Topological charge quantization via path integration: An application of the Kustaanheimo-Stiefel transformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Inomata, A.; Junker, G.; Wilson, R.

1993-08-01

The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bahn problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case. 32 refs.

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

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.

2006-07-01

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

BFV approach to geometric quantization

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1994-12-01

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Master equation for open two-band systems and its applications to Hall conductance

NASA Astrophysics Data System (ADS)

Shen, H. Z.; Zhang, S. S.; Dai, C. M.; Yi, X. X.

2018-02-01

Hall conductivity in the presence of a dephasing environment has recently been investigated with a dissipative term introduced phenomenologically. In this paper, we study the dissipative topological insulator (TI) and its topological transition in the presence of quantized electromagnetic environments. A Lindblad-type equation is derived to determine the dynamics of a two-band system. When the two-band model describes TIs, the environment may be the fluctuations of radiation that surround the TIs. We find the dependence of decay rates in the master equation on Bloch vectors in the two-band system, which leads to a mixing of the band occupations. Hence the environment-induced current is in general not perfectly topological in the presence of coupling to the environment, although deviations are small in the weak limit. As an illustration, we apply the Bloch-vector-dependent master equation to TIs and calculate the Hall conductance of tight-binding electrons in a two-dimensional lattice. The influence of environments on the Hall conductance is presented and discussed. The calculations show that the phase transition points of the TIs are robust against the quantized electromagnetic environment. The results might bridge the gap between quantum optics and topological photonic materials.

Probing the Topology of Density Matrices

NASA Astrophysics Data System (ADS)

Bardyn, Charles-Edouard; Wawer, Lukas; Altland, Alexander; Fleischhauer, Michael; Diehl, Sebastian

2018-01-01

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.

Noncommutative gerbes and deformation quantization

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Baković, Igor; Jurčo, Branislav; Schupp, Peter

2010-11-01

We define noncommutative gerbes using the language of star products. Quantized twisted Poisson structures are discussed as an explicit realization in the sense of deformation quantization. Our motivation is the noncommutative description of D-branes in the presence of topologically non-trivial background fields.

Quantized charge transport in chiral Majorana edge modes

NASA Astrophysics Data System (ADS)

Rachel, Stephan; Mascot, Eric; Cocklin, Sagen; Vojta, Matthias; Morr, Dirk K.

2017-11-01

Majorana fermions can be realized as quasiparticles in topological superconductors, with potential applications in topological quantum computing. Recently, lattices of magnetic adatoms deposited on the surface of s -wave superconductors—Shiba lattices—have been proposed as a new platform for topological superconductivity. These systems possess the great advantage that they are accessible via scanning-probe techniques and thus enable the local manipulation and detection of Majorana modes. Using a nonequilibrium Green's function technique we demonstrate that the topological Majorana edge modes of nanoscopic Shiba islands display universal electronic and transport properties. Most remarkably, these Majorana modes possess a quantized charge conductance that is proportional to the topological Chern number, C , and carry a supercurrent whose chirality reflects the sign of C . These results establish nanoscopic Shiba islands as promising components in future topology-based devices.

Probing topology by "heating": Quantized circular dichroism in ultracold atoms.

PubMed

Tran, Duc Thanh; Dauphin, Alexandre; Grushin, Adolfo G; Zoller, Peter; Goldman, Nathan

2017-08-01

We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic two-dimensional (2D) Chern insulator subjected to a circular time-periodic perturbation. Because of the system's chiral nature, the depletion rate is shown to depend on the orientation of the circular shake; taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number (ν) of the populated band: This "differential integrated rate" is directly related to the strength of the driving field through the quantized coefficient η 0 = ν/ ℏ 2 , where h = 2π ℏ is Planck's constant. Contrary to the integer quantum Hall effect, this quantized response is found to be nonlinear with respect to the strength of the driving field, and it explicitly involves interband transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the nonlinear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion rate measurements as a universal probe for topological order in quantum matter.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed

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.

The topological particle and Morse theory

NASA Astrophysics Data System (ADS)

Rogers, Alice

2000-09-01

Canonical BRST quantization of the topological particle defined by a Morse function h is described. Stochastic calculus, using Brownian paths which implement the WKB method in a new way providing rigorous tunnelling results even in curved space, is used to give an explicit and simple expression for the matrix elements of the evolution operator for the BRST Hamiltonian. These matrix elements lead to a representation of the manifold cohomology in terms of critical points of h along lines developed by Witten (Witten E 1982 J. Diff. Geom. 17 661-92).

Photoinduced half-integer quantized conductance plateaus in topological-insulator/superconductor heterostructures

NASA Astrophysics Data System (ADS)

Yap, Han Hoe; Zhou, Longwen; Lee, Ching Hua; Gong, Jiangbin

2018-04-01

The past few years have witnessed increased attention to the quest for Majorana-like excitations in the condensed matter community. As a promising candidate in this race, the one-dimensional chiral Majorana edge mode (CMEM) in topological insulator-superconductor heterostructures has gathered renewed interests after an experimental breakthrough [Q. L. He et al., Science 357, 294 (2017), 10.1126/science.aag2792]. In this work, we study computationally the quantum transport of topological insulator-superconductor hybrid devices subject to time-periodic modulation. We report half-integer quantized conductance plateaus at 1/2 e/2h and 3/2 e/2h upon applying the so-called sum rule in the theory of quantum transport in Floquet topological matter. In particular, in a photoinduced topological superconductor sandwiched between two Floquet Chern insulators, it is found that for each Floquet sideband, the CMEM admits equal probability for normal transmission and local Andreev reflection over a wide range of parameter regimes, yielding half-integer quantized plateaus that resist static and time-periodic disorder. While it is well-established that periodic driving fields can simultaneously create and manipulate multiple pairs of Majorana bound states, their detection scheme remains elusive, in part due to their being neutral excitations. Therefore the 3/2 e/2h plateau indicates the possibility to verify the generation of multiple pairs of photoinduced CMEMs via transport measurements. The robust and half-quantized conductance plateaus due to CMEMs are both fascinating and subtle because they only emerge after a summation over contributions from all Floquet sidebands. Our work may add insights into the transport properties of Floquet topological systems and stimulate further studies on the optical control of topological superconductivity.

Probing topology by “heating”: Quantized circular dichroism in ultracold atoms

PubMed Central

Tran, Duc Thanh; Dauphin, Alexandre; Grushin, Adolfo G.; Zoller, Peter; Goldman, Nathan

2017-01-01

We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic two-dimensional (2D) Chern insulator subjected to a circular time-periodic perturbation. Because of the system’s chiral nature, the depletion rate is shown to depend on the orientation of the circular shake; taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number (ν) of the populated band: This “differential integrated rate” is directly related to the strength of the driving field through the quantized coefficient η0 = ν/ℏ2, where h = 2π ℏ is Planck’s constant. Contrary to the integer quantum Hall effect, this quantized response is found to be nonlinear with respect to the strength of the driving field, and it explicitly involves interband transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the nonlinear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion rate measurements as a universal probe for topological order in quantum matter. PMID:28835930

Non-commutative Chern numbers for generic aperiodic discrete systems

NASA Astrophysics Data System (ADS)

Bourne, Chris; Prodan, Emil

2018-06-01

The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a unifying theoretical framework for topological electronic, photonic, phononic etc (aperiodic) systems. We then discuss, in physical terms, the philosophy behind an operator theoretic analysis used to systematize such systems. A model calculation of the Hall conductance of a 2-dimensional amorphous lattice is given, where we present numerical evidence of its quantization in the mobility gap regime. Motivated by such facts, we then present the main result of our work, which is the extension of the Chern number formulas to Hamiltonians associated to lattices without a canonical labeling of the sites, together with index theorems that assure the quantization and stability of these Chern numbers in the mobility gap regime. Our results cover a broad range of applications, in particular, those involving quasi-crystalline, amorphous as well as synthetic (i.e. algorithmically generated) lattices.

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

NASA Astrophysics Data System (ADS)

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.

Quantized circular photogalvanic effect in Weyl semimetals

NASA Astrophysics Data System (ADS)

de Juan, Fernando; Grushin, Adolfo G.; Morimoto, Takahiro; Moore, Joel E.

The circular photogalvanic effect (CPGE) is the part of a photocurrent that switches depending on the sense of circular polarization of the incident light. It has been consistently observed in systems without inversion symmetry and depends on non-universal material details. We find that in a class of Weyl semimetals (e.g. SrSi2) and three-dimensional Rashba materials (e.g. doped Te) without inversion and mirror symmetries, the CPGE trace is effectively Quantized in terms of the combination of fundamental constants e3/h2 cɛ0 with no material-dependent parameters. This is so because the CPGE directly measures the topological charge of Weyl points near the Fermi surface, and non-quantized corrections from disorder and additional bands can be small over a significant range of incident frequencies. Moreover, the magnitude of the CPGE induced by a Weyl node is relatively large, which enables the direct detection of the monopole charge with current techniques.

Quantized circular photogalvanic effect in Weyl semimetals

NASA Astrophysics Data System (ADS)

de Juan, Fernando; Grushin, Adolfo G.; Morimoto, Takahiro; Moore, Joel E.

2017-07-01

The circular photogalvanic effect (CPGE) is the part of a photocurrent that switches depending on the sense of circular polarization of the incident light. It has been consistently observed in systems without inversion symmetry and depends on non-universal material details. Here we find that in a class of Weyl semimetals (for example, SrSi2) and three-dimensional Rashba materials (for example, doped Te) without inversion and mirror symmetries, the injection contribution to the CPGE trace is effectively quantized in terms of the fundamental constants e, h, c and with no material-dependent parameters. This is so because the CPGE directly measures the topological charge of Weyl points, and non-quantized corrections from disorder and additional bands can be small over a significant range of incident frequencies. Moreover, the magnitude of the CPGE induced by a Weyl node is relatively large, which enables the direct detection of the monopole charge with current techniques.

Vortex creation during magnetic trap manipulations of spinor Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Itin, A. P.; Space Research Institute, RAS, Moscow; Morishita, T.

2006-06-15

We investigate several mechanisms of vortex creation during splitting of a spinor Bose-Einstein condensate (BEC) in a magnetic double-well trap controlled by a pair of current carrying wires and bias magnetic fields. Our study is motivated by a recent MIT experiment on splitting BECs with a similar trap [Y. Shin et al., Phys. Rev. A 72, 021604 (2005)], where an unexpected fork-like structure appeared in the interference fringes indicating the presence of a singly quantized vortex in one of the interfering condensates. It is well known that in a spin-1 BEC in a quadrupole trap, a doubly quantized vortex ismore » topologically produced by a 'slow' reversal of bias magnetic field B{sub z}. Since in the experiment a doubly quantized vortex had never been seen, Shin et al. ruled out the topological mechanism and concentrated on the nonadiabatic mechanical mechanism for explanation of the vortex creation. We find, however, that in the magnetic trap considered both mechanisms are possible: singly quantized vortices can be formed in a spin-1 BEC topologically (for example, during the magnetic field switching-off process). We therefore provide a possible alternative explanation for the interference patterns observed in the experiment. We also present a numerical example of creation of singly quantized vortices due to 'fast' splitting; i.e., by a dynamical (nonadiabatic) mechanism.« less

Robust transport signatures of topological superconductivity in topological insulator nanowires.

PubMed

de Juan, Fernando; Ilan, Roni; Bardarson, Jens H

2014-09-05

Finding a clear signature of topological superconductivity in transport experiments remains an outstanding challenge. In this work, we propose exploiting the unique properties of three-dimensional topological insulator nanowires to generate a normal-superconductor junction in the single-mode regime where an exactly quantized 2e2/h zero-bias conductance can be observed over a wide range of realistic system parameters. This is achieved by inducing superconductivity in half of the wire, which can be tuned at will from trivial to topological with a parallel magnetic field, while a perpendicular field is used to gap out the normal part, except for two spatially separated chiral channels. The combination of chiral mode transport and perfect Andreev reflection makes the measurement robust to moderate disorder, and the quantization of conductance survives to much higher temperatures than in tunnel junction experiments. Our proposal may be understood as a variant of a Majorana interferometer which is easily realizable in experiments.

Dirac’s magnetic monopole and the Kontsevich star product

NASA Astrophysics Data System (ADS)

Soloviev, M. A.

2018-03-01

We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial topology, and are constructed for two operator representations. In the first setting, the quantum operators act on the Hilbert space of sections of a nontrivial complex line bundle associated with the Hopf bundle, whereas the second approach uses instead a quaternionic Hilbert module of sections of a trivial quaternionic line bundle. We show that these two quantizations are naturally related by a bundle morphism and, as a consequence, induce the same phase-space star product. We obtain explicit expressions for the integral kernels of star-products corresponding to various operator orderings and calculate their asymptotic expansions up to the third order in the Planck constant \\hbar . We also show that the differential form of the magnetic Weyl product corresponding to the symmetric ordering agrees completely with the Kontsevich formula for deformation quantization of Poisson structures and can be represented by Kontsevich’s graphs.

General covariance, topological quantum field theories and fractional statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gamboa, J.

1992-01-20

Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. The authors study the relationship between both theories in 2 + 1 dimensions and the authors show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST-BFV quantization is reviewed in order tomore » understand the topological approach proposed here.« less

Study of Topological Effects Concerning the Lowest A″ and the Three A' States for the CO2(+) Ion.

