SO(N) reformulated link invariants from topological strings

International Nuclear Information System (INIS)

Borhade, Pravina; Ramadevi, P.

2005-01-01

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

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.

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 invariance of classical electromagnetism under Charge-conjugation, Parity and Time-reversal (CPT) transformations

Science.gov (United States)

Norbury, John W.

1989-01-01

The invariance of classical electromagnetism under charge-conjugation, parity, and time-reversal (CPT) is studied by considering the motion of a charged particle in electric and magnetic fields. Upon applying CPT transformations to various physical quantities and noting that the motion still behaves physically demonstrates invariance.

Spin foam diagrammatics and topological invariance

International Nuclear Information System (INIS)

Girelli, Florian; Oeckl, Robert; Perez, Alejandro

2002-01-01

We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3D pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, proposed as models of quantum gravity in 4D, under refinement of the cellular decomposition

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.

The imaginary-time path integral and non-time-reversal-invariant saddle points of the Euclidean action

International Nuclear Information System (INIS)

Dasgupta, I.

1998-01-01

We discuss new bounce-like (but non-time-reversal-invariant) solutions to Euclidean equations of motion, which we dub boomerons. In the Euclidean path integral approach to quantum theories, boomerons make an imaginary contribution to the vacuum energy. The fake vacuum instability can be removed by cancelling boomeron contributions against contributions from time reversed boomerons (anti-boomerons). The cancellation rests on a sign choice whose significance is not completely understood in the path integral method. (orig.)

Quantized Hall conductance as a topological invariant

International Nuclear Information System (INIS)

Niu, Q.; Thouless, Ds.J.; Wu, Y.S.

1984-10-01

Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by TKNN to the situation where many body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect we draw the conclusion that there must be a symmetry breaking in the many body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also carefully discussed. 19 references

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

International Nuclear Information System (INIS)

Lewis, H.R.

1990-01-01

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

Discover potential in a search for time-reversal invariance violation in nuclei

Energy Technology Data Exchange (ETDEWEB)

Gudkov, Vladimir, E-mail: gudkov@sc.edu; Song, Young-Ho [University of South Carolina, Department of Physics and Astronomy (United States)

2013-03-15

Time reversal invariance violating (TRIV) effects in low energy physics could be very important in searching for new physics, being complementary to neutron and atomic electric dipole moment (EDM) measurements. In this relation, we discuss a sensitivity of some TRIV observables to different models of time-reversal (CP) violation and their dependencies on nuclear structure. As a measure of a sensitivity of TRIV effects to the value of TRIV nucleon coupling constant, we introduce a coefficient of a 'discovery potential', which shows a possible factor for improving the current limits of the EDM experiments by measuring nuclear TRIV effects.

Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions

Science.gov (United States)

Wen, Xiao-Gang

2017-05-01

We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)-dimensional [(3+1)D] Z2-gauge theory with emergent fermionic Kramers doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in space-time without pin+ structure. The exactly soluble model also leads to a statistical transmutation in (3+1)D. In addition, we construct exactly soluble bosonic models that realize 2 types of time-reversal symmetry-enriched Z2 topological orders in 2+1 dimensions, and 20 types of simplest time-reversal symmetry-enriched topological (SET) orders which have only one nontrivial pointlike and stringlike topological excitation. Many physical properties of those topological states are calculated using the exactly soluble models. We find that some time-reversal SET orders have pointlike excitations that carry Kramers doublet, a fractionalized time-reversal symmetry. We also find that some Z2 SET orders have stringlike excitations that carry anomalous (nononsite) Z2 symmetry, which can be viewed as a fractionalization of Z2 symmetry on strings. Our construction is based on cochains and cocycles in algebraic topology, which is very versatile. In principle, it can also realize emergent topological field theory beyond the twisted gauge theory.

Test of feasibility of a novel high precision test of time reversal invariance

International Nuclear Information System (INIS)

Samuel, Deepak

2007-01-01

The first results of a feasibility test of a novel high precision test of time reversal invariance are reported. The Time Reversal Invariance test at COSY (TRIC) was planned to measure the time reversal violating observable A y,xz with an accuracy of 10 -6 in proton-deuteron (p-d) scattering. A novel technique for measuring total cross sections is introduced and the achievable precision of this measuring technique is tested. The correlation coefficient A y,y in p-d scattering fakes a time-reversal violating effect. This work reports the feasibility test of the novel method in the measurement of A y,y in p-p scattering. The first step in the experimental design was the development of a hard real-time data acquisition system. To meet stringent latency requirements, the capabilities of Windows XP had to be augmented with a real-time subsystem. The remote control feature of the data acquisition enables users to operate it from any place via an internet connection. The data acquisition proved its reliability in several beam times without any failures. The analysis of the data showed the presence of 1/f noise which substantially limits the quality of our measurements. The origin of 1/f noise was traced and found to be the Barkhausen noise from the ferrite core of the beam current transformer (BCT). A global weighted fitting technique based on a modified Wiener-Khinchin method was developed and used to suppress the influence of 1/f noise, which increased the error bar of the results by a factor 3. This is the only deviation from our expectations. The results are presented and discussed. (orig.)

Test of feasibility of a novel high precision test of time reversal invariance

Energy Technology Data Exchange (ETDEWEB)

Samuel, Deepak

2007-07-01

The first results of a feasibility test of a novel high precision test of time reversal invariance are reported. The Time Reversal Invariance test at COSY (TRIC) was planned to measure the time reversal violating observable A{sub y,xz} with an accuracy of 10{sup -6} in proton-deuteron (p-d) scattering. A novel technique for measuring total cross sections is introduced and the achievable precision of this measuring technique is tested. The correlation coefficient A{sub y,y} in p-d scattering fakes a time-reversal violating effect. This work reports the feasibility test of the novel method in the measurement of A{sub y,y} in p-p scattering. The first step in the experimental design was the development of a hard real-time data acquisition system. To meet stringent latency requirements, the capabilities of Windows XP had to be augmented with a real-time subsystem. The remote control feature of the data acquisition enables users to operate it from any place via an internet connection. The data acquisition proved its reliability in several beam times without any failures. The analysis of the data showed the presence of 1/f noise which substantially limits the quality of our measurements. The origin of 1/f noise was traced and found to be the Barkhausen noise from the ferrite core of the beam current transformer (BCT). A global weighted fitting technique based on a modified Wiener-Khinchin method was developed and used to suppress the influence of 1/f noise, which increased the error bar of the results by a factor 3. This is the only deviation from our expectations. The results are presented and discussed. (orig.)

Time reversal invariance - a test in free neutron decay

Energy Technology Data Exchange (ETDEWEB)

Lising, Laura Jean [Univ. of California, Berkeley, CA (United States)

1999-01-01

Time reversal invariance violation plays only a small role in the Standard Model, and the existence of a T-violating effect above the predicted level would be an indication of new physics. A sensitive probe of this symmetry in the weak interaction is the measurement of the T-violating ''D''-correlation in the decay of free neutrons. The triple-correlation Dσ_n∙p_e x p_v involves three kinematic variables, the neutron spin, electron momentu, and neutrino (or proton) momentum, and changes sign under time reversal. This experiment detects the decay products of a polarized cold neutron beam with an octagonal array of scintillation and solid-state detectors. Data from first run at NIST's Cold Neutron Research Facility give a D-coefficient of -0.1 ± 1.3(stat.) ± 0.7(syst) x 10^-3 This measurement has the greatest bearing on extensions to the Standard model that incorporate leptoquarks, although exotic fermion and lift-right symmetric models also allow a D as large as the present limit.

Torsional Topological Invariants (and their relevance for real life)

CERN Document Server

Chandia, O; Chandia, Osvaldo; Zanelli, Jorge

1997-01-01

The existence of topological invariants analogous to Chern/Pontryagin classes for a standard $SO(D)$ or SU(N) connection, but constructed out of the torsion tensor, is discussed. These invariants exhibit many of the features of the Chern/Pontryagin invariants: they can be expressed as integrals over the manifold of local densities and take integer values on compact spaces without boundary; their spectrum is determined by the homotopy groups determined by the connection bundle but depend also on the bundle of local orthonormal frames on the tangent space of the manifold. It is shown that in spacetimes with nonvanishing torsion there can occur topologically stable configurations associated with the frame bundle which are independent of the curvature. Explicit examples of topologically stable configurations carrying nonvanishing instanton number in four and eight dimensions are given, and they can be conjectured to exist in dimension $4k$. It is also shown that the chiral anomaly in a spacetime with torsion rece...

Time- and Site-Resolved Dynamics in a Topological Circuit

Directory of Open Access Journals (Sweden)

Jia Ningyuan

2015-06-01

Full Text Available From studies of exotic quantum many-body phenomena to applications in spintronics and quantum information processing, topological materials are poised to revolutionize the condensed-matter frontier and the landscape of modern materials science. Accordingly, there is a broad effort to realize topologically nontrivial electronic and photonic materials for fundamental science as well as practical applications. In this work, we demonstrate the first simultaneous site- and time-resolved measurements of a time-reversal-invariant topological band structure, which we realize in a radio-frequency photonic circuit. We control band-structure topology via local permutation of a traveling-wave capacitor-inductor network, increasing robustness by going beyond the tight-binding limit. We observe a gapped density of states consistent with a modified Hofstadter spectrum at a flux per plaquette of ϕ=π/2. In situ probes of the band gaps reveal spatially localized bulk states and delocalized edge states. Time-resolved measurements reveal dynamical separation of localized edge excitations into spin-polarized currents. The radio-frequency circuit paradigm is naturally compatible with nonlocal coupling schemes, allowing us to implement a Möbius strip topology inaccessible in conventional systems. This room-temperature experiment illuminates the origins of topology in band structure, and when combined with circuit quantum electrodynamics techniques, it provides a direct path to topologically ordered quantum matter.

Introduction to time reversal theory

International Nuclear Information System (INIS)

Henley, E.M.

1987-01-01

Theory and reaction mechanisms relevant to time reversal invariance are reviewed. Consequences of time reversal invariance are presented under the headings of CP tests, electromagnetic moments, weak emissions or absorptions, and scattering reactions. 8 refs., 4 figs

Test of time-reversal invariance at COSY

Energy Technology Data Exchange (ETDEWEB)

Valdau, Yury [Helmholtz Institut fuer Strahlen- und Kernphysik, Bonn Univ. (Germany); National Research Center ' ' Kurchatov Institute' ' Petersburg Nuclear Physics Institute B.P. Konstantinov, Gatchina (Russian Federation); Eversheim, Dieter [Helmholtz Institut fuer Strahlen- und Kernphysik, Bonn Univ. (Germany); Lorentz, Bernd [Forschungszentrum Juelich, Institute fuer Kernphysik (Germany)

2016-07-01

The experiment to test the Time Reversal Invariance at Cosy (TRIC) is under the preparation by the PAX collaboration. It is planned to improve present limit on the T-odd P-even interaction by at least one order of magnitude using a unique genuine null observable available in double polarized proton-deuteron scattering. The TRIC experiment is planned as a transmission experiment using a tensor polarized deuterium target placed at the internal target place of the Cooler-Synchrotron COSY-Juelich. Total double polarized cross section will be measured observing a beam current change due to the interaction of a polarized proton beam with an internal tensor polarized deuterium target from the PAX atomic beam source. Hence, in this experiment COSY will be used as an accelerator, detector and ideal zero degree spectrometer. In addition to the high intensity polarized proton beam and high density polarized deuterium target, a new high precision beam current measurement system will be prepared for the TRIC experiment. In this report status of all the activities of PAX collaboration towards realization of the TRIC experiment will be presented.

Topological excitations in U(1) -invariant theories

International Nuclear Information System (INIS)

Savit, R.

1977-01-01

A class of U(1) -invariant theories in d dimensions is introduced on a lattice. These theories are labeled by a simplex number s, with 1 < or = s < d. The case with s = 1 is the X-Y model; and s = 2 gives compact photodynamics. An exact duality transformation is applied to show that the U(1) -invariant theory in d dimensions with simplex number s is the same as a similar theory in d dimensions but which is Z /sub infinity/-invariant and has simplex number s = d-s. This dual theory describes the topological excitations of the original theory. These excitations are of dimension s - 1

Three-dimensional low-energy topological invariants

International Nuclear Information System (INIS)

Bakalarska, M.; Broda, B.

2000-01-01

A description of the one-loop approximation formula for the partition function of a three-dimensional abelian version of the Donaldson-Witten theory is proposed. The one-loop expression is shown to contain such topological invariants of a three-dimensional manifold M like the Reidemeister-Ray-Singer torsion τ R and Betti numbers. (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.

A class of P,T-invariant topological phases of interacting electrons

International Nuclear Information System (INIS)

Freedman, Michael; Nayak, Chetan; Shtengel, Kirill; Walker, Kevin; Wang Zhenghan

2004-01-01

We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding statistics. P and T invariance are maintained by a 'doubling' of the low-energy degrees of freedom which occurs naturally without doubling the underlying microscopic degrees of freedom. The simplest examples have been the subject of considerable interest as proposed mechanisms for high-T c superconductivity. One is the 'doubled' version of the chiral spin liquid. The chiral spin liquid gives rise to anyon superconductivity at finite doping and the corresponding field theory is U(1) Chern-Simons theory at coupling constant m=2. The 'doubled' theory is two copies of this theory, one with m=2 the other with m=-2. The second example corresponds to Z 2 gauge theory, which describes a scenario for spin-charge separation. Our main concern, with an eye towards applications to quantum computation, are richer models which support non-Abelian statistics. All of these models, richer or poorer, lie in a tightly organized discrete family indexed by the Baraha numbers, 2cos(π/(k+2)), for positive integer k. The physical inference is that a material manifesting the Z 2 gauge theory or a doubled chiral spin liquid might be easily altered to one capable of universal quantum computation. These phases of matter have a field-theoretic description in terms of gauge theories which, in their infrared limits, are topological field theories. We motivate these gauge theories using a parton model or slave-fermion construction and show how they can be solved exactly. The structure of the resulting Hilbert spaces can be understood in purely combinatorial terms. The highly constrained nature of this combinatorial construction, phrased in the language of the topology of curves on surfaces, lays the groundwork for a strategy for constructing microscopic

The Jones polynomial as a new invariant of topological fluid dynamics

International Nuclear Information System (INIS)

Ricca, Renzo L; Liu, Xin

2014-01-01

A new method based on the use of the Jones polynomial, a well-known topological invariant of knot theory, is introduced to tackle and quantify topological aspects of structural complexity of vortex tangles in ideal fluids. By re-writing the Jones polynomial in terms of helicity, the resulting polynomial becomes then function of knot topology and vortex circulation, providing thus a new invariant of topological fluid dynamics. Explicit computations of the Jones polynomial for some standard configurations, including the Whitehead link and the Borromean rings (whose linking numbers are zero), are presented for illustration. In the case of a homogeneous, isotropic tangle of vortex filaments with same circulation, the new Jones polynomial reduces to some simple algebraic expression, that can be easily computed by numerical methods. This shows that this technique may offer a new setting and a powerful tool to detect and compute topological complexity and to investigate relations with energy, by tackling fundamental aspects of turbulence research. (paper)

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.

Topological entropy for finite invariant sets of Y

International Nuclear Information System (INIS)

Li Shihai; Ye Xiangdong.

1992-12-01

Let Y be the space {z is an element of C:z 3 is an element of [0,1]} with a metric defined by the arc length. Suppose that f is an element of C(Y,Y) and P is a finite f-invariant set. The topological entropy of (P,f), h(P), is the infimum of the topological entropies of maps from C(Y,Y) which agree with f on P. In this paper we construct a function C P is an element of C(Y,Y) satisfying C P | P =f| P which achieves the topological entropy of (P,f). (author). 14 refs

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.

Bulk and boundary invariants for complex topological insulators from K-theory to physics

CERN Document Server

Prodan, Emil

2016-01-01

This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connect...

Nobel Lecture: Topological quantum matter*

Science.gov (United States)

Haldane, F. Duncan M.

2017-10-01

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

Gauge-theoretic invariants for topological insulators: a bridge between Berry, Wess-Zumino, and Fu-Kane-Mele

Science.gov (United States)

Monaco, Domenico; Tauber, Clément

2017-07-01

We establish a connection between two recently proposed approaches to the understanding of the geometric origin of the Fu-Kane-Mele invariant FKM\\in Z_2, arising in the context of two-dimensional time-reversal symmetric topological insulators. On the one hand, the Z_2 invariant can be formulated in terms of the Berry connection and the Berry curvature of the Bloch bundle of occupied states over the Brillouin torus. On the other, using techniques from the theory of bundle gerbes, it is possible to provide an expression for FKM containing the square root of the Wess-Zumino amplitude for a certain U( N)-valued field over the Brillouin torus. We link the two formulas by showing directly the equality between the above-mentioned Wess-Zumino amplitude and the Berry phase, as well as between their square roots. An essential tool of independent interest is an equivariant version of the adjoint Polyakov-Wiegmann formula for fields T^2 → U(N), of which we provide a proof employing only basic homotopy theory and circumventing the language of bundle gerbes.

Graph topology and gap topology for unstable systems

NARCIS (Netherlands)

Zhu, S.Q.

1989-01-01

A reformation is provided of the graph topology and the gap topology for a general setting (including lumped linear time-invariant systems and distributed linear time-invariant systems) in the frequency domain. Some essential properties and their comparisons are clearly presented in the

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

Science.gov (United States)

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

2015-01-23

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

The volume conjecture, perturbative knot invariants, and recursion relations for topological strings

NARCIS (Netherlands)

Dijkgraaf, R.; Fuji, H.; Manabe, M.

2011-01-01

We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the

Time-reversal symmetry breaking in quantum billiards

Energy Technology Data Exchange (ETDEWEB)

Schaefer, Florian

2009-01-26

The present doctoral thesis describes experimentally measured properties of the resonance spectra of flat microwave billiards with partially broken timereversal invariance induced by an embedded magnetized ferrite. A vector network analyzer determines the complex scattering matrix elements. The data is interpreted in terms of the scattering formalism developed in nuclear physics. At low excitation frequencies the scattering matrix displays isolated resonances. At these the effect of the ferrite on isolated resonances (singlets) and pairs of nearly degenerate resonances (doublets) is investigated. The hallmark of time-reversal symmetry breaking is the violation of reciprocity, i.e. of the symmetry of the scattering matrix. One finds that reciprocity holds in singlets; it is violated in doublets. This is modeled by an effective Hamiltonian of the resonator. A comparison of the model to the data yields time-reversal symmetry breaking matrix elements in the order of the level spacing. Their dependence on the magnetization of the ferrite is understood in terms of its magnetic properties. At higher excitation frequencies the resonances overlap and the scattering matrix elements fluctuate irregularly (Ericson fluctuations). They are analyzed in terms of correlation functions. The data are compared to three models based on random matrix theory. The model by Verbaarschot, Weidenmueller and Zirnbauer describes time-reversal invariant scattering processes. The one by Fyodorov, Savin and Sommers achieves the same for systems with complete time-reversal symmetry breaking. An extended model has been developed that accounts for partial breaking of time-reversal invariance. This extended model is in general agreement with the data, while the applicability of the other two models is limited. The cross-correlation function between forward and backward reactions determines the time-reversal symmetry breaking matrix elements of the Hamiltonian to up to 0.3 mean level spacings. Finally

Time-reversal symmetry breaking in quantum billiards

International Nuclear Information System (INIS)

Schaefer, Florian

2009-01-01

The present doctoral thesis describes experimentally measured properties of the resonance spectra of flat microwave billiards with partially broken timereversal invariance induced by an embedded magnetized ferrite. A vector network analyzer determines the complex scattering matrix elements. The data is interpreted in terms of the scattering formalism developed in nuclear physics. At low excitation frequencies the scattering matrix displays isolated resonances. At these the effect of the ferrite on isolated resonances (singlets) and pairs of nearly degenerate resonances (doublets) is investigated. The hallmark of time-reversal symmetry breaking is the violation of reciprocity, i.e. of the symmetry of the scattering matrix. One finds that reciprocity holds in singlets; it is violated in doublets. This is modeled by an effective Hamiltonian of the resonator. A comparison of the model to the data yields time-reversal symmetry breaking matrix elements in the order of the level spacing. Their dependence on the magnetization of the ferrite is understood in terms of its magnetic properties. At higher excitation frequencies the resonances overlap and the scattering matrix elements fluctuate irregularly (Ericson fluctuations). They are analyzed in terms of correlation functions. The data are compared to three models based on random matrix theory. The model by Verbaarschot, Weidenmueller and Zirnbauer describes time-reversal invariant scattering processes. The one by Fyodorov, Savin and Sommers achieves the same for systems with complete time-reversal symmetry breaking. An extended model has been developed that accounts for partial breaking of time-reversal invariance. This extended model is in general agreement with the data, while the applicability of the other two models is limited. The cross-correlation function between forward and backward reactions determines the time-reversal symmetry breaking matrix elements of the Hamiltonian to up to 0.3 mean level spacings. Finally

Experimental demonstration of anomalous Floquet topological insulator for sound

Science.gov (United States)

Peng, Yu-Gui; Qin, Cheng-Zhi; Zhao, De-Gang; Shen, Ya-Xi; Xu, Xiang-Yuan; Bao, Ming; Jia, Han; Zhu, Xue-Feng

2016-11-01

Time-reversal invariant topological insulator is widely recognized as one of the fundamental discoveries in condensed matter physics, for which the most fascinating hallmark is perhaps a spin-based topological protection, the absence of scattering of conduction electrons with certain spins on matter surface. Recently, it has created a paradigm shift for topological insulators, from electronics to photonics, phononics and mechanics as well, bringing about not only involved new physics but also potential applications in robust wave transport. Despite the growing interests in topologically protected acoustic wave transport, T-invariant acoustic topological insulator has not yet been achieved. Here we report experimental demonstration of anomalous Floquet topological insulator for sound: a strongly coupled metamaterial ring lattice that supports one-way propagation of pseudo-spin-dependent edge states under T-symmetry. We also demonstrate the formation of pseudo-spin-dependent interface states due to lattice dislocations and investigate the properties of pass band and band gap states.

Topology and Edge Modes in Quantum Critical Chains

Science.gov (United States)

Verresen, Ruben; Jones, Nick G.; Pollmann, Frank

2018-02-01

We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases. This is possible even without gapped degrees of freedom in the bulk—in contrast to recent work on edge modes in gapless chains. We present an intuitive picture for the existence of these edge modes in the case of noninteracting spinless fermions with time-reversal symmetry (BDI class of the tenfold way). The stability of this phenomenon relies on a topological invariant defined in terms of a complex function, counting its zeros and poles inside the unit circle. This invariant can prevent two models described by the same conformal field theory (CFT) from being smoothly connected. A full classification of critical phases in the noninteracting BDI class is obtained: Each phase is labeled by the central charge of the CFT, c ∈1/2 N , and the topological invariant, ω ∈Z . Moreover, c is determined by the difference in the number of edge modes between the phases neighboring the transition. Numerical simulations show that the topological edge modes of critical chains can be stable in the presence of interactions and disorder.

(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 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.

Topologically massive gauge theories and their dual factorized gauge-invariant formulation

International Nuclear Information System (INIS)

Bertrand, Bruno; Govaerts, Jan

2007-01-01

There exists a well-known duality between the Maxwell-Chern-Simons theory and the 'self-dual' massive model in (2 + 1) dimensions. This dual description may be extended to topologically massive gauge theories (TMGT) for forms of arbitrary rank and in any dimension. This communication introduces the construction of this type of duality through a reparametrization of the 'master' theory action. The dual action thereby obtained preserves the full gauge symmetry structure of the original theory. Furthermore, the dual action is factorized into a propagating sector of massive gauge-invariant variables and a decoupled sector of gauge-variant variables defining a pure topological field theory. Combining the results obtained within the Lagrangian and Hamiltonian formulations, a completed structure for a gauge-invariant dual factorization of TMGT is thus achieved. (fast track communication)

Tests of time reversal in neutron-nucleus scattering

International Nuclear Information System (INIS)

Bowman, J.D.

1988-01-01

Experiments to test time-reversal invariance are discussed. The experiments are based on observables constructed from the momentum and spin vectors of epithermal neutrons and from the spin of an aligned or polarized target. It is shown that the proposed tests are detailed balance tests of time-reversal invariance. The status of the experiments is briefly reviewed. 14 refs., 5 figs

Three-dimensional topological insulators and bosonization

Energy Technology Data Exchange (ETDEWEB)

Cappelli, Andrea [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Randellini, Enrico [INFN, Sezione di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Dipartimento di Fisica e Astronomia, Università di Firenze,Via G. Sansone 1, 50019 Sesto Fiorentino - Firenze (Italy); Sisti, Jacopo [Scuola Internazionale Superiore di Studi Avanzati (SISSA),Via Bonomea 265, 34136 Trieste (Italy)

2017-05-25

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

Polynomial invariants for torus knots and topological strings

International Nuclear Information System (INIS)

Labastida, J.M.F.

2001-01-01

We make a precision test of a recently proposed conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold. First, we develop a systematic procedure to extract string amplitudes from vacuum expectation values (vevs) of Wilson loops in Chern-Simons gauge theory, and then we evaluate these vevs in arbitrary irreducible representations of SU(N) for torus knots. We find complete agreement with the predictions derived from the target space interpretation of the string amplitudes. We also show that the structure of the free energy of topological open string theory gives further constraints on the Chern-Simons vevs. Our work provides strong evidence towards an interpretation of knot polynomial invariants as generating functions associated to enumerative problems. (orig.)

Topological insulators and superconductors: tenfold way and dimensional hierarchy

International Nuclear Information System (INIS)

Ryu, Shinsei; Schnyder, Andreas P; Furusaki, Akira; Ludwig, Andreas W W

2010-01-01

It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on the case, by a Z or a Z 2 topological invariant. This is an exhaustive classification. Here we construct representatives of topological insulators and superconductors for all five classes and in arbitrary spatial dimension d, in terms of Dirac Hamiltonians. Using these representatives we demonstrate how topological insulators (superconductors) in different dimensions and different classes can be related via 'dimensional reduction' by compactifying one or more spatial dimensions (in 'Kaluza-Klein'-like fashion). For Z-topological insulators (superconductors) this proceeds by descending by one dimension at a time into a different class. The Z 2 -topological insulators (superconductors), on the other hand, are shown to be lower-dimensional descendants of parent Z-topological insulators in the same class, from which they inherit their topological properties. The eightfold periodicity in dimension d that exists for topological insulators (superconductors) with Hamiltonians satisfying at least one reality condition (arising from time-reversal or charge-conjugation/particle-hole symmetries) is a reflection of the eightfold periodicity of the spinor representations of the orthogonal groups SO(N) (a form of Bott periodicity). Furthermore, we derive for general spatial dimensions a relation between the topological invariant that characterizes topological insulators and superconductors with chiral symmetry (i.e., the winding number) and the Chern-Simons invariant. For lower-dimensional cases, this formula relates the winding number to the electric polarization (d=1 spatial dimensions) or to the magnetoelectric polarizability (d=3 spatial dimensions). Finally, we also discuss topological field theories describing the spacetime theory of

Quasi-invariant modified Sobolev norms for semi linear reversible PDEs

International Nuclear Information System (INIS)

Faou, Erwan; Grébert, Benoît

2010-01-01

We consider a general class of infinite dimensional reversible differential systems. Assuming a nonresonance condition on linear frequencies, we construct for such systems almost invariant pseudo-norms that are close to Sobolev-like norms. This allows us to prove that if the Sobolev norm of index s of the initial data z 0 is sufficiently small (of order ε) then the Sobolev norm of the solution is bounded by 2ε over a very long time interval (of order ε −r with r arbitrary). It turns out that this theorem applies to a large class of reversible semi-linear partial differential equations (PDEs) including the nonlinear Schrödinger (NLS) equation on the d-dimensional torus. We also apply our method to a system of coupled NLS equations which is reversible but not Hamiltonian. We also note that for the same class of reversible systems we can prove a Birkhoff normal form theorem, which in turn implies the same bounds on the Sobolev norms. Nevertheless the techniques that we use to prove the existence of quasi-invariant pseudo-norms are much more simple and direct

Test of parity and time reversal invariance with low energy polarized neutrons

International Nuclear Information System (INIS)

Masaike, Akira

1996-01-01

Measurements of helicity asymmetries in slow neutron reactions on nuclei have been performed by transmission and capture γ-ray detection. Large enhancements of parity-violation effects have been observed on p-wave resonances of various medium and heavy nuclei. The weak matrix elements in hadron reactions have been deduced from these experimental results. Neutron spin precession near the p-wave resonance has been measured. In recent years violation of time reversal invariance is being searched for in the neutron reactions in which large enhancements of the parity violation effects have been observed. The measurement of the term σ n ·(k n x I) in a neutron reaction using polarized neutrons and a polarized target is an example of the test of T-violation. Polarizations of the neutron and lanthanum nucleus for these experiments are also presented. (author)

Topological Gyroscopic Metamaterials

Science.gov (United States)

Nash, Lisa Michelle

Topological materials are generally insulating in their bulk, with protected conducting states on their boundaries that are robust against disorder and perturbation of material property. The existence of these conducting edge states is characterized by an integer topological invariant. Though the phenomenon was first discovered in electronic systems, recent years have shown that topological states exist in classical systems as well. In this thesis we are primarily concerned with the topological properties of gyroscopic materials, which are created by coupling networks of fast-spinning objects. Through a series of simulations, numerical calculations, and experiments, we show that these materials can support topological edge states. We find that edge states in these gyroscopic metamaterials bear the hallmarks of topology related to broken time reversal symmetry: they transmit excitations unidirectionally and are extremely robust against experimental disorder. We also explore requirements for topology by studying several lattice configurations and find that topology emerges naturally in gyroscopic systems.A simple prescription can be used to create many gyroscopic lattices. Though many of our gyroscopic networks are periodic, we explore amorphous point-sets and find that topology also emerges in these networks.

