, 4 + k - a) is used to show that any solution of an algebraically closed differential system, that is generated from matrix Lie algebra valued 1-forms on a four-dimensional parameter space, will generate families of immersions of four-dimensional spacetimes R 4 in flat (4 + k)-dimensional spaces M 4+k with compatible signature. The algorithm is shown to work with local action of SO(a, 4 + k - a) replaced by local action of GL(4 + k). Immersions generated by local action of the Poincare group on the target spacetime are also obtained. Evaluations of the line elements, immersion loci and connection and curvature forms of these immersions are algebraic. Families of immersions that depend on one or more arbitrary functions are calculated for 1 ≤ k ≤ 4. Appropriate sections of graphs of the conformal factor for two and three interacting line singularities immersed in M 6 are given in appendix A. The local immersion theorem given in appendix B shows that all local solutions of the immersion problem are obtained by use of this method and an algebraic extension in exceptional cases

Topological susceptibility in lattice QCD with unimproved Wilson fermions

International Nuclear Information System (INIS)

Chowdhury, Abhishek; De, Asit K.; De Sarkar, Sangita; Harindranath, A.; Mondal, Santanu; Sarkar, Anwesa; Maiti, Jyotirmoy

2012-01-01

We address a long standing problem regarding topology in lattice simulations of QCD with unimproved Wilson fermions. Earlier attempt with unimproved Wilson fermions at β=5.6 to verify the suppression of topological susceptibility with decreasing quark mass (m q ) was unable to unambiguously confirm the suppression. We carry out systematic calculations for two degenerate flavours at two different lattice spacings (β=5.6 and 5.8). The effects of quark mass, lattice volume and the lattice spacing on the spanning of different topological sectors are presented. We unambiguously demonstrate the suppression of the topological susceptibility with decreasing quark mass, expected from chiral Ward identity and chiral perturbation theory.

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.

A Bioengineered Three-Dimensional Cell Culture Platform Integrated with Microfluidics To Address Antimicrobial Resistance in Tuberculosis

Directory of Open Access Journals (Sweden)

Magdalena K. Bielecka

2017-02-01

Full Text Available Antimicrobial resistance presents one of the most significant threats to human health, with the emergence of totally drug-resistant organisms. We have combined bioengineering, genetically modified bacteria, longitudinal readouts, and fluidics to develop a transformative platform to address the drug development bottleneck, utilizing Mycobacterium tuberculosis as the model organism. We generated microspheres incorporating virulent reporter bacilli, primary human cells, and an extracellular matrix by using bioelectrospray methodology. Granulomas form within the three-dimensional matrix, and mycobacterial stress genes are upregulated. Pyrazinamide, a vital first-line antibiotic for treating human tuberculosis, kills M. tuberculosis in a three-dimensional culture but not in a standard two-dimensional culture or Middlebrook 7H9 broth, demonstrating that antibiotic sensitivity within microspheres reflects conditions in patients. We then performed pharmacokinetic modeling by combining the microsphere system with a microfluidic plate and demonstrated that we can model the effect of dynamic antibiotic concentrations on mycobacterial killing. The microsphere system is highly tractable, permitting variation of cell content, the extracellular matrix, sphere size, the infectious dose, and the surrounding medium with the potential to address a wide array of human infections and the threat of antimicrobial resistance.

A TQFT associated to the LMO invariant of three-dimensional manifolds

DEFF Research Database (Denmark)

Cheptea, Dorin; Le, Thang

2007-01-01

We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This is ......We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category...

Topological insulators and C*-algebras: Theory and numerical practice

International Nuclear Information System (INIS)

Hastings, Matthew B.; Loring, Terry A.

2011-01-01

Research highlights: → We classify topological insulators using C* algebras. → We present new K-theory invariants. → We develop efficient numerical algorithms based on this technique. → We observe unexpected quantum phase transitions using our algorithm. - Abstract: We apply ideas from C*-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological obstructions to approximating these matrices by exactly commuting matrices, we are able to compute invariants quantifying different topological phases. We generalize previous two dimensional results to higher dimensions; we give a general expression for the topological invariants for arbitrary dimension and several symmetry classes, including chiral symmetry classes, and we present a detailed K-theory treatment of this expression for time reversal invariant three dimensional systems. We can use these results to show non-existence of localized Wannier functions for these systems. We use this approach to calculate the index for time-reversal invariant systems with spin-orbit scattering in three dimensions, on sizes up to 12 3 , averaging over a large number of samples. The results show an interesting separation between the localization transition and the point at which the average index (which can be viewed as an 'order parameter' for the topological insulator) begins to fluctuate from sample to sample, implying the existence of an unsuspected quantum phase transition separating two different delocalized phases in this system. One of the particular advantages of the C*-algebraic technique that we present is that it is significantly faster in practice than other methods of computing the index, allowing the study of larger systems. In this paper, we present a detailed discussion of numerical implementation of our method.

A four-dimensional variational chemistry data assimilation scheme for Eulerian chemistry transport modeling

Science.gov (United States)

Eibern, Hendrik; Schmidt, Hauke

1999-08-01

The inverse problem of data assimilation of tropospheric trace gas observations into an Eulerian chemistry transport model has been solved by the four-dimensional variational technique including chemical reactions, transport, and diffusion. The University of Cologne European Air Pollution Dispersion Chemistry Transport Model 2 with the Regional Acid Deposition Model 2 gas phase mechanism is taken as the basis for developing a full four-dimensional variational data assimilation package, on the basis of the adjoint model version, which includes the adjoint operators of horizontal and vertical advection, implicit vertical diffusion, and the adjoint gas phase mechanism. To assess the potential and limitations of the technique without degrading the impact of nonperfect meteorological analyses and statistically not established error covariance estimates, artificial meteorological data and observations are used. The results are presented on the basis of a suite of experiments, where reduced records of artificial "observations" are provided to the assimilation procedure, while other "data" is retained for performance control of the analysis. The paper demonstrates that the four-dimensional variational technique is applicable for a comprehensive chemistry transport model in terms of computational and storage requirements on advanced parallel platforms. It is further shown that observed species can generally be analyzed, even if the "measurements" have unbiased random errors. More challenging experiments are presented, aiming to tax the skill of the method (1) by restricting available observations mostly to surface ozone observations for a limited assimilation interval of 6 hours and (2) by starting with poorly chosen first guess values. In this first such application to a three-dimensional chemistry transport model, success was also achieved in analyzing not only observed but also chemically closely related unobserved constituents.