PubMed

Dhindhwal, Vikash; Baer, Michael; Sathyamurthy, N

2016-05-19

A study of the topological effects, viz., the Jahn-Teller (JT) and Renner-Teller (RT) effects, in CO2(+) has been carried out by calculating nonadiabatic coupling terms (NACTs) at the state-averaged CASSCF level using the cc-pVTZ basis set for the lowest three A' states and one A″ state along a circular contour. Using the NACTs, the privileged adiabatic-to-diabatic transformation (ADT) angles (γ12) for 1A' and 2A' states of CO2(+) have been calculated along various circular contours. Employing one of the oxygen atoms as the test particle exposed two conical intersections (ci) located on each side of the CO diatom. The main purpose of this study is to explore the possibility of forming reliable diabatic potential energy surfaces for this system. Success in achieving this goal is guaranteed by the ability to calculate quantized privileged ADT angles along closed contours covering large regions in configuration space (see, e.g., J. Phys. Chem. A 2014 , 118 , 6361 ). The calculations were carried out for two and three JT states. In most cases very nice quantization has been achieved although the calculations were frequently done, as required, for large regions in configuration space (sometimes ≥18 Å(2)). In one case, for which the quantization was not gratifying, the inclusion of the RT effect modified it considerably.

Infinite family of three-dimensional Floquet topological paramagnets

NASA Astrophysics Data System (ADS)

Potter, Andrew C.; Vishwanath, Ashvin; Fidkowski, Lukasz

2018-06-01

We uncover an infinite family of time-reversal symmetric 3 d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium and are governed by an infinite set of Z2-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3 d FTPMs are not captured by group cohomology methods and cannot be obtained from equilibrium classifications simply by treating the discrete time translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous Z2 (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2 d system without breaking time reversal symmetry.

Two dimensional topological insulator in quantizing magnetic fields

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

A Heisenberg Algebra Bundle of a Vector Field in Three-Space and its Weyl Quantization

NASA Astrophysics Data System (ADS)

Binz, Ernst; Pods, Sonja

2006-01-01

In these notes we associate a natural Heisenberg group bundle Ha with a singularity free smooth vector field X = (id,a) on a submanifold M in a Euclidean three-space. This bundle yields naturally an infinite dimensional Heisenberg group HX∞. A representation of the C*-group algebra of HX∞ is a quantization. It causes a natural Weyl-deformation quantization of X. The influence of the topological structure of M on this quantization is encoded in the Chern class of a canonical complex line bundle inside Ha.

Manipulating topological-insulator properties using quantum confinement

NASA Astrophysics Data System (ADS)

Kotulla, M.; Zülicke, U.

2017-07-01

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

Can chaos be observed in quantum gravity?

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Höhn, Philipp A.; Koslowski, Tim A.; Nelson, Mike I.

2017-06-01

Full general relativity is almost certainly 'chaotic'. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.

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

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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.

Quantum Hall effect with small numbers of vortices in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Byrnes, Tim; Dowling, Jonathan P.

2015-08-01

When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of 2 π . In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of m /2 h , where m is the mass of the atoms and h is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.

Massive Schwinger model at finite θ

NASA Astrophysics Data System (ADS)

Azcoiti, Vicente; Follana, Eduardo; Royo-Amondarain, Eduardo; Di Carlo, Giuseppe; Vaquero Avilés-Casco, Alejandro

2018-01-01

Using the approach developed by V. Azcoiti et al. [Phys. Lett. B 563, 117 (2003), 10.1016/S0370-2693(03)00601-4], we are able to reconstruct the behavior of the massive one-flavor Schwinger model with a θ term and a quantized topological charge. We calculate the full dependence of the order parameter with θ . Our results at θ =π are compatible with Coleman's conjecture on the phase diagram of this model.

Unconventional topological Hall effect in skyrmion crystals caused by the topology of the lattice

NASA Astrophysics Data System (ADS)

Göbel, Börge; Mook, Alexander; Henk, Jürgen; Mertig, Ingrid

2017-03-01

The hallmark of a skyrmion crystal (SkX) is the topological Hall effect (THE). In this article we predict and explain an unconventional behavior of the topological Hall conductivity in SkXs. In simple terms, the spin texture of the skyrmions causes an inhomogeneous emergent magnetic field whose associated Lorentz force acts on the electrons. By making the emergent field homogeneous, the THE is mapped onto the quantum Hall effect (QHE). Consequently, each electronic band of the SkX is assigned to a Landau level. This correspondence of THE and QHE allows us to explain the unconventional behavior of the THE of electrons in SkXs. For example, a skyrmion crystal on a triangular lattice exhibits a quantized topological Hall conductivity with steps of 2 .e2/h below and with steps of 1 .e2/h above the van Hove singularity. On top of this, the conductivity shows a prominent sign change at the van Hove singularity. These unconventional features are deeply connected to the topology of the structural lattice.

Quantized Majorana conductance

NASA Astrophysics Data System (ADS)

Zhang, Hao; Liu, Chun-Xiao; Gazibegovic, Sasa; Xu, Di; Logan, John A.; Wang, Guanzhong; van Loo, Nick; Bommer, Jouri D. S.; de Moor, Michiel W. A.; Car, Diana; Op Het Veld, Roy L. M.; van Veldhoven, Petrus J.; Koelling, Sebastian; Verheijen, Marcel A.; Pendharkar, Mihir; Pennachio, Daniel J.; Shojaei, Borzoyeh; Lee, Joon Sue; Palmstrøm, Chris J.; Bakkers, Erik P. A. M.; Sarma, S. Das; Kouwenhoven, Leo P.

2018-04-01

Majorana zero-modes—a type of localized quasiparticle—hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool for identifying the presence of Majorana zero-modes, for instance as a zero-bias peak in differential conductance. The height of the Majorana zero-bias peak is predicted to be quantized at the universal conductance value of 2e2/h at zero temperature (where e is the charge of an electron and h is the Planck constant), as a direct consequence of the famous Majorana symmetry in which a particle is its own antiparticle. The Majorana symmetry protects the quantization against disorder, interactions and variations in the tunnel coupling. Previous experiments, however, have mostly shown zero-bias peaks much smaller than 2e2/h, with a recent observation of a peak height close to 2e2/h. Here we report a quantized conductance plateau at 2e2/h in the zero-bias conductance measured in indium antimonide semiconductor nanowires covered with an aluminium superconducting shell. The height of our zero-bias peak remains constant despite changing parameters such as the magnetic field and tunnel coupling, indicating that it is a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins by investigating its robustness to electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of Majorana zero-modes in the system, consequently paving the way for future braiding experiments that could lead to topological quantum computing.

Quantized Majorana conductance.

PubMed

Zhang, Hao; Liu, Chun-Xiao; Gazibegovic, Sasa; Xu, Di; Logan, John A; Wang, Guanzhong; van Loo, Nick; Bommer, Jouri D S; de Moor, Michiel W A; Car, Diana; Op Het Veld, Roy L M; van Veldhoven, Petrus J; Koelling, Sebastian; Verheijen, Marcel A; Pendharkar, Mihir; Pennachio, Daniel J; Shojaei, Borzoyeh; Lee, Joon Sue; Palmstrøm, Chris J; Bakkers, Erik P A M; Sarma, S Das; Kouwenhoven, Leo P

2018-04-05

Majorana zero-modes-a type of localized quasiparticle-hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool for identifying the presence of Majorana zero-modes, for instance as a zero-bias peak in differential conductance. The height of the Majorana zero-bias peak is predicted to be quantized at the universal conductance value of 2e 2 /h at zero temperature (where e is the charge of an electron and h is the Planck constant), as a direct consequence of the famous Majorana symmetry in which a particle is its own antiparticle. The Majorana symmetry protects the quantization against disorder, interactions and variations in the tunnel coupling. Previous experiments, however, have mostly shown zero-bias peaks much smaller than 2e 2 /h, with a recent observation of a peak height close to 2e 2 /h. Here we report a quantized conductance plateau at 2e 2 /h in the zero-bias conductance measured in indium antimonide semiconductor nanowires covered with an aluminium superconducting shell. The height of our zero-bias peak remains constant despite changing parameters such as the magnetic field and tunnel coupling, indicating that it is a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins by investigating its robustness to electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of Majorana zero-modes in the system, consequently paving the way for future braiding experiments that could lead to topological quantum computing.

Topological formation of a multiply charged vortex in the Rb Bose-Einstein condensate: Effectiveness of the gravity compensation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumakura, M.; PRESTO, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012; CREST, JST, 4-1-8 Honcho Kawaguchi, Saitama 332-0012

2006-06-15

In a Bose-Einstein condensate of {sup 87}Rb (F=2,m{sub F}=2) atoms we have topologically created a quantized vortex with a charge of 4 by reversing the magnetic field of the trap. Experimental conditions of reversal time and initial magnetic field strength for the successful vortex creation were restricted within narrower ranges, compared to those in the case of the {sup 23}Na condensate. The experimental difficulty was explained in terms of a non-negligible gravitational sag arising from its large atomic mass. We have successfully stabilized the vortex formation by compensating gravity with a blue-detuned laser beam.

Splitting Times of Doubly Quantized Vortices in Dilute Bose-Einstein Condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huhtamaeki, J. A. M.; Pietilae, V.; Virtanen, S. M. M.

2006-09-15

Recently, the splitting of a topologically created doubly quantized vortex into two singly quantized vortices was experimentally investigated in dilute atomic cigar-shaped Bose-Einstein condensates [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)]. In particular, the dependency of the splitting time on the peak particle density was studied. We present results of theoretical simulations which closely mimic the experimental setup. We show that the combination of gravitational sag and time dependency of the trapping potential alone suffices to split the doubly quantized vortex in time scales which are in good agreement with the experiments.

Quantized Iterative Learning Consensus Tracking of Digital Networks With Limited Information Communication.

PubMed

Xiong, Wenjun; Yu, Xinghuo; Chen, Yao; Gao, Jie

2017-06-01

This brief investigates the quantized iterative learning problem for digital networks with time-varying topologies. The information is first encoded as symbolic data and then transmitted. After the data are received, a decoder is used by the receiver to get an estimate of the sender's state. Iterative learning quantized communication is considered in the process of encoding and decoding. A sufficient condition is then presented to achieve the consensus tracking problem in a finite interval using the quantized iterative learning controllers. Finally, simulation results are given to illustrate the usefulness of the developed criterion.

Probing Dirac fermion dynamics in topological insulator Bi2Se3 films with a scanning tunneling microscope.

PubMed

Song, Can-Li; Wang, Lili; He, Ke; Ji, Shuai-Hua; Chen, Xi; Ma, Xu-Cun; Xue, Qi-Kun

2015-05-01

Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi2Se3 ultrathin films. At the two-dimensional limit, bulk electrons become quantized and the quantization can be controlled by the film thickness at a single quintuple layer level. By studying the spatial decay of standing waves (quasiparticle interference patterns) off steps, we measure directly the energy and film thickness dependence of the phase relaxation length lϕ and inelastic scattering lifetime τ of topological surface-state electrons. We find that τ exhibits a remarkable (E - EF)(-2) energy dependence and increases with film thickness. We show that the features revealed are typical for electron-electron scattering between surface and bulk states.

Theory of the Quantized Hall Conductance in Periodic Systems: a Topological Analysis.

NASA Astrophysics Data System (ADS)

Czerwinski, Michael Joseph

The integral quantization of the Hall conductance in two-dimensional periodic systems is investigated from a topological point of view. Attention is focused on the contributions from the electronic sub-bands which arise from perturbed Landau levels. After reviewing the theoretical work leading to the identification of the Hall conductance as a topological quantum number, both a determination and interpretation of these quantized values for the sub-band conductances is made. It is shown that the Hall conductance of each sub-band can be regarded as the sum of two terms which will be referred to as classical and nonclassical. Although each of these contributions individually leads to a fractional conductance, the sum of these two contributions does indeed yield an integer. These integral conductances are found to be given by the solution of a simple Diophantine equation which depends on the periodic perturbation. A connection between the quantized value of the Hall conductance and the covering of real space by the zeroes of the sub-band wavefunctions allows for a determination of these conductances under more general potentials. A method is described for obtaining the conductance values from only those states bordering the Brillouin zone, and not the states in its interior. This method is demonstrated to give Hall conductances in agreement with those obtained from the Diophantine equation for the sinusoidal potential case explored earlier. Generalizing a simple gauge invariance argument from real space to k-space, a k-space 'vector potential' is introduced. This allows for a explicit identification of the Hall conductance with the phase winding number of the sub-band wavefunction around the Brillouin zone. The previously described division of the Hall conductance into classical and nonclassical contributions is in this way made more rigorous; based on periodicity considerations alone, these terms are identified as the winding numbers associated with (i) the basis states and (ii) the coefficients of these basis states, respectively. In this way a general Diophantine equation, independent of the periodic potential, is obtained. Finally, the use of the 'parallel transport' of state vectors in the determination of an overall phase convention for these states is described. This is seen to lead to a simple and straightforward method for determining the Hall conductance. This method is based on the states directly, without reference to the particular component wavefunctions of these states. Mention is made of the generality of calculations of this type, within the context of the geometric (or Berry) phases acquired by systems under an adiabatic modification of their environment.