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

Classification of crystalline topological semimetals with an application to Na3Bi

International Nuclear Information System (INIS)

Chiu, Ching-Kai; Schnyder, Andreas P

2015-01-01

Topological phases can not only be protected by internal symmetries (e.g., time-reversal symmetry), but also by crystalline symmetries, such as reflection or rotation symmetry. Recently a complete topological classification of reflection symmetric insulators, superconductors, nodal semimetals, and nodal superconductors has been established. In this article, after a brief review of the classification of reflection-symmetry-protected semimetals and nodal superconductors, we discuss an example of a three-dimensional topological Dirac semimetal, which exhibits time-reversal symmetry as well as reflection and rotation symmetries. We compute the surface state spectrum of this Dirac semimetal and identify the crystal lattice symmetries that lead to the protection of the surface states. We discuss the implications of our findings for the stability of the Fermi arc surface states of the Dirac material Na 3 Bi. Our analysis suggests that the Fermi arc of Na 3 Bi is gapped except at time-reversal invariant surface momenta, which is in agreement with recent photoemission measurements. (paper)

Cubic systems with invariant affine straight lines of total parallel multiplicity seven

Directory of Open Access Journals (Sweden)

Alexandru Suba

2013-12-01

Full Text Available In this article, we study the planar cubic differential systems with invariant affine straight lines of total parallel multiplicity seven. We classify these system according to their geometric properties encoded in the configurations of invariant straight lines. We show that there are only 17 different topological phase portraits in the Poincar\\'e disc associated to this family of cubic systems up to a reversal of the sense of their orbits, and we provide representatives of every class modulo an affine change of variables and rescaling of the time variable.

Neutral meson tests of time-reversal symmetry invariance

OpenAIRE

Bevan, Adrian; Inguglia, Gianluca; Zoccali, Michele

2013-01-01

The laws of quantum physics can be studied under the mathematical operation T that inverts the direction of time. Strong and electromagnetic forces are known to be invariant under temporal inversion, however the weak force is not. The BaBar experiment recently exploited the quantum-correlated production of pairs of B0 mesons to show that T is a broken symmetry. Here we show that it is possible to perform a wide range of tests of quark flavour changing processes under T in order to validate th...

Constraints on a parity-even/time-reversal-odd interaction

International Nuclear Information System (INIS)

Oers, Willem T.H. van

2000-01-01

Time-Reversal-Invariance non-conservation has for the first time been unequivocally demonstrated in a direct measurement, one of the results of the CPLEAR experiment. What is the situation then with regard to time-reversal-invariance non-conservation in systems other than the neutral kaon system? Two classes of tests of time-reversal-invariance need to be distinguished: the first one deals with parity violating (P-odd)/time-reversal-invariance non-conserving (T-odd) interactions, while the second one deals with P-even/T-odd interactions (assuming CPT conservation this implies C-conjugation non-conservation). Limits on a P-odd/T-odd interaction follow from measurements of the electric dipole moment of the neutron. This in turn provides a limit on a P-odd/T-odd pion-nucleon coupling constant which is 10 -4 times the weak interaction strength. Limits on a P-even/T-odd interaction are much less stringent. The better constraint stems also from the measurement of the electric dipole moment of the neutron. Of all the other tests, measurements of charge-symmetry breaking in neutron-proton elastic scattering provide the next better constraint. The latter experiments were performed at TRIUMF (at 477 and 347 MeV) and at IUCF (at 183 MeV). Weak decay experiments (the transverse polarization of the muon in K + →π 0 μ + ν μ and the transverse polarization of the positrons in polarized muon decay) have the potential to provide comparable or possibly better constraints

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.

Unitarity and time reversal in the Glauber model

International Nuclear Information System (INIS)

Lazard, C.; Lombard, R.J.

1984-12-01

It has been pointed out by Formanek (1976-1980) that for incident energies above the particle production threshold the usual Glauber formulation of particle-nucleus scattering violates unitarity and time reversal invariance. We propose a simple method for recovering T-invariance and we discuss unitarity in view of the proposed modification. Numerical estimates are given to check the importance of T-invariance effects

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

International Nuclear Information System (INIS)

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

1988-09-01

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

The polarized atomic-beam target for the EDDA experiment and the time-reversal invariance test at COSY

International Nuclear Information System (INIS)

Eversheim, P.D.; Altmeier, M.; Felden, O.

1996-01-01

For the the EDDA experiment, which was set up to measure the p-vector - p-vector excitation function during the acceleration ramp of the cooler synchrotron COSY at Juelich, a polarized atomic-beam target was designed regarding the restrictions imposed by the geometry of the EDDA detector. Later, when the time-reversal invariance experiment is to be performed, the EDDA detector will serve as efficient internal polarimeter and the source has to deliver tensor polarized deuterons. The modular design of this polarized atomic-beam target that allows to meet these conditions are discussed in comparison to other existing polarized atomic-beam targets. (orig.)

Time reversal in polarized neutron decay: the emiT experiment

CERN Document Server

Jones, G L; Anaya, J M; Bowles, T J; Chupp, T E; Coulter, K P; Dewey, M S; Freedman, S J; Fujikawa, B K; García, A; Greene, G L; Hwang, S R; Lising, L J; Mumm, H P; Nico, J S; Robertson, R G H; Steiger, T D; Teasdale, W A; Thompson, A K; Wasserman, E G; Wietfeldt, F E; Wilkerson, J F

2000-01-01

The standard electro-weak model predicts negligible violation of time-reversal invariance in light quark processes. We report on an experimental test of time-reversal invariance in the beta decay of polarized neutrons as a search for physics beyond the standard model. The emiT collaboration has measured the time-reversal-violating triple-correlation in neutron beta decay between the neutron spin, electron momentum, and neutrino momentum often referred to as the D coefficient. The first run of the experiment produced 14 million events which are currently being analyzed. However, a second run with improved detectors should provide greater statistical precision and reduced systematic uncertainties.

Topological Photonics for Continuous Media

Science.gov (United States)

Silveirinha, Mario

Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.

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

CERN Document Server

Asbóth, János K; Pályi, András

2016-01-01

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

Topological acoustic polaritons: robust sound manipulation at the subwavelength scale

International Nuclear Information System (INIS)

Yves, Simon; Fleury, Romain; Lemoult, Fabrice; Fink, Mathias; Lerosey, Geoffroy

2017-01-01

Topological insulators, a hallmark of condensed matter physics, have recently reached the classical realm of acoustic waves. A remarkable property of time-reversal invariant topological insulators is the presence of unidirectional spin-polarized propagation along their edges, a property that could lead to a wealth of new opportunities in the ability to guide and manipulate sound. Here, we demonstrate and study the possibility to induce topologically non-trivial acoustic states at the deep subwavelength scale, in a structured two-dimensional metamaterial composed of Helmholtz resonators. Radically different from previous designs based on non-resonant sonic crystals, our proposal enables robust sound manipulation on a surface along predefined, subwavelength pathways of arbitrary shapes. (paper)

Topological acoustic polaritons: robust sound manipulation at the subwavelength scale

Science.gov (United States)

Yves, Simon; Fleury, Romain; Lemoult, Fabrice; Fink, Mathias; Lerosey, Geoffroy

2017-07-01

Topological insulators, a hallmark of condensed matter physics, have recently reached the classical realm of acoustic waves. A remarkable property of time-reversal invariant topological insulators is the presence of unidirectional spin-polarized propagation along their edges, a property that could lead to a wealth of new opportunities in the ability to guide and manipulate sound. Here, we demonstrate and study the possibility to induce topologically non-trivial acoustic states at the deep subwavelength scale, in a structured two-dimensional metamaterial composed of Helmholtz resonators. Radically different from previous designs based on non-resonant sonic crystals, our proposal enables robust sound manipulation on a surface along predefined, subwavelength pathways of arbitrary shapes.

The polarized atomic-beam target for the EDDA experiment and the time-reversal invariance test at COSY

Science.gov (United States)

Eversheim, P. D.; Altmeier, M.; Felden, O.

1997-02-01

For the the EDDA experiment, which was set up to measure the p¯-p¯ excitation function during the acceleration ramp of the cooler synchrotron COSY at Jülich, a polarized atomic-beam target was designed regarding the restrictions imposed by the geometry of the EDDA detector. Later, when the time-reversal invariance experiment is to be performed, the EDDA detector will serve as efficient internal polarimeter and the source has to deliver tensor polarized deuterons. The modular design of this polarized atomic-beam target that allows to meet these conditions will be discussed in comparison to other existing polarized atomic-beam targets.

Cohomological invariants in Galois cohomology

CERN Document Server

Garibaldi, Skip; Serre, Jean Pierre

2003-01-01

This volume is concerned with algebraic invariants, such as the Stiefel-Whitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of �tale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the Hasse-Witt invariant of quadratic forms. The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of G-torsors with values in H^3(\\mathbb{Q}/\\mathbb{Z}(2)), when G is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant. This is the first time that most of this material appears in print.

The criterion for time symmetry of probabilistic theories and the reversibility of quantum mechanics

International Nuclear Information System (INIS)

Holster, A T

2003-01-01

Physicists routinely claim that the fundamental laws of physics are 'time symmetric' or 'time reversal invariant' or 'reversible'. In particular, it is claimed that the theory of quantum mechanics is time symmetric. But it is shown in this paper that the orthodox analysis suffers from a fatal conceptual error, because the logical criterion for judging the time symmetry of probabilistic theories has been incorrectly formulated. The correct criterion requires symmetry between future-directed laws and past-directed laws. This criterion is formulated and proved in detail. The orthodox claim that quantum mechanics is reversible is re-evaluated. The property demonstrated in the orthodox analysis is shown to be quite distinct from time reversal invariance. The view of Satosi Watanabe that quantum mechanics is time asymmetric is verified, as well as his view that this feature does not merely show a de facto or 'contingent' asymmetry, as commonly supposed, but implies a genuine failure of time reversal invariance of the laws of quantum mechanics. The laws of quantum mechanics would be incompatible with a time-reversed version of our universe

Generating functional for Donaldson invariants and operator algebra in topological D=4 Yang-Mills theory

International Nuclear Information System (INIS)

Johansen, A.A.

1992-01-01

It is shown, that under the certain constraints the generating functional for the Donaldson invariants in the D=4 topological Yang-Mills theory can be interpreted as a partition function for the renormalizable theory. 20 refs

Constraints of a parity-conserving/time-reversal-non-conserving interaction

International Nuclear Information System (INIS)

Oers, Willem T.H. van

2002-01-01

Time-Reversal-Invariance non-conservation has for the first time been unequivocally demonstrated in a direct measurement at CPLEAR. One then can ask the question: What about tests of time-reversal-invariance in systems other than the kaon system? Tests of time-reversal-invariance can be distinguished as belonging to two classes: the first one deals with time-reversal-invariance-non-conserving (T-odd)/parity violating (P-odd) interactions, while the second one deals with T-odd/P-even interactions (assuming CPT conservation this implies C-conjugation non-conservation). Limits on a T-odd/P-odd interaction follow from measurements of the electric dipole moment of the neutron ( -26 e.cm [95% C.L.]). It provides a limit on a T-odd/P-odd pion-nucleon coupling constant which is less than 10 -4 times the weak interaction strength. Experimental limits on a T-odd/P-even interaction are much less stringent. Following the standard approach of describing the nucleon-nucleon interaction in terms of meson exchanges, it can be shown that only charged ρ-meson exchange and A 1 -meson exchange can lead to a T-odd/P-even interaction. The better constraints stem from measurements of the electric dipole moment of the neutron and from measurements of charge-symmetry breaking in neutron-proton elastic scattering. The latter experiments were executed at TRIUMF (497 and 347 MeV) and at IUCF (183 MeV). All other experiments, like detailed balance experiments, polarization - analyzing power difference determinations, and five-fold correlation experiments with polarized incident nucleons and aligned nuclear targets, have been shown to be at least an order to magnitude less sensitive. Is there room for further experimentation?

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

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

International Nuclear Information System (INIS)

Zois, I.P.

2016-01-01

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

Electric–magnetic duality of lattice systems with topological order

Energy Technology Data Exchange (ETDEWEB)

Buerschaper, Oliver [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5 (Canada); Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching (Germany); Christandl, Matthias [Institute for Theoretical Physics, ETH Zurich, 8093 Zurich (Switzerland); Kong, Liang, E-mail: kong.fan.liang@gmail.com [Institute for Advanced Study (Science Hall), Tsinghua University, Beijing 100084 (China); Department of Mathematics and Statistics University of New Hampshire, Durham, NH 03824 (United States); Aguado, Miguel [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching (Germany)

2013-11-11

We investigate the duality structure of quantum lattice systems with topological order, a collective order also appearing in fractional quantum Hall systems. We define electromagnetic (EM) duality for all of Kitaev's quantum double models based on discrete gauge theories with Abelian and non-Abelian groups, and identify its natural habitat as a new class of topological models based on Hopf algebras. We interpret these as extended string-net models, whereupon Levin and Wen's string-nets, which describe all intrinsic topological orders on the lattice with parity and time-reversal invariance, arise as magnetic and electric projections of the extended models. We conjecture that all string-net models can be extended in an analogous way, using more general algebraic and tensor-categorical structures, such that EM duality continues to hold. We also identify this EM duality with an invertible domain wall. Physical applications include topology measurements in the form of pairs of dual tensor networks.

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 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.

Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials

Science.gov (United States)

Shapourian, Hassan; Wang, Yuxuan; Ryu, Shinsei

2018-03-01

We study the intrinsic fully gapped odd-parity superconducting order in doped nodal-loop materials with a torus-shaped Fermi surface. We show that the mirror symmetry, which protects the nodal loop in the normal state, also protects the superconducting state as a topological crystalline superconductor. As a result, the surfaces preserving the mirror symmetry host gapless Majorana cones. Moreover, for a Weyl-loop system (twofold degenerate at the nodal loop), the surfaces that break the mirror symmetry (those parallel to the bulk nodal loop) contribute a Chern (winding) number to the quasi-two-dimensional system in a slab geometry, which leads to a quantized thermal Hall effect and a single Majorana zero mode bound at a vortex line penetrating the system. This Chern number can be viewed as a higher-order topological invariant, which supports hinge modes in a cubic sample when mirror symmetry is broken. For a Dirac-loop system (fourfold degenerate at the nodal loop), the fully gapped odd-parity state can be either time-reversal symmetry-breaking or symmetric, similar to the A and B phases of 3He. In a slab geometry, the A phase has a Chern number two, while the B phase carries a nontrivial Z2 invariant. We discuss the experimental relevance of our results to nodal-loop materials such as CaAgAs.

A simple proof of the existence of adiabatic invariants for perturbed reversible problems

International Nuclear Information System (INIS)

Chartier, P; Faou, E

2008-01-01

In this paper, we give a simple proof of the existence of invariants for reversible perturbations of action-angle systems. The originality of this proof is that it does not rely on canonical transformations that bring the system gradually closer to a normal form, but rather on a formal development of the invariant itself

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

Computation by symmetry operations in a structured model of the brain: Recognition of rotational invariance and time reversal

Science.gov (United States)

McGrann, John V.; Shaw, Gordon L.; Shenoy, Krishna V.; Leng, Xiaodan; Mathews, Robert B.

1994-06-01

Symmetries have long been recognized as a vital component of physical and biological systems. What we propose here is that symmetry operations are an important feature of higher brain function and result from the spatial and temporal modularity of the cortex. These symmetry operations arise naturally in the trion model of the cortex. The trion model is a highly structured mathematical realization of the Mountcastle organizational principle [Mountcastle, in The Mindful Brain (MIT, Cambridge, 1978)] in which the cortical column is the basic neural network of the cortex and is comprised of subunit minicolumns, which are idealized as trions with three levels of firing. A columnar network of a small number of trions has a large repertoire of quasistable, periodic spatial-temporal firing magic patterns (MP's), which can be excited. The MP's are related by specific symmetries: Spatial rotation, parity, ``spin'' reversal, and time reversal as well as other ``global'' symmetry operations in this abstract internal language of the brain. These MP's can be readily enhanced (as well as inherent categories of MP's) by only a small change in connection strengths via a Hebb learning rule. Learning introduces small breaking of the symmetries in the connectivities which enables a symmetry in the patterns to be recognized in the Monte Carlo evolution of the MP's. Examples of the recognition of rotational invariance and of a time-reversed pattern are presented. We propose the possibility of building a logic device from the hardware implementation of a higher level architecture of trion cortical columns.

Observation of elastic topological states in soft materials.

Science.gov (United States)

Li, Shuaifeng; Zhao, Degang; Niu, Hao; Zhu, Xuefeng; Zang, Jianfeng

2018-04-10

Topological elastic metamaterials offer insight into classic motion law and open up opportunities in quantum and classic information processing. Theoretical modeling and numerical simulation of elastic topological states have been reported, whereas the experimental observation remains relatively unexplored. Here we present an experimental observation and numerical simulation of tunable topological states in soft elastic metamaterials. The on-demand reversible switch in topological phase has been achieved by changing filling ratio, tension, and/or compression of the elastic metamaterials. By combining two elastic metamaterials with distinct topological invariants, we further demonstrate the formation and dynamic tunability of topological interface states by mechanical deformation, and the manipulation of elastic wave propagation. Moreover, we provide a topological phase diagram of elastic metamaterials under deformation. Our approach to dynamically control interface states in soft materials paves the way to various phononic systems involving thermal management and soft robotics requiring better use of energy.

Properties of invariant modelling and invariant glueing of vector fields

International Nuclear Information System (INIS)

Petukhov, V.R.

1987-01-01

Invariant modelling and invariant glueing of both continuous (rates and accelerations) and descrete vector fields, gradient and divergence cases are considered. The following appendices are discussed: vector fields in crystals, crystal disclinations, topological charges and their fields

Time-Reversal Generation of Rogue Waves

Science.gov (United States)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

A topological approach unveils system invariances and broken symmetries in the brain.

Science.gov (United States)

Tozzi, Arturo; Peters, James F

2016-05-01

Symmetries are widespread invariances underscoring countless systems, including the brain. A symmetry break occurs when the symmetry is present at one level of observation but is hidden at another level. In such a general framework, a concept from algebraic topology, namely, the Borsuk-Ulam theorem (BUT), comes into play and sheds new light on the general mechanisms of nervous symmetries. The BUT tells us that we can find, on an n-dimensional sphere, a pair of opposite points that have the same encoding on an n - 1 sphere. This mapping makes it possible to describe both antipodal points with a single real-valued vector on a lower dimensional sphere. Here we argue that this topological approach is useful for the evaluation of hidden nervous symmetries. This means that symmetries can be found when evaluating the brain in a proper dimension, although they disappear (are hidden or broken) when we evaluate the same brain only one dimension lower. In conclusion, we provide a topological methodology for the evaluation of the most general features of brain activity, i.e., the symmetries, cast in a physical/biological fashion that has the potential to be operationalized. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Time-reversal breaking and spin transport induced by magnetic impurities in a 2D topological insulator

International Nuclear Information System (INIS)

Derakhshan, V; Ketabi, S A; Moghaddam, A G

2016-01-01

We employed the formalism of bond currents, expressed in terms of non-equilibrium Green’s function to obtain the local currents and transport features of zigzag silicene ribbon in the presence of magnetic impurity. When only intrinsic and Rashba spin–orbit interactions are present, silicene behaves as a two-dimensional topological insulator with gapless edge states. But in the presence of finite intrinsic spin–orbit interaction, the edge states start to penetrate into the bulk of the sample by increasing Rashba interaction strength. The exchange interaction induced by local impurities breaks the time-reversal symmetry of the gapless edge states and influences the topological properties strongly. Subsequently, the singularity of partial Berry curvature disappears and the silicene nanoribbon becomes a trivial insulator. On the other hand, when the concentration of the magnetic impurities is low, the edge currents are not affected significantly. In this case, when the exchange field lies in the x – y plane, the spin mixing around magnetic impurity is more profound rather than the case in which the exchange field is directed along the z -axis. Nevertheless, when the exchange field of magnetic impurities is placed in the x – y plane, a spin-polarized conductance is observed. The resulting conductance polarization can be tuned by the concentration of the impurities and even completely polarized spin transport is achievable. (paper)

Finite-time consensus for leader-following multi-agent systems over switching network topologies

International Nuclear Information System (INIS)

Sun Feng-Lan; Zhu Wei

2013-01-01

Finite-time consensus problem of the leader-following multi-agent system under switching network topologies is studied in this paper. Based on the graph theory, matrix theory, homogeneity with dilation, and LaSalle's invariance principle, the control protocol of each agent using local information is designed, and the detailed analysis of the leader-following finite-time consensus is provided. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results

Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator

Science.gov (United States)

Zhang, Zhiwang; Tian, Ye; Cheng, Ying; Liu, Xiaojun; Christensen, Johan

2017-12-01

Topologically protected wave engineering in artificially structured media resides at the frontier of ongoing metamaterials research, which is inspired by quantum mechanics. Acoustic analogs of electronic topological insulators have recently led to a wealth of new opportunities in manipulating sound propagation by means of robust edge mode excitations through analogies drawn to exotic quantum states. A variety of artificial acoustic systems hosting topological edge states have been proposed analogous to the quantum Hall effect, topological insulators, and Floquet topological insulators in electronic systems. However, those systems were characterized by a fixed geometry and a very narrow frequency response, which severely hinders the exploration and design of useful applications. Here we establish acoustic multipolar pseudospin states as an engineering degree of freedom in time-reversal invariant flow-free phononic crystals and develop reconfigurable topological insulators through rotation of their meta-atoms and reshaping of the metamolecules. Specifically, we show how rotation forms man-made snowflakelike molecules, whose topological phase mimics pseudospin-down (pseudospin-up) dipolar and quadrupolar states, which are responsible for a plethora of robust edge confined properties and topological controlled refraction disobeying Snell's law.

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

2012-07-01

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

Topological properties and global structure of space-time

International Nuclear Information System (INIS)

Bergmann, P.G.; De Sabbata, V.

1986-01-01

This book presents information on the following topics: measurement of gravity and gauge fields using quantum mechanical probes; gravitation at spatial infinity; field theories on supermanifolds; supergravities and Kaluza-Klein theories; boundary conditions at spatial infinity; singularities - global and local aspects; matter at the horizon of the Schwarzschild black hole; introluction to string theories; cosmic censorship and the strengths of singularities; conformal quantisation in singular spacetimes; solar system tests in transition; integration and global aspects of supermanifolds; the space-time of the bimetric general relativity theory; gravitation without Lorentz invariance; a uniform static magnetic field in Kaluza-Klein theory; introduction to topological geons; and a simple model of a non-asymptotically flat Schwarzschild black hole

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.

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.

Nonlinear Time-Reversal in a Wave Chaotic System

Science.gov (United States)

Frazier, Matthew; Taddese, Biniyam; Ott, Edward; Antonsen, Thomas; Anlage, Steven

2012-02-01

Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)

Time-reversal and Bayesian inversion

Science.gov (United States)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

Asymmetric Cherenkov acoustic reverse in topological insulators

Science.gov (United States)

Smirnov, Sergey

2014-09-01

A general phenomenon of the Cherenkov radiation known in optics or acoustics of conventional materials is a formation of a forward cone of, respectively, photons or phonons emitted by a particle accelerated above the speed of light or sound in those materials. Here we suggest three-dimensional topological insulators as a unique platform to fundamentally explore and practically exploit the acoustic aspect of the Cherenkov effect. We demonstrate that by applying an in-plane magnetic field to a surface of a three-dimensional topological insulator one may suppress the forward Cherenkov sound up to zero at a critical magnetic field. Above the critical field the Cherenkov sound acquires pure backward nature with the polar distribution differing from the forward one generated below the critical field. Potential applications of this asymmetric Cherenkov reverse are in the design of low energy electronic devices such as acoustic ratchets or, in general, in low power design of electronic circuits with a magnetic field control of the direction and magnitude of the Cherenkov dissipation.

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...

Wilson loop invariants from WN conformal blocks

Directory of Open Access Journals (Sweden)

Oleg Alekseev

2015-12-01

Full Text Available Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.

Tunable Topological Phononic Crystals

KAUST Repository

Chen, Zeguo

2016-05-27

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

Tunable Topological Phononic Crystals

KAUST Repository

Chen, Zeguo; Wu, Ying

2016-01-01

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

Analytic invariants of boundary links

OpenAIRE

Garoufalidis, Stavros; Levine, Jerome

2001-01-01

Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. Farber.

Braiding knots with topological strings

International Nuclear Information System (INIS)

Gu, Jie

2015-08-01

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

Majorana bound states in two-channel time-reversal-symmetric nanowire systems

DEFF Research Database (Denmark)

Gaidamauskas, Erikas; Paaske, Jens; Flensberg, Karsten

2014-01-01

We consider time-reversal-symmetric two-channel semiconducting quantum wires proximity coupled to a conventional s-wave superconductor. We analyze the requirements for a non-trivial topological phase, and find that necessary conditions are 1) the determinant of the pairing matrix in channel space...

Topological Aspects of Solitons in Ferromagnets

International Nuclear Information System (INIS)

Ren Jirong; Wang Jibiao; Li Ran; Xu Donghui; Duan Yishi

2008-01-01

Two kinds of topological soliton (skyrmion and magnetic vortex ring) in ferromagnets are studied. They have the common topological origin, a tensor H αβ = n-vector · (∂ α n-vector x ∂ β n-vector ), which describes the non-trivial distribution of local orientation of magnetization n-vector at large distances in space. The topological stability of skyrmion is protected by the winding number. Knot-like topological defect as magnetic vortex rings is also studied. On the assumption that magnetic vortex rings are geometric lines, we present their δ-function distribution in ferromagnetic materials. Furthermore, it is briefly shown that Hopf invariant is a proper topological invariant to describe the topology of magnetic vortex rings

Multiperiod Maximum Loss is time unit invariant.

Science.gov (United States)

Kovacevic, Raimund M; Breuer, Thomas

2016-01-01

Time unit invariance is introduced as an additional requirement for multiperiod risk measures: for a constant portfolio under an i.i.d. risk factor process, the multiperiod risk should equal the one period risk of the aggregated loss, for an appropriate choice of parameters and independent of the portfolio and its distribution. Multiperiod Maximum Loss over a sequence of Kullback-Leibler balls is time unit invariant. This is also the case for the entropic risk measure. On the other hand, multiperiod Value at Risk and multiperiod Expected Shortfall are not time unit invariant.

Topological and non-topological soliton solutions to some time

Indian Academy of Sciences (India)

Topological and non-topological soliton solutions to some time-fractional differential equations ... These equations have been widely applied in many branches of nonlinear ... Department of Engineering Sciences, Faculty of Technology and ...

Theta, time reversal and temperature

Energy Technology Data Exchange (ETDEWEB)

Gaiotto, Davide [Perimeter Institute for Theoretical Physics,Waterloo, Ontario, N2L 2Y5 (Canada); Kapustin, Anton [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Komargodski, Zohar [Department of Particle Physics and Astrophysics, Weizmann Institute of Science,Rehovot 76100 (Israel); Seiberg, Nathan [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States)

2017-05-17

SU(N) gauge theory is time reversal invariant at θ=0 and θ=π. We show that at θ=π there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at θ=π the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at θ=0 is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at θ=π, several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for SU(2) gauge theory. The underlying symmetry at θ=π is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two O(2)-symmetric fixed points. It may also be that the four-dimensional theory around θ=π is gapless, e.g. a Coulomb phase could match the underlying anomalies.

Theta, time reversal and temperature

International Nuclear Information System (INIS)

Gaiotto, Davide; Kapustin, Anton; Komargodski, Zohar; Seiberg, Nathan

2017-01-01

SU(N) gauge theory is time reversal invariant at θ=0 and θ=π. We show that at θ=π there is a discrete ’t Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at θ=π the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at θ=0 is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at θ=π, several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for SU(2) gauge theory. The underlying symmetry at θ=π is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two O(2)-symmetric fixed points. It may also be that the four-dimensional theory around θ=π is gapless, e.g. a Coulomb phase could match the underlying anomalies.

Morse theory interpretation of topological quantum field theories

International Nuclear Information System (INIS)

Labastida, J.M.F.

1989-01-01

Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: Topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained. (orig.)

Magnetic topology and the problem of its invariant definition

International Nuclear Information System (INIS)

Hornig, G.; Schindler, K.

1996-01-01

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

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.

Computer calculation of Witten's 3-manifold invariant

International Nuclear Information System (INIS)

Freed, D.S.; Gompf, R.E.

1991-01-01

Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)

Darboux integrability and rational reversibility in cubic systems with two invariant straight lines

Directory of Open Access Journals (Sweden)

Dumitru Cozma

2013-01-01

Full Text Available We find conditions for a singular point O(0,0 of a center or a focus type to be a center, in a cubic differential system with two distinct invariant straight lines. The presence of a center at O(0,0 is proved by using the method of Darboux integrability and the rational reversibility.

Lectures on the Topological Vertex

CERN Document Server

Mariño, M

2008-01-01

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

N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant

International Nuclear Information System (INIS)

Blau, M.; Thompson, G.