Nonlinear Dirac cones

NASA Astrophysics Data System (ADS)

Bomantara, Raditya Weda; Zhao, Wenlei; Zhou, Longwen; Gong, Jiangbin

2017-09-01

Physics arising from two-dimensional (2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such 2D Dirac cones are often characterized by a π Berry phase and are destroyed by a perturbative mass term. By considering mean-field nonlinearity in a minimal two-band Chern insulator model, we obtain a different type of Dirac cone that is robust to local perturbations without symmetry restrictions. Due to a different pseudospin texture, the Berry phase of the Dirac cone is no longer quantized in π , and can be continuously tuned as an order parameter. Furthermore, in an Aharonov-Bohm (AB) interference setup to detect such Dirac cones, the adiabatic AB phase is found to be π both theoretically and computationally, offering an observable topological invariant and a fascinating example where the Berry phase and AB phase are fundamentally different. We hence discover a nonlinearity-induced quantum phase transition from a known topological insulating phase to an unusual gapless topological phase.

Skyrme insulators: insulators at the brink of superconductivity

DOE PAGES

Ertem, Onur; Chang, Po -Yao; Coleman, Piers; ...

2017-08-04

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected, quantized circulation. When this topological protection is absent, as in the case of 3He-A, the coherent quantum state no longer supports persistent superflow. In this paper, we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. Specifically, we introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex vector order parameter. Here, we apply this idea to the case ofmore » SmB6, arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood as a realization of this state. Our theory enables us to understand the linear specific heat of SmB6 in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.« less

Skyrme Insulators: Insulators at the Brink of Superconductivity

NASA Astrophysics Data System (ADS)

Erten, Onur; Chang, Po-Yao; Coleman, Piers; Tsvelik, Alexei M.

2017-08-01

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected quantized circulation. When this topological protection is absent, as in the case of 3He -A , the coherent quantum state no longer supports persistent superflow. Here, we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. We specifically introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex-vector order parameter. We apply this idea to the case of SmB6 , arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood as a realization of this state. Our theory enables us to understand the linear specific heat of SmB6 in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB6 will develop a Meissner effect.

Topological Anderson insulator phase in a Dirac-semimetal thin film

NASA Astrophysics Data System (ADS)

Chen, Rui; Xu, Dong-Hui; Zhou, Bin

2017-06-01

The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three-dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that the quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either a normal insulator or quantum spin Hall insulator, depending on the thin-film thickness. We present the study of disorder effects in a thin film of Dirac semimetals. It is found that moderate Anderson disorder strength can drive a topological phase transition from a normal band insulator to a topological Anderson insulator in a Dirac-semimetal thin film. The numerical calculation based on the model parameters of Dirac semimetal Na3Bi shows that in the topological Anderson insulator phase, a quantized conductance plateau occurs in the bulk gap of the band insulator, and the distributions of local currents further confirm that the quantized conductance plateau arises from the helical edge states induced by disorder. Finally, an effective medium theory based on the Born approximation fits the numerical data.

New excitations in the Thirring model

NASA Astrophysics Data System (ADS)

Cortés, J. L.; Gamboa, J.; Schmidt, I.; Zanelli, J.

1998-12-01

The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate x- in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Right-handed fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.

Quantized Algebras of Functions on Homogeneous Spaces with Poisson Stabilizers

NASA Astrophysics Data System (ADS)

Neshveyev, Sergey; Tuset, Lars

2012-05-01

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0 < q < 1. We study a quantization C( G q / K q ) of the algebra of continuous functions on G/ K. Using results of Soibelman and Dijkhuizen-Stokman we classify the irreducible representations of C( G q / K q ) and obtain a composition series for C( G q / K q ). We describe closures of the symplectic leaves of G/ K refining the well-known description in the case of flag manifolds in terms of the Bruhat order. We then show that the same rules describe the topology on the spectrum of C( G q / K q ). Next we show that the family of C*-algebras C( G q / K q ), 0 < q ≤ 1, has a canonical structure of a continuous field of C*-algebras and provides a strict deformation quantization of the Poisson algebra {{C}[G/K]} . Finally, extending a result of Nagy, we show that C( G q / K q ) is canonically KK-equivalent to C( G/ K).

On Correspondence of BRST-BFV, Dirac, and Refined Algebraic Quantizations of Constrained Systems

NASA Astrophysics Data System (ADS)

Shvedov, O. Yu.

2002-11-01

The correspondence between BRST-BFV, Dirac, and refined algebraic (group averaging, projection operator) approaches to quantizing constrained systems is analyzed. For the closed-algebra case, it is shown that the component of the BFV wave function corresponding to maximal (minimal) value of number of ghosts and antighosts in the Schrodinger representation may be viewed as a wave function in the refined algebraic (Dirac) quantization approach. The Giulini-Marolf group averaging formula for the inner product in the refined algebraic quantization approach is obtained from the Batalin-Marnelius prescription for the BRST-BFV inner product, which should be generally modified due to topological problems. The considered prescription for the correspondence of states is observed to be applicable to the open-algebra case. The refined algebraic quantization approach is generalized then to the case of nontrivial structure functions. A simple example is discussed. The correspondence of observables for different quantization methods is also investigated.

Application of path-integral quantization to indistinguishable particle systems topologically confined by a magnetic field

NASA Astrophysics Data System (ADS)

Jacak, Janusz E.

2018-01-01

We demonstrate an original development of path-integral quantization in the case of a multiply connected configuration space of indistinguishable charged particles on a 2D manifold and exposed to a strong perpendicular magnetic field. The system occurs to be exceptionally homotopy-rich and the structure of the homotopy essentially depends on the magnetic field strength resulting in multiloop trajectories at specific conditions. We have proved, by a generalization of the Bohr-Sommerfeld quantization rule, that the size of a magnetic field flux quantum grows for multiloop orbits like (2 k +1 ) h/c with the number of loops k . Utilizing this property for electrons on the 2D substrate jellium, we have derived upon the path integration a complete FQHE hierarchy in excellent consistence with experiments. The path integral has been next developed to a sum over configurations, displaying various patterns of trajectory homotopies (topological configurations), which in the nonstationary case of quantum kinetics, reproduces some unclear formerly details in the longitudinal resistivity observed in experiments.

Plateau-Plateau Transitions in Disordered Topological Chern Insulators

NASA Astrophysics Data System (ADS)

Su, Ying; Avishai, Yshai; Wang, Xiangrong

Occurrence of the topological Anderson insulator (TAI) in the HgTe quantum well demonstrates that topological phase transition can be driven by disorder, where re-entrant 2e2 / h quantized conductance is contributed by helical edge states. Within a certain extension of the disordered Kane-Mele model for magnetic materials that violate time-reversal symmetry and inversion symmetry, it is shown that the physics of TAI becomes even richer due to lifted spin and valley degeneracies. Tuning either disorder or Fermi energy (in both topologically trivial and nontrivial phases) makes it possible to drive plateau-plateau transitions between distinct TAI phases characterized by different Chern numbers, marked by jumps of the quantized conductance from 0 to e2 / h and from e2 / h to 2e2 / h . An effective medium theory based on the Born approximation yields an accurate description of different TAI phases in parameter space. This work is supported by NSF of China Grant (No. 11374249) and Hong Kong RGC Grants (No. 163011151 and No. 605413). The research of Y.A. is partially supported by Israel Science Foundation Grant No. 400/2012.

Observation of the Quantum Hall Effect in Confined Films of the Three-Dimensional Dirac Semimetal Cd3 As2

NASA Astrophysics Data System (ADS)

Schumann, Timo; Galletti, Luca; Kealhofer, David A.; Kim, Honggyu; Goyal, Manik; Stemmer, Susanne

2018-01-01

The magnetotransport properties of epitaxial films of Cd3 As2 , a paradigm three-dimensional Dirac semimetal, are investigated. We show that an energy gap opens in the bulk electronic states of sufficiently thin films and, at low temperatures, carriers residing in surface states dominate the electrical transport. The carriers in these states are sufficiently mobile to give rise to a quantized Hall effect. The sharp quantization demonstrates surface transport that is virtually free of parasitic bulk conduction and paves the way for novel quantum transport studies in this class of topological materials. Our results also demonstrate that heterostructuring approaches can be used to study and engineer quantum states in topological semimetals.

Observation of Conductance Quantization in InSb Nanowire Networks

PubMed Central

2017-01-01

Majorana zero modes (MZMs) are prime candidates for robust topological quantum bits, holding a great promise for quantum computing. Semiconducting nanowires with strong spin orbit coupling offer a promising platform to harness one-dimensional electron transport for Majorana physics. Demonstrating the topological nature of MZMs relies on braiding, accomplished by moving MZMs around each other in a certain sequence. Most of the proposed Majorana braiding circuits require nanowire networks with minimal disorder. Here, the electronic transport across a junction between two merged InSb nanowires is studied to investigate how disordered these nanowire networks are. Conductance quantization plateaus are observed in most of the contact pairs of the epitaxial InSb nanowire networks: the hallmark of ballistic transport behavior. PMID:28665621

Disorder-induced half-integer quantized conductance plateau in quantum anomalous Hall insulator-superconductor structures

NASA Astrophysics Data System (ADS)

Huang, Yingyi; Setiawan, F.; Sau, Jay D.

2018-03-01

A weak superconducting proximity effect in the vicinity of the topological transition of a quantum anomalous Hall system has been proposed as a venue to realize a topological superconductor (TSC) with chiral Majorana edge modes (CMEMs). A recent experiment [Science 357, 294 (2017), 10.1126/science.aag2792] claimed to have observed such CMEMs in the form of a half-integer quantized conductance plateau in the two-terminal transport measurement of a quantum anomalous Hall-superconductor junction. Although the presence of a superconducting proximity effect generically splits the quantum Hall transition into two phase transitions with a gapped TSC in between, in this Rapid Communication we propose that a nearly flat conductance plateau, similar to that expected from CMEMs, can also arise from the percolation of quantum Hall edges well before the onset of the TSC or at temperatures much above the TSC gap. Our Rapid Communication, therefore, suggests that, in order to confirm the TSC, it is necessary to supplement the observation of the half-quantized conductance plateau with a hard superconducting gap (which is unlikely for a disordered system) from the conductance measurements or the heat transport measurement of the transport gap. Alternatively, the half-quantized thermal conductance would also serve as a smoking-gun signature of the TSC.

Topological Quantum Phase Transition and Local Topological Order in a Strongly Interacting Light-Matter System.

PubMed

Sarkar, Sujit

2017-05-12

An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of nonlinear cavities. Topological quantum phase transition occurs with massless excitation only for the finite detuning process. We present a few results based on the exact analytical calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non-topological state. Finally, we study the quantized Berry phase (topological order) and its connection to the topological number (winding number).

Effective vacua for Floquet topological phases: A numerical perspective on the switch-function formalism

NASA Astrophysics Data System (ADS)

Tauber, C.

2018-05-01

We propose a general edge index definition for two-dimensional Floquet topological phases based on a switch-function formalism. When the Floquet operator has a spectral gap, the index covers both clean and disordered phases, anomalous or not, and does not require the bulk to be fully localized. It is interpreted as a nonadiabatic charge pumping that is quantized when the sample is placed next to an effective vacuum. This vacuum is gap-dependent and obtained from a Floquet Hamiltonian. The choice of a vacuum provides a simple and alternative gap-selection mechanism. Inspired by the model from Rudner et al. we then illustrate these concepts on Floquet disordered phases. Switch-function formalism is usually restricted to infinite samples in the thermodynamic limit. Here we circumvent this issue and propose a numerical implementation of the edge index that could be adapted to any bulk or edge index expressed in terms of switch functions, already existing for many topological phases.

Topological phase transition measured in a dissipative metamaterial

NASA Astrophysics Data System (ADS)

Rosenthal, Eric I.; Ehrlich, Nicole K.; Rudner, Mark S.; Higginbotham, Andrew P.; Lehnert, K. W.

2018-06-01

We construct a metamaterial from radio-frequency harmonic oscillators, and find two topologically distinct phases resulting from dissipation engineered into the system. These phases are distinguished by a quantized value of bulk energy transport. The impulse response of our circuit is measured and used to reconstruct the band structure and winding number of circuit eigenfunctions around a dark mode. Our results demonstrate that dissipative topological transport can occur in a wider class of physical systems than considered before.

Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms

NASA Astrophysics Data System (ADS)

Nobukane, Hiroyoshi; Matsuyama, Toyoki; Tanda, Satoshi

2017-01-01

The quantum anomaly that breaks the symmetry, for example the parity and the chirality, in the quantization leads to a physical quantity with a topological Chern invariant. We report the observation of a Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms by employing electric transport. We observed the superconductor-to-insulator transition by reducing the thickness of Sr2RuO4 single crystals. The appearance of a gap structure in the insulating phase implies local superconductivity. Fractional quantized conductance was observed without an external magnetic field. We found an anomalous induced voltage with temperature and thickness dependence, and the induced voltage exhibited switching behavior when we applied a magnetic field. We suggest that there was fractional magnetic-field-induced electric polarization in the interlayer. These anomalous results are related to topological invariance. The fractional axion angle Θ = π/6 was determined by observing the topological magneto-electric effect in the Bose-insulating phase of Sr2RuO4 nanofilms.

Fuzzy spaces topology change and BH thermodynamics

NASA Astrophysics Data System (ADS)

Silva, C. A. S.; Landim, R. R.

2014-03-01

What is the ultimate fate of something that falls into a black hole? From this question arises one of the most intricate problems of modern theoretical physics: the black hole information loss paradox. Bekenstein and Hawking have been shown that the entropy in a black hole is proportional to the surface area of its event horizon, which should be quantized in a multiple of the Planck area. This led G.'t Hooft and L. Susskind to propose the holographic principle which states that all the information inside the black hole can be stored on its event horizon. From this results, one may think if the solution to the information paradox could lies in the quantum properties of the black hole horizon. One way to quantize the event horizon is to see it as a fuzzy sphere, which posses a closed relation with Hopf algebras. This relation makes possible a topology change process where a fuzzy sphere splits in two others. In this work it will be shown that, if one quantize the black hole event horizon as a fuzzy sphere taking into account its quantum symmetry properties, a topology change process to black holes can be defined without break unitarity or locality, and we can obtain a possible solution to the information paradox. Moreover, we show that this model can explain the origin of the black hole entropy, and why black holes obey a generalized second law of thermodynamics.

Pseudospins and Topological Effects of Phonons in a Kekulé Lattice

NASA Astrophysics Data System (ADS)

Liu, Yizhou; Lian, Chao-Sheng; Li, Yang; Xu, Yong; Duan, Wenhui

2017-12-01

The search for exotic topological effects of phonons has attracted enormous interest for both fundamental science and practical applications. By studying phonons in a Kekulé lattice, we find a new type of pseudospin characterized by quantized Berry phases and pseudoangular momenta, which introduces various novel topological effects, including topologically protected pseudospin-polarized interface states and a phonon pseudospin Hall effect. We further demonstrate a pseudospin-contrasting optical selection rule and a pseudospin Zeeman effect, giving a complete generation-manipulation-detection paradigm of the phonon pseudospin. The pseudospin and topology-related physics revealed for phonons is general and applicable for electrons, photons, and other particles.

Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings

NASA Astrophysics Data System (ADS)

Sciarappa, Antonio

2016-10-01

Bethe/Gauge correspondence as it is usually stated is ill-defined in five dimensions and needs a "non-perturbative" completion; a related problem also appears in three dimensions. It has been suggested that this problem, probably due to incompleteness of Omega background regularization in odd dimension, may be solved if we consider gauge theory on compact S 5 and S 3 geometries. We will develop this idea further by giving a full Bethe/Gauge correspondence dictionary on S 5 and S 3 focussing mainly on the eigenfunctions of (open and closed) relativistic 2-particle Toda chain and its quantized spectral curve: these are most properly written in terms of non-perturbatively completed NS open topological strings. A key ingredient is Faddeev's modular double structure which is naturally implemented by the S 5 and S 3 geometries.

Topological Floquet-Thouless Energy Pump

NASA Astrophysics Data System (ADS)

Kolodrubetz, Michael H.; Nathan, Frederik; Gazit, Snir; Morimoto, Takahiro; Moore, Joel E.

2018-04-01

We explore adiabatic pumping in the presence of a periodic drive, finding a new phase in which the topologically quantized pumped quantity is energy rather than charge. The topological invariant is given by the winding number of the micromotion with respect to time within each cycle, momentum, and adiabatic tuning parameter. We show numerically that this pump is highly robust against both disorder and interactions, breaking down at large values of either in a manner identical to the Thouless charge pump. Finally, we suggest experimental protocols for measuring this phenomenon.

Spontaneously broken topological SL(5,R) gauge theory with standard gravity emerging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mielke, Eckehard W.

2011-02-15

A completely metric-free sl(5,R) gauge framework is developed in four dimensions. After spontaneous symmetry breaking of the corresponding topological BF scheme, Einstein spaces with a tiny cosmological constant emerge, similarly as in (anti-)de Sitter gauge theories of gravity. The induced {Lambda} is related to the scale of the symmetry breaking. A ''background'' metric surfaces from a Higgs-like mechanism. The finiteness of such a topological scheme converts into asymptotic safeness after quantization of the spontaneously broken model.

Semiclassical theory of Landau levels and magnetic breakdown in topological metals

NASA Astrophysics Data System (ADS)

Alexandradinata, A.; Glazman, Leonid

2018-04-01

The Bohr-Sommerfeld quantization rule lies at the heart of the semiclassical theory of a Bloch electron in a magnetic field. This rule is predictive of Landau levels and de Haas-van Alphen oscillations for conventional metals, as well as for a host of topological metals which have emerged in the recent intercourse between band theory, crystalline symmetries, and topology. The essential ingredients in any quantization rule are connection formulas that match the semiclassical (WKB) wave function across regions of strong quantum fluctuations. Here, we propose (a) a multicomponent WKB wave function that describes transport within degenerate-band subspaces, and (b) the requisite connection formulas for saddle points and type-II Dirac points, where tunneling respectively occurs within the same band, and between distinct bands. (a) and (b) extend previous works by incorporating phase corrections that are subleading in powers of the field; these corrections include the geometric Berry phase, and account for the orbital magnetic moment and the Zeeman coupling. A comprehensive symmetry analysis is performed for such phase corrections occurring in closed orbits, which is applicable to solids in any (magnetic) space group. We have further formulated a graph-theoretic description of semiclassical orbits. This allows us to systematize the construction of quantization rules for a large class of closed orbits (with or without tunneling), as well as to formulate the notion of a topological invariant in semiclassical magnetotransport—as a quantity that is invariant under continuous deformations of the graph. Landau levels in the presence of tunneling are generically quasirandom, i.e., disordered on the scale of nearest-neighbor level spacings but having longer-ranged correlations; we develop a perturbative theory to determine Landau levels in such quasirandom spectra.

Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas (Author’s Manuscript)

DTIC Science & Technology

2017-01-27

Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas Yong Xu,∗ Sheng-Tao Wang, and L.-M. Duan Department of Physics, University...atomic gas trapped in an optical lattice. Recently, condensed matter systems have proven to be a powerful platform to study low energy gapless...possess a nonzero quantized Chern number. This leads to a natural question of whether there exists a topological ring exhibiting both a quantized Chern

Geometry, topology, and response in condensed matter systems

NASA Astrophysics Data System (ADS)

Varjas, Daniel

Topological order provides a new paradigm to view phases of matter. Unlike conventional symmetry breaking order, these states are not distinguished by different patterns of symmetry breaking, instead by their intricate mathematical structure, topology. By the bulk-boundary correspondence, the nontrivial topology of the bulk results in robust gapless excitations on symmetry preserving surfaces. We utilize both of these views to study topological phases together with the analysis of their quantized physical responses to perturbations. First we study the edge excitations of strongly interacting abelian fractional quantum Hall liquids on an infinite strip geometry. We use the infinite density matrix renormalization group method to numerically measure edge exponents in model systems, including subleading orders. Using analytic methods we derive a generalized Luttinger's theorem that relates momenta of edge excitations. Next we consider topological crystalline insulators protected by space group symmetry. After reviewing the general formalism, we present results about the quantization of the magnetoelectric response protected by orientation-reversing space group symmetries. We construct and analyze insulating and superconducting tight-binding models with glide symmetry in three dimensions to illustrate the general result. Following this, we derive constraints on weak indices of three dimensional topological insulators imposed by space group symmetries. We focus on spin-orbit coupled insulators with and without time reversal invariance and consider both symmorphic and nonsymmorphic symmetries. Finally, we calculate the response of metals and generalize the notion of the magnetoelectric effect to noninteracting gapless systems. We use semiclassical dynamics to study the magnetopiezoelectric effect, the current response to elastic strain in static external magnetic fields.

Hidden topological constellations and polyvalent charges in chiral nematic droplets

NASA Astrophysics Data System (ADS)

Posnjak, Gregor; Čopar, Simon; Muševič, Igor

2017-02-01

Topology has an increasingly important role in the physics of condensed matter, quantum systems, material science, photonics and biology, with spectacular realizations of topological concepts in liquid crystals. Here we report on long-lived hidden topological states in thermally quenched, chiral nematic droplets, formed from string-like, triangular and polyhedral constellations of monovalent and polyvalent singular point defects. These topological defects are regularly packed into a spherical liquid volume and stabilized by the elastic energy barrier due to the helical structure and confinement of the liquid crystal in the micro-sphere. We observe, for the first time, topological three-dimensional point defects of the quantized hedgehog charge q=-2, -3. These higher-charge defects act as ideal polyvalent artificial atoms, binding the defects into polyhedral constellations representing topological molecules.

Hidden topological constellations and polyvalent charges in chiral nematic droplets

PubMed Central

Posnjak, Gregor; Čopar, Simon; Muševič, Igor

2017-01-01

Topology has an increasingly important role in the physics of condensed matter, quantum systems, material science, photonics and biology, with spectacular realizations of topological concepts in liquid crystals. Here we report on long-lived hidden topological states in thermally quenched, chiral nematic droplets, formed from string-like, triangular and polyhedral constellations of monovalent and polyvalent singular point defects. These topological defects are regularly packed into a spherical liquid volume and stabilized by the elastic energy barrier due to the helical structure and confinement of the liquid crystal in the micro-sphere. We observe, for the first time, topological three-dimensional point defects of the quantized hedgehog charge q=−2, −3. These higher-charge defects act as ideal polyvalent artificial atoms, binding the defects into polyhedral constellations representing topological molecules. PMID:28220770

Global synchronization of complex dynamical networks through digital communication with limited data rate.

PubMed

Wang, Yan-Wu; Bian, Tao; Xiao, Jiang-Wen; Wen, Changyun

2015-10-01

This paper studies the global synchronization of complex dynamical network (CDN) under digital communication with limited bandwidth. To realize the digital communication, the so-called uniform-quantizer-sets are introduced to quantize the states of nodes, which are then encoded and decoded by newly designed encoders and decoders. To meet the requirement of the bandwidth constraint, a scaling function is utilized to guarantee the quantizers having bounded inputs and thus achieving bounded real-time quantization levels. Moreover, a new type of vector norm is introduced to simplify the expression of the bandwidth limit. Through mathematical induction, a sufficient condition is derived to ensure global synchronization of the CDNs. The lower bound on the sum of the real-time quantization levels is analyzed for different cases. Optimization method is employed to relax the requirements on the network topology and to determine the minimum of such lower bound for each case, respectively. Simulation examples are also presented to illustrate the established results.

Unique Fock quantization of scalar cosmological perturbations

NASA Astrophysics Data System (ADS)

Fernández-Méndez, Mikel; Mena Marugán, Guillermo A.; Olmedo, Javier; Velhinho, José M.

2012-05-01

We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lemaître-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a three-sphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter-field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined.

A general diagrammatic algorithm for contraction and subsequent simplification of second-quantized expressions.

PubMed

Bochevarov, Arteum D; Sherrill, C David

2004-08-22

We present a general computer algorithm to contract an arbitrary number of second-quantized expressions and simplify the obtained analytical result. The functions that perform these operations are a part of the program Nostromo which facilitates the handling and analysis of the complicated mathematical formulas which are often encountered in modern quantum-chemical models. In contrast to existing codes of this kind, Nostromo is based solely on the Goldstone-diagrammatic representation of algebraic expressions in Fock space and has capabilities to work with operators as well as scalars. Each Goldstone diagram is internally represented by a line of text which is easy to interpret and transform. The calculation of matrix elements does not exploit Wick's theorem in a direct way, but uses diagrammatic techniques to produce only nonzero terms. The identification of equivalent expressions and their subsequent factorization in the final result is performed easily by analyzing the topological structure of the diagrammatic expressions. (c) 2004 American Institute of Physics

Cross-entropy embedding of high-dimensional data using the neural gas model.

PubMed

Estévez, Pablo A; Figueroa, Cristián J; Saito, Kazumi

2005-01-01

A cross-entropy approach to mapping high-dimensional data into a low-dimensional space embedding is presented. The method allows to project simultaneously the input data and the codebook vectors, obtained with the Neural Gas (NG) quantizer algorithm, into a low-dimensional output space. The aim of this approach is to preserve the relationship defined by the NG neighborhood function for each pair of input and codebook vectors. A cost function based on the cross-entropy between input and output probabilities is minimized by using a Newton-Raphson method. The new approach is compared with Sammon's non-linear mapping (NLM) and the hierarchical approach of combining a vector quantizer such as the self-organizing feature map (SOM) or NG with the NLM recall algorithm. In comparison with these techniques, our method delivers a clear visualization of both data points and codebooks, and it achieves a better mapping quality in terms of the topology preservation measure q(m).

Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms

PubMed Central

Nobukane, Hiroyoshi; Matsuyama, Toyoki; Tanda, Satoshi

2017-01-01

The quantum anomaly that breaks the symmetry, for example the parity and the chirality, in the quantization leads to a physical quantity with a topological Chern invariant. We report the observation of a Chern structure in the Bose-insulating phase of Sr2RuO4 nanofilms by employing electric transport. We observed the superconductor-to-insulator transition by reducing the thickness of Sr2RuO4 single crystals. The appearance of a gap structure in the insulating phase implies local superconductivity. Fractional quantized conductance was observed without an external magnetic field. We found an anomalous induced voltage with temperature and thickness dependence, and the induced voltage exhibited switching behavior when we applied a magnetic field. We suggest that there was fractional magnetic-field-induced electric polarization in the interlayer. These anomalous results are related to topological invariance. The fractional axion angle Θ = π/6 was determined by observing the topological magneto-electric effect in the Bose-insulating phase of Sr2RuO4 nanofilms. PMID:28112269

Irrational Charge from Topological Order

NASA Astrophysics Data System (ADS)

Moessner, R.; Sondhi, S. L.