1991-11-01

Gauge theory with a topological N=2 symmetry is discussed. This theory captures the de Rahm complex and Riemannian geometry of some underlying moduli space M and the partition function equals the Euler number χ (M) of M. Moduli spaces of instantons and of flat connections in 2 and 3 dimensions are explicitly dealt with. To motivate the constructions the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics are explained and a new kind of supersymmetric quantum mechanics is introduced, based on the Gauss-Codazzi equations. The gauge theory actions are interpreted from the Atiyah-Jeffrey point of view and related to super-symmetric quantum mechanics on spaces of connections. As a consequence of these considerations the Euler number χ (M) of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. The possibility of constructing a topological version of the Penner matrix model is also commented. (author). 63 refs

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.

Statistics of resonances and time reversal reconstruction in aluminum acoustic chaotic cavities

NARCIS (Netherlands)

Antoniuk, O.; Sprik, R.

2010-01-01

The statistical properties of wave propagation in classical chaotic systems are of fundamental interest in physics and are the basis for diagnostic tools in materials science. The statistical properties depend in particular also on the presence of time reversal invariance in the system, which can be

Edge topology and flows in the reversed-field pinch

International Nuclear Information System (INIS)

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

2012-01-01

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

Topological expansion of mixed correlations in the Hermitian 2-matrix model and x-y symmetry of the Fg algebraic invariants

International Nuclear Information System (INIS)

Eynard, B; Orantin, N

2008-01-01

We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. a generating function for counting bicolored discrete surfaces with non-uniform boundary conditions. As an application, we prove the x-y symmetry of Eynard and Orantin (2007 Invariants of algebraic curves and topological expansion Preprint math-ph/0702045)

Two-dimensional topological photonic systems

Science.gov (United States)

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

2017-09-01

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

Additivity for parametrized topological Euler characteristic and Reidemeister torsion

OpenAIRE

Badzioch, Bernard; Dorabiala, Wojciech

2005-01-01

Dwyer, Weiss, and Williams have recently defined the notions of parametrized topological Euler characteristic and parametrized topological Reidemeister torsion which are invariants of bundles of compact topological manifolds. We show that these invariants satisfy additivity formulas paralleling the additive properties of the classical Euler characteristic and Reidemeister torsion of finite CW-complexes.

Geometric model of topological insulators from the Maxwell algebra

Science.gov (United States)

Palumbo, Giandomenico

2017-11-01

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

Estimating Turaev-Viro three-manifold invariants is universal for quantum computation

International Nuclear Information System (INIS)

Alagic, Gorjan; Reichardt, Ben W.; Jordan, Stephen P.; Koenig, Robert

2010-01-01

The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-dimensional topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently decidable by a quantum computer. Thus approximating certain Turaev-Viro invariants of manifolds presented by Heegaard splittings is a universal problem for quantum computation. This establishes a relation between the task of distinguishing nonhomeomorphic 3-manifolds and the power of a general quantum computer.

Are the invariance principles really truly Lorentz covariant?

International Nuclear Information System (INIS)

Arunasalam, V.

1994-02-01

It is shown that some sections of the invariance (or symmetry) principles such as the space reversal symmetry (or parity P) and time reversal symmetry T (of elementary particle and condensed matter physics, etc.) are not really truly Lorentz covariant. Indeed, I find that the Dirac-Wigner sense of Lorentz invariance is not in full compliance with the Einstein-Minkowski reguirements of the Lorentz covariance of all physical laws (i.e., the world space Mach principle)

The ABCD of topological recursion

DEFF Research Database (Denmark)

Andersen, Jorgen Ellegaard; Borot, Gaëtan; Chekhov, Leonid O.

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of math-ph/0702045, seeing it as a quantization of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial data a quantum Airy structure...... the 2d TQFT partition function as a special case), non-commutative Frobenius algebras, loop spaces of Frobenius algebras and a Z2-invariant version of the latter. This Z2-invariant version in the case of a semi-simple Frobenius algebra corresponds to the topological recursion of math-ph/0702045....

Persistent topological features of dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Maletić, Slobodan, E-mail: slobodan@hitsz.edu.cn [Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen (China); Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade (Serbia); Zhao, Yi, E-mail: zhao.yi@hitsz.edu.cn [Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen (China); Rajković, Milan, E-mail: milanr@vinca.rs [Institute of Nuclear Sciences Vinča, University of Belgrade, Belgrade (Serbia)

2016-05-15

Inspired by an early work of Muldoon et al., Physica D 65, 1–16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network.

Finite type invariants and fatgraphs

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry

2010-01-01

–Murakami–Ohtsuki of the link invariant of Andersen–Mattes–Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., G establishes an isomorphism...

Construction of time-dependent dynamical invariants: A new approach

International Nuclear Information System (INIS)

Bertin, M. C.; Pimentel, B. M.; Ramirez, J. A.

2012-01-01

We propose a new way to obtain polynomial dynamical invariants of the classical and quantum time-dependent harmonic oscillator from the equations of motion. We also establish relations between linear and quadratic invariants, and discuss how the quadratic invariant can be related to the Ermakov invariant.

The local Gromov-Witten invariants of configurations of rational curves

CERN Document Server

Karp, D; Marino, M; CERN. Geneva; Karp, Dagan; Liu, Chiu-Chu Melissa; Marino, Marcos

2005-01-01

We compute the local Gromov-Witten invariants of certain configurations of rational curves in a Calabi-Yau threefold. These configurations are connected subcurves of the ``minimal trivalent configuration'', which is a particular tree of CP^1's with specified formal neighborhood. We show that these local invariants are equal to certain global or ordinary Gromov-Witten invariants of a blowup of CP^3 at points, and we compute these ordinary invariants using the geometry of the Cremona transform. We also realize the configurations in question as formal toric schemes and compute their formal Gromov-Witten invariants using the mathematical and physical theories of the topological vertex. In particular, we provide further evidence equating the vertex amplitudes derived from physical and mathematical theories of the topological vertex.

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)

Topological superfluids confined in a nanoscale slab geometry

Science.gov (United States)

Saunders, John

2013-03-01

Nanofluidic samples of superfluid 3He provide a route to explore odd-parity topological superfluids and their surface, edge and defect-bound excitations under well controlled conditions. We have cooled superfluid 3He confined in a precisely defined nano-fabricated cavity to well below 1 mK for the first time. We fingerprint the order parameter by nuclear magnetic resonance, exploiting a SQUID NMR spectrometer of exquisite sensitivity. We demonstrate that dimensional confinement, at length scales comparable to the superfluid Cooper-pair diameter, has a profound influence on the superfluid order of 3He. The chiral A-phase is stabilized at low pressures, in a cavity of height 650 nm. At higher pressures we observe 3He-B with a surface induced planar distortion. 3He-B is a time-reversal invariant topological superfluid, supporting gapless Majorana surface states. In the presence of the small symmetry breaking NMR static magnetic field we observe two possible B-phase states of the order parameter manifold, which can coexist as domains. Non-linear NMR on these states enables a measurement of the surface induced planar distortion, which determines the spectral weight of the surface excitations. The expected structure of the domain walls is such that, at the cavity surface, the line separating the two domains is predicted to host fermion zero modes, protected by symmetry and topology. Increasing confinement should stabilize new p-wave superfluid states of matter, such as the quasi-2D gapped A phase, which breaks time reversal symmetry, has a protected chiral edge mode, and may host half-quantum vortices with a Majorana zero-mode at the core. We discuss experimental progress toward this phase, through measurements on a 100 nm cavity. On the other hand, a cavity height of 1000 nm may stabilize a novel ``striped'' superfluid with spatially modulated order parameter. Supported by EPSRC (UK) GR/J022004/1 and European Microkelvin Consortium, FP7 grant 228464

On topological properties of sierpinski networks

International Nuclear Information System (INIS)

Imran, Muhammad; Sabeel-e-Hafi; Gao, Wei; Reza Farahani, Mohammad

2017-01-01

Sierpinski graphs constitute an extensively studied class of graphs of fractal nature applicable in topology, mathematics of Tower of Hanoi, computer science, and elsewhere. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, biological activity, etc. are determined by the chemical applications of graph theory. These properties can be characterized by certain graph invariants referred to as topological indices. In QRAR/QSPR study these graph invariants has played a vital role. In this paper, we study the molecular topological properties of Sierpinski networks and derive the analytical closed formulas for the atom-bond connectivity (ABC) index, geometric-arithmetic (GA) index, and fourth and fifth version of these topological indices for Sierpinski networks denoted by S(n, k).

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.

Equivariant topological quantum field theory and symmetry protected topological phases

Energy Technology Data Exchange (ETDEWEB)

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

2017-03-01

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

Test of time reversal invariance in p-p elastic scattering at 198.5 MeV

International Nuclear Information System (INIS)

Davis, C.A.; Greeniaus, L.G.; Moss, G.A.

1986-01-01

A precise measurement of the polarization-analyzing power difference in p-p elastic scattering has been made at 198.5 MeV to improve the experimental limits on time reversal violation in proton-proton scattering in this energy region. The experiment was performed in a kinematic regime where sensitivities to time reversal violating amplitudes should be high. Experimental methods which eliminated the need to refer to absolute values of the beam polarization or to the analyzing power of a polarimeter were used. The result is (P-A) = 0.0047 with a statistical uncertainty of +- 0.0025 and a systematic uncertainty of +- 0.0015

CFT and topological recursion

CERN Document Server

Kostov, Ivan

2010-01-01

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

Quantum condensates and topological bosons in coupled light-matter excitations

Energy Technology Data Exchange (ETDEWEB)

Janot, Alexander

2016-02-29

Motivated by the sustained interest in Bose Einstein condensates and the recent progress in the understanding of topological phases in condensed matter systems, we study quantum condensates and possible topological phases of bosons in coupled light-matter excitations, so-called polaritons. These bosonic quasi-particles emerge if electronic excitations (excitons) couple strongly to photons. In the first part of this thesis a polariton Bose Einstein condensate in the presence of disorder is investigated. In contrast to the constituents of a conventional condensate, such as cold atoms, polaritons have a finite life time. Then, the losses have to be compensated by continued pumping, and a non-thermal steady state can build up. We discuss how static disorder affects this non-equilibrium condensate, and analyze the stability of the superfluid state against disorder. We find that disorder destroys the quasi-long range order of the condensate wave function, and that the polariton condensate is not a superfluid in the thermodynamic limit, even for weak disorder, although superfluid behavior would persist in small systems. Furthermore, we analyze the far field emission pattern of a polariton condensate in a disorder environment in order to compare directly with experiments. In the second part of this thesis features of polaritons in a two-dimensional quantum spin Hall cavity with time reversal symmetry are discussed. We propose a topological invariant which has a nontrivial value if the quantum spin Hall insulator is topologically nontrivial. Furthermore, we analyze emerging polaritonic edge states, discuss their relation to the underlying electronic structure, and develop an effective edge state model for polaritons.

On the gauge invariant and topological nature of the localization determining the Quantum Hall Effect plateaus

CERN Document Server

Cabo-Montes de Oca, Alejandro

2002-01-01

It is shown how the electromagnetic response of 2DEG under Quantum Hall Effect regime, characterized by the Chern-Simons topological action, transforms the sample impurities and defects in charge-reservoirs that stabilize the Hall conductivity plateaus. The results determine the basic dynamical origin of the singular properties of localization under the occurrence of the Quantum Hall Effect obtained in the pioneering works of Laughlin and of Joynt and Prange, by means of a gauge invariance argument and a purely electronic analysis, respectively. The common intuitive picture of electrons moving along the equipotential lines gets an analytical realization through the Chern-Simons current and charge densities.

Topological invariants and the dynamics of an axial vector torsion field

International Nuclear Information System (INIS)

Drechsler, W.

1983-01-01

A generalized throry of gravitation is discussed which is based on a Riemann-Cartan space-time, U 4 , with an axial vector torsion field. Besides Einstein's equations determining the metric of the U 4 a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for the U 4 space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic. (author)

Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy

KAUST Repository

Majumdar, Apala; Robbins, J.M.; Zyskin, Maxim

2009-01-01

energy, E (H), for continuous tangent maps of arbitrary homotopy type H. The expression for E (H) involves a topological invariant - the spelling length - associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S2 - {s1

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.

New Limit on Time-Reversal Violation in Beta Decay

International Nuclear Information System (INIS)

Mumm, H. P.; Chupp, T. E.; Cooper, R. L.; Coulter, K. P.; Freedman, S. J.; Fujikawa, B. K.; Garcia, A.; Jones, G. L.; Nico, J. S.; Thompson, A. K.; Trull, C. A.; Wietfeldt, F. E.; Wilkerson, J. F.

2011-01-01

We report the results of an improved determination of the triple correlation DP·(p e xp v ) that can be used to limit possible time-reversal invariance in the beta decay of polarized neutrons and constrain extensions to the standard model. Our result is D=[-0.96±1.89(stat)±1.01(sys)]x10 -4 . The corresponding phase between g A and g V is φ AV =180.013 deg. ±0.028 deg. (68% confidence level). This result represents the most sensitive measurement of D in nuclear β decay.

Superconducting Coset Topological Fluids in Josephson Junction Arrays

CERN Document Server

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

2006-01-01

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

Topological pregauge-pregeometry

International Nuclear Information System (INIS)

Akama, Keiichi; Oda, Ichiro.

1990-12-01

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

Attainable conditions and exact invariant for the time-dependent harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)

2006-09-22

The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.

Attainable conditions and exact invariant for the time-dependent harmonic oscillator

International Nuclear Information System (INIS)

Guasti, Manuel Fernandez

2006-01-01

The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system

On null tests of time-reversal invariance in scattering and reactions

International Nuclear Information System (INIS)

Conzett, H.E.

1993-01-01

There have been suggestions in the literature, both recently and in the more distant past, that, in the lowest-order Born approximation, time-reversal (T)-odd experimental observables in certain reactions are required by T-symmetry to vanish. These observables are the final-state spin-correlation coefficient C xy in the reaction e + e - → τ + τ - and the target analysing power A oy in the inclusive process ep → eX with a polarized proton target. These assertions are in direct conflict with a theorem that states that there can be no null-test of T-symmetry in such processes; that is, T-symmetry does not require any single observable to vanish. This talk addresses the resolution of that conflict

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

Unidirectional transmission in 1D nonlinear photonic crystal based on topological phase reversal by optical nonlinearity

Directory of Open Access Journals (Sweden)

Chong Li

2017-02-01

Full Text Available We propose a scheme of unidirectional transmission in a 1D nonlinear topological photonic crystal based on the topological edge state and three order optical nonlinearity. The 1D photonic crystals consists of a nonlinear photonic crystal L and a linear photonic crystal R. In the backward direction, light is totally reflected for the photons transmission prohibited by the bandgap. While in the forward direction, light interacts with the nonlinear photonic crystal L by optical Kerr effect, bringing a topological phase reversal and results the topological edge mode arising at the interface which could transmit photons through the bandgaps both of the photonic crystal L and R. When the signal power intensity larger than a moderate low threshold value of 10.0 MW/cm2, the transmission contrast ratio could remain at 30 steadily.

Analyzing vortex breakdown flow structures by assignment of colors to tensor invariants.

Science.gov (United States)

Rütten, Markus; Chong, Min S

2006-01-01

Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.

Electrically tuned magnetic order and magnetoresistance in a topological insulator.

Science.gov (United States)

Zhang, Zuocheng; Feng, Xiao; Guo, Minghua; Li, Kang; Zhang, Jinsong; Ou, Yunbo; Feng, Yang; Wang, Lili; Chen, Xi; He, Ke; Ma, Xucun; Xue, Qikun; Wang, Yayu

2014-09-15

The interplay between topological protection and broken time reversal symmetry in topological insulators may lead to highly unconventional magnetoresistance behaviour that can find unique applications in magnetic sensing and data storage. However, the magnetoresistance of topological insulators with spontaneously broken time reversal symmetry is still poorly understood. In this work, we investigate the transport properties of a ferromagnetic topological insulator thin film fabricated into a field effect transistor device. We observe a complex evolution of gate-tuned magnetoresistance, which is positive when the Fermi level lies close to the Dirac point but becomes negative at higher energies. This trend is opposite to that expected from the Berry phase picture, but is intimately correlated with the gate-tuned magnetic order. The underlying physics is the competition between the topology-induced weak antilocalization and magnetism-induced negative magnetoresistance. The simultaneous electrical control of magnetic order and magnetoresistance facilitates future topological insulator based spintronic devices.

Local topology via the invariants of the velocity gradient tensor within vortex clusters and intense Reynolds stress structures in turbulent channel flow

International Nuclear Information System (INIS)

Buchner, Abel-John; Kitsios, Vassili; Atkinson, Callum; Soria, Julio; Lozano-Durán, Adrián

2016-01-01

Previous works have shown that momentum transfer in the wall–normal direction within turbulent wall–bounded flows occurs primarily within coherent structures defined by regions of intense Reynolds stress [1]. Such structures may be classified into wall–attached and wall–detached structures with the latter being typically weak, small–scale, and isotropically oriented, while the former are larger and carry most of the Reynolds stresses. The mean velocity fluctuation within each structure may also be used to separate structures by their dynamic properties. This study aims to extract information regarding the scales, kinematics and dynamics of these structures within the topological framework of the invariants of the velocity gradient tensor (VGT). The local topological characteristics of these intense Reynolds stress structures are compared to the topological characteristics of vortex clusters defined by the discriminant of the velocity gradient tensor. The alignment of vorticity with the principal strain directions within these structures is also determined, and the implications of these findings are discussed. (paper)

Duality and topology

Science.gov (United States)

Sacramento, P. D.; Vieira, V. R.

2018-04-01

Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.

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....

First direct observation of time-reversal non-invariance in the neutral-kaon system

CERN Document Server

Angelopoulos, Angelos; Aslanides, Elie; Backenstoss, Gerhard; Bargassa, P; Behnke, O; Benelli, A; Bertin, V; Blanc, F; Bloch, P; Carlson, P J; Carroll, M; Cawley, E; Chertok, M B; Danielsson, M; Dejardin, M; Derré, J; Ealet, A; Eleftheriadis, C; Faravel, L; Fetscher, W; Fidecaro, Maria; Filipcic, A; Francis, D; Fry, J; Gabathuler, Erwin; Gamet, R; Gerber, H J; Go, A; Haselden, A; Hayman, P J; Henry-Coüannier, F; Hollander, R W; Jon-And, K; Kettle, P R; Kokkas, P; Kreuger, R; Le Gac, R; Leimgruber, F; Mandic, I; Manthos, N; Marel, Gérard; Mikuz, M; Miller, J; Montanet, François; Müller, A; Nakada, Tatsuya; Pagels, B; Papadopoulos, I M; Pavlopoulos, P; Polivka, G; Rickenbach, R; Roberts, B L; Ruf, T; Santoni, C; Schäfer, M; Schaller, L A; Schietinger, T; Schopper, A; Tauscher, Ludwig; Thibault, C; Touchard, F; Touramanis, C; van Eijk, C W E; Vlachos, S; Weber, P; Wigger, O; Wolter, M; Zavrtanik, D; Zimmerman, D

1998-01-01

We report on the first observation of time-reversal symmetry violation through a comparison of the probabilities of $\\bar{K}^0$ transforming into $K^0$ and $K^0$ into $\\bar{K}^0$ as a function of the neutral-kaon eigentime $t$. The comparison is based on the analysis of the neutral-kaon semileptonic decays recorded in the CPLEAR experiment. There, the strangeness of the neutral kaon at time $t=0$ was tagged by the kaon charge in the reaction $p\\bar{p} \\rightarrow K^{\\pm} \\pi^{\\mp} K^0(\\bar{K}^0)$ at rest, whereas the strangeness of the kaon at the decay time $t=\\tau$ was tagged by the lepton charge in the final state. An average decay-rate asymmetry \\begin{equation*} \\langle^{R(\\bar{K}^0_{t=0} \\to e^+\\pi^-\

The Causes of Preference Reversal.

OpenAIRE

Tversky, Amos; Slovic, Paul; Kahneman, Daniel

1990-01-01

Observed preference reversal cannot be adequately explained by violations of independence, the reduction axiom, or transitivity. The primary cause of preference reversal is the failure of procedure invariance, especially the overpricing of low-probability, high-payoff bets. This result violates regret theory and generalized (nonindependent) utility models. Preference reversal and a new reversal involving time preferences are explained by scale compatibility, which implies that payoffs are wei...

Spectroscopic Visualization of Inversion and Time-Reversal Symmetry Breaking Weyl Semi-metals

Science.gov (United States)

Beidenkopf, Haim

A defining property of a topological material is the existence of surface bands that cannot be realized but as the termination of a topological bulk. In a Weyl semi-metal these surface states are in the form of Fermi-arcs. Their open-contour Fermi-surface curves between pairs of surface projections of bulk Weyl cones. Such Dirac-like bulk bands, as opposed to the gapped bulk of topological insulators, land a unique opportunity to examine the deep notion of bulk to surface correspondence. We study the intricate properties both of inversion symmetry broken and of time-reversal symmetry broken Weyl semimetals using scanning tunneling spectroscopy. We visualize the Fermi arc states on the surface of the non-centrosymmetric Weyl semi-metal TaAs. Using the distinct structure and spatial distribution of the wavefunctions associated with the different topological and trivial bands we detect the scattering processes that involve Fermi arcs. Each of these imaged scattering processes entails information on the unique nature of Fermi arcs and their correspondence to the topological bulk. We further visualize the magnetic response of the candidate magnetic Weyl semimetal GdPtBi in which the magnetic order parameter is coupled to the topological classification. European Research Council (ERC-StG no. 678702, TOPO-NW\\x9D), the Israel Science Foundation (ISF), and the United States-Israel Binational Science Foundation (BSF).

Tunable topological phases in photonic and phononic crystals

KAUST Repository

Chen, Zeguo

2018-02-18

Topological photonics/phononics, inspired by the discovery of topological insulators, is a prosperous field of research, in which remarkable one-way propagation edge states are robust against impurities or defect without backscattering. This dissertation discusses the implementation of multiple topological phases in specific designed photonic and phononic crystals. First, it reports a tunable quantum Hall phase in acoustic ring-waveguide system. A new three-band model focused on the topological transitions at the Γ point is studied, which gives the functionality that nontrivial topology can be tuned by changing the strengths of the couplings and/or the broken time-reversal symmetry. The resulted tunable topological edge states are also numerically verified. Second, based on our previous studied acoustic ring-waveguide system, we introduce anisotropy by tuning the couplings along different directions. We find that the bandgap topology is related to the frequency and directions. We report our proposal on a frequency filter designed from such an anisotropic topological phononic crystal. Third, motivated by the recent progress on quantum spin Hall phases, we propose a design of time-reversal symmetry broken quantum spin Hall insulators in photonics, in which a new quantum anomalous Hall phase emerges. It supports a chiral edge state with certain spin orientations, which is robust against the magnetic impurities. We also report the realization of the quantum anomalous Hall phase in phononics.

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

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...

Andreev spectrum with high spin-orbit interactions: Revealing spin splitting and topologically protected crossings

Science.gov (United States)

Murani, A.; Chepelianskii, A.; Guéron, S.; Bouchiat, H.

2017-10-01

In order to point out experimentally accessible signatures of spin-orbit interaction, we investigate numerically the Andreev spectrum of a multichannel mesoscopic quantum wire (N) with high spin-orbit interaction coupled to superconducting electrodes (S), contrasting topological and nontopological behaviors. In the nontopological case (square lattice with Rashba interactions), we find that the Kramers degeneracy of Andreev levels is lifted by a phase difference between the S reservoirs except at multiples of π , when the normal quantum wires can host several conduction channels. The level crossings at these points invariant by time-reversal symmetry are not lifted by disorder. Whereas the dc Josephson current is insensitive to these level crossings, the high-frequency admittance (susceptibility) at finite temperature reveals these level crossings and the lifting of their degeneracy at π by a small Zeeman field. We have also investigated the hexagonal lattice with intrinsic spin-orbit interaction in the range of parameters where it is a two-dimensional topological insulator with one-dimensional helical edges protected against disorder. Nontopological superconducting contacts can induce topological superconductivity in this system characterized by zero-energy level crossing of Andreev levels. Both Josephson current and finite-frequency admittance carry then very specific signatures at low temperature of this disorder-protected Andreev level crossing at π and zero energy.

Universality of the topology of period doubling dynamical systems

International Nuclear Information System (INIS)

Beiersdorfer, P.

1983-10-01

The evolution of the topology of the invariant manifolds of the attractors of 3-D autonomous dynamical systems during period doubling is shown to be universal. The overall topology of the nth attractor is shown to depend only on the topology of the first attractor at birth

Time-reversal asymmetry: polarization and analyzing power in nuclear reactions

International Nuclear Information System (INIS)

Rioux, C.; Roy, R.; Slobodrian, R.J.; Conzett, H.E.

1984-01-01

Measurements of the proton polarization in the reactions 7 Li( 3 He, p vector) 9 Be and 9 Be( 3 He, p vector) 11 B and of the analyzing powers in the inverse reactions, initiated by polarized protons at the same center-of-mass energies, show significant differences. This implies the failure of the polarization-analyzing-power theorem and, prima facie, of time-reversal invariance in these reactions. The reaction 2 H( 3 He, p vector) 4 He and its inverse have also been investigated and show smaller differences. A discussion of instrumental asymmetries is presented

Geometric Model of Topological Insulators from the Maxwell Algebra

Science.gov (United States)

Palumbo, Giandomenico

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

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)

Real topological string amplitudes

Energy Technology Data Exchange (ETDEWEB)

Narain, K.S. [The Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, Trieste, 34151 (Italy); Piazzalunga, N. [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794-3636 (United States); International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy); Tanzini, A. [International School for Advanced Studies (SISSA) and INFN, Sez. di Trieste,via Bonomea 265, Trieste, 34136 (Italy)

2017-03-15

We discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude G{sub χ}, at fixed worldsheet Euler characteristic χ. This corresponds in the low-energy effective action to N=2 Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power g{sup ′}=−χ+1. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude F{sub g}.

The noncommutative index theorem and the periodic table for disordered topological insulators and superconductors

Science.gov (United States)

Katsura, Hosho; Koma, Tohru

2018-03-01

We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions d ≥ 1. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of the topological invariant, are protected by certain symmetries of the Hamiltonian against disorder. This generic feature is characterized by a generalized index theorem which is a noncommutative analog of the Atiyah-Singer index theorem. The noncommutative index defined in terms of a pair of projections gives a precise formula for the topological invariant in each symmetry class in any dimension (d ≥ 1). Under the assumption on the nonvanishing spectral or mobility gap, we prove that the index formula reproduces Bott periodicity and all of the possible values of topological invariants in the classification table of topological insulators and superconductors. We also prove that the indices are robust against perturbations that do not break the symmetry of the unperturbed Hamiltonian.

Gauge invariance of the Rayleigh--Schroedinger time-independent perturbation theory

International Nuclear Information System (INIS)

Yang, K.H.

1977-08-01

It is shown that the Rayleigh-Schroedinger time-independent perturbation theory is gauge invariant when the operator concerned is the particle's instantaneous energy operator H/sub B/ = (1/2m)[vector p - (e/c) vector A] 2 + eV 0 . More explicitly, it is shown that the energy perturbation corrections of each individual order of every state is gauge invariant. When the vector potential is curlless, the energy corrections of all orders are shown to vanish identically regardless of the explicit form of the vector potential. The relation between causality and gauge invariance is investigated. It is shown that gauge invariance guarantees conformity with causality and violation of gauge invariance implies violation of causality

Quantum invariants of knots and 3-manifolds. 2. rev. ed.

International Nuclear Information System (INIS)

Turaev, Vladimir G.

2010-01-01

Due to the strong appeal and wide use of this monograph, it is now available in its second revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. From the contents: - Invariants of graphs in Euclidean 3-space and of closed 3-manifolds - Foundations of topological quantum field theory - Three-dimensional topological quantum field theory - Two-dimensional modular functors - 6j-symbols - Simplicial state sums on 3-manifolds - Shadows of manifolds and state sums on shadows - Constructions of modular categories. (orig.)

Search for time reversal violation in neutron decay; Recherche d'une violation de l'invariance sous le renversement du temps dans la desintegration du neutron

Energy Technology Data Exchange (ETDEWEB)

Gorel, P

2006-06-15

The topic of this thesis is the implementation of an experimental setup designed to measure the R- and N-parameters in polarized neutron decay, together with the data analysis. Four observables are necessary for this measurement: the neutron polarization, the electron momentum and both transverse components of the electron polarization. These last two are measured using a Mott polarimeter. The other observables are determined using the same detectors. The precision to be reached on the R-parameter is 0.5%. A non zero value would sign a time reversal invariance violation and therefore would be a hint of physics beyond the Standard Model. This document presents the work done to prepare and optimize the experimental setup before the data acquisition run performed in 2004. Particular care was taken on the scintillator walls, used to trigger the acquisition and measure the electron energy. The second part concerns the implementation of methods to extract R and N from the data, and the study of the background recorded simultaneously. (author)

A first course in topology continuity and dimension

CERN Document Server

McCleary, John

2006-01-01

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincar� argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time. The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended fo...

Chern Numbers Hiding in Time of Flight Images

Science.gov (United States)

Satija, Indubala; Zhao, Erhai; Ghosh, Parag; Bray-Ali, Noah

2011-03-01

Since the experimental realization of synthetic magnetic fields in neural ultracold atoms, transport measurement such as quantized Hall conductivity remains an open challenge. Here we propose a novel and feasible scheme to measure the topological invariants, namely the chern numbers, in the time of flight images. We study both the commensurate and the incommensurate flux, with the later being the main focus here. The central concept underlying our proposal is the mapping between the chern numbers and the size of the dimerized states that emerge when the two-dimensional hopping is tuned to the highly anisotropic limit. In a uncoupled double quantum Hall system exhibiting time reversal invariance, only odd-sized dimer correlation functions are non-zero and hence encode quantized spin current. Finally, we illustrate that inspite of highly fragmented spectrum, a finite set of chern numbers are meaningful. Our results are supported by direct numerical computation of transverse conductivity. NBA acknowledges support from a National Research Council postdoctoral research associateship.

Invariants of the Dirichlet/Voronoi Tilings of Hyperspheres in Rn and their Dual Delone/Delaunay Graphs

DEFF Research Database (Denmark)

Antón Castro, Francesc/François

2015-01-01

In this paper, we are addressing the geometric and topological invariants that arise in the exact computation of the Delone (Delaunay) graph and the Dirichlet/Voronoi tiling of N-dimensional hyperspheres using Ritt-Wu's algorithm. Our main contribution is a methodology for automated derivation...... of geometric and topological invariants of the Dirichlet tiling of N + 1-dimenional hyperspheres and its dual Delone graph from the invariants of the Dirichlet tiling of N-dimensional hyperspheres and its dual Delone graph (starting from N = 3)....

Invariants of the dirichlet/voronoi tilings of hyperspheres in RN and their dual delone/delaunay graphs

DEFF Research Database (Denmark)

Anton, François

In this paper, we are addressing the geometric and topological invariants that arise in the exact computation of the Delone (Delaunay) graph and the Dirichlet/Voronoi tiling of n-dimensional hyperspheres using Ritt-Wu's algorithm. Our main contribution is a methodology for automated derivation...... of geometric and topological invariants of the Dirichlet tiling of N + 1-dimenional hyperspheres and its dual Delone graph from the invariants of the Dirichlet tiling of N-dimensional hyperspheres and its dual Delone graph (starting from N = 3)....

On fermionic representation of the framed topological vertex

International Nuclear Information System (INIS)

Deng, Fusheng; Zhou, Jian

2015-01-01

The Gromov-Witten invariants of ℂ"3 with branes is encoded in the topological vertex which has a very complicated combinatorial expression. A simple formula for the topological vertex was proposed by Aganagic et al. in the fermionic picture. We will propose a similar formula for the framed topological vertex and prove it in the case when there are one or two branes.

Aspects of Majorana Bound States in One-Dimensional Systems with and without Time-Reversal Symmetry

DEFF Research Database (Denmark)

Wölms, Konrad Udo Hannes

In recent years there has been a lot of interest in topological phases of matter. Unlike conventional phases of matter, topological phases are not distinguished by symmetries, but by so-called topological invariants which have more subtle physical implications. It comes therefore as no surprise...... phase the edge excitations are called Majorana bound states and they are interesting in themselves. There has been a lot of eort in detecting Majorana bound states in the lab. One reason is that these excitations provide evidence that a system is indeed in a topological phase. It is therefore required...... to have unambiguous experimental evidence for the presence Majorana bound states, which in turn requires a good theoretical understanding of the physics associated with Majorana bound states. In particular for the most common experimental methods that are used to study them, the signature of Majorana...

Interfacial Dirac cones from alternating topological invariant superlattice structures of Bi2Se3.

Science.gov (United States)

Song, Jung-Hwan; Jin, Hosub; Freeman, Arthur J

2010-08-27

When the three-dimensional topological insulators Bi2Se3 and Bi2Te3 have an interface with vacuum, i.e., a surface, they show remarkable features such as topologically protected and spin-momentum locked surface states. However, for practical applications, one often requires multiple interfaces or channels rather than a single surface. Here, for the first time, we show that an interfacial and ideal Dirac cone is realized by alternating band and topological insulators. The multichannel Dirac fermions from the superlattice structures open a new way for applications such as thermoelectric and spintronics devices. Indeed, utilizing the interfacial Dirac fermions, we also demonstrate the possible power factor improvement for thermoelectric applications.

The separating topology for the space-times of general relativity

International Nuclear Information System (INIS)

Lindstroem, U.

1977-08-01

The separating topology, first suggested by Zeeman, is defined for the space-times of general relativity. It is defined by a basis. A number of properties are derived. The topology induces the ordinary Euclidean topology on space-like hypersurfaces as well as on timelike curves and the discrete topology on null-cones. The group of auto-homeomorphisms is found to be the group of smooth conformal diffeomorphisms if the space-time is strongly causal. (author)

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.

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

Science.gov (United States)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

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

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.

Topological superconductivity in the extended Kitaev-Heisenberg model

Science.gov (United States)

Schmidt, Johann; Scherer, Daniel D.; Black-Schaffer, Annica M.

2018-01-01

We study superconducting pairing in the doped Kitaev-Heisenberg model by taking into account the recently proposed symmetric off-diagonal exchange Γ . By performing a mean-field analysis, we classify all possible superconducting phases in terms of symmetry, explicitly taking into account effects of spin-orbit coupling. Solving the resulting gap equations self-consistently, we map out a phase diagram that involves several topologically nontrivial states. For Γ breaking chiral phase with Chern number ±1 and a time-reversal symmetric nematic phase that breaks the rotational symmetry of the lattice. On the other hand, for Γ ≥0 we find a time-reversal symmetric phase that preserves all the lattice symmetries, thus yielding clearly distinguishable experimental signatures for all superconducting phases. Both of the time-reversal symmetric phases display a transition to a Z2 nontrivial phase at high doping levels. Finally, we also include a symmetry-allowed spin-orbit coupling kinetic energy and show that it destroys a tentative symmetry-protected topological order at lower doping levels. However, it can be used to tune the time-reversal symmetric phases into a Z2 nontrivial phase even at lower doping.

A computational non-commutative geometry program for disordered topological insulators

CERN Document Server

Prodan, Emil

2017-01-01

This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the co...

Recent Progress in the Study of Topological Semimetals

Science.gov (United States)

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

2018-04-01

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

Topological constraints and their breakdown in dynamical evolution

International Nuclear Information System (INIS)

Goldstein, Raymond E; Moffatt, H Keith; Pesci, Adriana I

2012-01-01

A variety of physical and biological systems exhibit dynamical behaviour that has some explicit or implicit topological features. Here, the term ‘topological’ is meant to convey the idea of structures, e.g. physical knots, links or braids, that have some measure of invariance under continuous deformation. Dynamical evolution is then subject to the topological constraints that express this invariance. The simplest problem arising in these systems is the determination of minimum-energy structures (and routes towards these structures) permitted by such constraints, and elucidation of mechanisms by which the constraints may be broken. In more complex nonequilibrium cases there can be recurring singularities associated with topological rearrangements driven by continuous injection of energy. In this brief overview, motivated by an upcoming program on ‘Topological Dynamics in the Physical and Biological Sciences’ at the Isaac Newton Institute for Mathematical Sciences, we present a summary of this class of dynamical systems and discuss examples of important open problems. (invited articles)

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.

Compound-nuclear tests of time reversal invariance in the nucleon-nucleon interaction

International Nuclear Information System (INIS)

French, J.B.; Pandey, A.; Smith, J.

1987-01-01

The theory for the effects of time-reversal noninvariance (TRNI) in complex systems is reviewed. Applied to the compound-nuclear data for energy-level, width and cross-section fluctuations (the latter for detailed-balance pairs of reactions proceeding through the compound nucleus) this gives bounds on multiparticle TRNI Hamiltonian matrix elements. Using a fluctuation-free form of statistical spectroscopy the results are reduced to bounds on α, the relative magnitude of the TRNI nucleon-nucleon interaction. The level and width analyses for heavy nuclei gave α ≤ 2 x 10 -3 at high (∼99%) statistical confidence; preliminary calculations for detailed balance with 24 Mg(α,p) 27 Al and its inverse gives α ≤ 4 x 10 -3 at the same high confidence, but ≤0.2 x 10 -3 at 80% confidence. Suggestions are made about experiments which should yield sharper bounds. 28 refs., 1 tab

Time-scale invariance as an emergent property in a perceptron with realistic, noisy neurons.

Science.gov (United States)

Buhusi, Catalin V; Oprisan, Sorinel A

2013-05-01

In most species, interval timing is time-scale invariant: errors in time estimation scale up linearly with the estimated duration. In mammals, time-scale invariance is ubiquitous over behavioral, lesion, and pharmacological manipulations. For example, dopaminergic drugs induce an immediate, whereas cholinergic drugs induce a gradual, scalar change in timing. Behavioral theories posit that time-scale invariance derives from particular computations, rules, or coding schemes. In contrast, we discuss a simple neural circuit, the perceptron, whose output neurons fire in a clockwise fashion based on the pattern of coincidental activation of its input neurons. We show numerically that time-scale invariance emerges spontaneously in a perceptron with realistic neurons, in the presence of noise. Under the assumption that dopaminergic drugs modulate the firing of input neurons, and that cholinergic drugs modulate the memory representation of the criterion time, we show that a perceptron with realistic neurons reproduces the pharmacological clock and memory patterns, and their time-scale invariance, in the presence of noise. These results suggest that rather than being a signature of higher order cognitive processes or specific computations related to timing, time-scale invariance may spontaneously emerge in a massively connected brain from the intrinsic noise of neurons and circuits, thus providing the simplest explanation for the ubiquity of scale invariance of interval timing. Copyright © 2013 Elsevier B.V. All rights reserved.

Quasi-topological Ricci polynomial gravities

Science.gov (United States)

Li, Yue-Zhou; Liu, Hai-Shan; Lü, H.

2018-02-01

Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where g tt g rr is constant. The third type is the linearized quasitopological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.

Topological Rankings in Communication Networks

DEFF Research Database (Denmark)

Aabrandt, Andreas; Hansen, Vagn Lundsgaard; Træholt, Chresten

2015-01-01

In the theory of communication the central problem is to study how agents exchange information. This problem may be studied using the theory of connected spaces in topology, since a communication network can be modelled as a topological space such that agents can communicate if and only...... if they belong to the same path connected component of that space. In order to study combinatorial properties of such a communication network, notions from algebraic topology are applied. This makes it possible to determine the shape of a network by concrete invariants, e.g. the number of connected components...

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

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

Science.gov (United States)

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

2018-03-01

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

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.

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.

Decentralized control of discrete-time linear time invariant systems with input saturation

NARCIS (Netherlands)

Deliu, C.; Deliu, Ciprian; Malek, Babak; Roy, Sandip; Saberi, Ali; Stoorvogel, Antonie Arij

We study decentralized stabilization of discrete-time linear time invariant (LTI) systems subject to actuator saturation, using LTI controllers. The requirement of stabilization under both saturation constraints and decentralization impose obvious necessary conditions on the open-loop plant, namely

Decentralized control of discrete-time linear time invariant systems with input saturation

NARCIS (Netherlands)

Deliu, Ciprian; Deliu, C.; Malek, Babak; Roy, Sandip; Saberi, Ali; Stoorvogel, Antonie Arij

2009-01-01

We study decentralized stabilization of discrete time linear time invariant (LTI) systems subject to actuator saturation, using LTI controllers. The requirement of stabilization under both saturation constraints and decentralization impose obvious necessary conditions on the open-loop plant, namely

Tokunaga self-similarity arises naturally from time invariance

Science.gov (United States)

Kovchegov, Yevgeniy; Zaliapin, Ilya

2018-04-01

The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching process G (s ) that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of G (s ) with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region where the process satisfies the Tokunaga condition (and hence is time invariant), G (s ) enjoys many of the symmetries observed in a critical binary Galton-Watson branching process and reproduces the latter for a particular parameter value.

Polar Kerr effect studies of time reversal symmetry breaking states in heavy fermion superconductors

Energy Technology Data Exchange (ETDEWEB)

Schemm, E.R., E-mail: eschemm@alumni.stanford.edu [Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305 (United States); Levenson-Falk, E.M. [Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305 (United States); Department of Physics, Stanford University, Stanford, CA 94305 (United States); Kapitulnik, A. [Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305 (United States); Department of Physics, Stanford University, Stanford, CA 94305 (United States); Department of Applied Physics, Stanford University, Stanford, CA 94305 (United States); Stanford Institute of Energy and Materials Science, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025 (United States)

2017-04-15

Highlights: • Polar Kerr effect (PKE) probes broken time-reversal symmetry (TRS) in superconductors. • Absence of PKE below Tc in CeCoIn{sub 5} is consistent with dx2-y2 order parameter symmetry. • PKE in the B phase of the multiphase superconductor UPt3 agrees with an E2u model. • Data on URu2Si2 show broken TRS and additional structure in the superconducting state. - Abstract: The connection between chiral superconductivity and topological order has emerged as an active direction in research as more instances of both have been identified in condensed matter systems. With the notable exception of {sup 3}He-B, all of the known or suspected chiral – that is to say time-reversal symmetry-breaking (TRSB) – superfluids arise in heavy fermion superconductors, although the vast majority of heavy fermion superconductors preserve time-reversal symmetry. Here we review recent experimental efforts to identify TRSB states in heavy fermion systems via measurement of polar Kerr effect, which is a direct consequence of TRSB.

Cognitive Invariants of Geographic Event Conceptualization: What Matters and What Refines?

Science.gov (United States)

Klippel, Alexander; Li, Rui; Hardisty, Frank; Weaver, Chris

Behavioral experiments addressing the conceptualization of geographic events are few and far between. Our research seeks to address this deficiency by developing an experimental framework on the conceptualization of movement patterns. In this paper, we report on a critical experiment that is designed to shed light on the question of cognitively salient invariants in such conceptualization. Invariants have been identified as being critical to human information processing, particularly for the processing of dynamic information. In our experiment, we systematically address cognitive invariants of one class of geographic events: single entity movement patterns. To this end, we designed 72 animated icons that depict the movement patterns of hurricanes around two invariants: size difference and topological equivalence class movement patterns endpoints. While the endpoint hypothesis, put forth by Regier (2007), claims a particular focus of human cognition to ending relations of events, other research suggests that simplicity principles guide categorization and, additionally, that static information is easier to process than dynamic information. Our experiments show a clear picture: Size matters. Nonetheless, we also find categorization behaviors consistent with experiments in both the spatial and temporal domain, namely that topology refines these behaviors and that topological equivalence classes are categorized consistently. These results are critical steppingstones in validating spatial formalism from a cognitive perspective and cognitively grounding work on ontologies.

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

Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice

Science.gov (United States)

Khanikaev, Alexander B.; Fleury, Romain; Mousavi, S. Hossein; Alù, Andrea

2015-10-01

Topological insulators do not allow conduction in the bulk, yet they support edge modes that travel along the boundary only in one direction, determined by the carried electron spin, with inherent robustness to defects and disorder. Topological insulators have inspired analogues in photonics and optics, in which one-way edge propagation in topologically protected two-dimensional materials is achieved breaking time-reversal symmetry with a magnetic bias. Here, we introduce the concept of topological order in classical acoustics, realizing robust topological protection and one-way edge propagation of sound in a suitably designed resonator lattice biased with angular momentum, forming the acoustic analogue of a magnetically biased graphene layer. Extending the concept of an acoustic nonreciprocal circulator based on angular-momentum bias, time-reversal symmetry is broken here using moderate rotational motion of air within each element of the lattice, which takes the role of the electron spin in determining the direction of modal edge propagation.

Phylogenetic mixtures and linear invariants for equal input models.

Science.gov (United States)

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

Inflation and Topological Phase Transition Driven by Exotic Smoothness

Directory of Open Access Journals (Sweden)

Torsten Asselmeyer-Maluga

2014-01-01

Full Text Available We will discuss a model which describes the cause of inflation by a topological transition. The guiding principle is the choice of an exotic smoothness structure for the space-time. Here we consider a space-time with topology S3×ℝ. In case of an exotic S3×ℝ, there is a change in the spatial topology from a 3-sphere to a homology 3-sphere which can carry a hyperbolic structure. From the physical point of view, we will discuss the path integral for the Einstein-Hilbert action with respect to a decomposition of the space-time. The inclusion of the boundary terms produces fermionic contributions to the partition function. The expectation value of an area (with respect to some surface shows an exponential increase; that is, we obtain inflationary behavior. We will calculate the amount of this increase to be a topological invariant. Then we will describe this transition by an effective model, the Starobinski or R2 model which is consistent with the current measurement of the Planck satellite. The spectral index and other observables are also calculated.

First direct observation of time-reversal violation

International Nuclear Information System (INIS)

Angelopoulos, A.; Apostolakis, A.; Aslanides, E.; Bertin, V.; Ealet, A.; Henry-Couannier, F.; Le Gac, R.; Montanet, F.; Touchard, F.; Backenstoss, G.; Benelli, A.; Kokkas, P.; Leimgruber, F.; Pavlopoulos, P.; Polivka, G.; Rickenbach, R.; Schietinger, T.; Tauscher, L.; Vlachos, S.; Bargassa, P.

2000-01-01

Using its unique capability of strangeness tagging at K 0 production in pp-bar→K ± π ± K 0 (K-bar) 0 ) and at decay with the lepton charge in semileptonic decays CPLEAR measured the semileptonic decay-rate asymmetry (R(K-bar) 0 →e + π - ν)-R(K 0 →e - π + ν-bar)/R(K-bar) 0 →e + π - ν)+R(K 0 →e - π + ν-bar). The asymmetry, fitted over the eigentime interval 1-20 τ S , yielded a non-zero result of (6.6±1.3 stat ±1.1 syst )x10 -3 . A thorough phenomenological analysis identifies T violation in K 0 mixing and/or CPT violation in semileptonic decays as possible interpretations. A confrontation with world data on neutral kaon decays, however, excludes the latter with sufficient precision to establish the result as the first direct observation of time reversal non-invariance

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

International Nuclear Information System (INIS)

Fu Jingli; Jimenez, Salvador; Tang Yifa; Vazquez, Luis

2008-01-01

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Fu Jingli [Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)], E-mail: sqfujingli@163.com; Jimenez, Salvador [Departamento de Matematica Aplicada TTII, E.T.S.I. Telecomunicacion, Universidad Politecnica de Madrid, 28040 Madrid (Spain); Tang Yifa [State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Vazquez, Luis [Departamento de Matematica Aplicada Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de Astrobiologia (CSIC-INTA), Torrejon de Ardoz, 28850 Madrid (Spain)

2008-03-03

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out.

Search for time reversal violation in neutron decay; Recherche d'une violation de l'invariance sous le renversement du temps dans la desintegration du neutron

Energy Technology Data Exchange (ETDEWEB)

Gorel, P

2006-06-15

The topic of this thesis is the implementation of an experimental setup designed to measure the R- and N-parameters in polarized neutron decay, together with the data analysis. Four observables are necessary for this measurement: the neutron polarization, the electron momentum and both transverse components of the electron polarization. These last two are measured using a Mott polarimeter. The other observables are determined using the same detectors. The precision to be reached on the R-parameter is 0.5%. A non zero value would sign a time reversal invariance violation and therefore would be a hint of physics beyond the Standard Model. This document presents the work done to prepare and optimize the experimental setup before the data acquisition run performed in 2004. Particular care was taken on the scintillator walls, used to trigger the acquisition and measure the electron energy. The second part concerns the implementation of methods to extract R and N from the data, and the study of the background recorded simultaneously. (author)

New technique for real-time distortion-invariant multiobject recognition and classification

Science.gov (United States)

Hong, Rutong; Li, Xiaoshun; Hong, En; Wang, Zuyi; Wei, Hongan

2001-04-01

A real-time hybrid distortion-invariant OPR system was established to make 3D multiobject distortion-invariant automatic pattern recognition. Wavelet transform technique was used to make digital preprocessing of the input scene, to depress the noisy background and enhance the recognized object. A three-layer backpropagation artificial neural network was used in correlation signal post-processing to perform multiobject distortion-invariant recognition and classification. The C-80 and NOA real-time processing ability and the multithread programming technology were used to perform high speed parallel multitask processing and speed up the post processing rate to ROIs. The reference filter library was constructed for the distortion version of 3D object model images based on the distortion parameter tolerance measuring as rotation, azimuth and scale. The real-time optical correlation recognition testing of this OPR system demonstrates that using the preprocessing, post- processing, the nonlinear algorithm os optimum filtering, RFL construction technique and the multithread programming technology, a high possibility of recognition and recognition rate ere obtained for the real-time multiobject distortion-invariant OPR system. The recognition reliability and rate was improved greatly. These techniques are very useful to automatic target recognition.

Calculating topological entropy for transient chaos with an application to communicating with chaos

International Nuclear Information System (INIS)

Jacobs, J.; Ott, E.; Hunt, B.R.

1998-01-01

Recent work on communicating with chaos provides a practical motivation for being able to determine numerically the topological entropy for chaotic invariant sets. In this paper we discuss numerical methods for evaluating topological entropy. To assess the accuracy and convergence of the methods, we test them in situations where the topological entropy is known independently. We also discuss the entropy of invariant chaotic saddles formed by those points in a given attractor that never visit some forbidden 'gap' region. Such gaps have been proposed as a means of providing noise immunity in schemes for communication with chaos, and we discuss the dependence of the topological entropy on the size of the gap. copyright 1998 The American Physical Society

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.

A topological extension of GR: Black holes induce dark energy

International Nuclear Information System (INIS)

Spaans, M

2013-01-01

A topological extension of general relativity is presented. The superposition principle of quantum mechanics, as formulated by the Feynman path integral, is taken as a starting point. It is argued that the trajectories that enter this path integral are distinct and thus that space-time topology is multiply connected. Specifically, space-time at the Planck scale consists of a lattice of three-tori that facilitates many distinct paths for particles to travel along. To add gravity, mini black holes are attached to this lattice. These mini black holes represent Wheeler's quantum foam and result from the fact that GR is not conformally invariant. The number of such mini black holes in any time-slice through four-space is found to be equal to the number of macroscopic (so long-lived) black holes in the entire universe. This connection, by which macroscopic black holes induce mini black holes, is a topological expression of Mach's principle. The proposed topological extension of GR can be tested because, if correct, the dark energy density of the universe should be proportional the total number of macroscopic black holes in the universe at any time. This prediction, although strange, agrees with current astrophysical observations.

On topological approach to local theory of surfaces in Calabi-Yau threefolds

DEFF Research Database (Denmark)

Gukov, Sergei; Liu, Chiu-Chu Melissa; Sheshmani, Artan

2017-01-01

We study the web of dualities relating various enumerative invariants, notably Gromov-Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson-Thomas gauge theory and its reductions to D=4 and D=2 which are relevant to the local theory of surfaces...

Building blocks of topological quantum chemistry: Elementary band representations

Science.gov (United States)

Cano, Jennifer; Bradlyn, Barry; Wang, Zhijun; Elcoro, L.; Vergniory, M. G.; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei

2018-01-01

The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time reversal in his theory of "elementary" band representations. In a recent paper [Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268] we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wave functions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.

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

Effective Hamiltonian for protected edge states in graphene

International Nuclear Information System (INIS)

Winkler, R.; Deshpande, H.

2017-01-01

Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.

Embedded graph invariants in Chern-Simons theory

International Nuclear Information System (INIS)

Major, Seth A.

1999-01-01

Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices

Topological vortices in gauge models of graphene

Science.gov (United States)

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

2018-06-01

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

A Relation Between Topological Quantum Field Theory and the Kodama State

OpenAIRE

Oda, Ichiro

2003-01-01

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

Scale-invariant Green-Kubo relation for time-averaged diffusivity

Science.gov (United States)

Meyer, Philipp; Barkai, Eli; Kantz, Holger

2017-12-01

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function. The time-averaged mean-squared displacement is given by 〈δ2¯〉 ˜2 DνtβΔν -β , where t is the total measurement time and Δ is the lag time. Here ν is the anomalous diffusion exponent obtained from ensemble-averaged measurements 〈x2〉 ˜tν , while β ≥-1 marks the growth or decline of the kinetic energy 〈v2〉 ˜tβ . Thus, we establish a connection between exponents that can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant Dν. We demonstrate our results with nonstationary scale-invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. If the averaged kinetic energy is finite, β =0 , the time scaling of 〈δ2¯〉 and 〈x2〉 are identical; however, the time-averaged transport coefficient Dν is not identical to the corresponding ensemble-averaged diffusion constant.

Superconductivity and ferromagnetism in topological insulators

Science.gov (United States)

Zhang, Duming

Topological insulators, a new state of matter discovered recently, have attracted great interest due to their novel properties. They are insulating inside the bulk, but conducting at the surface or edges. This peculiar behavior is characterized by an insulating bulk energy gap and gapless surface or edge states, which originate from strong spin-orbit coupling and time-reversal symmetry. The spin and momentum locked surface states not only provide a model system to study fundamental physics, but can also lead to applications in spintronics and dissipationless electronics. While topological insulators are interesting by themselves, more exotic behaviors are predicted when an energy gap is induced at the surface. This dissertation explores two types of surface state gap in topological insulators, a superconducting gap induced by proximity effect and a magnetic gap induced by chemical doping. The first three chapters provide introductory theory and experimental details of my research. Chapter 1 provides a brief introduction to the theoretical background of topological insulators. Chapter 2 is dedicated to material synthesis principles and techniques. I will focus on two major synthesis methods: molecular beam epitaxy for the growth of Bi2Se3 thin films and chemical vapor deposition for the growth of Bi2Se3 nanoribbons and nanowires. Material characterization is discussed in Chapter 3. I will describe structural, morphological, magnetic, electrical, and electronic characterization techniques used to study topological insulators. Chapter 4 discusses the experiments on proximity-induced superconductivity in topological insulator (Bi2Se3) nanoribbons. This work is motivated by the search for the elusive Majorana fermions, which act as their own antiparticles. They were proposed by Ettore Majorara in 1937, but have remained undiscovered. Recently, Majorana's concept has been revived in condensed matter physics: a condensed matter analog of Majorana fermions is predicted to

Theory and computation of disturbance invariant sets for discrete-time linear systems

Directory of Open Access Journals (Sweden)

Kolmanovsky Ilya

1998-01-01

Full Text Available This paper considers the characterization and computation of invariant sets for discrete-time, time-invariant, linear systems with disturbance inputs whose values are confined to a specified compact set but are otherwise unknown. The emphasis is on determining maximal disturbance-invariant sets X that belong to a specified subset Γ of the state space. Such d-invariant sets have important applications in control problems where there are pointwise-in-time state constraints of the form χ ( t ∈ Γ . One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic-based, nonlinear multimode regulator. For plants with disturbance inputs and state-control constraints it enlarges the constraint-admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.

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

Time-scale invariances in preseismic electromagnetic radiation, magnetization and damage evolution of rocks

Directory of Open Access Journals (Sweden)

Y. Kawada

2007-10-01

Full Text Available We investigate the time-scale invariant changes in electromagnetic and mechanical energy releases prior to a rock failure or a large earthquake. The energy release processes are caused by damage evolutions such as crack propagation, motion of charged dislocation, area-enlargement of sheared asperities and repetitive creep-rate changes. Damage mechanics can be used to represent the time-scale invariant evolutions of both brittle and plastic damages. Irreversible thermodynamics applied to the damage mechanics reveals that the damage evolution produces the variations in charge, dipole and electromagnetic signals in addition to mechanical energy release, and yields the time-scale invariant patterns of Benioff electromagnetic radiation and cumulative Benioff strain-release. The irreversible thermodynamic framework of damage mechanics is also applicable to the seismo-magnetic effect, and the time-scale invariance is recognized in the remanent magnetization change associated with damage evolution prior to a rock failure.

Multiple topological phases in phononic crystals

KAUST Repository

Chen, Zeguo; Wu, Ying

2017-01-01

We report a new topological phononic crystal in a ring-waveguide acoustic system. In the previous reports on topological phononic crystals, there are two types of topological phases: quantum Hall phase and quantum spin Hall phase. A key point in achieving quantum Hall insulator is to break the time-reversal (TR) symmetry, and for quantum spin Hall insulator, the construction of pseudo-spin is necessary. We build such pseudo-spin states under particular crystalline symmetry (C-6v) and then break the degeneracy of the pseudo-spin states by introducing airflow to the ring. We study the topology evolution by changing both the geometric parameters of the unit cell and the strength of the applied airflow. We find that the system exhibits three phases: quantum spin Hall phase, conventional insulator phase and a new quantum anomalous Hall phase.

Multiple topological phases in phononic crystals

KAUST Repository

Chen, Zeguo

2017-11-20

We report a new topological phononic crystal in a ring-waveguide acoustic system. In the previous reports on topological phononic crystals, there are two types of topological phases: quantum Hall phase and quantum spin Hall phase. A key point in achieving quantum Hall insulator is to break the time-reversal (TR) symmetry, and for quantum spin Hall insulator, the construction of pseudo-spin is necessary. We build such pseudo-spin states under particular crystalline symmetry (C-6v) and then break the degeneracy of the pseudo-spin states by introducing airflow to the ring. We study the topology evolution by changing both the geometric parameters of the unit cell and the strength of the applied airflow. We find that the system exhibits three phases: quantum spin Hall phase, conventional insulator phase and a new quantum anomalous Hall phase.

Frozen reaction fronts in steady flows: A burning-invariant-manifold perspective

Science.gov (United States)

Mahoney, John R.; Li, John; Boyer, Carleen; Solomon, Tom; Mitchell, Kevin A.

2015-12-01

The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the reacted domain is static, and the front appears "frozen." Our central result is that these frozen fronts in the two-dimensional fluid are composed of segments of burning invariant manifolds, invariant manifolds of front-element dynamics in x y θ space, where θ is the front orientation. Burning invariant manifolds (BIMs) have been identified previously as important local barriers to front propagation in fluid flows. The relevance of BIMs for frozen fronts rests in their ability, under appropriate conditions, to form global barriers, separating reacted domains from nonreacted domains for all time. The second main result of this paper is an understanding of bifurcations that lead from a nonfrozen state to a frozen state, as well as bifurcations that change the topological structure of the frozen front. Although the primary results of this study apply to general fluid flows, our analysis focuses on a chain of vortices in a channel flow with an imposed wind. For this system, we present both experimental and numerical studies that support the theoretical analysis developed here.