2010-10-01

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

Disorder-Induced Topological State Transition in Photonic Metamaterials

NASA Astrophysics Data System (ADS)

Liu, Changxu; Gao, Wenlong; Yang, Biao; Zhang, Shuang

2017-11-01

The topological state transition has been widely studied based on the quantized topological band invariant such as the Chern number for the system without intense randomness that may break the band structures. We numerically demonstrate the disorder-induced state transition in the photonic topological systems for the first time. Instead of applying the ill-defined topological band invariant in a disordered system, we utilize an empirical parameter to unambiguously illustrate the state transition of the topological metamaterials. Before the state transition, we observe a robust surface state with well-confined electromagnetic waves propagating unidirectionally, immune to the disorder from permittivity fluctuation up to 60% of the original value. During the transition, a hybrid state composed of a quasiunidirectional surface mode and intensively localized hot spots is established, a result of the competition between the topological protection and Anderson localization.

Topological Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

Zhang, Pengfei; Zhai, Hui

2018-05-01

In this Rapid Communication, we construct a large-N exactly solvable model to study the interplay between interaction and topology, by connecting the Sachdev-Ye-Kitaev (SYK) model with constant hopping. The hopping forms a band structure that can exhibit both topologically trivial and nontrivial phases. Starting from a topologically trivial insulator with zero Hall conductance, we show that the interaction can drive a phase transition to a topologically nontrivial insulator with quantized nonzero Hall conductance, and a single gapless Dirac fermion emerges when the interaction is fine tuned to the critical point. The finite temperature effect is also considered, and we show that the topological phase with a stronger interaction is less stable against temperature. Our model provides a concrete example to illustrate the interacting topological phases and phase transitions, and can shed light on similar problems in physical systems.

Dissipationless conductance in a topological coaxial cable

NASA Astrophysics Data System (ADS)

Schuster, Thomas; Iadecola, Thomas; Chamon, Claudio; Jackiw, Roman; Pi, So-Young

2016-09-01

We present a dynamical mechanism leading to dissipationless conductance, whose quantized value is controllable in a (3+1)-dimensional electronic system. The mechanism is exemplified by a theory of Weyl fermions coupled to a Higgs field, also known as an axion insulator. We show that the insertion of an axial gauge flux can induce vortex lines in the Higgs field, similar to the development of vortices in a superconductor upon the insertion of magnetic flux. We further show that the necessary axial gauge flux can be generated using Rashba spin-orbit coupling or a magnetic field. Vortex lines in the Higgs field are known to bind chiral fermionic modes, each of which serves as a one-way channel for electric charge with conductance e2/h . Combining these elements, we present a physical picture, the "topological coaxial cable," illustrating how the value of the quantized conductance could be controlled in such an axion insulator.

Robustness of topological Hall effect of nontrivial spin textures

NASA Astrophysics Data System (ADS)

Jalil, Mansoor B. A.; Tan, Seng Ghee

2014-05-01

We analyze the topological Hall conductivity (THC) of topologically nontrivial spin textures like magnetic vortices and skyrmions and investigate its possible application in the readback for magnetic memory based on those spin textures. Under adiabatic conditions, such spin textures would theoretically yield quantized THC values, which are related to topological invariants such as the winding number and polarity, and as such are insensitive to fluctuations and smooth deformations. However, in a practical setting, the finite size of spin texture elements and the influence of edges may cause them to deviate from their ideal configurations. We calculate the degree of robustness of the THC output in practical magnetic memories in the presence of edge and finite size effects.

Topological Valley Currents in Gapped Dirac Materials

NASA Astrophysics Data System (ADS)

Lensky, Yuri D.; Song, Justin C. W.; Samutpraphoot, Polnop; Levitov, Leonid S.

2015-06-01

Gapped 2D Dirac materials, in which inversion symmetry is broken by a gap-opening perturbation, feature a unique valley transport regime. Topological valley currents in such materials are dominated by bulk currents produced by electronic states just beneath the gap rather than by edge modes. The system ground state hosts dissipationless persistent valley currents existing even when topologically protected edge modes are absent. Valley currents induced by an external bias are characterized by a quantized half-integer valley Hall conductivity. The undergap currents dominate magnetization and the charge Hall effect in a light-induced valley-polarized state.

Topos quantum theory on quantization-induced sheaves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Kunji, E-mail: nakayama@law.ryukoku.ac.jp

2014-10-15

In this paper, we construct a sheaf-based topos quantum theory. It is well known that a topos quantum theory can be constructed on the topos of presheaves on the category of commutative von Neumann algebras of bounded operators on a Hilbert space. Also, it is already known that quantization naturally induces a Lawvere-Tierney topology on the presheaf topos. We show that a topos quantum theory akin to the presheaf-based one can be constructed on sheaves defined by the quantization-induced Lawvere-Tierney topology. That is, starting from the spectral sheaf as a state space of a given quantum system, we construct sheaf-basedmore » expressions of physical propositions and truth objects, and thereby give a method of truth-value assignment to the propositions. Furthermore, we clarify the relationship to the presheaf-based quantum theory. We give translation rules between the sheaf-based ingredients and the corresponding presheaf-based ones. The translation rules have “coarse-graining” effects on the spaces of the presheaf-based ingredients; a lot of different proposition presheaves, truth presheaves, and presheaf-based truth-values are translated to a proposition sheaf, a truth sheaf, and a sheaf-based truth-value, respectively. We examine the extent of the coarse-graining made by translation.« less

TBA-like integral equations from quantized mirror curves

NASA Astrophysics Data System (ADS)

Okuyama, Kazumi; Zakany, Szabolcs

2016-03-01

Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in certain cases, this resolvent function satisfies a system of non-linear integral equations whose structure is very similar to the Thermodynamic Bethe Ansatz (TBA) systems. This can be used to compute spectral traces, both exactly and as a semiclassical expansion. As a main example, we consider the system related to the quantized mirror curve of local P2. According to a recent proposal, the traces of this operator are determined by the refined BPS indices of the underlying CY. We use our non-linear integral equations to test that proposal.

Theory of the disordered ν =5/2 quantum thermal Hall state: Emergent symmetry and phase diagram

NASA Astrophysics Data System (ADS)

Lian, Biao; Wang, Juven

2018-04-01

Fractional quantum Hall (FQH) system at Landau level filling fraction ν =5 /2 has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance σx y=5 e2/2 h . Thermal Hall conductances of the Pf and APf states are quantized at κx y=7 /2 and κx y=3 /2 , respectively, in a proper unit. However, a recent experiment shows the thermal Hall conductance of ν =5 /2 FQH state is κx y=5 /2 . It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a κx y=5 /2 phase. In this paper, we do perturbative and nonperturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold Λ1, which is lowered to an emergent U (1 )×U (1) symmetry at energy scales between Λ1 and a higher value Λ2, and is finally lowered to the composite fermion parity symmetry Z2F above Λ2. Based on the emergent symmetries, we propose a phase diagram of the disordered ν =5 /2 FQH system and show that a κx y=5 /2 phase arises at disorder energy scales Λ >Λ1 . Furthermore, we show the gapped double-semion sector of ND compact domain walls contributes nonlocal topological degeneracy 2ND-1, causing a low-temperature peak in the heat capacity. We implement a nonperturbative method to bootstrap generic topological 1 +1 D domain walls (two-surface defects) applicable to any 2 +1 D non-Abelian topological order. We also identify potentially relevant spin topological quantum field theories (TQFTs) for various ν =5 /2 FQH states in terms of fermionic version of U (1) ±8 Chern-Simons theory ×Z8 -class TQFTs.

Topological quantization of energy transport in micromechanical and nanomechanical lattices

NASA Astrophysics Data System (ADS)

Chien, Chih-Chun; Velizhanin, Kirill A.; Dubi, Yonatan; Ilic, B. Robert; Zwolak, Michael

2018-03-01

Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nanomechanical lattices in the classical regime, i.e., essentially "masses and springs." We show that the thermal conductance factorizes into topological and nontopological components. The former takes on three discrete values and arises due to the appearance of edge modes that prevent good contact between the heat reservoirs and the bulk, giving a length-independent reduction of the conductance. In essence, energy input at the boundary mostly stays there, an effect robust against disorder and nonlinearity. These results bridge two seemingly disconnected disciplines of physics, namely topology and thermal transport, and suggest ways to engineer thermal contacts, opening a direction to explore the ramifications of topological properties on nanoscale technology.

Stabilizing the false vacuum: Mott skyrmions

PubMed Central

Kanász-Nagy, M.; Dóra, B.; Demler, E. A.; Zaránd, G.

2015-01-01

Topological excitations keep fascinating physicists since many decades. While individual vortices and solitons emerge and have been observed in many areas of physics, their most intriguing higher dimensional topological relatives, skyrmions (smooth, topologically stable textures) and magnetic monopoles emerging almost necessarily in any grand unified theory and responsible for charge quantization remained mostly elusive. Here we propose that loading a three-component nematic superfluid such as 23Na into a deep optical lattice and thereby creating an insulating core, one can create topologically stable skyrmion textures. The skyrmion's extreme stability and its compact geometry enable one to investigate the skyrmion's structure, and the interplay of topology and excitations in detail. In particular, the superfluid's excitation spectrum as well as the quantum numbers are demonstrated to change dramatically due to the skyrmion, and reflect the presence of a trapped monopole, as imposed by the skyrmion's topology. PMID:25582915

Stabilizing the false vacuum. Mott skyrmions

DOE PAGES

Kanász-Nagy, M.; Dóra, B.; Demler, E. A.; ...

2015-01-13

Topological excitations keep fascinating physicists since many decades. While individual vortices and solitons emerge and have been observed in many areas of physics, their most intriguing higher dimensional topological relatives, skyrmions (smooth, topologically stable textures) and magnetic monopoles emerging almost necessarily in any grand unified theory and responsible for charge quantization remained mostly elusive. Here we propose that loading a three-component nematic superfluid such as 23Na into a deep optical lattice and thereby creating an insulating core, one can create topologically stable skyrmion textures. The skyrmion’s extreme stability and its compact geometry enable one to investigate the skyrmion’s structure, andmore » the interplay of topology and excitations in detail. In particular, the superfluid’s excitation spectrum as well as the quantum numbers are demonstrated to change dramatically due to the skyrmion, and reflect the presence of a trapped monopole, as imposed by the skyrmion’s topology.« less

Modeling shape and topology of low-resolution density maps of biological macromolecules.

PubMed Central

De-Alarcón, Pedro A; Pascual-Montano, Alberto; Gupta, Amarnath; Carazo, Jose M

2002-01-01

In the present work we develop an efficient way of representing the geometry and topology of volumetric datasets of biological structures from medium to low resolution, aiming at storing and querying them in a database framework. We make use of a new vector quantization algorithm to select the points within the macromolecule that best approximate the probability density function of the original volume data. Connectivity among points is obtained with the use of the alpha shapes theory. This novel data representation has a number of interesting characteristics, such as 1) it allows us to automatically segment and quantify a number of important structural features from low-resolution maps, such as cavities and channels, opening the possibility of querying large collections of maps on the basis of these quantitative structural features; 2) it provides a compact representation in terms of size; 3) it contains a subset of three-dimensional points that optimally quantify the densities of medium resolution data; and 4) a general model of the geometry and topology of the macromolecule (as opposite to a spatially unrelated bunch of voxels) is easily obtained by the use of the alpha shapes theory. PMID:12124252

Experimental Observation of a Generalized Thouless Pump with a Single Spin

NASA Astrophysics Data System (ADS)

Ma, Wenchao; Zhou, Longwen; Zhang, Qi; Li, Min; Cheng, Chunyang; Geng, Jianpei; Rong, Xing; Shi, Fazhan; Gong, Jiangbin; Du, Jiangfeng

2018-03-01

Adiabatic cyclic modulation of a one-dimensional periodic potential will result in quantized charge transport, which is termed the Thouless pump. In contrast to the original Thouless pump restricted by the topology of the energy band, here we experimentally observe a generalized Thouless pump that can be extensively and continuously controlled. The extraordinary features of the new pump originate from interband coherence in nonequilibrium initial states, and this fact indicates that a quantum superposition of different eigenstates individually undergoing quantum adiabatic following can also be an important ingredient unavailable in classical physics. The quantum simulation of this generalized Thouless pump in a two-band insulator is achieved by applying delicate control fields to a single spin in diamond. The experimental results demonstrate all principal characteristics of the generalized Thouless pump. Because the pumping in our system is most pronounced around a band-touching point, this work also suggests an alternative means to detect quantum or topological phase transitions.

Quantized edge modes in atomic-scale point contacts in graphene

NASA Astrophysics Data System (ADS)

Kinikar, Amogh; Phanindra Sai, T.; Bhattacharyya, Semonti; Agarwala, Adhip; Biswas, Tathagata; Sarker, Sanjoy K.; Krishnamurthy, H. R.; Jain, Manish; Shenoy, Vijay B.; Ghosh, Arindam

2017-07-01

The zigzag edges of single- or few-layer graphene are perfect one-dimensional conductors owing to a set of gapless states that are topologically protected against backscattering. Direct experimental evidence of these states has been limited so far to their local thermodynamic and magnetic properties, determined by the competing effects of edge topology and electron-electron interaction. However, experimental signatures of edge-bound electrical conduction have remained elusive, primarily due to the lack of graphitic nanostructures with low structural and/or chemical edge disorder. Here, we report the experimental detection of edge-mode electrical transport in suspended atomic-scale constrictions of single and multilayer graphene created during nanomechanical exfoliation of highly oriented pyrolytic graphite. The edge-mode transport leads to the observed quantization of conductance close to multiples of G0 = 2e2/h. At the same time, conductance plateaux at G0/2 and a split zero-bias anomaly in non-equilibrium transport suggest conduction via spin-polarized states in the presence of an electron-electron interaction.

Quantized edge modes in atomic-scale point contacts in graphene.

PubMed

Kinikar, Amogh; Phanindra Sai, T; Bhattacharyya, Semonti; Agarwala, Adhip; Biswas, Tathagata; Sarker, Sanjoy K; Krishnamurthy, H R; Jain, Manish; Shenoy, Vijay B; Ghosh, Arindam

2017-07-01

The zigzag edges of single- or few-layer graphene are perfect one-dimensional conductors owing to a set of gapless states that are topologically protected against backscattering. Direct experimental evidence of these states has been limited so far to their local thermodynamic and magnetic properties, determined by the competing effects of edge topology and electron-electron interaction. However, experimental signatures of edge-bound electrical conduction have remained elusive, primarily due to the lack of graphitic nanostructures with low structural and/or chemical edge disorder. Here, we report the experimental detection of edge-mode electrical transport in suspended atomic-scale constrictions of single and multilayer graphene created during nanomechanical exfoliation of highly oriented pyrolytic graphite. The edge-mode transport leads to the observed quantization of conductance close to multiples of G 0  = 2e 2 /h. At the same time, conductance plateaux at G 0 /2 and a split zero-bias anomaly in non-equilibrium transport suggest conduction via spin-polarized states in the presence of an electron-electron interaction.

Emergent Topological Phenomena in Thin Films of Pyrochlore Iridates

NASA Astrophysics Data System (ADS)

Yang, Bohm-Jung; Nagaosa, Naoto

2014-06-01

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

Controlling charge quantization with quantum fluctuations.

PubMed

Jezouin, S; Iftikhar, Z; Anthore, A; Parmentier, F D; Gennser, U; Cavanna, A; Ouerghi, A; Levkivskyi, I P; Idrisov, E; Sukhorukov, E V; Glazman, L I; Pierre, F

2016-08-04

In 1909, Millikan showed that the charge of electrically isolated systems is quantized in units of the elementary electron charge e. Today, the persistence of charge quantization in small, weakly connected conductors allows for circuits in which single electrons are manipulated, with applications in, for example, metrology, detectors and thermometry. However, as the connection strength is increased, the discreteness of charge is progressively reduced by quantum fluctuations. Here we report the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometre-scale metallic island to a circuit, we explore the complete evolution of charge quantization while scanning the entire range of connection strengths, from a very weak (tunnel) to a perfect (ballistic) contact. We observe, when approaching the ballistic limit, that charge quantization is destroyed by quantum fluctuations, and scales as the square root of the residual probability for an electron to be reflected across the quantum channel; this scaling also applies beyond the different regimes of connection strength currently accessible to theory. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization and in a universal square-root scaling, valid for all connection strengths, in agreement with expectations. Besides being pertinent for the improvement of single-electron circuits and their applications, and for the metal-semiconductor hybrids relevant to topological quantum computing, knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices.

First- and second-order metal-insulator phase transitions and topological aspects of a Hubbard-Rashba system

NASA Astrophysics Data System (ADS)

Marcelino, Edgar

2017-05-01

This paper considers a model consisting of a kinetic term, Rashba spin-orbit coupling and short-range Coulomb interaction at zero temperature. The Coulomb interaction is decoupled by a mean-field approximation in the spin channel using field theory methods. The results feature a first-order phase transition for any finite value of the chemical potential and quantum criticality for vanishing chemical potential. The Hall conductivity is also computed using the Kubo formula in a mean-field effective Hamiltonian. In the limit of infinite mass the kinetic term vanishes and all the phase transitions are of second order; in this case the spontaneous symmetry-breaking mechanism adds a ferromagnetic metallic phase to the system and features a zero-temperature quantization of the Hall conductivity in the insulating one.

Finite energy quantization on a topology changing spacetime

NASA Astrophysics Data System (ADS)

Krasnikov, S.

2016-08-01

The "trousers" spacetime is a pair of flat two-dimensional cylinders ("legs") merging into a single one ("trunk"). In spite of its simplicity this spacetime has a few features (including, in particular, a naked singularity in the "crotch") each of which is presumably unphysical, but for none of which a mechanism is known able to prevent its occurrence. Therefore, it is interesting and important to study the behavior of the quantum fields in such a space. Anderson and DeWitt were the first to consider the free scalar field in the trousers spacetime. They argued that the crotch singularity produces an infinitely bright flash, which was interpreted as evidence that the topology of space is dynamically preserved. Similar divergencies were later discovered by Manogue, Copeland, and Dray who used a more exotic quantization scheme. Later yet the same result obtained within a somewhat different approach led Sorkin to the conclusion that the topological transition in question is suppressed in quantum gravity. In this paper I show that the Anderson-DeWitt divergence is an artifact of their choice of the Fock space. By choosing a different one-particle Hilbert space one gets a quantum state in which the components of the stress-energy tensor (SET) are bounded in the frame of a free-falling observer.

Quantization and superselection sectors III: Multiply connected spaces and indistinguishable particles

NASA Astrophysics Data System (ADS)

Landsman, N. P. Klaas

2016-09-01

We reconsider the (non-relativistic) quantum theory of indistinguishable particles on the basis of Rieffel’s notion of C∗-algebraic (“strict”) deformation quantization. Using this formalism, we relate the operator approach of Messiah and Greenberg (1964) to the configuration space approach pioneered by Souriau (1967), Laidlaw and DeWitt-Morette (1971), Leinaas and Myrheim (1977), and others. In dimension d > 2, the former yields bosons, fermions, and paraparticles, whereas the latter seems to leave room for bosons and fermions only, apparently contradicting the operator approach as far as the admissibility of parastatistics is concerned. To resolve this, we first prove that in d > 2 the topologically non-trivial configuration spaces of the second approach are quantized by the algebras of observables of the first. Secondly, we show that the irreducible representations of the latter may be realized by vector bundle constructions, among which the line bundles recover the results of the second approach. Mathematically speaking, representations on higher-dimensional bundles (which define parastatistics) cannot be excluded, which render the configuration space approach incomplete. Physically, however, we show that the corresponding particle states may always be realized in terms of bosons and/or fermions with an unobserved internal degree of freedom (although based on non-relativistic quantum mechanics, this conclusion is analogous to the rigorous results of the Doplicher-Haag-Roberts analysis in algebraic quantum field theory, as well as to the heuristic arguments which led Gell-Mann and others to QCD (i.e. Quantum Chromodynamics)).

Flows with fractional quantum circulation in Bose-Einstein condensates induced by nontopological phase defects

NASA Astrophysics Data System (ADS)

Kanai, Toshiaki; Guo, Wei; Tsubota, Makoto

2018-01-01

It is a common view that rotational motion in a superfluid can exist only in the presence of topological defects, i.e., quantized vortices. However, in our numerical studies on the merging of two concentric Bose-Einstein condensates with axial symmetry in two-dimensional space, we observe the emergence of a spiral dark soliton when one condensate has a nonzero initial angular momentum. This spiral dark soliton enables the transfer of angular momentum between the condensates and allows the merged condensate to rotate even in the absence of quantized vortices. Our examination of the flow field around the soliton strikingly reveals that its sharp endpoint can induce flow like a vortex point but with a fraction of a quantized circulation. This interesting nontopological "phase defect" may generate broad interest since rotational motion is essential in many quantum transport processes.

Floquet Engineering of Optical Solenoids and Quantized Charge Pumping along Tailored Paths in Two-Dimensional Chern Insulators

NASA Astrophysics Data System (ADS)

Wang, Botao; Ünal, F. Nur; Eckardt, André

2018-06-01

The insertion of a local magnetic flux, as the one created by a thin solenoid, plays an important role in gedanken experiments of quantum Hall physics. By combining Floquet engineering of artificial magnetic fields with the ability of single-site addressing in quantum gas microscopes, we propose a scheme for the realization of such local solenoid-type magnetic fields in optical lattices. We show that it can be employed to manipulate and probe elementary excitations of a topological Chern insulator. This includes quantized adiabatic charge pumping along tailored paths inside the bulk, as well as the controlled population of edge modes.

Canonical quantization of general relativity in discrete space-times.

PubMed

Gambini, Rodolfo; Pullin, Jorge

2003-01-17

It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.

Majorana fermions from Landau quantization in a superconductor and topological-insulator hybrid structure.

PubMed

Tiwari, Rakesh P; Zülicke, U; Bruder, C

2013-05-03

We show that the interplay of cyclotron motion and Andreev reflection experienced by massless-Dirac-like charge carriers in topological-insulator surface states generates a Majorana-particle excitation. On the basis of an envelope-function description of the Dirac-Andreev edge states, we discuss the kinematic properties of the Majorana mode and find them to be tunable by changing the superconductor's chemical potential and/or the magnitude of the perpendicular magnetic field. Our proposal opens up new possibilities for studying Majorana fermions in a controllable setup.

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

NASA Astrophysics Data System (ADS)

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

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

Stochastic dynamics of extended objects in driven systems II: Current quantization in the low-temperature limit

NASA Astrophysics Data System (ADS)

Catanzaro, Michael J.; Chernyak, Vladimir Y.; Klein, John R.

2016-12-01

Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of observables to describe their non-equilibrium steady states. Here we consider stochastic motion of a (k - 1) -dimensional object, which sweeps out a k-dimensional trajectory, and gives rise to a higher k-dimensional current. By employing the low-temperature (low-noise) limit, we reduce the problem to a discrete Markov chain model on a CW complex, a topological construction which generalizes the notion of a graph. This reduction allows the mean fluxes and currents of the process to be expressed in terms of solutions to the discrete Supersymmetric Fokker-Planck (SFP) equation. Taking the adiabatic limit, we show that generic driving leads to rational quantization of the generated higher dimensional current. The latter is achieved by implementing the recently developed tools, coined the higher-dimensional Kirchhoff tree and co-tree theorems. This extends the study of motion of extended objects in the continuous setting performed in the prequel (Catanzaro et al.) to this manuscript.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Topology, edge states, and zero-energy states of ultracold atoms in one-dimensional optical superlattices with alternating on-site potentials or hopping coefficients

NASA Astrophysics Data System (ADS)

He, Yan; Wright, Kevin; Kouachi, Said; Chien, Chih-Chun

2018-02-01

One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices allow a systematic study of those properties in superlattices with or without boundaries. While superlattices with additional modulating parameters are shown to have quantized topological invariants in the augmented parameter space, we also found localized or zero-energy states associated with symmetries of the Hamiltonians. Probing those states in ultracold atoms is possible by utilizing recently proposed methods analyzing particle depletion or the local density of states. Moreover, we summarize feasible realizations of configurable optical superlattices using currently available techniques.

Topological gaps without masses in driven graphene-like systems

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Neupert, Titus; Chamon, Claudio

2014-03-01

We illustrate the possibility of realizing band gaps in graphene-like systems that fall outside the existing classification of gapped Dirac Hamiltonians in terms of masses. As our primary example we consider a band gap arising due to time-dependent distortions of the honeycomb lattice. By means of an exact, invertible, and transport-preserving mapping to a time-independent Hamiltonian, we show that the system exhibits Chern-insulating phases with quantized Hall conductivities +/-e2 / h . The chirality of the corresponding gapless edge modes is controllable by both the frequency of the driving and the manner in which sublattice symmetry is broken by the dynamical lattice modulations. We demonstrate that, while these phases are in the same topological sector as the Haldane model, they are nevertheless separated from the latter by a gap-closing transition unless an extra parameter is added to the Hamiltonian. Finally, we discuss a promising possible realization of this physics in photonic lattices. This work is supported in part by DOE Grant DEF-06ER46316 (T.I. and C.C.).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bestwick, A. J.; Fox, E. J.; Kou, Xufeng

In this study, we report a nearly ideal quantum anomalous Hall effect in a three-dimensional topological insulator thin film with ferromagnetic doping. Near zero applied magnetic field we measure exact quantization in the Hall resistance to within a part per 10,000 and a longitudinal resistivity under 1 Ω per square, with chiral edge transport explicitly confirmed by nonlocal measurements. Deviations from this behavior are found to be caused by thermally activated carriers, as indicated by an Arrhenius law temperature dependence. Using the deviations as a thermometer, we demonstrate an unexpected magnetocaloric effect and use it to reach near-perfect quantization bymore » cooling the sample below the dilution refrigerator base temperature in a process approximating adiabatic demagnetization refrigeration.« less

Thermal Simulations, Open Boundary Conditions and Switches

NASA Astrophysics Data System (ADS)

Burnier, Yannis; Florio, Adrien; Kaczmarek, Olaf; Mazur, Lukas

2018-03-01

SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

Gauge symmetry and constraints structure for topologically massive AdS gravity: a symplectic viewpoint

NASA Astrophysics Data System (ADS)

Rodríguez-Tzompantzi, Omar; Escalante, Alberto

2018-05-01

By applying the Faddeev-Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant Λ , elegantly encoded in the zero-modes of the symplectic matrix, can be identified. Thereafter, via a suitable partial gauge-fixing procedure, the time gauge, we calculate the quantization bracket structure (generalized Faddeev-Jackiw brackets) for the dynamic variables and confirm that the number of physical degrees of freedom is one. This approach provides an alternative to explore the dynamical content of massive gravity models.