Topological dimension and dynamical systems

CERN Document Server

Coornaert, Michel

2015-01-01

Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner’s characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active ar...

Gauge symmetries, topology, and quantisation

International Nuclear Information System (INIS)

Balachandran, A.P.

1994-01-01

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

Topological 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...

Inferring network topology from complex dynamics

International Nuclear Information System (INIS)

Shandilya, Srinivas Gorur; Timme, Marc

2011-01-01

Inferring the network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method for inferring the structural connection topology of a network, given an observation of one collective dynamical trajectory. The general theoretical framework is applicable to arbitrary network dynamical systems described by ordinary differential equations. No interference (external driving) is required and the type of dynamics is hardly restricted in any way. In particular, the observed dynamics may be arbitrarily complex; stationary, invariant or transient; synchronous or asynchronous and chaotic or periodic. Presupposing a knowledge of the functional form of the dynamical units and of the coupling functions between them, we present an analytical solution to the inverse problem of finding the network topology from observing a time series of state variables only. Robust reconstruction is achieved in any sufficiently long generic observation of the system. We extend our method to simultaneously reconstructing both the entire network topology and all parameters appearing linear in the system's equations of motion. Reconstruction of network topology and system parameters is viable even in the presence of external noise that distorts the original dynamics substantially. The method provides a conceptually new step towards reconstructing a variety of real-world networks, including gene and protein interaction networks and neuronal circuits.

Exact scale-invariant background of gravitational waves from cosmic defects.

Science.gov (United States)

Figueroa, Daniel G; Hindmarsh, Mark; Urrestilla, Jon

2013-03-08

We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early universe, are such a scaling source. We emphasize that the result is independent of the topology of the cosmic defects, the order of phase transition, and the nature of the symmetry broken, global or gauged. As an example, using large-scale numerical simulations, we calculate the scale-invariant gravitational wave power spectrum generated by the dynamics of a global O(N) scalar theory. The result approaches the large N theoretical prediction as N(-2), albeit with a large coefficient. The signal from global cosmic strings is O(100) times larger than the large N prediction.

Symplectic invariants of some families of Lagrangian T3-fibrations

International Nuclear Information System (INIS)

Castano Bernard, R.

2003-12-01

We construct families of Lagrangian 3-torus fibrations resembling the topology of some of the singularities in Topological Mirror Symmetry. We perform a detailed analysis of the affine structure on the base of these fibrations near their discriminant loci. This permits us to classify the aforementioned families up to fibre preserving symplectomorphism. The kind of degenerations we investigate give rise to a large number of symplectic invariants. (author)

Superspace gauge fixing of topological Yang-Mills theories

Energy Technology Data Exchange (ETDEWEB)

Constantinidis, Clisthenis P; Piguet, Olivier [Universidade Federal do Espirito Santo (UFES) (Brazil); Spalenza, Wesley [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro (Brazil)

2004-03-01

We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ''shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (orig.)

Superspace gauge fixing of topological Yang-Mills theories

International Nuclear Information System (INIS)

Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley

2004-01-01

We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ''shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (orig.)

Biaxially mechanical tuning of 2-D reversible and irreversible surface topologies through simultaneous and sequential wrinkling.

Science.gov (United States)

Yin, Jie; Yagüe, Jose Luis; Boyce, Mary C; Gleason, Karen K

2014-02-26

Controlled buckling is a facile means of structuring surfaces. The resulting ordered wrinkling topologies provide surface properties and features desired for multifunctional applications. Here, we study the biaxially dynamic tuning of two-dimensional wrinkled micropatterns under cyclic mechanical stretching/releasing/restretching simultaneously or sequentially. A biaxially prestretched PDMS substrate is coated with a stiff polymer deposited by initiated chemical vapor deposition (iCVD). Applying a mechanical release/restretch cycle in two directions loaded simultaneously or sequentially to the wrinkled system results in a variety of dynamic and tunable wrinkled geometries, the evolution of which is investigated using in situ optical profilometry, numerical simulations, and theoretical modeling. Results show that restretching ordered herringbone micropatterns, created through sequential release of biaxial prestrain, leads to reversible and repeatable surface topography. The initial flat surface and the same wrinkled herringbone pattern are obtained alternatively after cyclic release/restretch processes, owing to the highly ordered structure leaving no avenue for trapping irregular topological regions during cycling as further evidenced by the uniformity of strains distributions and negligible residual strain. Conversely, restretching disordered labyrinth micropatterns created through simultaneous release shows an irreversible surface topology whether after sequential or simultaneous restretching due to creation of irregular surface topologies with regions of highly concentrated strain upon formation of the labyrinth which then lead to residual strains and trapped topologies upon cycling; furthermore, these trapped topologies depend upon the subsequent strain histories as well as the cycle. The disordered labyrinth pattern varies after each cyclic release/restretch process, presenting residual shallow patterns instead of achieving a flat state. The ability to

Chern-Simons invariants on hyperbolic manifolds and topological quantum field theories

Energy Technology Data Exchange (ETDEWEB)

Bonora, L. [International School for Advanced Studies (SISSA/ISAS), Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A.; Goncalves, A.E. [Universidade Estadual de Londrina, Departamento de Fisica, Londrina-Parana (Brazil)

2016-11-15

We derive formulas for the classical Chern-Simons invariant of irreducible SU(n)-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of the Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities. (orig.)

Search for time reversal violation in neutron decay

International Nuclear Information System (INIS)

Gorel, P.

2006-06-01

The topic of this thesis is the implementation of an experimental setup designed to measure the R- and N-parameters in polarized neutron decay, together with the data analysis. Four observables are necessary for this measurement: the neutron polarization, the electron momentum and both transverse components of the electron polarization. These last two are measured using a Mott polarimeter. The other observables are determined using the same detectors. The precision to be reached on the R-parameter is 0.5%. A non zero value would sign a time reversal invariance violation and therefore would be a hint of physics beyond the Standard Model. This document presents the work done to prepare and optimize the experimental setup before the data acquisition run performed in 2004. Particular care was taken on the scintillator walls, used to trigger the acquisition and measure the electron energy. The second part concerns the implementation of methods to extract R and N from the data, and the study of the background recorded simultaneously. (author)

Strain-induced topological magnon phase transitions: applications to kagome-lattice ferromagnets

Science.gov (United States)

Owerre, S. A.

2018-06-01

A common feature of topological insulators is that they are characterized by topologically invariant quantity such as the Chern number and the index. This quantity distinguishes a nontrivial topological system from a trivial one. A topological phase transition may occur when there are two topologically distinct phases, and it is usually defined by a gap closing point where the topologically invariant quantity is ill-defined. In this paper, we show that the magnon bands in the strained (distorted) kagome-lattice ferromagnets realize an example of a topological magnon phase transition in the realistic parameter regime of the system. When spin–orbit coupling (SOC) is neglected (i.e. no Dzyaloshinskii–Moriya interaction), we show that all three magnon branches are dispersive with no flat band, and there exists a critical point where tilted Dirac and semi-Dirac point coexist in the magnon spectra. The critical point separates two gapless magnon phases as opposed to the usual phase transition. Upon the inclusion of SOC, we realize a topological magnon phase transition point at the critical strain , where D and J denote the perturbative SOC and the Heisenberg spin exchange interaction respectively. It separates two distinct topological magnon phases with different Chern numbers for and for . The associated anomalous thermal Hall conductivity develops an abrupt change at , due to the divergence of the Berry curvature in momentum space. The proposed topological magnon phase transition is experimentally feasible by applying external perturbations such as uniaxial strain or pressure.

The duality in the topological vector spaces and the linear physical system theory

International Nuclear Information System (INIS)

Oliveira Castro, F.M. de.

1980-01-01

The excitation-response relation in a linear, passive, and causal physical system who has the property of this relation be invariant for a time translation is univocally determined by the general form of the linear and continuous functionals defined on the linear topological space chosen for the representation of the excitations. (L.C.) [pt

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.

Demystifying the constancy of the Ermakov-Lewis invariant for a time-dependent oscillator

Science.gov (United States)

Padmanabhan, T.

2018-03-01

It is well known that the time-dependent harmonic oscillator (TDHO) possesses a conserved quantity, usually called Ermakov-Lewis invariant. I provide a simple physical interpretation of this invariant as well as a whole family of related invariants. This interpretation does not seem to have been noticed in the literature before. The procedure also allows one to tackle some key conceptual issues which arise in the study of quantum fields in the external, time-dependent backgrounds like in the case of particle production in an expanding universe and Schwinger effect.

d $\\leq$ 1 U d $\\geq$ 25 and W constraints from BRST invariance in the C $\

CERN Document Server

Gato-Rivera, Beatriz

1992-01-01

The BRST invariance condition in a highest-weight representation of the topological ($\\equiv$ twisted $N=2$) algebra captures the `invariant' content of two-dimensional gravity coupled to matter. The standard DDK formulation is recovered by splitting the topological generators into $c=-26$ reparametrization ghosts+matter +`Liouville', while a similar splitting involving $c=-2$ ghosts gives rise to the matter dressed in exactly the way required in order that the theory be equivalent to Virasoro constraints on the KP hierarchy. The two dressings of matter with the `Liouville' differ also by their `ghost numbers', which is similar to the existence of representatives of BRST cohomologies with different ghost numbers. The topological central charge $\\ctop\

Time-Scale Invariant Audio Data Embedding

Directory of Open Access Journals (Sweden)

Mansour Mohamed F

2003-01-01

Full Text Available We propose a novel algorithm for high-quality data embedding in audio. The algorithm is based on changing the relative length of the middle segment between two successive maximum and minimum peaks to embed data. Spline interpolation is used to change the lengths. To ensure smooth monotonic behavior between peaks, a hybrid orthogonal and nonorthogonal wavelet decomposition is used prior to data embedding. The possible data embedding rates are between 20 and 30 bps. However, for practical purposes, we use repetition codes, and the effective embedding data rate is around 5 bps. The algorithm is invariant after time-scale modification, time shift, and time cropping. It gives high-quality output and is robust to mp3 compression.

Field transformations, collective coordinates and BRST invariance

International Nuclear Information System (INIS)

Alfaro, J.; Damgaard, P.H.

1989-12-01

A very large class of general field transformations can be viewed as a field theory generalization of the method of collective coordinates. The introduction of new variables induces a gauge invariance in the transformed theory, and the freedom left in gauge fixing this new invariance can be used to find equivalent formulations of the same theory. First the Batalin-Fradkin-Vilkovisky formalism is applied to the Hamiltonian formulation of physical systems that can be described in terms of collective coordinates. We then show how this type of collective coordinate scheme can be generalized to field transformations, and discuss the War Identities of the associated BRST invariance. For Yang-Mills theory a connection to topological field theory and the background field method is explained in detail. In general the resulting BRST invariance we find hidden in any quantum field theory can be viewed as a consequence of our freedom in choosing a basis of coordinates φ(χ) in the action S[φ]. (orig.)

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.

Time-varying and time-invariant dimensions of depression in children and adolescents: Implications for cross-informant agreement.

Science.gov (United States)

Cole, David A; Martin, Joan M; Jacquez, Farrah M; Tram, Jane M; Zelkowitz, Rachel; Nick, Elizabeth A; Rights, Jason D

2017-07-01

The longitudinal structure of depression in children and adolescents was examined by applying a Trait-State-Occasion structural equation model to 4 waves of self, teacher, peer, and parent reports in 2 age groups (9 to 13 and 13 to 16 years old). Analyses revealed that the depression latent variable consisted of 2 longitudinal factors: a time-invariant dimension that was completely stable over time and a time-varying dimension that was not perfectly stable over time. Different sources of information were differentially sensitive to these 2 dimensions. Among adolescents, self- and parent reports better reflected the time-invariant aspects. For children and adolescents, peer and teacher reports better reflected the time-varying aspects. Relatively high cross-informant agreement emerged for the time-invariant dimension in both children and adolescents. Cross-informant agreement for the time-varying dimension was high for adolescents but very low for children. Implications emerge for theoretical models of depression and for its measurement, especially when attempting to predict changes in depression in the context of longitudinal studies. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

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.

Quantum states with topological properties via dipolar interactions

Energy Technology Data Exchange (ETDEWEB)

Peter, David

2015-06-25

This thesis proposes conceptually new ways to realize materials with topological properties by using dipole-dipole interactions. First, we study a system of ultracold dipolar fermions, where the relaxation mechanism of dipolar spins can be used to reach the quantum Hall regime. Second, in a system of polar molecules in an optical lattice, dipole-dipole interactions induce spin-orbit coupling terms for the rotational excitations. In combination with time-reversal symmetry breaking this leads to topological bands with Chern numbers greater than one.

Precise discussion of time-reversal asymmetries in B-meson decays

International Nuclear Information System (INIS)

Morozumi, Takuya; Okane, Hideaki; Umeeda, Hiroyuki

2015-01-01

BaBar collaboration announced that they observed time reversal (T) asymmetry through B meson system. In the experiment, time dependencies of two distinctive processes, B_−→ (B"0)-bar and (B"0)-bar →B_− (− expresses CP value) are compared with each other. In our study, we examine event number difference of these two processes. In contrast to the BaBar asymmetry, the asymmetry of events number includes the overall normalization difference for rates. Time dependence of the asymmetry is more general and it includes terms absent in one used by BaBar collaboration. Both of the BaBar asymmetry and ours are naively thought to be T-odd since two processes compared are related with flipping time direction. We investigate the time reversal transformation property of our asymmetry. Using our notation, one can see that the asymmetry is not precisely a T-odd quantity, taking into account indirect CP and CPT violation of K meson systems. The effect of ϵ_K is extracted and gives rise to O(10"−"3) contribution. The introduced parameters are invariant under rephasing of quarks so that the coefficients of our asymmetry are expressed as phase convention independent quantities. Some combinations of the asymmetry enable us to extract parameters for wrong sign decays of B_d meson, CPT violation, etc. We also study the reason why the T-even terms are allowed to contribute to the asymmetry, and find that several conditions are needed for the asymmetry to be a T-odd quantity.

Topological symmetry breakdown in cholesterics, nematics, and 3He

International Nuclear Information System (INIS)

Balachandran, A.P.; Lizzi, F.; Rodgers, V.G.J.

1984-01-01

Cholesterics, uniaxial and biaxial nematics, and the dipole-free A phase of superfluid 3 He are characterized by order parameters which are left invariant by suitable ''symmetry'' groups H. We show that in the presence of defects, the full group H may not be implementable on the states because of topological obstructions. Thus H is topologically broken in the presence of suitable defects

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.

Superspace gauge fixing of topological Yang-Mills theories

International Nuclear Information System (INIS)

Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley

2003-10-01

We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of 'shift supersymmetry' generators, using a superspace formalism. The super-B F structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and B F gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (author)

Superspace gauge fixing of topological Yang-Mills theories

Energy Technology Data Exchange (ETDEWEB)

Constantinidis, Clisthenis P; Piguet, Olivier [Espirito Santo Univ. (UFES), Vitoria, ES (Brazil); Spalenza, Wesley

2003-10-15

We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of 'shift supersymmetry' generators, using a superspace formalism. The super-B F structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and B F gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (author)

Topological chaos, braiding and bifurcation of almost-cyclic sets.

Science.gov (United States)

Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj

2012-12-01

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.

Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation

CERN Document Server

Qin, Hong

2005-01-01

Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

Topological gravity from a transgression gauge field theory

International Nuclear Information System (INIS)

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

2010-01-01

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

Membrane topology of hedgehog acyltransferase.

Science.gov (United States)

Matevossian, Armine; Resh, Marilyn D

2015-01-23

Hedgehog acyltransferase (Hhat) is a multipass transmembrane enzyme that mediates the covalent attachment of the 16-carbon fatty acid palmitate to the N-terminal cysteine of Sonic Hedgehog (Shh). Palmitoylation of Shh by Hhat is critical for short and long range signaling. Knowledge of the topological organization of Hhat transmembrane helices would enhance our understanding of Hhat-mediated Shh palmitoylation. Bioinformatics analysis of transmembrane domains within human Hhat using 10 different algorithms resulted in highly consistent predictions in the C-terminal, but not in the N-terminal, region of Hhat. To empirically determine the topology of Hhat, we designed and exploited Hhat constructs containing either terminal or 12 different internal epitope tags. We used selective permeabilization coupled with immunofluorescence as well as a protease protection assay to demonstrate that Hhat contains 10 transmembrane domains and 2 re-entrant loops. The invariant His and highly conserved Asp residues within the membrane-bound O-acyltransferase (MBOAT) homology domain are segregated on opposite sides of the endoplasmic reticulum membrane. The localization of His-379 on the lumenal membrane surface is consistent with a role for this invariant residue in catalysis. Analysis of the activity and stability of the Hhat constructs revealed that the C-terminal MBOAT domain is especially sensitive to manipulation. Moreover, there was remarkable similarity in the overall topological organization of Hhat and ghrelin O-acyltransferase, another MBOAT family member. Knowledge of the topological organization of Hhat could serve as an important tool for further design of selective Hhat inhibitors. © 2015 by The American Society for Biochemistry and Molecular Biology, Inc.

QUIPS: Time-dependent properties of quasi-invariant self-gravitating polytropes

International Nuclear Information System (INIS)

Munier, A.; Feix, M.R.

1983-01-01

Quasi-invariance, a method based on group tranformations, is used to obtain time-dependent solutions for the expansion and/or contraction of a self-gravitating sphere of perfect gas with polytopic index n. Quasi-invariance transforms the equations of hydrodynamics into ''dual equations'' exhibiting extra terms such as a friction, a mass source or sink term, and a centripetal/centrifugal force. The search for stationary solutions in this ''dual space'' leads to a new class of time-dependent solutions, the QUIP (for Quasi-invariant polytrope), which generalizes Emden's static model and introduces a characteristic frequency a related to Jean's frequency. The second order differential equation describing the solution is integrated numerically. A critical point is seen always to exist for nnot =3. Solutions corresponding in the ''dual space'' to a time-dependent generalization of Eddington's standard model (n = 3) are discussed. These solutions conserve both the total mass and the energy. A transition between closed and open structures is seen to take place at a particular frequency a/sub c/. For n = 3, no critical point arises in the ''dual space'' due to the self-similar motion of the fluid. A new time-dependent mass-radius relation and a generalized Betti-Ritter relation are obtained. Conclusions about the existence of a minimum Q-factor are presented

M-Polynomial and Related Topological Indices of Nanostar Dendrimers

Directory of Open Access Journals (Sweden)

Mobeen Munir

2016-09-01

Full Text Available Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.

Topological networks for quantum communication between distant qubits

Science.gov (United States)

Lang, Nicolai; Büchler, Hans Peter

2017-11-01

Efficient communication between qubits relies on robust networks, which allow for fast and coherent transfer of quantum information. It seems natural to harvest the remarkable properties of systems characterized by topological invariants to perform this task. Here, we show that a linear network of coupled bosonic degrees of freedom, characterized by topological bands, can be employed for the efficient exchange of quantum information over large distances. Important features of our setup are that it is robust against quenched disorder, all relevant operations can be performed by global variations of parameters, and the time required for communication between distant qubits approaches linear scaling with their distance. We demonstrate that our concept can be extended to an ensemble of qubits embedded in a two-dimensional network to allow for communication between all of them.

Closed 1-forms in topology and geometric group theory

Energy Technology Data Exchange (ETDEWEB)

Farber, Michael; Schuetz, Dirk [University of Durham, Durham (United Kingdom); Geoghegan, Ross [State University of New York, New York (United States)

2010-01-01

In this article we describe relations of the topology of closed 1-forms to the group-theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW-complexes and show that many properties of the group-theoretic version have analogous statements. In particular, we show the relation between Sigma invariants and finiteness properties of certain infinite covering spaces. We also discuss applications of these invariants to the Lusternik-Schnirelmann category of a closed 1-form and to the existence of a non-singular closed 1-form in a given cohomology class on a high-dimensional closed manifold. Bibliography: 32 titles.

Topological transitions at finite temperatures: A real-time numerical approach

International Nuclear Information System (INIS)

Grigoriev, D.Yu.; Rubakov, V.A.; Shaposhnikov, M.E.

1989-01-01

We study topological transitions at finite temperatures within the (1+1)-dimensional abelian Higgs model by a numerical simulation in real time. Basic ideas of the real-time approach are presented and some peculiarities of the Metropolis technique are discussed. It is argued that the processes leading to topological transitions are of classical origin; the transitions can be observed by solving the classical field equations in real time. We show that the topological transitions actually pass via the sphaleron configuration. The transition rate as a function of temperature is found to be in good agreement with the analytical predictions. No extra suppression of the rate is observed. The conditions of applicability of our approach are discussed. The temperature interval where the low-temperature broken phase persists is estimated. (orig.)

A new topology for curved space--time which incorporates the causal, differential, and conformal structures

International Nuclear Information System (INIS)

Hawking, S.W.; King, A.R.; McCarthy, P.J.

1976-01-01

A new topology is proposed for strongly causal space--times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal, differential, and conformal structures of space--time. The topology is more appealing, physical, and manageable than the topology previously proposed by Zeeman for Minkowski space. It thus seems that many calculations involving the above structures may be made purely topological

Integrable topological billiards and equivalent dynamical systems

Science.gov (United States)

Vedyushkina, V. V.; Fomenko, A. T.

2017-08-01

We consider several topological integrable billiards and prove that they are Liouville equivalent to many systems of rigid body dynamics. The proof uses the Fomenko-Zieschang theory of invariants of integrable systems. We study billiards bounded by arcs of confocal quadrics and their generalizations, generalized billiards, where the motion occurs on a locally planar surface obtained by gluing several planar domains isometrically along their boundaries, which are arcs of confocal quadrics. We describe two new classes of integrable billiards bounded by arcs of confocal quadrics, namely, non-compact billiards and generalized billiards obtained by gluing planar billiards along non-convex parts of their boundaries. We completely classify non-compact billiards bounded by arcs of confocal quadrics and study their topology using the Fomenko invariants that describe the bifurcations of singular leaves of the additional integral. We study the topology of isoenergy surfaces for some non-convex generalized billiards. It turns out that they possess exotic Liouville foliations: the integral trajectories of the billiard that lie on some singular leaves admit no continuous extension. Such billiards appear to be leafwise equivalent to billiards bounded by arcs of confocal quadrics in the Minkowski metric.

Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator.

Science.gov (United States)

Wu, Liang; Salehi, M; Koirala, N; Moon, J; Oh, S; Armitage, N P

2016-12-02

Topological insulators have been proposed to be best characterized as bulk magnetoelectric materials that show response functions quantized in terms of fundamental physical constants. Here, we lower the chemical potential of three-dimensional (3D) Bi 2 Se 3 films to ~30 meV above the Dirac point and probe their low-energy electrodynamic response in the presence of magnetic fields with high-precision time-domain terahertz polarimetry. For fields higher than 5 tesla, we observed quantized Faraday and Kerr rotations, whereas the dc transport is still semiclassical. A nontrivial Berry's phase offset to these values gives evidence for axion electrodynamics and the topological magnetoelectric effect. The time structure used in these measurements allows a direct measure of the fine-structure constant based on a topological invariant of a solid-state system. Copyright © 2016, American Association for the Advancement of Science.

Interferometry with particles of non-zero rest mass: topological experiments

International Nuclear Information System (INIS)

Opat, G.I.

1994-01-01

Interferometry as a space-time process is described, together with its topology. Starting from this viewpoint, a convenient unified formalism for the phase shifts which arise in particle interferometry is developed. This formalism is based on a covariant form of Hamilton's action principle and Lagrange's equations of motion. It will be shown that this Lorentz invariant formalism yields a simple perturbation theoretic expression for the general phase shift that arises in matter-wave interferometry. The Lagrangian formalism is compared with the more usual formalism based on the wave propagation vector and frequency. The resulting formalism will be used to analyse the Sagnac effect, gravitational field measurements, and several Aharonov-Bohm-like topological phase shifts. Several topological interferometric experiments using particles of non-zero rest mass are discussed. These experiments involve the use of electrons, neutrons and neutral atoms. Neutron experiments will be emphasised. 45 refs., 15 figs

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

Towards topological quantum computer

Science.gov (United States)

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

2018-01-01

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

Towards topological quantum computer

Directory of Open Access Journals (Sweden)

D. Melnikov

2018-01-01

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

Even-dimensional topological gravity from Chern-Simons gravity

International Nuclear Information System (INIS)

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

2009-01-01

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

Topology-Preserving Rigid Transformation of 2D Digital Images.

Science.gov (United States)

Ngo, Phuc; Passat, Nicolas; Kenmochi, Yukiko; Talbot, Hugues

2014-02-01

We provide conditions under which 2D digital images preserve their topological properties under rigid transformations. We consider the two most common digital topology models, namely dual adjacency and well-composedness. This paper leads to the proposal of optimal preprocessing strategies that ensure the topological invariance of images under arbitrary rigid transformations. These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping.

Riemann, topology, and physics

CERN Document Server

Monastyrsky, Michael I

2008-01-01

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

Algebraic topology a primer

CERN Document Server

Deo, Satya

2018-01-01

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

One-way propagation of bulk states and robust edge states in photonic crystals with broken inversion and time-reversal symmetries

Science.gov (United States)

Lu, Jin-Cheng; Chen, Xiao-Dong; Deng, Wei-Min; Chen, Min; Dong, Jian-Wen

2018-07-01

The valley is a flexible degree of freedom for light manipulation in photonic systems. In this work, we introduce the valley concept in magnetic photonic crystals with broken inversion symmetry. One-way propagation of bulk states is demonstrated by exploiting the pseudo-gap where bulk states only exist at one single valley. In addition, the transition between Hall and valley-Hall nontrivial topological phases is also studied in terms of the competition between the broken inversion and time-reversal symmetries. At the photonic boundary between two topologically distinct photonic crystals, we illustrate the one-way propagation of edge states and demonstrate their robustness against defects.

Broadband Control of Topological Nodes in Electromagnetic Fields

Science.gov (United States)

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

2018-05-01

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

Invariant set computation for constrained uncertain discrete-time systems

NARCIS (Netherlands)

Athanasopoulos, N.; Bitsoris, G.

2010-01-01

In this article a novel approach to the determination of polytopic invariant sets for constrained discrete-time linear uncertain systems is presented. First, the problem of stabilizing a prespecified initial condition set in the presence of input and state constraints is addressed. Second, the

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...

Topological quantum phase transitions in the spin–singlet superconductor with Rashba and Dresselhaus (110) spin–orbit couplings

Energy Technology Data Exchange (ETDEWEB)

You, Jia-Bin, E-mail: jiabinyou@gmail.com [Centre for Quantum Technologies, National University of Singapore, 117543 (Singapore); Chan, A.H. [Department of Physics, National University of Singapore, 117542 (Singapore); Oh, C.H., E-mail: phyohch@nus.edu.sg [Centre for Quantum Technologies, National University of Singapore, 117543 (Singapore); Department of Physics, National University of Singapore, 117542 (Singapore); Vedral, Vlatko [Centre for Quantum Technologies, National University of Singapore, 117543 (Singapore); Department of Physics, National University of Singapore, 117542 (Singapore); Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU (United Kingdom)

2014-10-15

We examine the topological properties of a spin–singlet superconductor with Rashba and Dresselhaus (110) spin–orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov–de Gennes (BdG) Hamiltonian by symmetry analysis. In particular, the Pfaffian invariant P for the particle–hole symmetry can be used to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, an edge index, namely the Pfaffian invariant P(k{sub y}) or the winding number W(k{sub y}), is needed to make them topologically stable. These edge indices can also be used in determining the location of the Majorana flat bands. - Highlights: • Majorana fermion can emerge in the spin–orbit coupled singlet superconductor. • Pfaffian invariant and 1D winding number can be used to identify the nontrivial topological phase where Majorana flat band exists. • All the possible phase diagrams in the spin–orbit coupled singlet superconductor are demonstrated. • Majorana flat band only exists in the y direction in our model. • Majorana flat band has a significant experimental signature in the tunneling conductance measurement.

The volume conjecture and topological strings

NARCIS (Netherlands)

Dijkgraaf, R.; Fuji, H.

2009-01-01

In this paper, we discuss a relation between Jones-Witten theory of knot invariants and topological open string theory on the basis of the volume conjecture. We find a similar Hamiltonian structure for both theories, and interpret the AJ conjecture as the D-module structure for a D-brane partition

Observables in topological Yang-Mills theories with extended shift supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Constantinidis, Clisthenis P; Piguet, Olivier [Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil); Spalenza, Wesley [Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste (Italy); Centro Brasileiro de Pesquisas Fsicas (CBPF), Rio de Janeiro (Brazil)

2006-01-01

We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator. (orig.)

Testing Lorentz invariance in β decay

Directory of Open Access Journals (Sweden)

Sytema A.

2014-03-01

Experimentally we exploit the Gamow-Teller transition of polarized 20Na, where we can test the dependence of the β-decay rate on the spin orientation of 20Na. The polarization degree is measured using the β asymmetry, while the decay rate is measured by the γ yield. A change in the γ rate, when reversing the spin, implies Lorentz invariance violation. The decay rate should depend on sidereal time and the polarization direction relative to the rotation axis of the earth. The method of the measurement will be presented, together with the first results.