Topological transport in Dirac nodal-line semimetals

NASA Astrophysics Data System (ADS)

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.

Index theorem for the flat Andreev bound states at a dirty surface of a nodal superconductor

NASA Astrophysics Data System (ADS)

Ikegaya, Satoshi; Asano, Yasuhiro

2018-03-01

We discuss the stability of at-band Andreev bound states appearing at a surface of a nodal unconventional superconductor. In the clean limit, the existence of the surface bound states is topologically characterized by a momentum-dependent topological invariant: one-dimensional winding number de ned in the restricted Brillouin zone. Thus, such topological invariant is ill-defined in the presence of potential disorder which is inevitable in experiments. By paying attention to chiral symmetry of the Hamiltonian, we provide an alternative topological index N ZES that predicts the number of Andreev bound states at a dirty surface of an unconventional superconductor. Moreover, we demonstrate that the zero-bias differential conductance in a normal metal/unconventional superconductor junction is quantized at (4e 2 /h)|N ZES | in the limit of strong impurity scattering in the normal metal.

Quasiparticle Interference Studies of Quantum Materials.

PubMed

Avraham, Nurit; Reiner, Jonathan; Kumar-Nayak, Abhay; Morali, Noam; Batabyal, Rajib; Yan, Binghai; Beidenkopf, Haim

2018-06-03

Exotic electronic states are realized in novel quantum materials. This field is revolutionized by the topological classification of materials. Such compounds necessarily host unique states on their boundaries. Scanning tunneling microscopy studies of these surface states have provided a wealth of spectroscopic characterization, with the successful cooperation of ab initio calculations. The method of quasiparticle interference imaging proves to be particularly useful for probing the dispersion relation of the surface bands. Herein, how a variety of additional fundamental electronic properties can be probed via this method is reviewed. It is demonstrated how quasiparticle interference measurements entail mesoscopic size quantization and the electronic phase coherence in semiconducting nanowires; helical spin protection and energy-momentum fluctuations in a topological insulator; and the structure of the Bloch wave function and the relative insusceptibility of topological electronic states to surface potential in a topological Weyl semimetal. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

STM Studies of Spin-­Orbit Coupled Phases in Real-­ and Momentum-­Space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Madhavan, Vidya

The recently discovered class of spin-orbit coupled materials with interesting topological character are fascinating both from fundamental as well as application point of view. Two striking examples are 3D topological insulators (TIs) and topological crystalline insulators (TCIs). These materials host linearly dispersing (Dirac like) surface states with an odd number of Dirac nodes and are predicted to carry a quantized half-integer value of the axion field. The non-trivial topological properties of TIs and TCIs arise from strong spin-orbit coupling leading to an inverted band structure; which also leads to the chiral spin texture in momentum space. In this project wemore » used low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) to study materials with topological phases in real- and momentum-space. We studied both single crystals and thin films of topological materials which are susceptible to being tuned by doping, strain or gating, allowing us to explore their physical properties in the most interesting regimes and set the stage for future technological applications. .« less

Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times

NASA Astrophysics Data System (ADS)

Finster, Felix; Strohmaier, Alexander

2015-08-01

We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the time-slice axiom, and the corresponding vacuum states satisfy the microlocal spectrum condition. We also give an explicit construction of ground states on ultrastatic space-times. Unlike previous constructions, our method does not require a spectral gap or the absence of zero modes. The only requirement, the absence of zero-resonance states, is shown to be stable under compact perturbations of topology and metric. Usual deformation arguments based on the time-slice axiom then lead to a construction of Gupta-Bleuler representations on a large class of globally hyperbolic space-times. As usual, the field algebra is represented on an indefinite inner product space, in which the physical states form a positive semi-definite subspace. Gauge transformations are incorporated in such a way that the field can be coupled perturbatively to a Dirac field. Our approach does not require any topological restrictions on the underlying space-time.

Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems

NASA Astrophysics Data System (ADS)

Harada, Hiromitsu; Mouchet, Amaury; Shudo, Akira

2017-10-01

The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann surface provides complete information on the topology of complex paths, which allows us to enumerate all the possible candidates contributing to the semiclassical sum formula for tunnelling splittings. This naturally leads to action relations among classically disjoined regions, revealing entirely non-local nature in the quantization condition. The importance of the proper treatment of Stokes phenomena is also discussed in Hamiltonians in the normal form.

Symplectic analysis of three-dimensional Abelian topological gravity

NASA Astrophysics Data System (ADS)

Cartas-Fuentevilla, R.; Escalante, Alberto; Herrera-Aguilar, Alfredo

2017-02-01

A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; we show that this formalism is equivalent and more economical than Dirac's method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide with each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory at the chiral point, and the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.

Topological defects in mixtures of superconducting condensates with different charges

NASA Astrophysics Data System (ADS)

Garaud, Julien; Babaev, Egor

2014-06-01

We investigate the topological defects in phenomenological models describing mixtures of charged condensates with commensurate electric charges. Such situations are expected to appear for example in liquid metallic deuterium. This is modeled by a multicomponent Ginzburg-Landau theory where the condensates are coupled to the same gauge field by different coupling constants whose ratio is a rational number. We also briefly discuss the case where electric charges are incommensurate. Flux quantization and finiteness of the energy per unit length dictate that the different condensates have different winding and thus different number of (fractional) vortices. Competing attractive and repulsive interactions lead to molecule-like bound states between fractional vortices. Such bound states have finite energy and carry integer flux quanta. These can be characterized by the CP1 topological invariant that motivates their denomination as skyrmions.

Magnetic Susceptibility and Quantum Oscillations in a Buckled Honeycomb Lattice

NASA Astrophysics Data System (ADS)

Tabert, Calvin; Carbotte, Jules; Nicol, Elisabeth

2015-03-01

We calculate the magnetic response of a low-buckled honeycomb lattice with intrinsic spin-orbit coupling which is described by the Kane-Mele Hamiltonian (a model which would describe the low-energy physics of a material like silicene). Included in the Hamiltonian, is a sublattice potential difference term which may be induced by a perpendicular electric field; this field can tune the system from a topological insulator (TI), through a valley-spin polarized metal, to a trivial band insulator (BI). In an external magnetic field, a distinct signature of the phase transition is seen in the derivative of the magnetization with respect to chemical potential; this gives the quantization of the Hall plateaus through the Streda relation. The results are compared with the zero-frequency conductivity obtained from the Kubo formula. The magnetic susceptibility also displays signatures of the different topological phases. We also explore the de-Haas van-Alphen effect. At the transition point between the TI and BI, magnetic oscillations exist for any value of chemical potential. Away from the critical point, the chemical potential must be larger than the minimum gap. For large chemical potential (or small but finite sublattice potential difference), there is a strong beating pattern.

Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition

DOE PAGES

Wang, Jing; Zhou, Quan; Lian, Biao; ...

2015-08-31

Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional s -wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance willmore » be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between e 2 /2h and e2 /h with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.« less

Chiral topological superconductor and half-integer conductance plateau from quantum anomalous Hall plateau transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Jing; Zhou, Quan; Lian, Biao

Here, we propose to realize a two-dimensional chiral topological superconducting (TSC) state from the quantum anomalous Hall plateau transition in a magnetic topological insulator thin film through the proximity effect to a conventional s -wave superconductor. This state has a full pairing gap in the bulk and a single chiral Majorana mode at the edge. The optimal condition for realizing such chiral TSC is to have inequivalent superconducting pairing amplitudes on top and bottom surfaces of the doped magnetic topological insulator. We further propose several transport experiments to detect the chiral TSC. One unique signature is that the conductance willmore » be quantized into a half-integer plateau at the coercive field in this hybrid system. In particular, with the point contact formed by a superconducting junction, the conductance oscillates between e 2 /2h and e2 /h with the frequency determined by the voltage across the junction. We close by discussing the feasibility of these experimental proposals.« less

Asynchronous State Estimation for Discrete-Time Switched Complex Networks With Communication Constraints.

PubMed

Zhang, Dan; Wang, Qing-Guo; Srinivasan, Dipti; Li, Hongyi; Yu, Li

2018-05-01

This paper is concerned with the asynchronous state estimation for a class of discrete-time switched complex networks with communication constraints. An asynchronous estimator is designed to overcome the difficulty that each node cannot access to the topology/coupling information. Also, the event-based communication, signal quantization, and the random packet dropout problems are studied due to the limited communication resource. With the help of switched system theory and by resorting to some stochastic system analysis method, a sufficient condition is proposed to guarantee the exponential stability of estimation error system in the mean-square sense and a prescribed performance level is also ensured. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem. Finally, the effectiveness of the proposed design approach is demonstrated by a simulation example.

Generalized Skyrme model with the loosely bound potential

NASA Astrophysics Data System (ADS)

Gudnason, Sven Bjarke; Zhang, Baiyang; Ma, Nana

2016-12-01

We study a generalization of the loosely bound Skyrme model which consists of the Skyrme model with a sixth-order derivative term—motivated by its fluidlike properties—and the second-order loosely bound potential—motivated by lowering the classical binding energies of higher-charged Skyrmions. We use the rational map approximation for the Skyrmion of topological charge B =4 , calculate the binding energy of the latter, and estimate the systematic error in using this approximation. In the parameter space that we can explore within the rational map approximation, we find classical binding energies as low as 1.8%, and once taking into account the contribution from spin-isospin quantization, we obtain binding energies as low as 5.3%. We also calculate the contribution from the sixth-order derivative term to the electric charge density and axial coupling.

Quantization of Electromagnetic Fields in Cavities

NASA Technical Reports Server (NTRS)

Kakazu, Kiyotaka; Oshiro, Kazunori

1996-01-01

A quantization procedure for the electromagnetic field in a rectangular cavity with perfect conductor walls is presented, where a decomposition formula of the field plays an essential role. All vector mode functions are obtained by using the decomposition. After expanding the field in terms of the vector mode functions, we get the quantized electromagnetic Hamiltonian.

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons.

PubMed

Cardano, Filippo; D'Errico, Alessio; Dauphin, Alexandre; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo; Lewenstein, Maciej; Massignan, Pietro

2017-06-01

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems.

Weyl nodes in Andreev spectra of multiterminal Josephson junctions: Chern numbers, conductances, and supercurrents

NASA Astrophysics Data System (ADS)

Xie, Hong-Yi; Vavilov, Maxim G.; Levchenko, Alex

2018-02-01

We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When the scattering matrix of the normal region connecting superconducting leads is energy independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The corresponding fluxes are quantified by Chern numbers that translate into a quantized nonlocal conductance that we compute explicitly for the time-reversal-symmetric scattering matrix. The topological regime can also be identified by supercurrents as Josephson current-phase relationships exhibit pronounced nonanalytic behavior and discontinuities near Weyl points that can be controllably accessed in experiments.

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

PubMed Central

Cardano, Filippo; D’Errico, Alessio; Dauphin, Alexandre; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo; Lewenstein, Maciej; Massignan, Pietro

2017-01-01

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems. PMID:28569741

ER = EPR and non-perturbative action integrals for quantum gravity

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina

In this paper, we construct and calculate non-perturbative path integrals in a multiply-connected spacetime. This is done by summing over homotopy classes of paths. The topology of the spacetime is defined by Einstein-Rosen bridges (ERB) forming from the entanglement of quantum foam described by virtual black holes. As these “bubbles” are entangled, they are connected by Planckian ERBs because of the ER = EPR conjecture. Hence, the spacetime will possess a large first Betti number B1. For any compact 2-surface in the spacetime, the topology (in particular the homotopy) of that surface is non-trivial due to the large number of Planckian ERBs that define homotopy through this surface. The quantization of spacetime with this topology — along with the proper choice of the 2-surfaces — is conjectured to allow non-perturbative path integrals of quantum gravity theory over the spacetime manifold.

Topological gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Cook, Ashley; Repellin, Cécile; Regnault, Nicolas; Neupert, Titus

We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. We focus on a time-reversal symmetric bilayer fractional quantum Hall system of Laughlin ν = 1 / 3 states. The fully gapped edges carry a topological parafermionic degree of freedom that can encode quantum information protected against local perturbations. We numerically simulate such a system using exact diagonalization by restricting the calculation to the Laughlin quasihole subspace. We study the quantization of the total charge on each edge and show that the ground states are permuted by spin flux insertion and the parafermionic Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The full affiliation for Author 3 is: Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris.

Selective equal spin Andreev reflection at vortex core center in magnetic semiconductor-superconductor heterostructure.