Filtration of the classical knot concordance group and Casson-Gordon invariants

Science.gov (United States)

Kim, Taehee

2004-09-01

It is known that if every prime power branched cyclic cover of a knot in S(3) is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in S(3) whose prime power branched cyclic covers are homology spheres. We show that these knots generate an infinite rank subgroup of scrf_{(1.0)}/scrf_{(1.5)} for which Casson-Gordon invariants vanish in Cochran-Orr-Teichner's filtration of the classical knot concordance group. As a corollary, it follows that Casson-Gordon invariants are not a complete set of obstructions to a second layer of Whitney disks.

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

Energy Technology Data Exchange (ETDEWEB)

Jehle, H.

1977-01-01

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

Topology identification of the complex networks with non-delayed and delayed coupling

International Nuclear Information System (INIS)

Guo Wanli; Chen Shihua; Sun Wen

2009-01-01

In practical situation, there exists many uncertain information in complex networks, such as the topological structures. So the topology identification is an important issue in the research of the complex networks. Based on LaSalle's invariance principle, in this Letter, an adaptive controlling method is proposed to identify the topology of a weighted general complex network model with non-delayed and delayed coupling. Finally, simulation results show that the method is effective.

Real-time trajectory analysis using stacked invariance methods

OpenAIRE

Kitts, B.

1998-01-01

Invariance methods are used widely in pattern recognition as a preprocessing stage before algorithms such as neural networks are applied to the problem. A pattern recognition system has to be able to recognise objects invariant to scale, translation, and rotation. Presumably the human eye implements some of these preprocessing transforms in making sense of incoming stimuli, for example, placing signals onto a log scale. This paper surveys many of the commonly used invariance methods, and asse...

Topological quantum field theory and four manifolds

CERN Document Server

Marino, Marcos

2005-01-01

The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the ...

Gauge groups and topological invariants of vacuum manifolds

International Nuclear Information System (INIS)

Golo, V.L.; Monastyrsky, M.I.

1978-01-01

The paper is concerned with topological properties of the vacuum manifolds in the theories with the broken gauge symmetry for the groups of the type SO(k) x U(n), SO(k) x SO(p) x U(r). For the Ginsburg-Landau theory of the superfluid 3 He the gauge transformations are discussed. They provide the means to indicate all possible types of the vacuum manifolds, which are likely to correspond to distinct phases of the superfluid 3 He. Conditions on the existence of the minimums of the Ginsburg-Landau functional are discussed

Impact source identification in finite isotropic plates using a time-reversal method: theoretical study

International Nuclear Information System (INIS)

Chen, Chunlin; Yuan, Fuh-Gwo

2010-01-01

This paper aims to identify impact sources on plate-like structures based on the synthetic time-reversal (T-R) concept using an array of sensors. The impact source characteristics, namely, impact location and impact loading time history, are reconstructed using the invariance of time-reversal concept, reciprocal theory, and signal processing algorithms. Numerical verification for two finite isotropic plates under low and high velocity impacts is performed to demonstrate the versatility of the synthetic T-R method for impact source identification. The results show that the impact location and time history of the impact force with various shapes and frequency bands can be readily obtained with only four sensors distributed around the impact location. The effects of time duration and the inaccuracy in the estimated impact location on the accuracy of the time history of the impact force using the T-R method are investigated. Since the T-R technique retraces all the multi-paths of reflected waves from the geometrical boundaries back to the impact location, it is well suited for quantifying the impact characteristics for complex structures. In addition, this method is robust against noise and it is suggested that a small number of sensors is sufficient to quantify the impact source characteristics through simple computation; thus it holds promise for the development of passive structural health monitoring (SHM) systems for impact monitoring in near real-time

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.

Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators

Directory of Open Access Journals (Sweden)

Michael Hermele

2016-10-01

Full Text Available We introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry-enriched topological (SET phases. We focus on bosonic systems with Z_{2} topological order and a symmetry group of the form G=U(1⋊G^{′}, where G^{′} is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly d=2 systems but can occur at surfaces of d=3 symmetry-protected topological (SPT phases. This observation leads to examples of d=3 bosonic topological crystalline insulators (TCIs that, to our knowledge, have not previously been identified. In some cases, these d=3 bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by nontrivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1 symmetry and to show that some fractionalization patterns cannot be extended to a consistent action of G^{′} symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to d=1 SPT phases. We apply our method to several different symmetry groups with nontrivial anomalies, including G=U(1×Z_{2}^{T} and G=U(1×Z_{2}^{P}, where Z_{2}^{T} and Z_{2}^{P} are time-reversal and d=2 reflection symmetry, respectively.

Exact invariants in the form of momentum resonances for particle motion in one-dimensional, time-dependent potentials

International Nuclear Information System (INIS)

Goedert, J.; Lewis, H.R.

1984-01-01

A momentum-resonance ansatz of Lewis and Leach was used to study exact invariants for time-dependent, one-dimensional potentials. This ansatz provides a framework for finding invariants admitted by a larger class of time-dependent potentials that was known previously. For a potential that admits an exact invariant in this resonance form, we have shown how to construct the invariant as a functional of the potential in terms of the solution of a definite linear algebraic system of equations. We have found a necessary and sufficient condition on the potential for the existence of an invariant with a given number of resonances. There exist more potentials that admit invariants with two resonances than were previously known and we have found an example in parametric form of such a potential. We have also found examples of potentials that admit invariants with three resonances

WKB solutions of difference equations and reconstruction by the topological recursion

Science.gov (United States)

Marchal, Olivier

2018-01-01

The purpose of this article is to analyze the connection between Eynard-Orantin topological recursion and formal WKB solutions of a \\hbar -difference equation: \\Psi(x+\\hbar)=≤ft(e\\hbar\\fracd{dx}\\right) \\Psi(x)=L(x;\\hbar)\\Psi(x) with L(x;\\hbar)\\in GL_2( ({C}(x))[\\hbar]) . In particular, we extend the notion of determinantal formulas and topological type property proposed for formal WKB solutions of \\hbar -differential systems to this setting. We apply our results to a specific \\hbar -difference system associated to the quantum curve of the Gromov-Witten invariants of {P}1 for which we are able to prove that the correlation functions are reconstructed from the Eynard-Orantin differentials computed from the topological recursion applied to the spectral curve y=\\cosh-1\\frac{x}{2} . Finally, identifying the large x expansion of the correlation functions, proves a recent conjecture made by Dubrovin and Yang regarding a new generating series for Gromov-Witten invariants of {P}1 .

Topology Identification of General Dynamical Network with Distributed Time Delays

International Nuclear Information System (INIS)

Zhao-Yan, Wu; Xin-Chu, Fu

2009-01-01

General dynamical networks with distributed time delays are studied. The topology of the networks are viewed as unknown parameters, which need to be identified. Some auxiliary systems (also called the network estimators) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied in designing these network estimators. Based on linear matrix inequalities and the Lyapunov function method, the sufficient condition for the achievement of topology identification is obtained. This method can also better monitor the switching topology of dynamical networks. Illustrative examples are provided to show the effectiveness of this method. (general)

The topology of geodesically complete space-times

International Nuclear Information System (INIS)

Lee, C.W.

1983-01-01

Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic to S 3 then the part of space-time that it encloses must be simply connected. (author)

Time-warp invariant pattern detection with bursting neurons

International Nuclear Information System (INIS)

Gollisch, Tim

2008-01-01

Sound patterns are defined by the temporal relations of their constituents, individual acoustic cues. Auditory systems need to extract these temporal relations to detect or classify sounds. In various cases, ranging from human speech to communication signals of grasshoppers, this pattern detection has been found to display invariance to temporal stretching or compression of the sound signal ('linear time-warp invariance'). In this work, a four-neuron network model is introduced, designed to solve such a detection task for the example of grasshopper courtship songs. As an essential ingredient, the network contains neurons with intrinsic bursting dynamics, which allow them to encode durations between acoustic events in short, rapid sequences of spikes. As shown by analytical calculations and computer simulations, these neuronal dynamics result in a powerful mechanism for temporal integration. Finally, the network reads out the encoded temporal information by detecting equal activity of two such bursting neurons. This leads to the recognition of rhythmic patterns independent of temporal stretching or compression

Evaluation of scaling invariance embedded in short time series.

Directory of Open Access Journals (Sweden)

Xue Pan

Full Text Available Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2. Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03 and sharp confidential interval (standard deviation ≤0.05. Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.

Evaluation of scaling invariance embedded in short time series.

Science.gov (United States)

Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping

2014-01-01

Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2). Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03) and sharp confidential interval (standard deviation ≤0.05). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.

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.

A strong-topological-metal material with multiple Dirac cones

OpenAIRE

Ji, Huiwen; Pletikosić, I; Gibson, Q. D.; Sahasrabudhe, Girija; Valla, T.; Cava, R. J.

2015-01-01

We report a new, cleavable, strong-topological-metal, Zr2Te2P, which has the same tetradymite-type crystal structure as the topological insulator Bi2Te2Se. Instead of being a semiconductor, however, Zr2Te2P is metallic with a pseudogap between 0.2 and 0.7 eV above the fermi energy (EF). Inside this pseudogap, two Dirac dispersions are predicted: one is a surface-originated Dirac cone protected by time-reversal symmetry (TRS), while the other is a bulk-originated and slightly gapped Dirac cone...

Conformal geometry and invariants of 3-strand Brownian braids

International Nuclear Information System (INIS)

Nechaev, Sergei; Voituriez, Raphael

2005-01-01

We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the properties of conformal maps of doubly-punctured plane z to the universal covering surface. The special attention is paid to the case of indistinguishable particles. Our method of conformal maps allows us to investigate the statistical properties of the topological complexity of a bunch of 3-strand Brownian braids and to compute the expectation value of the irreducible braid length in the non-Abelian case

Reversible perspective and splitting in time.

Science.gov (United States)

Hart, Helen Schoenhals

2012-01-01

The element of time--the experience of it and the defensive use of it--is explored in conjunction with the use of reversible perspective as a psychotic defense. Clinical material from a long analysis illustrates how a psychotic patient used the reversible perspective, with its static splitting, to abolish the experience of time. When he improved and the reversible perspective became less effective for him, he replaced it with a more dynamic splitting mechanism using time gaps. With further improvement, the patient began to experience the passage of time, and along with it the excruciating pain of separation, envy, and loss.

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.

Topological Phases in the Real World

Science.gov (United States)

Hsu, Yi-Ting

The experimental discovery and subsequent theoretical understanding of the integer quantum Hall effect, the first known topological phase, has started a revolutionary breakthrough in understanding states of matter since its discovery four decades ago. Topological phases are predicted to have many generic signatures resulting from their underlying topological nature, such as quantized Hall transport, robust boundary states, and possible fractional excitations. The intriguing nature of these signatures and their potential applications in quantum computation has intensely fueled the efforts of the physics community to materialize topological phases. Among various topological phases initially predicted on theoretical grounds, chiral topological superconductors and time-reversal symmetric topological insulators (TI) in three dimension (3D) are two promising candidates for experimental realization and application. The family of materials, Bi2X3 (X = Se, Te), has been predicted and shown experimentally to be time-reversal symmetric 3D TIs through the observation of robust Dirac surface states with Rashba-type spin-winding. Due to their robust surface states with spin-windings, these 3D TIs are expected to be promising materials for producing large spin-transfer torques which are advantageous for spintronics application. As for topological superconductors, despite the exotic excitations that have been extensively proposed as qubits for topological quantum computing, materials hosting topological superconductivity are rare to date and the leading candidate in two dimensions (2D), Sr 2RuO4, has a low transition temperature (Tc ). The goal of my phd study is to push forward the current status of realization of topological phases by materializing higher Tc topological superconductors and investigating the stability of Dirac surface states in 3D TIs. In the first part of this thesis, I will discuss our double-pronged objective for topological superconductors: to propose how to

Anomalous Z2 antiferromagnetic topological phase in pressurized SmB6

Science.gov (United States)

Chang, Kai-Wei; Chen, Peng-Jen

2018-05-01

Antiferromagnetic materials, whose time-reversal symmetry is broken, can be classified into the Z2 topology if they respect some specific symmetry. Since the theoretical proposal, however, no materials have been found to host such Z2 antiferromagnetic topological (Z2-AFT ) phase to date. Here we demonstrate that the topological Kondo insulator SmB6 can be a Z2-AFT system when pressurized to undergo an antiferromagnetic phase transition. In addition to proposing the possible candidate for a Z2-AFT material, in this work we also illustrate the anomalous topological surface states of the Z2-AFT phase which have not been discussed before. Originating from the interplay between the topological properties and the antiferromagnetic surface magnetization, the topological surface states of the Z2-AFT phase behave differently as compared with those of a topological insulator. Besides, the Z2-AFT insulators are also found promising in the generation of tunable spin currents, which is an important application in spintronics.

Circular symmetry in topologically massive gravity

International Nuclear Information System (INIS)

Deser, S; Franklin, J

2010-01-01

We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null. (note)

Circular symmetry in topologically massive gravity

Energy Technology Data Exchange (ETDEWEB)

Deser, S [Physics Department, Brandeis University, Waltham, MA 02454 (United States); Franklin, J, E-mail: deser@brandeis.ed, E-mail: jfrankli@reed.ed [Reed College, Portland, OR 97202 (United States)

2010-05-21

We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null. (note)

Time reversibility in the quantum frame

Energy Technology Data Exchange (ETDEWEB)

Masot-Conde, Fátima [Escuela Superior Ingenieros, Dpt. Física Aplicada III, Universidad de Sevilla Isla Mágica, 41092- Sevilla (Spain)

2014-12-04

Classic Mechanics and Electromagnetism, conventionally taken as time-reversible, share the same concept of motion (either of mass or charge) as the basis of the time reversibility in their own fields. This paper focuses on the relationship between mobile geometry and motion reversibility. The goal is to extrapolate the conclusions to the quantum frame, where matter and radiation behave just as elementary mobiles. The possibility that the asymmetry of Time (Time’s arrow) is an effect of a fundamental quantum asymmetry of elementary particles, turns out to be a consequence of the discussion.

Filtration of the classical knot concordance group and Casson-Gordon invariants

OpenAIRE

Kim, Taehee

2002-01-01

It is known that if any prime power branched cyclic cover of a knot in the 3-sphere is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in the 3-sphere whose prime power branched cyclic covers are homology spheres. We show that these knots generate an infinite rank subgroup of F_(1.0)/F_(1.5) for which Casson-Gordon invariants vanish in Cochran-Orr-Teichner's filtration of the classical knot conco...

EMPLOYEE COMMITMENT ACROSS COUNTRIES AND TIMES - MEASUREMENT INVARIANCE

Directory of Open Access Journals (Sweden)

Dana Mesner Andolšek

2015-01-01

Full Text Available Employee organisational commitment has been long and extensively studied until now (Meyer & Allen, 1997; Jaussi, 2007.An emphasis of current analysis was to verify its measurement characteristics, for the purpose of comparisons of levels of commitment across time and countries. A limited set of countries was chosen among those available in a sample from the data on Work Orientations II, ISSP 1997, purpose fully selected to reflect cultural and structural differences that was expected to affect change in levels of organisational commitment. With the use of structural equations models we first confirmed that a model for configural invariance for two factors measuring conceptually distinct components of Affective commitment (AC and Continuance commitment (CC respectively has better support than of one factor model. Metric and error term invariance was subsequently confirmed. Scalar equivalence, needed for valid comparison of mean levels of both components of commitment, was confirmed as well, with the exception of two country specific Tau coefficient. Finally, a model thus established was applied additionally on data from2005 ISSP. Acceptable fit was achieved for a common model containing both points in time and all countries, which allowed making more firm conclusions about the changes in AC and CC in different countries.

Topologically protected bound states in photonic parity-time-symmetric crystals.

Science.gov (United States)

Weimann, S; Kremer, M; Plotnik, Y; Lumer, Y; Nolte, S; Makris, K G; Segev, M; Rechtsman, M C; Szameit, A

2017-04-01

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

Topological and conventional order of spinless fermions in 2D lattices

International Nuclear Information System (INIS)

Kourtis, Stefanos

2014-01-01

After an introduction to the quintessential properties characterizing quantum Hall effects and topological phases in Part I of the present text, Part II has ventured into the less explored realm of correlated topological states in lattices. Haldane-like models were doped to fractional fillings of the gapped lower band and short-range interactions were used to induce lattice reincarnations of fractional quantum Hall states, called fractional Chern insulators (FCI). In Chapter 5, it was shown that band dispersion, which is usually taken to be zero to mimic Landau levels, can affect the competition between CDW and FCI states and actually favor the latter against the former. Furthermore, a first rudimentary look at the effect of magnetic disorder on a fractionally quantized topological invariant indicated that, even though the impact of disorder is intricate, the quantization of the invariant remains intact. The results presented in Chapter 6 demonstrate that FCI states do not necessarily need to come purely from a single Chern band, since strong interactions that mix bands seem to enhance their stability. The possibility for obtaining exotic correlated topological states was exemplified by the topological pinball liquid - a composite quantum state comprising of a CDW and a FCI - in Chapter 7. The conclusions of the preceding Chapters can be now set forth as answers to the questions posed in the beginning of Part II: - Are weak or strong interactions more favorable to correlated topological states? - Are insulators or semiconductors more suitable hosts? - Are dispersive or flat bands more susceptible to topological order? - Are correlated topological phases beyond the fractional quantum Hall paradigm possible in single-species many-particle systems?

Topological and conventional order of spinless fermions in 2D lattices

Energy Technology Data Exchange (ETDEWEB)

Kourtis, Stefanos

2014-10-15

After an introduction to the quintessential properties characterizing quantum Hall effects and topological phases in Part I of the present text, Part II has ventured into the less explored realm of correlated topological states in lattices. Haldane-like models were doped to fractional fillings of the gapped lower band and short-range interactions were used to induce lattice reincarnations of fractional quantum Hall states, called fractional Chern insulators (FCI). In Chapter 5, it was shown that band dispersion, which is usually taken to be zero to mimic Landau levels, can affect the competition between CDW and FCI states and actually favor the latter against the former. Furthermore, a first rudimentary look at the effect of magnetic disorder on a fractionally quantized topological invariant indicated that, even though the impact of disorder is intricate, the quantization of the invariant remains intact. The results presented in Chapter 6 demonstrate that FCI states do not necessarily need to come purely from a single Chern band, since strong interactions that mix bands seem to enhance their stability. The possibility for obtaining exotic correlated topological states was exemplified by the topological pinball liquid - a composite quantum state comprising of a CDW and a FCI - in Chapter 7. The conclusions of the preceding Chapters can be now set forth as answers to the questions posed in the beginning of Part II: - Are weak or strong interactions more favorable to correlated topological states? - Are insulators or semiconductors more suitable hosts? - Are dispersive or flat bands more susceptible to topological order? - Are correlated topological phases beyond the fractional quantum Hall paradigm possible in single-species many-particle systems?.

Hamiltonian Dynamics and Adiabatic Invariants for Time-Dependent Superconducting Qubit-Oscillators and Resonators in Quantum Computing Systems

Directory of Open Access Journals (Sweden)

Jeong Ryeol Choi

2015-01-01

Full Text Available An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.

Accessing the topological susceptibility via the Gribov horizon

Science.gov (United States)

Dudal, D.; Felix, C. P.; Guimaraes, M. S.; Sorella, S. P.

2017-10-01

The topological susceptibility, χ4 , following the work of Witten and Veneziano, plays a key role in identifying the relative magnitude of the η' mass, the so-called U (1 )A problem. A nonzero χ4 is caused by the Veneziano ghost, the occurrence of an unphysical massless pole in the correlation function of the topological current Kμ. In this paper, we investigate the topological susceptibility, χ4, in S U (3 ) and S U (2 ) Euclidean Yang-Mills theory using an appropriate Padé approximation tool and a nonperturbative gluon propagator, within a Becchi-Rouet-Stora-Tyutin invariant framework and by taking into account Gribov copies in a general linear covariant gauge.

Topology reconstruction for B-Rep modeling from 3D mesh in reverse engineering applications

Science.gov (United States)

Bénière, Roseline; Subsol, Gérard; Gesquière, Gilles; Le Breton, François; Puech, William

2012-03-01

Nowadays, most of the manufactured objects are designed using CAD (Computer-Aided Design) software. Nevertheless, for visualization, data exchange or manufacturing applications, the geometric model has to be discretized into a 3D mesh composed of a finite number of vertices and edges. But, in some cases, the initial model may be lost or unavailable. In other cases, the 3D discrete representation may be modified, for example after a numerical simulation, and does not correspond anymore to the initial model. A reverse engineering method is then required to reconstruct a 3D continuous representation from the discrete one. In previous work, we have presented a new approach for 3D geometric primitive extraction. In this paper, to complete our automatic and comprehensive reverse engineering process, we propose a method to construct the topology of the retrieved object. To reconstruct a B-Rep model, a new formalism is now introduced to define the adjacency relations. Then a new process is used to construct the boundaries of the object. The whole process is tested on 3D industrial meshes and bring a solution to recover B-Rep models.

Engineering Topological Many-Body Materials in Microwave Cavity Arrays

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Brandon M. Anderson

2016-12-01

Full Text Available We present a scalable architecture for the exploration of interacting topological phases of photons in arrays of microwave cavities, using established techniques from cavity and circuit quantum electrodynamics. A time-reversal symmetry-breaking (nonreciprocal flux is induced by coupling the microwave cavities to ferrites, allowing for the production of a variety of topological band structures including the α=1/4 Hofstadter model. To induce photon-photon interactions, the cavities are coupled to superconducting qubits; we find these interactions are sufficient to stabilize a ν=1/2 bosonic Laughlin puddle. Exact diagonalization studies demonstrate that this architecture is robust to experimentally achievable levels of disorder. These advances provide an exciting opportunity to employ the quantum circuit toolkit for the exploration of strongly interacting topological materials.

On the invariance of world time reference system

International Nuclear Information System (INIS)

Asanov, G.S.

1978-01-01

A universal reference system is studied. It is shown that time differentiation acquires an invariant meaning in the covariant theory of a curved space-time. All the principal covariant equations of the Einstein gravitational field theory can be interpreted successively relative to a universal reference system, whose base congruence is the S-congruence. The Lorentz calibration conditions determine the base tetrades of the universal reference system with an accuracy to rigid spatial rotations with constant coefficients. The use of rigid tetrades eliminates the ambiguity in the interpretation of the value of the energy momentum of a gravitational field

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.

Non-commutative tools for topological insulators

International Nuclear Information System (INIS)

Prodan, Emil

2010-01-01

This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have nontrivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, a relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.

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.

The ATLAS Level-1 Topological Trigger performance in Run 2

CERN Document Server

AUTHOR|(INSPIRE)INSPIRE-00120419; The ATLAS collaboration

2017-01-01

The Level-1 trigger is the first event rate reducing step in the ATLAS detector trigger system, with an output rate of up to 100 kHz and decision latency smaller than 2.5 μs. During the LHC shutdown after Run 1, the Level-1 trigger system was upgraded at hardware, firmware and software levels. In particular, a new electronics sub-system was introduced in the real-time data processing path: the Level-1 Topological trigger system. It consists of a single electronics shelf equipped with two Level-1 Topological processor blades. They receive real-time information from the Level-1 calorimeter and muon triggers, which is processed to measure angles between trigger objects, invariant masses or other kinematic variables. Complementary to other requirements, these measurements are taken into account in the final Level-1 trigger decision. The system was installed and commissioning started in 2015 and continued during 2016. As part of the commissioning, the decisions from individual algorithms were simulated and compar...

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.

Topological Classification of Crystalline Insulators through Band Structure Combinatorics

Science.gov (United States)

Kruthoff, Jorrit; de Boer, Jan; van Wezel, Jasper; Kane, Charles L.; Slager, Robert-Jan

2017-10-01

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-unitary symmetries. The results presented match the mathematical structure underlying the topological classification of these crystals in terms of K -theory and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify all allowed topological phases of spinless particles in crystals in class A . Employing this classification, we study transitions between topological phases within class A that are driven by band inversions at high-symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure and to identify whether or not they give rise to intermediate Weyl semimetallic phases.

Topological mechanics: from metamaterials to active matter

Science.gov (United States)

Vitelli, Vincenzo

2015-03-01

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

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...

Quantum phase transitions of a disordered antiferromagnetic topological insulator

Science.gov (United States)

Baireuther, P.; Edge, J. M.; Fulga, I. C.; Beenakker, C. W. J.; Tworzydło, J.

2014-01-01

We study the effect of electrostatic disorder on the conductivity of a three-dimensional antiferromagnetic insulator (a stack of quantum anomalous Hall layers with staggered magnetization). The phase diagram contains regions where the increase of disorder first causes the appearance of surface conduction (via a topological phase transition), followed by the appearance of bulk conduction (via a metal-insulator transition). The conducting surface states are stabilized by an effective time-reversal symmetry that is broken locally by the disorder but restored on long length scales. A simple self-consistent Born approximation reliably locates the boundaries of this so-called "statistical" topological phase.

Developmental time windows for axon growth influence neuronal network topology.

Science.gov (United States)

Lim, Sol; Kaiser, Marcus

2015-04-01

Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation during early development, either starting at the same time for all neurons (parallel, i.e., maximally overlapped time windows) or occurring for each neuron separately one neuron after another (serial, i.e., no overlaps in time windows). For both cases, the number of potential and established synapses remained comparable. Topological and spatial properties, however, differed: Neurons that started axon growth early on in serial growth achieved higher out-degrees, higher local efficiency and longer axon lengths while neurons demonstrated more homogeneous connectivity patterns for parallel growth. Second, connection probability decreased more rapidly with distance between neurons for parallel growth than for serial growth. Third, bidirectional connections were more numerous for parallel growth. Finally, we tested our predictions with C. elegans data. Together, this indicates that time windows for axon growth influence the topological and spatial properties of neuronal networks opening up the possibility to a posteriori estimate developmental mechanisms based on network properties of a developed network.

Symmetries and invariants of the oscillator and envelope equations with time-dependent frequency

Directory of Open Access Journals (Sweden)

Hong Qin

2006-05-01

Full Text Available The single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant, a fundamental concept in accelerator physics, is fundamentally a result of the corresponding symmetry admitted by the harmonic oscillator equation with linear time-dependent frequency. It is demonstrated that the Lie algebra of the symmetry group for the oscillator equation with time-dependent frequency is eight dimensional, and is composed of four independent subalgebras. A detailed analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. As an application to accelerator physics, the symmetries of the envelope equation enable a fast numerical algorithm for finding matched solutions without using the conventional iterative Newton’s method, where the envelope equation needs to be numerically integrated once for every iteration, and the Jacobi matrix needs to be calculated for the envelope perturbation.

High-order computer-assisted estimates of topological entropy

Science.gov (United States)

Grote, Johannes

The concept of Taylor Models is introduced, which offers highly accurate C0-estimates for the enclosures of functional dependencies, combining high-order Taylor polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified interval arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly nonlinear dynamical systems. A method to obtain sharp rigorous enclosures of Poincare maps for certain types of flows and surfaces is developed and numerical examples are presented. Differential algebraic techniques allow the efficient and accurate computation of polynomial approximations for invariant curves of certain planar maps around hyperbolic fixed points. Subsequently we introduce a procedure to extend these polynomial curves to verified Taylor Model enclosures of local invariant manifolds with C0-errors of size 10-10--10 -14, and proceed to generate the global invariant manifold tangle up to comparable accuracy through iteration in Taylor Model arithmetic. Knowledge of the global manifold structure up to finite iterations of the local manifold pieces enables us to find all homoclinic and heteroclinic intersections in the generated manifold tangle. Combined with the mapping properties of the homoclinic points and their ordering we are able to construct a subshift of finite type as a topological factor of the original planar system to obtain rigorous lower bounds for its topological entropy. This construction is fully automatic and yields homoclinic tangles with several hundred homoclinic points. As an example rigorous lower bounds for the topological entropy of the Henon map are computed, which to the best knowledge of the authors yield the largest such estimates published so far.

Time-invariant PT product and phase locking in PT -symmetric lattice models

Science.gov (United States)

Joglekar, Yogesh N.; Onanga, Franck Assogba; Harter, Andrew K.

2018-01-01

Over the past decade, non-Hermitian, PT -symmetric Hamiltonians have been investigated as candidates for both a fundamental, unitary, quantum theory and open systems with a nonunitary time evolution. In this paper, we investigate the implications of the former approach in the context of the latter. Motivated by the invariance of the PT (inner) product under time evolution, we discuss the dynamics of wave-function phases in a wide range of PT -symmetric lattice models. In particular, we numerically show that, starting with a random initial state, a universal, gain-site location dependent locking between wave-function phases at adjacent sites occurs in the PT -symmetry-broken region. Our results pave the way towards understanding the physically observable implications of time invariants in the nonunitary dynamics produced by PT -symmetric Hamiltonians.

Invariant operator theory for the single-photon energy in time-varying media

International Nuclear Information System (INIS)

Jeong-Ryeol, Choi

2010-01-01

After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis–Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions, ε(i) = ε(0), μ(t) = μ(0), and σ(t) = 0 simultaneously. The use of the Lewis–Riesenfeld invariant operator method in quantum optics leads to a marvelous result: the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency. (general)

Tolerance of topological surface state towards adsorbed magnetic moments: Fe on Bi{sub 2}Te{sub 3}

Energy Technology Data Exchange (ETDEWEB)

Scholz, Markus; Marchenko, Dmitry; Sanchez-Barriga, Jaime; Varykhalov, Andrei; Rader, Oliver [Helmholtz-Zentrum fuer Materialien und Energie, Berlin (Germany); Volykhov, Andrei; Yashina, Lada [Moscow State University, Moskau, Russland (Russian Federation)

2011-07-01

Topological surface states on Bi{sub 2}Se{sub 3} and Bi{sub 2}Te{sub 3} are protected by time reversal symmetry. Magnetic fields break time-reversal symmetry, and they have been used in two-dimensional spin quantum-Hall systems to destroy the topological edge states. Another possibility is to introduce magnetic moments. This has been done by substitution of Mn and Fe into the bulk. For Fe a small gap of 44meV was created, however, at very large amounts (12%). In this work, we deposit Fe directly onto the surface where the topological surface state is localized. We show for coverages of 0.25 and 1 ML Fe that the Dirac point remains intact and no gap appears. Core level spectroscopy of Bi and Te states gives insight into the interaction between substrate and adatoms. In addition, extra surface states appear at the Fermi energy which show a large Rashba-type spin-orbit splitting. The orientation of the spin of both, the topological as well as the Rashba-type split surface states is analysed.

Probing the Topology of Density Matrices

Directory of Open Access Journals (Sweden)

Charles-Edouard Bardyn

2018-02-01

Full Text Available The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the “ensemble geometric phase” (EGP—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities (“purity-gap” closing points of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

NOTE: Circular symmetry in topologically massive gravity

Science.gov (United States)

Deser, S.; Franklin, J.

2010-05-01

We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null.

Edge instabilities of topological superconductors

Energy Technology Data Exchange (ETDEWEB)

Hofmann, Johannes S. [Institut fuer Theoretische Physik und Astrophysik, Universitaet Wuerzburg (Germany); Max-Planck-Institut fuer Festkoerperforschung, Stuttgart (Germany); Assaad, Fakher F. [Institut fuer Theoretische Physik und Astrophysik, Universitaet Wuerzburg (Germany); Schnyder, Andreas P. [Max-Planck-Institut fuer Festkoerperforschung, Stuttgart (Germany)

2016-07-01

Nodal topological superconductors display zero-energy Majorana flat bands at generic edges. The flatness of these edge bands, which is protected by time-reversal and translation symmetry, gives rise to an extensive ground state degeneracy and a diverging density of states. Therefore, even arbitrarily weak interactions lead to an instability of the flat-band edge states towards time-reversal and translation-symmetry broken phases, which lift the ground-state degeneracy. Here, we employ Monte Carlo simulations combined with mean-field considerations to examine the instabilities of the flat-band edge states of d{sub xy}-wave superconductors. We find that attractive interactions induce a complex s-wave pairing instability together with a density wave instability. Repulsive interactions, on the other hand, lead to ferromagnetism mixed with spin-triplet pairing at the edge. We discuss the implications of our findings for experiments on cuprate high-temperature superconductors.

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.

Dual kinetic curves in reversible electrochemical systems.

Directory of Open Access Journals (Sweden)

Michael J Hankins

Full Text Available We introduce dual kinetic chronoamperometry, in which reciprocal relations are established between the kinetic curves of electrochemical reactions that start from symmetrical initial conditions. We have performed numerical and experimental studies in which the kinetic curves of the electron-transfer processes are analyzed for a reversible first order reaction. Experimental tests were done with the ferrocyanide/ferricyanide system in which the concentrations of each component could be measured separately using the platinum disk/gold ring electrode. It is shown that the proper ratio of the transient kinetic curves obtained from cathodic and anodic mass transfer limited regions give thermodynamic time invariances related to the reaction quotient of the bulk concentrations. Therefore, thermodynamic time invariances can be observed at any time using the dual kinetic curves for reversible reactions. The technique provides a unique possibility to extract the non-steady state trajectory starting from one initial condition based only on the equilibrium constant and the trajectory which starts from the symmetrical initial condition. The results could impact battery technology by predicting the concentrations and currents of the underlying non-steady state processes in a wide domain from thermodynamic principles and limited kinetic information.

Gauge-Invariant Formulation of Time-Dependent Configuration Interaction Singles Method

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Takeshi Sato

2018-03-01

Full Text Available We propose a gauge-invariant formulation of the channel orbital-based time-dependent configuration interaction singles (TDCIS method [Phys. Rev. A, 74, 043420 (2006], one of the powerful ab initio methods to investigate electron dynamics in atoms and molecules subject to an external laser field. In the present formulation, we derive the equations of motion (EOMs in the velocity gauge using gauge-transformed time-dependent, not fixed, orbitals that are equivalent to the conventional EOMs in the length gauge using fixed orbitals. The new velocity-gauge EOMs avoid the use of the length-gauge dipole operator, which diverges at large distance, and allows us to exploit computational advantages of the velocity-gauge treatment over the length-gauge one, e.g., a faster convergence in simulations with intense and long-wavelength lasers, and the feasibility of exterior complex scaling as an absorbing boundary. The reformulated TDCIS method is applied to an exactly solvable model of one-dimensional helium atom in an intense laser field to numerically demonstrate the gauge invariance. We also discuss the consistent method for evaluating the time derivative of an observable, which is relevant, e.g., in simulating high-harmonic generation.

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.

Explicit Minkowski invariance and differential calculus in the quantum space-time

International Nuclear Information System (INIS)

Xu Zhan.

1991-11-01

In terms of the R-circumflex matrix of the quantum group SL q (2), the explicit Minkowski coordinate commutation relations in the four-dimensional quantum space-time are given, and the invariance of the Minkowski metric is shown. The differential calculus in this quantum space-time is discussed and the corresponding commutation relations are proposed. (author). 17 refs

A gauge invariant theory for time dependent heat current

International Nuclear Information System (INIS)

Chen, Jian; ShangGuan, Minhui; Wang, Jian

2015-01-01

In this work, we develop a general gauge-invariant theory for AC heat current through multi-probe systems. Using the non-equilibrium Green’s function, a general expression for time-dependent electrothermal admittance is obtained where we include the internal potential due to the Coulomb interaction explicitly. We show that the gauge-invariant condition is satisfied for heat current if the self-consistent Coulomb interaction is considered. It is known that the Onsager relation holds for dynamic charge conductance. We show in this work that the Onsager relation for electrothermal admittance is violated, except for a special case of a quantum dot system with a single energy level. We apply our theory to a nano capacitor where the Coulomb interaction plays an essential role. We find that, to the first order in frequency, the heat current is related to the electrochemical capacitance as well as the phase accumulated in the scattering event. (paper)

A geometric view on topologically massive gauge theories

International Nuclear Information System (INIS)

Horvathy, P.A.; Nash, C.

1985-01-01

The topologically massive gauge theory of Deser, Jackiw and Templeton is understood from Souriau's Principle of General Covariance. The non-gauge invariant mass term corresponds to a non-trivial class in the first cohomology group of configuration space, generated by the Chern-Simons secondary characteristic class. Quantization requires this class to be integral

Adiabatic photo-steering theory in topological insulators

Science.gov (United States)

Inoue, Jun-ichi

2014-12-01

Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane-Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed.

Adiabatic photo-steering theory in topological insulators

International Nuclear Information System (INIS)

Inoue, Jun-ichi

2014-01-01

Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane–Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed. (focus issue review)

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.

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

Time in Science: Reversibility vs. Irreversibility

Science.gov (United States)

Pomeau, Yves

To discuss properly the question of irreversibility one needs to make a careful distinction between reversibility of the equations of motion and the choice of the initial conditions. This is also relevant for the rather confuse philosophy of the wave packet reduction in quantum mechanics. The explanation of this reduction requires also to make precise assumptions on what initial data are accessible in our world. Finally I discuss how a given (and long) time record can be shown in an objective way to record an irreversible or reversible process. Or: can a direction of time be derived from its analysis? This leads quite naturally to examine if there is a possible spontaneous breaking of the time reversal symmetry in many body systems, a symmetry breaking that would be put in evidence objectively by looking at certain specific time correlations.

The Real Topological String on a local Calabi-Yau

CERN Document Server

Krefl, Daniel

2009-01-01

We study the topological string on local P2 with O-plane and D-brane at its real locus, using three complementary techniques. In the A-model, we refine localization on the moduli space of maps with respect to the torus action preserved by the anti-holomorphic involution. This leads to a computation of open and unoriented Gromov-Witten invariants that can be applied to any toric Calabi-Yau with involution. We then show that the full topological string amplitudes can be reproduced within the topological vertex formalism. We obtain the real topological vertex with trivial fixed leg. Finally, we verify that the same results derive in the B-model from the extended holomorphic anomaly equation, together with appropriate boundary conditions. The expansion at the conifold exhibits a gap structure that belongs to a so far unidentified universality class.

On the sighting of unicorns: A variational approach to computing invariant sets in dynamical systems

Science.gov (United States)

Junge, Oliver; Kevrekidis, Ioannis G.

2017-06-01

We propose to compute approximations to invariant sets in dynamical systems by minimizing an appropriate distance between a suitably selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments, that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topology, dimension, and stability, such as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function, which yields more evenly distributed approximating finite point sets, and illustrate the procedure through corresponding numerical experiments.

Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective

Science.gov (United States)

Locke, Rory A.; Mahoney, John R.; Mitchell, Kevin A.

2018-01-01

Fronts propagating in two-dimensional advection-reaction-diffusion systems exhibit a rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using the so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.

Foundations of combinatorial topology

CERN Document Server

Pontryagin, L S

2015-01-01

Hailed by The Mathematical Gazette as ""an extremely valuable addition to the literature of algebraic topology,"" this concise but rigorous introductory treatment focuses on applications to dimension theory and fixed-point theorems. The lucid text examines complexes and their Betti groups, including Euclidean space, application to dimension theory, and decomposition into components; invariance of the Betti groups, with consideration of the cone construction and barycentric subdivisions of a complex; and continuous mappings and fixed points. Proofs are presented in a complete, careful, and eleg

Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators.

Science.gov (United States)

Tse, Wang-Kong; MacDonald, A H

2010-07-30

Topological insulators can exhibit strong magneto-electric effects when their time-reversal symmetry is broken. In this Letter we consider the magneto-optical Kerr and Faraday effects of a topological insulator thin film weakly exchange coupled to a ferromagnet. We find that its Faraday rotation has a universal value at low frequencies θF=tan(-1)α, where α is the vacuum fine structure constant, and that it has a giant Kerr rotation θK=π/2. These properties follow from a delicate interplay between thin-film cavity confinement and the surface Hall conductivity of a topological insulator's helical quasiparticles.

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.

Expository lectures on topology, geometry, and gauge theories

International Nuclear Information System (INIS)

Akyildiz, Y.

1983-01-01

The article provides an extremely useful and clear explanation of applications of topology and differential geometry in modern gauge theories. Basic concepts like invariants, manifolds, (co)homology, etc. are explained. The author has prepared this lecture with physicists in mind and the level of mathematical sophistication has been kept to a minimum. (S.J.P.)

Topological data analysis of financial time series: Landscapes of crashes

Science.gov (United States)

Gidea, Marian; Katz, Yuri

2018-02-01

We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, to which we associate a topological space. We detect transient loops that appear in this space, and we measure their persistence. This is encoded in real-valued functions referred to as a 'persistence landscapes'. We quantify the temporal changes in persistence landscapes via their Lp-norms. We test this procedure on multidimensional time series generated by various non-linear and non-equilibrium models. We find that, in the vicinity of financial meltdowns, the Lp-norms exhibit strong growth prior to the primary peak, which ascends during a crash. Remarkably, the average spectral density at low frequencies of the time series of Lp-norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03/10/2000, or to the Lehman bankruptcy on 09/15/2008. Our study suggests that TDA provides a new type of econometric analysis, which complements the standard statistical measures. The method can be used to detect early warning signals of imminent market crashes. We believe that this approach can be used beyond the analysis of financial time series presented here.

Strings reinterpreted as topological elements of space time

International Nuclear Information System (INIS)

Ne'eman, Y.

1986-01-01

In 1974, Scherk and Schwarz suggested a reinterpretation of string dynamics as a theory of quantum gravity with unification. We suggest completing the transition through the reinterpretation of the strings themselves as Feynman-paths, spanning the topology of space time in the Hawking-King-McCarthy model. This explains the emergency of gravity

Asymmetries of various P- and T-parities in angular distributions of products of cold-polarized-neutron-induced binary and ternary fission of oriented nuclei and T-invariance

Energy Technology Data Exchange (ETDEWEB)

Kadmensky, S. G., E-mail: kadmensky@phys.vsu.ru; Kostryukov, P. V. [Voronezh State University (Russian Federation)

2016-09-15

It is shown that a quantum system whose Hamiltonian is independent of time is T -invariant if this Hamiltonian contains only those terms that do not change sign upon time reversal. It is also shown that the coincidence of the amplitudes for multistep direct and statistical nuclear reactions with the timereversed amplitudes for the reactions being studied is a condition that ensures the T -invariance of the amplitudes in question, the transition from the original amplitudes to their time-reversed counterparts being accomplished, first, upon introducing the inverse-reactionmatrices T instead of the original-reaction matrix T and, second, upon replacing the wave functions for the initial, final, and intermediate states of the system by the respective time-reversed functions. It is found that the T -even (T -odd) asymmetries in cross sections for nuclear reactions stem from the interference between the amplitudes characterizing these reactions and having identical (opposite) T -parities. It is shown that the T -invariance condition for the above T -even (T -odd) asymmetries is related to the conservation of (change in) the sign of these asymmetries upon going over from original to inverse nuclear reactions. Mechanisms underlying the appearance of possible T -even and T-odd asymmetries in the cross sections for the cold-polarizedneutron- induced binary and ternary fission of oriented target nuclei are analyzed for the case of employing T -invariant Hamiltonians for the systems under study. It is also shown that the asymmetries in question satisfy the T -invariance condition if the reactions being considered have a sequential multistep statistical character. It is concluded that T -invariance is violated in the limiting case where, in ternary nuclear fission, the emission of a light third particle froma fissile compound nucleus formed upon incident-neutron capture by a target nucleus and its separation to two fission fragments are simultaneous events.

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.

Measurement Invariance of a Summative Achievement Assessment over Time: Is Status Really Ready for Growth?

Science.gov (United States)

Viger, Steven Guy

2014-01-01

The current study investigates the phenomenon of measurement invariance by examining the construct stability of a summative mathematics achievement instrument over time gleaned from an existing data set. In doing so, not only is the general question of measurement invariance of the particular instrument addressed, but also in the context of growth…

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.

Optical Time Reversal from Time-Dependent Epsilon-Near-Zero Media

Science.gov (United States)

Vezzoli, Stefano; Bruno, Vincenzo; DeVault, Clayton; Roger, Thomas; Shalaev, Vladimir M.; Boltasseva, Alexandra; Ferrera, Marcello; Clerici, Matteo; Dubietis, Audrius; Faccio, Daniele

2018-01-01

Materials with a spatially uniform but temporally varying optical response have applications ranging from magnetic field-free optical isolators to fundamental studies of quantum field theories. However, these effects typically become relevant only for time variations oscillating at optical frequencies, thus presenting a significant hurdle that severely limits the realization of such conditions. Here we present a thin-film material with a permittivity that pulsates (uniformly in space) at optical frequencies and realizes a time-reversing medium of the form originally proposed by Pendry [Science 322, 71 (2008), 10.1126/science.1162087]. We use an optically pumped, 500 nm thick film of epsilon-near-zero (ENZ) material based on Al-doped zinc oxide. An incident probe beam is both negatively refracted and time reversed through a reflected phase-conjugated beam. As a result of the high nonlinearity and the refractive index that is close to zero, the ENZ film leads to time reversed beams (simultaneous negative refraction and phase conjugation) with near-unit efficiency and greater-than-unit internal conversion efficiency. The ENZ platform therefore presents the time-reversal features required, e.g., for efficient subwavelength imaging, all-optical isolators and fundamental quantum field theory studies.

A multi-element cosmological model with a complex space-time topology

Science.gov (United States)

Kardashev, N. S.; Lipatova, L. N.; Novikov, I. D.; Shatskiy, A. A.

2015-02-01

Wormhole models with a complex topology having one entrance and two exits into the same space-time of another universe are considered, as well as models with two entrances from the same space-time and one exit to another universe. These models are used to build a model of a multi-sheeted universe (a multi-element model of the "Multiverse") with a complex topology. Spherical symmetry is assumed in all the models. A Reissner-Norström black-hole model having no singularity beyond the horizon is constructed. The strength of the central singularity of the black hole is analyzed.

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.

Gauge invariance in the theoretical description of time-resolved angle-resolved pump/probe photoemission spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Freericks, J. K.; Krishnamurthy, H. R.; Sentef, M. A.; Devereaux, T. P.

2015-10-01

Nonequilibrium calculations in the presence of an electric field are usually performed in a gauge, and need to be transformed to reveal the gauge-invariant observables. In this work, we discuss the issue of gauge invariance in the context of time-resolved angle-resolved pump/probe photoemission. If the probe is applied while the pump is still on, one must ensure that the calculations of the observed photocurrent are gauge invariant. We also discuss the requirement of the photoemission signal to be positive and the relationship of this constraint to gauge invariance. We end by discussing some technical details related to the perturbative derivation of the photoemission spectra, which involve processes where the pump pulse photoexcites electrons due to nonequilibrium effects.

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai; Schuster, Gerard T.

2016-01-01

Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.

Elastic least-squares reverse time migration

KAUST Repository

Feng, Zongcai

2016-09-06

Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.

Geometrical interpretation of the topological recursion, and integrable string theories

CERN Document Server

Eynard, Bertrand

2009-01-01

Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative geometry like maps, partitions, Hurwitz numbers, intersection numbers, Gromov-Witten invariants... The problem is thus to understand what they count, or in other words, given a spectral curve, construct an enumerative geometry problem. This is what we do in a semi-heuristic approach in this article. Starting from a spectral curve, i.e. an integrable system, we use its flat connection and flat coordinates, to define a family of worldsheets, whose enumeration is indeed solved by the topological recursion and symplectic invariants. In other words, for any spectral curve, we construct a corresponding string theory, whose target space is a submanifold of the Jacobian.

Topological interface states and effects for next generation of innovative devices

International Nuclear Information System (INIS)

Kantser, Valeriu; Carlig, Sergiu

2013-01-01

Topological insulators (TI) have opened a gateway to search new quantum electronic phase of the condensed matter as well as to pave new platform of modern technology. This stems mainly on their unique surface states that are protected by time-reversal symmetry, show the Dirac cones connecting the inverted conduction and valence bands and exhibit unique spin-momentum locking property. Increasing the surface state contribution in proportion to the bulk of material is critical to investigate the surface states and for future innovative device applications. The way to achieve this is to configure topological insulators into nanostructures, which at the same time in combination with others materials significantly enlarge the variety of new states and phenomena. This article reviews the recent progress made in topological insulator nano heterostructures electronic states investigation. The state of art of different new scenario of engineering topologically interface states in the TI heterostructures are revealed, in particular by using polarization fields and antiferromagnetic ordering. Some of new proposals for innovative electronic devices are discussed. (authors)

Extended holomorphic anomaly and loop amplitudes in open topological string

International Nuclear Information System (INIS)

Walcher, Johannes

2009-01-01

Open topological string amplitudes on compact Calabi-Yau threefolds are shown to satisfy an extension of the holomorphic anomaly equation of Bershadsky, Cecotti, Ooguri and Vafa. The total topological charge of the D-brane configuration must vanish in order to satisfy tadpole cancellation. The boundary state of such D-branes is holomorphically captured by a Hodge theoretic normal function. Its Griffiths' infinitesimal invariant is the analogue of the closed string Yukawa coupling and plays the role of the terminator in a Feynman diagram expansion for the topological string with D-branes. The holomorphic anomaly equation is solved and the holomorphic ambiguity is fixed for some representative worldsheets of low genus and with few boundaries on the real quintic.

Topological edge modes in multilayer graphene systems

KAUST Repository

Ge, Lixin

2015-08-10

Plasmons can be supported on graphene sheets as the Dirac electrons oscillate collectively. A tight-binding model for graphene plasmons is a good description as the field confinement in the normal direction is strong. With this model, the topological properties of plasmonic bands in multilayer graphene systems are investigated. The Zak phases of periodic graphene sheet arrays are obtained for different configurations. Analogous to Su-Schrieffer-Heeger (SSH) model in electronic systems, topological edge plasmon modes emerge when two periodic graphene sheet arrays with different Zak phases are connected. Interestingly, the dispersion of these topological edge modes is the same as that in the monolayer graphene and is invariant as the geometric parameters of the structure such as the separation and period change. These plasmonic edge states in multilayer graphene systems can be further tuned by electrical gating or chemical doping. © 2015 Optical Society of America.

Time reversal communication system

Science.gov (United States)

Candy, James V.; Meyer, Alan W.

2008-12-02

A system of transmitting a signal through a channel medium comprises digitizing the signal, time-reversing the digitized signal, and transmitting the signal through the channel medium. The channel medium may be air, earth, water, tissue, metal, and/or non-metal.

On the BRST invariance of field deformations

International Nuclear Information System (INIS)

Alfaro, J.; Damgaard, P.H.; Latorre, J.I.; Montano, D.

1989-08-01

Topological quantum field theories are distinguished by a BRST symmetry corresponding to local field deformations. We investigate in this letter to what extent an arbitrary quantum field theory may be related to this BRST invariance. We demonstrate that at the expense of having to add extra variables (but without changing the physics) one may always extend to symmetry of an arbitrary action to include local field deformations. New avenues for gauge-fixing are then available. Examples are worked out for Yang-Mills theories. (orig.)

Topological solitons in 8-spinor mie electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Rybakov, Yu. P., E-mail: soliton4@mail.ru [Peoples' Friendship University of Russia, Department of Theoretical Physics (Russian Federation)

2013-10-15

We investigate the effective 8-spinor field model suggested earlier as the generalization of nonlinear Mie electrodynamics. We first study in pure spinorial model the existence of topological solitons endowed with the nontrivial Hopf invariant Q{sub H}, which can be interpreted as the lepton number. Electromagnetic field being included as the perturbation, we estimate the energy and the spin of the localized charged configuration.

A Novel Topology of Hybrid HVDC Circuit Breaker for VSC-HVDC Application

Directory of Open Access Journals (Sweden)

Van-Vinh Nguyen

2017-10-01

Full Text Available The use of high voltage direct current (HVDC circuit breakers (CBs with the capabilities of bidirectional fault interruption, reclosing, and rebreaking can improve the reliable and safe operation of HVDC grids. Although several topologies of CBs have been proposed to perform these capabilities, the limitation of these topologies is either high on-state losses or long time interruption in the case bidirectional fault current interruption. Long time interruption results in the large magnitude of the fault current in the voltage source converter based HVDC (VSC-HVDC system due to the high rate of rise of fault current. This paper proposes a new topology of hybrid CB (HCB with lower conduction loss and lower interruption time to solve the problems. The proposed topology is based on the inverse current injection method, which uses the capacitor to enforce the fault current to zero. In the case of the bidirectional fault current interruption, the capacitor does not change its polarity after identifying the direction of fault current, which can reduce the interruption time accordingly. A switching control algorithm for the proposed topology is presented in detail. Different operation modes of proposed HCB, such as normal current mode, breaking fault current mode, discharging, and reversing capacitor voltage modes after clearing the fault, are considered in the proposed algorithm. The proposed topology with the switching control algorithm is tested in a simulation-based system. Different simulation scenarios such as temporary and permanent faults are carried out to verify the performance of the proposed topology. The simulation is performed in the Matlab/Simulink environment.

Conformal invariance self-avoiding walks in the plane or on a random surface

International Nuclear Information System (INIS)

Duplantier, B.

1988-01-01

The two-dimensional (2D) properties of polymers embedded in a solvent, are studied. They are modeled on a lattice by self-avoiding walks. The polymer properties either in the plane with a fixed metric, or on a random 2D surface, where the metric has critical fluctuations, are considered. In the scope of the work, the following topics are discussed: the watermelon topology; the O(n) model and Coulomb gas technique; the model and critical behaviours of polymers on a two-dimensional random lattice; the conformal invariance in a random surface and higher topologies

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

International Nuclear Information System (INIS)

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

2015-01-01

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

Hinge-free topology optimization with embedded translation-invariant differentiable wavelet shrinkage

DEFF Research Database (Denmark)

Yoon, G. H.; Kim, Y. Y.; Bendsøe, Martin P.

2004-01-01

In topology optimization applications for the design of compliant mechanisms, the formation of hinges is typically encountered. Often such hinges are unphysical artifacts that appear due to the choice of discretization spaces for design and analysis. The objective of this work is to present a new...... two-dimensional compliant mechanism design problems....

Time reversibility of quantum diffusion in small-world networks

Science.gov (United States)

Han, Sung-Guk; Kim, Beom Jun

2012-02-01

We study the time-reversal dynamics of a tight-binding electron in the Watts-Strogatz (WS) small-world networks. The localized initial wave packet at time t = 0 diffuses as time proceeds until the time-reversal operation, together with the momentum perturbation of the strength η, is made at the reversal time T. The time irreversibility is measured by I = |Π( t = 2 T) - Π( t = 0)|, where Π is the participation ratio gauging the extendedness of the wavefunction and for convenience, t is measured forward even after the time reversal. When η = 0, the time evolution after T makes the wavefunction at t = 2 T identical to the one at t = 0, and we find I = 0, implying a null irreversibility or a complete reversibility. On the other hand, as η is increased from zero, the reversibility becomes weaker, and we observe enhancement of the irreversibility. We find that I linearly increases with increasing η in the weakly-perturbed region, and that the irreversibility is much stronger in the WS network than in the local regular network.

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.

Topological triplon modes and bound states in a Shastry-Sutherland magnet

Science.gov (United States)

McClarty, P. A.; Krüger, F.; Guidi, T.; Parker, S. F.; Refson, K.; Parker, A. W.; Prabhakaran, D.; Coldea, R.

2017-08-01

The twin discoveries of the quantum Hall effect, in the 1980s, and of topological band insulators, in the 2000s, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries have taught us that quantum mechanical wavefunctions in crystalline solids may carry nontrivial topological invariants which have ramifications for the observable physics. One of the side effects of the recent topological insulator revolution has been that such physics is much more widespread than was appreciated ten years ago. For example, while topological insulators were originally studied in the context of electron wavefunctions, recent work has initiated a hunt for topological insulators in bosonic systems: in photonic crystals, in the vibrational modes of crystals, and in the excitations of ordered magnets. Using inelastic neutron scattering along with theoretical calculations, we demonstrate that, in a weak magnetic field, the dimerized quantum magnet SrCu2(BO3)2 is a bosonic topological insulator with topologically protected chiral edge modes of triplon excitations.

Topological regularizations of the triple collision singularity in the 3-vortex problem

International Nuclear Information System (INIS)

Hiraoka, Yasuaki

2008-01-01

The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition k 1 -1 +k 2 -1 +k 3 -1 =0 for vorticities to have the triple collision, the main results are summarized as follows: (i) For k 1 = k 2 , the triple collision singularity is topologically regularizable. (ii) For 0 1 − k 2 | < ε with a sufficiently small ε, the triple collision singularity is not topologically regularizable. First of all, in order to prove these statements, all singularities in the 3-vortex problem are classified. Then, we introduce a dynamical system by blowing up the triple collision singularity with an appropriate time scaling. Roughly speaking, it corresponds to pasting an invariant manifold at the triple collision singularity on the original phase space. This technique is well known as McGehee's collision manifold (1974 Inventions Math. 27 191–227) in the N-body problem of celestial mechanics. Finally, by adopting the viewpoint of Easton (1971 J. Diff. Eqns 10 92–9), topological regularizations of the triple collision singularity are studied in detail

Interactive Spacecraft Trajectory Design Strategies Featuring Poincare Map Topology

Science.gov (United States)

Schlei, Wayne R.

Space exploration efforts are shifting towards inexpensive and more agile vehicles. Versatility regarding spacecraft trajectories refers to the agility to correct deviations from an intended path or even the ability to adapt the future path to a new destination--all with limited spaceflight resources (i.e., small DeltaV budgets). Trajectory design methods for such nimble vehicles incorporate equally versatile procedures that allow for rapid and interactive decision making while attempting to reduce Delta V budgets, leading to a versatile trajectory design platform. A versatile design paradigm requires the exploitation of Poincare map topology , or the interconnected web of dynamical structures, existing within the chaotic dynamics of multi-body gravitational models to outline low-Delta V transfer options residing nearby to a current path. This investigation details an autonomous procedure to extract the periodic orbits (topology nodes) and correlated asymptotic flow structures (or the invariant manifolds representing topology links). The autonomous process summarized in this investigation (termed PMATE) overcomes discontinuities on the Poincare section that arise in the applied multi-body model (the planar circular restricted three-body problem) and detects a wide variety of novel periodic orbits. New interactive capabilities deliver a visual analytics foundation for versatile spaceflight design, especially for initial guess generation and manipulation. Such interactive strategies include the selection of states and arcs from Poincare section visualizations and the capabilities to draw and drag trajectories to remove dependency on initial state input. Furthermore, immersive selection is expanded to cull invariant manifold structures, yielding low-DeltaV or even DeltaV-free transfers between periodic orbits. The application of interactive design strategies featuring a dense extraction of Poincare map topology is demonstrated for agile spaceflight with a simple

Tracking of time-varying genomic regulatory networks with a LASSO-Kalman smoother

OpenAIRE

Khan, Jehandad; Bouaynaya, Nidhal; Fathallah-Shaykh, Hassan M

2014-01-01

It is widely accepted that cellular requirements and environmental conditions dictate the architecture of genetic regulatory networks. Nonetheless, the status quo in regulatory network modeling and analysis assumes an invariant network topology over time. In this paper, we refocus on a dynamic perspective of genetic networks, one that can uncover substantial topological changes in network structure during biological processes such as developmental growth. We propose a novel outlook on the inf...

Reverse time migration by Krylov subspace reduced order modeling

Science.gov (United States)

Basir, Hadi Mahdavi; Javaherian, Abdolrahim; Shomali, Zaher Hossein; Firouz-Abadi, Roohollah Dehghani; Gholamy, Shaban Ali

2018-04-01

Imaging is a key step in seismic data processing. To date, a myriad of advanced pre-stack depth migration approaches have been developed; however, reverse time migration (RTM) is still considered as the high-end imaging algorithm. The main limitations associated with the performance cost of reverse time migration are the intensive computation of the forward and backward simulations, time consumption, and memory allocation related to imaging condition. Based on the reduced order modeling, we proposed an algorithm, which can be adapted to all the aforementioned factors. Our proposed method benefit from Krylov subspaces method to compute certain mode shapes of the velocity model computed by as an orthogonal base of reduced order modeling. Reverse time migration by reduced order modeling is helpful concerning the highly parallel computation and strongly reduces the memory requirement of reverse time migration. The synthetic model results showed that suggested method can decrease the computational costs of reverse time migration by several orders of magnitudes, compared with reverse time migration by finite element method.

Chern-Simons Theory, Matrix Models, and Topological Strings

International Nuclear Information System (INIS)

Walcher, J

2006-01-01

This book is a find. Marino meets the challenge of filling in less than 200 pages the need for an accessible review of topological gauge/gravity duality. He is one of the pioneers of the subject and a clear expositor. It is no surprise that reading this book is a great pleasure. The existence of dualities between gauge theories and theories of gravity remains one of the most surprising recent discoveries in mathematical physics. While it is probably fair to say that we do not yet understand the full reach of such a relation, the impressive amount of evidence that has accumulated over the past years can be regarded as a substitute for a proof, and will certainly help to delineate the question of what is the most fundamental quantum mechanical theory. Here is a brief summary of the book. The journey begins with matrix models and an introduction to various techniques for the computation of integrals including perturbative expansion, large-N approximation, saddle point analysis, and the method of orthogonal polynomials. The second chapter, on Chern-Simons theory, is the longest and probably the most complete one in the book. Starting from the action we meet Wilson loop observables, the associated perturbative 3-manifold invariants, Witten's exact solution via the canonical duality to WZW models, the framing ambiguity, as well as a collection of results on knot invariants that can be derived from Chern-Simons theory and the combinatorics of U (∞) representation theory. The chapter also contains a careful derivation of the large-N expansion of the Chern-Simons partition function, which forms the cornerstone of its interpretation as a closed string theory. Finally, we learn that Chern-Simons theory can sometimes also be represented as a matrix model. The story then turns to the gravity side, with an introduction to topological sigma models (chapter 3) and topological string theory (chapter 4). While this presentation is necessarily rather condensed (and the beginner may

Invariance of the Berry phase under unitary transformations: application to the time-dependent generalized harmonic oscillator

International Nuclear Information System (INIS)

Kobe, D.H.

1989-01-01

The Berry phase is derived in a manifestly gauge-invariant way, without adiabatic or cyclic requirements. It is invariant under unitary transformations, contrary to recent assertions. A time-dependent generalized harmonic oscillator is taken as an example. The energy of the system is not in general the Hamiltonian. An energy, the time derivative of which is the power, is obtained from the equation of motion. When the system is quantized, the Berry phase is zero, and is invariant under unitary transformations. If the energy is chosen incorrectly to be the Hamiltonian, a nonzero Berry phase is obtained. In this case the total phase, the sun of the dynamical and Berry phases, is equal to the correct total phase through first order in perturbation theory. (author)

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.)

A topological approach to migration and visualization of time-varying volume data

International Nuclear Information System (INIS)

Fujishiro, Issei; Otsuka, Rieko; Hamaoka, Aya; Takeshima, Yuriko; Takahashi, Shigeo

2004-01-01

Rapid advance in high performance computing and measurement technologies has recently made it possible to produce a stupendous amount of time-varying volume datasets in various disciplines. However, there exist a few known visual exploration tools which allow us to investigate the core of their complex behavior effectively. In this article, our previous approach to topological volume skeletonization is extended to capture the topological skeleton of a 4D volumetric field in terms of critical timing. A cyclic information drilldown scheme, termed T-map, is presented, where a wide choice of information visualization techniques are deployed so that the users are allowed to repeatedly squeeze partial spatiotemporal domains of interest until the size gets fitted into an available computing storage space, prior to topologically-accentuated visualization of the pinpointed volumetric domains. A case study with datasets from atomic collision research is performed to illustrate the feasibility of the present method. (author)

Membrane morphology and topology for fouling control in Reverse Osmosis filtration systems

Science.gov (United States)

Ling, Bowen; Battiato, Ilenia

2017-11-01

Reverse Osmosis Membrane (ROM) filtration systems are widely utilized in waste-water recovery, seawater desalination, landfill water treatment, etc. During filtration, the system performance is dramatically affected by membrane fouling which causes a significant decrease in permeate flux as well as an increase in the energy input required to operate the system. Design and optimization of ROM filtration systems aim at reducing membrane fouling by studying the coupling between membrane structure, local flow field and foulant adsorption patterns. Yet, current studies focus exclusively on oversimplified steady-state models that ignore any dynamic coupling between fluid flow and transport through the membrane. In this work, we develop a customized solver (SUMembraneFoam) under OpenFOAM to solve the transient equations. The simulation results not only predict macroscopic quantities (e.g. permeate flux, pressure drop, etc.) but also show an excellent agreement with the fouling patterns observed in experiments. It is observed that foulant deposition is strongly controlled by the local shear stress on the membrane, and channel morphology or membrane topology can be modified to control the shear stress distribution and reduce fouling. Finally, we identify optimal regimes for design.

Property - preserving convergent sequences of invariant sets for linear discrete - time systems

NARCIS (Netherlands)

Athanasopoulos, N.; Lazar, M.; Bitsoris, G.

2014-01-01

Abstract: New sequences of monotonically increasing sets are introduced, for linear discrete-time systems subject to input and state constraints. The elements of the set sequences are controlled invariant and admissible regions of stabilizability. They are generated from the iterative application of

Link between the photonic and electronic topological phases in artificial graphene

Science.gov (United States)

Lannebère, Sylvain; Silveirinha, Mário G.

2018-04-01

In recent years the study of topological phases of matter has emerged as a very exciting field of research, both in photonics and in electronics. However, up to now the electronic and photonic properties have been regarded as totally independent. Here we establish a link between the electronic and the photonic topological phases of the same material system and theoretically demonstrate that they are intimately related. We propose a realization of the Haldane model as a patterned two-dimensional electron gas and determine its optical response using the Kubo formula. It is shown that the electronic and photonic phase diagrams of the patterned electron gas are strictly related. In particular, the system has a trivial photonic topology when the inversion symmetry is the prevalent broken symmetry, whereas it has a nontrivial photonic topology for a dominant broken time-reversal symmetry, similar to the electronic case. To confirm these predictions, we numerically demonstrate the emergence of topologically protected unidirectional electromagnetic edge states at the interface with a trivial photonic material.

A first theoretical realization of honeycomb topological magnon insulator.

Science.gov (United States)

Owerre, S A

2016-09-28

It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon-magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion symmetry of the lattice is broken by introducing a next-nearest neighbour Dzyaloshinskii-Moriya (DM) interaction. Thus, the system realizes magnon edge states similar to the Haldane model for quantum anomalous Hall effect in electronic systems. However, in contrast to electronic spin current where dissipation can be very large due to Ohmic heating, noninteracting topological magnons can propagate for a long time without dissipation as magnons are uncharged particles. We observe the same magnon edge states for the XY model on the honeycomb lattice. Remarkably, in this case the model maps to interacting hardcore bosons on the honeycomb lattice. Quantum magnetic systems with nontrivial magnon edge states are called topological magnon insulators. They have been studied theoretically on the kagome lattice and recently observed experimentally on the kagome magnet Cu(1-3, bdc) with three magnon bulk bands. Our results for the honeycomb lattice suggests an experimental procedure to search for honeycomb topological magnon insulators within a class of 2D quantum magnets and ultracold atoms trapped in honeycomb optical lattices. In 3D lattices, Dirac and Weyl points were recently studied theoretically, however, the criteria that give rise to them were not well-understood. We argue that the low-energy Hamiltonian near the Weyl points should break time-reversal symmetry of the pseudo spins

Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface

Directory of Open Access Journals (Sweden)

Meng Cheng

2016-12-01

Full Text Available The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a “spinon” excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of “anyonic spin-orbit coupling,” which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by on-site symmetry.

Topological visual mapping in robotics.

Science.gov (United States)

Romero, Anna; Cazorla, Miguel

2012-08-01

A key problem in robotics is the construction of a map from its environment. This map could be used in different tasks, like localization, recognition, obstacle avoidance, etc. Besides, the simultaneous location and mapping (SLAM) problem has had a lot of interest in the robotics community. This paper presents a new method for visual mapping, using topological instead of metric information. For that purpose, we propose prior image segmentation into regions in order to group the extracted invariant features in a graph so that each graph defines a single region of the image. Although others methods have been proposed for visual SLAM, our method is complete, in the sense that it makes all the process: it presents a new method for image matching; it defines a way to build the topological map; and it also defines a matching criterion for loop-closing. The matching process will take into account visual features and their structure using the graph transformation matching (GTM) algorithm, which allows us to process the matching and to remove out the outliers. Then, using this image comparison method, we propose an algorithm for constructing topological maps. During the experimentation phase, we will test the robustness of the method and its ability constructing topological maps. We have also introduced new hysteresis behavior in order to solve some problems found building the graph.

Time reversal imaging, Inverse problems and Adjoint Tomography}

Science.gov (United States)

Montagner, J.; Larmat, C. S.; Capdeville, Y.; Kawakatsu, H.; Fink, M.

2010-12-01

With the increasing power of computers and numerical techniques (such as spectral element methods), it is possible to address a new class of seismological problems. The propagation of seismic waves in heterogeneous media is simulated more and more accurately and new applications developed, in particular time reversal methods and adjoint tomography in the three-dimensional Earth. Since the pioneering work of J. Claerbout, theorized by A. Tarantola, many similarities were found between time-reversal methods, cross-correlations techniques, inverse problems and adjoint tomography. By using normal mode theory, we generalize the scalar approach of Draeger and Fink (1999) and Lobkis and Weaver (2001) to the 3D- elastic Earth, for theoretically understanding time-reversal method on global scale. It is shown how to relate time-reversal methods on one hand, with auto-correlations of seismograms for source imaging and on the other hand, with cross-correlations between receivers for structural imaging and retrieving Green function. Time-reversal methods were successfully applied in the past to acoustic waves in many fields such as medical imaging, underwater acoustics, non destructive testing and to seismic waves in seismology for earthquake imaging. In the case of source imaging, time reversal techniques make it possible an automatic location in time and space as well as the retrieval of focal mechanism of earthquakes or unknown environmental sources . We present here some applications at the global scale of these techniques on synthetic tests and on real data, such as Sumatra-Andaman (Dec. 2004), Haiti (Jan. 2010), as well as glacial earthquakes and seismic hum.

The geometric Hopf invariant and surgery theory

CERN Document Server

Crabb, Michael

2017-01-01

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .

Manifold-splitting regularization, self-linking, twisting, writhing numbers of space-time ribbons

International Nuclear Information System (INIS)

Tze, C.H.

1988-01-01

The authors present an alternative formulation of Polyakov's regularization of Gauss' integral formula for a single closed Feynman path. A key element in his proof of the D = 3 fermi-bose transmutations induced by topological gauge fields, this regularization is linked here with the existence and properties of a nontrivial topological invariant for a closed space ribbon. This self-linking coefficient, an integer, is the sum of two differential characteristics of the ribbon, its twisting and writhing numbers. These invariants form the basis for a physical interpretation of our regularization. Their connection to Polyakov's spinorization is discussed. The authors further generalize their construction to the self-linking, twisting and writhing of higher dimensional d = eta(odd) submanifolds in D = (2eta + 1) space-time

Comparing topological charge definitions using topology fixing actions

International Nuclear Information System (INIS)

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

2009-05-01

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

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

KAUST Repository

Tahir, M.

2012-12-06

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

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

KAUST Repository

Tahir, M.; Schwingenschlö gl, Udo

2012-01-01

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

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

Science.gov (United States)

Fösel, Thomas; Peano, Vittorio; Marquardt, Florian

2017-11-01

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

The character of free topological groups II

Directory of Open Access Journals (Sweden)

Peter Nickolas

2005-04-01

Full Text Available A systematic analysis is made of the character of the free and free abelian topological groups on metrizable spaces and compact spaces, and on certain other closely related spaces. In the first case, it is shown that the characters of the free and the free abelian topological groups on X are both equal to the “small cardinal” d if X is compact and metrizable, but also, more generally, if X is a non-discrete k!-space all of whose compact subsets are metrizable, or if X is a non-discrete Polish space. An example is given of a zero-dimensional separable metric space for which both characters are equal to the cardinal of the continuum. In the case of a compact space X, an explicit formula is derived for the character of the free topological group on X involving no cardinal invariant of X other than its weight; in particular the character is fully determined by the weight in the compact case. This paper is a sequel to a paper by the same authors in which the characters of the free groups were analysed under less restrictive topological assumptions.

Space-Time Foam in 2D and the Sum Over Topologies

International Nuclear Information System (INIS)

Loll, R.; Westra, W.

2003-01-01

It is well-known that the sum over topologies in quantum gravity is ill-defined, due to a super-exponential growth of the number of geometries as a function of the space-time volume, leading to a badly divergent gravitational path integral. Not even in dimension 2, where a non-perturbative quantum gravity theory can be constructed explicitly from a (regularized) path integral, has this problem found a satisfactory solution. In the present work, we extend a previous 2d Lorentzian path integral, regulated in terms of Lorentzian random triangulations, to include space-times with an arbitrary number of handles. We show that after the imposition of physically motivated causality constraints, the combined sum over geometries and topologies is well-defined and possesses a continuum limit which yields a concrete model of space-time foam in two dimensions. (author)

Winding around the winding number in topology, geometry, and analysis

CERN Document Server

Roe, John

2015-01-01

The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra), guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem), explain why ever

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.

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

International Nuclear Information System (INIS)

Finn, John M.

2015-01-01

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012

Remote Whispering Applying Time Reversal

Energy Technology Data Exchange (ETDEWEB)

Anderson, Brian Eric [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-07-16

The purpose of this project was to explore the use of time reversal technologies as a means for communication to a targeted individual or location. The idea is to have the privacy of whispering in one’s ear, but to do this remotely from loudspeakers not located near the target. Applications of this work include communicating with hostages and survivors in rescue operations, communicating imaging and operational conditions in deep drilling operations, monitoring storage of spent nuclear fuel in storage casks without wires, or clandestine activities requiring signaling between specific points. This technology provides a solution in any application where wires and radio communications are not possible or not desired. It also may be configured to self calibrate on a regular basis to adjust for changing conditions. These communications allow two people to converse with one another in real time, converse in an inaudible frequency range or medium (i.e. using ultrasonic frequencies and/or sending vibrations through a structure), or send information for a system to interpret (even allowing remote control of a system using sound). The time reversal process allows one to focus energy to a specific location in space and to send a clean transmission of a selected signal only to that location. In order for the time reversal process to work, a calibration signal must be obtained. This signal may be obtained experimentally using an impulsive sound, a known chirp signal, or other known signals. It may also be determined from a numerical model of a known environment in which the focusing is desired or from passive listening over time to ambient noise.

From topological quantum field theories to supersymmetric gauge theories

International Nuclear Information System (INIS)

Bossard, G.

2007-10-01

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

An edge index for the quantum spin-Hall effect

International Nuclear Information System (INIS)

Prodan, Emil

2009-01-01

Quantum spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the quantum Hall systems where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open problem to find the observable whose edge current is quantized. In this paper, we define a particular observable and the edge current corresponding to this observable. We show that this current is quantized and that the quantization is given by the index of a certain Fredholm operator. This provides a new topological invariant that is shown to take the generic values 0 and 2, in line with the Z 2 topological classification of time-reversal invariant systems. The result gives an effective tool for the investigation of the edge structure in quantum spin-Hall systems. Based on a reasonable assumption, we also show that the edge conducting channels are not destroyed by a random edge. (fast track communication)

Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers, and Quantum Spin Chains

Science.gov (United States)

Cao, Ting; Zhao, Fangzhou; Louie, Steven G.

2017-08-01

We show that semiconducting graphene nanoribbons (GNRs) of different width, edge, and end termination (synthesizable from molecular precursors with atomic precision) belong to different electronic topological classes. The topological phase of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formulas for their topological invariants and shown that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants, such as a periodic array of boron atoms. In a superlattice consisting of segments of doped and pristine GNRs, the junction states are stable spin centers, forming a Heisenberg antiferromagnetic spin 1 /2 chain with tunable exchange interaction. The discoveries here not only are of scientific interest for studies of quasi-one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.

Surface states on a topologically nontrivial semimetal: The case of Sb(110)

DEFF Research Database (Denmark)

Bianchi, Marco; Guan, Dandan; Strózecka, Anna

2012-01-01

The electronic structure of Sb(110) is studied by angle-resolved photoemission spectroscopy and first-principles calculations, revealing several electronic surface states in the projected bulk band gaps around the Fermi energy. The dispersion of the states can be interpreted in terms of a strong...... spin-orbit splitting. The bulk band structure of Sb has the characteristics of a strong topological insulator with a Z2 invariant ν0 = 1. This puts constraints on the existence of metallic surface states and the expected topology of the surface Fermi contour. However, bulk Sb is a semimetal......, not an insulator, and these constraints are therefore partly relaxed. This relation of bulk topology and expected surface-state dispersion for semimetals is discussed....

Algebraic K- and L-theory and applications to the topology of manifolds

Energy Technology Data Exchange (ETDEWEB)

Hambleton, I [Department of Mathematics and Statistics, McMaster University, Hamilton (Canada)

2002-08-15

The development of geometric topology has led to the identification of specific algebraic structures of great richness and usefulness. A common theme in this area is the study of algebraic invariants of discrete groups or rings by topological methods. The resulting subject is now called algebraic K-theory. The purpose of these lecture notes is to survey some of the main constructions and techniques in algebraic K-theory, together with an indication of the topological backnd and applications. More details about proofs can be found in the references. The material is organized into some introductory sections, concerning linear and unitary K-theory, followed by descriptions of four important geometric problems and their related algebraic methods.

Translation invariant time-dependent solutions to massive gravity II

Science.gov (United States)

Mourad, J.; Steer, D. A.

2014-06-01

This paper is a sequel to JCAP 12 (2013) 004 and is also devoted to translation-invariant solutions of ghost-free massive gravity in its moving frame formulation. Here we consider a mass term which is linear in the vielbein (corresponding to a β3 term in the 4D metric formulation) in addition to the cosmological constant. We determine explicitly the constraints, and from the initial value formulation show that the time-dependent solutions can have singularities at a finite time. Although the constraints give, as in the β1 case, the correct number of degrees of freedom for a massive spin two field, we show that the lapse function can change sign at a finite time causing a singular time evolution. This is very different to the β1 case where time evolution is always well defined. We conclude that the β3 mass term can be pathological and should be treated with care.

Topological sound in active-liquid metamaterials

Science.gov (United States)

Souslov, Anton; van Zuiden, Benjamin C.; Bartolo, Denis; Vitelli, Vincenzo

2017-11-01

Liquids composed of self-propelled particles have been experimentally realized using molecular, colloidal or macroscopic constituents. These active liquids can flow spontaneously even in the absence of an external drive. Unlike spontaneous active flow, the propagation of density waves in confined active liquids is not well explored. Here, we exploit a mapping between density waves on top of a chiral flow and electrons in a synthetic gauge field to lay out design principles for artificial structures termed topological active metamaterials. We design metamaterials that break time-reversal symmetry using lattices composed of annular channels filled with a spontaneously flowing active liquid. Such active metamaterials support topologically protected sound modes that propagate unidirectionally, without backscattering, along either sample edges or domain walls and despite overdamped particle dynamics. Our work illustrates how parity-symmetry breaking in metamaterial structure combined with microscopic irreversibility of active matter leads to novel functionalities that cannot be achieved using only passive materials.

Fermions and link invariants

International Nuclear Information System (INIS)

Kauffman, L.; Saleur, H.

1991-01-01

Various aspects of knot theory are discussed when fermionic degrees of freedom are taken into account in the braid group representations and in the state models. It is discussed how the R matrix for the Alexander polynomial arises from the Fox differential calculus, and how it is related to the quantum group U q gl(1,1). New families of solutions of the Yang Baxter equation obtained from ''linear'' representations of the braid group and exterior algebra are investigated. State models associated with U q sl(n,m), and in the case n=m=1 a state model for the multivariable Alexander polynomial are studied. Invariants of links in solid handlebodies are considered and it is shown how the non trivial topology lifts the boson fermion degeneracy is present in S 3 . (author) 36 refs

Time reversal technique for gas leakage detection.

Science.gov (United States)

Maksimov, A O; Polovinka, Yu A

2015-04-01

The acoustic remote sensing of subsea gas leakage traditionally uses sonars as active acoustic sensors and hydrophones picking up the sound generated by a leak as passive sensors. When gas leaks occur underwater, bubbles are produced and emit sound at frequencies intimately related to their sizes. The experimental implementation of an acoustic time-reversal mirror (TRM) is now well established in underwater acoustics. In the basic TRM experiment, a probe source emits a pulse that is received on an array of sensors, time reversed, and re-emitted. After time reversal, the resulting field focuses back at the probe position. In this study, a method for enhancing operation of the passive receiving system has been proposed by using it in the regime of TRM. Two factors, the local character of the acoustic emission signal caused by the leakage and a resonant nature of the bubble radiation at their birth, make particularly effective scattering with the conjugate wave (CW). Analytical calculations are performed for the scattering of CW wave on a single bubble when CW is formed by bubble birthing wail received on an array, time reversed, and re-emitted. The quality of leakage detection depends on the spatio-temporal distribution of ambient noise.

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.

Complete axiomatization of the stutter-invariant fragment of the linear time µ-calculus

NARCIS (Netherlands)

Gheerbrant, A.

2010-01-01

The logic µ(U) is the fixpoint extension of the "Until"-only fragment of linear-time temporal logic. It also happens to be the stutter-invariant fragment of linear-time µ-calculus µ(◊). We provide complete axiomatizations of µ(U) on the class of finite words and on the class of ω-words. We introduce

Underwater Time Service and Synchronization Based on Time Reversal Technique

Science.gov (United States)

Lu, Hao; Wang, Hai-bin; Aissa-El-Bey, Abdeldjalil; Pyndiah, Ramesh

2010-09-01

Real time service and synchronization are very important to many underwater systems. But the time service and synchronization in existence cannot work well due to the multi-path propagation and random phase fluctuation of signals in the ocean channel. The time reversal mirror technique can realize energy concentration through self-matching of the ocean channel and has very good spatial and temporal focusing properties. Based on the TRM technique, we present the Time Reversal Mirror Real Time service and synchronization (TRMRT) method which can bypass the processing of multi-path on the server side and reduce multi-path contamination on the client side. So TRMRT can improve the accuracy of time service. Furthermore, as an efficient and precise method of time service, TRMRT could be widely used in underwater exploration activities and underwater navigation and positioning systems.

Voltage-driven magnetization control in topological insulator/magnetic insulator heterostructures

Directory of Open Access Journals (Sweden)

Michael E. Flatté

2017-05-01

Full Text Available A major barrier to the development of spin-based electronics is the transition from current-driven spin torque, or magnetic-field-driven magnetization reversal, to a more scalable voltage-driven magnetization reversal. To achieve this, multiferroic materials appear attractive, however the effects in current materials occur at very large voltages or at low temperatures. Here the potential of a new class of hybrid multiferroic materials is described, consisting of a topological insulator adjacent to a magnetic insulator, for which an applied electric field reorients the magnetization. As these materials lack conducting states at the chemical potential in their bulk, no dissipative charge currents flow in the bulk. Surface states at the interface, if present, produce effects similar to surface recombination currents in bipolar devices, but can be passivated using magnetic doping. Even without conducting states at the chemical potential, for a topological insulator there is a finite spin Hall conductivity provided by filled bands below the chemical potential. Spin accumulation at the interface with the magnetic insulator provides a torque on the magnetization. Properly timed voltage pulses can thus reorient the magnetic moment with only the flow of charge current required in the leads to establish the voltage. If the topological insulator is sufficiently thick the resulting low capacitance requires little charge current.

The Dynamical Invariant of Open Quantum System

OpenAIRE

Wu, S. L.; Zhang, X. Y.; Yi, X. X.

2015-01-01

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...

Anomalous quantum numbers and topological properties of field theories

International Nuclear Information System (INIS)

Polychronakos, A.P.

1987-01-01

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

Chern-Simons topological Lagrangians in odd dimensions and their Kaluza-Klein reduction

International Nuclear Information System (INIS)

Wu, Y.

1984-01-01

Clarifying the behavior of generic Chern-Simons secondary invariants under infinitesimal variation and finite gauge transformation, it is proved that they are eligible to be a candidate term in the Lagrangian in odd dimensions (2k-1 for gauge theories and 4k-1 for gravity). The coefficients in front of these terms may be quantized because of topological reasons. As a possible application, the dimensional reduction of such actions in Kaluza-Klein theory is discussed. The difficulty in defining the Chern-Simons action for topologically nontrivial field configurations is pointed out and resolved

Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories

Science.gov (United States)

Wang, Tenghui; Zhang, Zhenxing; Xiang, Liang; Gong, Zhihao; Wu, Jianlan; Yin, Yi

2018-04-01

The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the "shortcut to adiabaticity" (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.

Far-field detection of sub-wavelength Tetris without extra near-field metal parts based on phase prints of time-reversed fields with intensive background interference.

Science.gov (United States)

Chen, Yingming; Wang, Bing-Zhong

2014-07-14

Time-reversal (TR) phase prints are first used in far-field (FF) detection of sub-wavelength (SW) deformable scatterers without any extra metal structure positioned in the vicinity of the target. The 2D prints derive from discrete short-time Fourier transform of 1D TR electromagnetic (EM) signals. Because the time-invariant intensive background interference is effectively centralized by TR technique, the time-variant weak indication from FF SW scatterers can be highlighted. This method shows a different use of TR technique in which the focus peak of TR EM waves is unusually removed and the most useful information is conveyed by the other part.

Strain-induced topological quantum phase transition in phosphorene oxide

Science.gov (United States)

Kang, Seoung-Hun; Park, Jejune; Woo, Sungjong; Kwon, Young-Kyun

Using ab initio density functional theory, we investigate the structural stability and electronic properties of phosphorene oxides (POx) with different oxygen compositions x. A variety of configurations are modeled and optimized geometrically to search for the equilibrium structure for each x value. Our electronic structure calculations on the equilibrium configuration obtained for each x reveal that the band gap tends to increase with the oxygen composition of x 0.5. We further explore the strain effect on the electronic structure of the fully oxidized phosphorene, PO, with x = 1. At a particular strain without spin-orbit coupling (SOC) is observed a band gap closure near the Γ point in the k space. We further find the strain in tandem with SOC induces an interesting band inversion with a reopened very small band gap (5 meV), and thus gives rise to a topological quantum phase transition from a normal insulator to a topological insulator. Such a topological phase transition is confirmed by the wave function analysis and the band topology identified by the Z2 invariant calculation.

On the Prognostic Efficiency of Topological Descriptors for Magnetograms of Active Regions

Science.gov (United States)

Knyazeva, I. S.; Urtiev, F. A.; Makarenko, N. G.

2017-12-01

Solar flare prediction remains an important practical task of space weather. An increase in the amount and quality of observational data and the development of machine-learning methods has led to an improvement in prediction techniques. Additional information has been retrieved from the vector magnetograms; these have been recently supplemented by traditional line-of-sight (LOS) magnetograms. In this work, the problem of the comparative prognostic efficiency of features obtained on the basis of vector data and LOS magnetograms is discussed. Invariants obtained from a topological analysis of LOS magnetograms are used as complexity characteristics of magnetic patterns. Alternatively, the so-called SHARP parameters were used; they were calculated by the data analysis group of the Stanford University Laboratory on the basis of HMI/SDO vector magnetograms and are available online at the website (http://jsoc.stanford.edu/) with the solar dynamics observatory (SDO) database for the entire history of SDO observations. It has been found that the efficiency of large-flare prediction based on topological descriptors of LOS magnetograms in epignosis mode is at least s no worse than the results of prognostic schemes based on vector features. The advantages of the use of topological invariants based on LOS data are discussed.

On Topological Indices of Certain Families of Nanostar Dendrimers.

Science.gov (United States)

Husin, Mohamad Nazri; Hasni, Roslan; Arif, Nabeel Ezzulddin; Imran, Muhammad

2016-06-24

A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR)/quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Randić connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are used to predict the bioactivity of different chemical compounds. A dendrimer is an artificially manufactured or synthesized molecule built up from the branched units called monomers. In this paper, the fourth version of ABC index and the fifth version of GA index of certain families of nanostar dendrimers are investigated. We derive the analytical closed formulas for these families of nanostar dendrimers. The obtained results can be of use in molecular data mining, particularly in researching the uniqueness of tested (hyper-branched) molecular graphs.