PubMed

Li, Chuang; Hu, Lun-Hui; Zhou, Yi; Zhang, Fu-Chun

2018-05-18

Sau, Lutchyn, Tewari and Das Sarma (SLTD) proposed a heterostructure consisting of a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator and showed possible Majorana zero mode. Here we study spin polarization of the vortex core states and spin selective Andreev reflection at the vortex center of the SLTD model. In the topological phase, the differential conductance at the vortex center contributed from the Andreev reflection, is spin selective and has a quantized value [Formula: see text] at zero bias. In the topological trivial phase, [Formula: see text] at the lowest quasiparticle energy of the vortex core is spin selective due to the spin-orbit coupling (SOC). Unlike in the topological phase, [Formula: see text] is suppressed in the Giaever limit and vanishes exactly at zero bias due to the quantum destruction interference.

Quantization selection in the high-throughput H.264/AVC encoder based on the RD

NASA Astrophysics Data System (ADS)

Pastuszak, Grzegorz

2013-10-01

In the hardware video encoder, the quantization is responsible for quality losses. On the other hand, it allows the reduction of bit rates to the target one. If the mode selection is based on the rate-distortion criterion, the quantization can also be adjusted to obtain better compression efficiency. Particularly, the use of Lagrangian function with a given multiplier enables the encoder to select the most suitable quantization step determined by the quantization parameter QP. Moreover, the quantization offset added before discarding the fraction value after quantization can be adjusted. In order to select the best quantization parameter and offset in real time, the HD/SD encoder should be implemented in the hardware. In particular, the hardware architecture should embed the transformation and quantization modules able to process the same residuals many times. In this work, such an architecture is used. Experimental results show what improvements in terms of compression efficiency are achievable for Intra coding.

Controlling neutron orbital angular momentum

NASA Astrophysics Data System (ADS)

Clark, Charles W.; Barankov, Roman; Huber, Michael G.; Arif, Muhammad; Cory, David G.; Pushin, Dmitry A.

2015-09-01

The quantized orbital angular momentum (OAM) of photons offers an additional degree of freedom and topological protection from noise. Photonic OAM states have therefore been exploited in various applications ranging from studies of quantum entanglement and quantum information science to imaging. The OAM states of electron beams have been shown to be similarly useful, for example in rotating nanoparticles and determining the chirality of crystals. However, although neutrons--as massive, penetrating and neutral particles--are important in materials characterization, quantum information and studies of the foundations of quantum mechanics, OAM control of neutrons has yet to be achieved. Here, we demonstrate OAM control of neutrons using macroscopic spiral phase plates that apply a `twist' to an input neutron beam. The twisted neutron beams are analysed with neutron interferometry. Our techniques, applied to spatially incoherent beams, demonstrate both the addition of quantum angular momenta along the direction of propagation, effected by multiple spiral phase plates, and the conservation of topological charge with respect to uniform phase fluctuations. Neutron-based studies of quantum information science, the foundations of quantum mechanics, and scattering and imaging of magnetic, superconducting and chiral materials have until now been limited to three degrees of freedom: spin, path and energy. The optimization of OAM control, leading to well defined values of OAM, would provide an additional quantized degree of freedom for such studies.

No chiral truncation of quantum log gravity?

NASA Astrophysics Data System (ADS)

Andrade, Tomás; Marolf, Donald

2010-03-01

At the classical level, chiral gravity may be constructed as a consistent truncation of a larger theory called log gravity by requiring that left-moving charges vanish. In turn, log gravity is the limit of topologically massive gravity (TMG) at a special value of the coupling (the chiral point). We study the situation at the level of linearized quantum fields, focussing on a unitary quantization. While the TMG Hilbert space is continuous at the chiral point, the left-moving Virasoro generators become ill-defined and cannot be used to define a chiral truncation. In a sense, the left-moving asymptotic symmetries are spontaneously broken at the chiral point. In contrast, in a non-unitary quantization of TMG, both the Hilbert space and charges are continuous at the chiral point and define a unitary theory of chiral gravity at the linearized level.

An incompressible state of a photo-excited electron gas

PubMed Central

Chepelianskii, Alexei D.; Watanabe, Masamitsu; Nasyedkin, Kostyantyn; Kono, Kimitoshi; Konstantinov, Denis

2015-01-01

Two-dimensional electrons in a magnetic field can form new states of matter characterized by topological properties and strong electronic correlations as displayed in the integer and fractional quantum Hall states. In these states, the electron liquid displays several spectacular characteristics, which manifest themselves in transport experiments with the quantization of the Hall resistance and a vanishing longitudinal conductivity or in thermodynamic equilibrium when the electron fluid becomes incompressible. Several experiments have reported that dissipationless transport can be achieved even at weak, non-quantizing magnetic fields when the electrons absorb photons at specific energies related to their cyclotron frequency. Here we perform compressibility measurements on electrons on liquid helium demonstrating the formation of an incompressible electronic state under these resonant excitation conditions. This new state provides a striking example of irradiation-induced self-organization in a quantum system. PMID:26007282

Electronic properties of one-dimensional nanostructures of the Bi2Se3 topological insulator

NASA Astrophysics Data System (ADS)

Virk, Naunidh; Autès, Gabriel; Yazyev, Oleg V.

2018-04-01

We theoretically study the electronic structure and spin properties of one-dimensional nanostructures of the prototypical bulk topological insulator Bi2Se3 . Realistic models of experimentally observed Bi2Se3 nanowires and nanoribbons are considered using the tight-binding method. At low energies, the band structures are composed of a series of evenly spaced degenerate subbands resulting from circumferential confinement of the topological surface states. The direct band gaps due to the nontrivial π Berry phase show a clear dependence on the circumference. The spin-momentum locking of the topological surface states results in a pronounced 2 π spin rotation around the circumference with the degree of spin polarization dependent on the momentum along the nanostructure. Overall, the band structures and spin textures are more complicated for nanoribbons, which expose two distinct facets. The effects of reduced dimensionality are rationalized with the help of a simple model that considers circumferential quantization of the topological surface states. Furthermore, the surface spin density induced by an electric current along the nanostructure shows a pronounced oscillatory dependence on the charge-carrier energy, which can be exploited in spintronics applications.

3D Quantum Hall Effect of Fermi Arc in Topological Semimetals

NASA Astrophysics Data System (ADS)

Wang, C. M.; Sun, Hai-Peng; Lu, Hai-Zhou; Xie, X. C.

2017-09-01

The quantum Hall effect is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution, giving an example of (d -2 )-dimensional boundary states. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hall conductivity evolves from the 1 /B dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd3 As2 , or Na3Bi . This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.

Interplay between topology, gauge fields and gravity

NASA Astrophysics Data System (ADS)

Corichi Rodriguez Gil, Alejandro

In this thesis we consider several physical systems that illustrate an interesting interplay between quantum theory, connections and knot theory. It can be divided into two parts. In the first one, we consider the quantization of the free Maxwell field. We show that there is an important role played by knot theory, and in particular the Gauss linking number, in the quantum theory. This manifestation is twofold. The first occurs at the level of the algebra of observables given by fluxes of electric and magnetic field across surfaces. The commutator of the operators, and thus the basic uncertainty relations, are given in terms of the linking number of the loops that bound the surfaces. Next, we consider the quantization of the Maxwell field based on self-dual connections in the loop representation. We show that the measure which determines the quantum inner product can be expressed in terms of the self linking number of thickened loops. Therefore, the linking number manifests itself at two key points of the theory: the Heisenberg uncertainty principle and the inner product. In the second part, we bring gravity into play. First we consider quantum test particles on certain stationary space-times. We demonstrate that a geometric phase exists for those space-times and focus on the example of a rotating cosmic string. The geometric phase can be explicitly computed, providing a fully relativistic gravitational Aharonov-Bohm effect. Finally, we consider 3-dimensional gravity with non-vanishing cosmological constant in the connection dynamics formulation. We restrict our attention to Lorentzian gravity with positive cosmological constant and Euclidean signature with negative cosmological constant. A complex transformation is performed in phase space that makes the constraints simple. The reduced phase space is characterized as the moduli space of flat complex connections. We construct the quantization of the theory when the initial hyper-surface is a torus. Two important issues relevant to full 3 + 1 gravity are clarified, namely, the incorporation of the 'reality conditions' in the quantum theory and the role played by the signature of the classical metric in the quantum theory.

Bipartite charge fluctuations in one-dimensional Z2 superconductors and insulators

NASA Astrophysics Data System (ADS)

Herviou, Loïc; Mora, Christophe; Le Hur, Karyn

2017-09-01

Bipartite charge fluctuations (BCFs) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems) and can be measured experimentally. We study the BCFs in generic one-dimensional Z2 (topological) models including the Kitaev superconducting wire model, the Ising chain, or various topological insulators such as the Su-Schrieffer-Heeger model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCFs probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a subdominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the X Y Z model.

Topologically protected charge transfer along the edge of a chiral p -wave superconductor

NASA Astrophysics Data System (ADS)

Gnezdilov, N. V.; van Heck, B.; Diez, M.; Hutasoit, Jimmy A.; Beenakker, C. W. J.

2015-09-01

The Majorana fermions propagating along the edge of a topological superconductor with px+i py pairing deliver a shot noise power of 1/2 ×e2/h per eV of voltage bias. We calculate the full counting statistics of the transferred charge and find that it becomes trinomial in the low-temperature limit, distinct from the binomial statistics of charge-e transfer in a single-mode nanowire or charge-2 e transfer through a normal-superconductor interface. All even-order correlators of current fluctuations have a universal quantized value, insensitive to disorder and decoherence. These electrical signatures are experimentally accessible, because they persist for temperatures and voltages large compared to the Thouless energy.

Magnetically Defined Qubits on 3D Topological Insulators

NASA Astrophysics Data System (ADS)

Ferreira, Gerson J.; Loss, Daniel

2014-03-01

We explore potentials that break time-reversal symmetry to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states predicted to show the quantum anomalous Hall effect. Here, we show that confinement can also occur at magnetic domain heterostructures, with states extended in the inner domain, as well as interfacial QAHE states at the surrounding domain walls. The proposed geometry allows the isolation of the wire and dot from spurious circumventing surface states. For the quantum dots, we find that highly spin-polarized quantized QAHE states at the dot edge constitute a promising candidate for quantum computing qubits. See [Ferreira and Loss, Phys. Rev. Lett. 111, 106802 (2013)]. We explore potentials that break time-reversal symmetry to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states predicted to show the quantum anomalous Hall effect. Here, we show that confinement can also occur at magnetic domain heterostructures, with states extended in the inner domain, as well as interfacial QAHE states at the surrounding domain walls. The proposed geometry allows the isolation of the wire and dot from spurious circumventing surface states. For the quantum dots, we find that highly spin-polarized quantized QAHE states at the dot edge constitute a promising candidate for quantum computing qubits. See [Ferreira and Loss, Phys. Rev. Lett. 111, 106802 (2013)]. We acknowledge support from the Swiss NSF, NCCR Nanoscience, NCCR QSIT, and the Brazillian Research Support Center Initiative (NAP Q-NANO) from Pró-Reitoria de Pesquisa (PRP/USP).

Unique Fock quantization of a massive fermion field in a cosmological scenario

NASA Astrophysics Data System (ADS)

Cortez, Jerónimo; Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Velhinho, José M.

2016-04-01

It is well known that the Fock quantization of field theories in general spacetimes suffers from an infinite ambiguity, owing to the inequivalent possibilities in the selection of a representation of the canonical commutation or anticommutation relations, but also owing to the freedom in the choice of variables to describe the field among all those related by linear time-dependent transformations, including the dependence through functions of the background. In this work we remove this ambiguity (up to unitary equivalence) in the case of a massive Dirac free field propagating in a spacetime with homogeneous and isotropic spatial sections of spherical topology. Two physically reasonable conditions are imposed in order to arrive at this result: (a) The invariance of the vacuum under the spatial isometries of the background, and (b) the unitary implementability of the dynamical evolution that dictates the Dirac equation. We characterize the Fock quantizations with a nontrivial fermion dynamics that satisfy these two conditions. Then, we provide a complete proof of the unitary equivalence of the representations in this class under very mild requirements on the time variation of the background, once a criterion to discern between particles and antiparticles has been set.

Electrical probing of field-driven cascading quantized transitions of skyrmion cluster states in MnSi nanowires

NASA Astrophysics Data System (ADS)

Du, Haifeng; Liang, Dong; Jin, Chiming; Kong, Lingyao; Stolt, Matthew J.; Ning, Wei; Yang, Jiyong; Xing, Ying; Wang, Jian; Che, Renchao; Zang, Jiadong; Jin, Song; Zhang, Yuheng; Tian, Mingliang

2015-07-01

Magnetic skyrmions are topologically stable whirlpool-like spin textures that offer great promise as information carriers for future spintronic devices. To enable such applications, particular attention has been focused on the properties of skyrmions in highly confined geometries such as one-dimensional nanowires. Hitherto, it is still experimentally unclear what happens when the width of the nanowire is comparable to that of a single skyrmion. Here, we achieve this by measuring the magnetoresistance in ultra-narrow MnSi nanowires. We observe quantized jumps in magnetoresistance versus magnetic field curves. By tracking the size dependence of the jump number, we infer that skyrmions are assembled into cluster states with a tunable number of skyrmions, in agreement with the Monte Carlo simulations. Our results enable an electric reading of the number of skyrmions in the cluster states, thus laying a solid foundation to realize skyrmion-based memory devices.

Argyres-Douglas theories, chiral algebras and wild Hitchin characters

NASA Astrophysics Data System (ADS)

Fredrickson, Laura; Pei, Du; Yan, Wenbin; Ye, Ke

2018-01-01

We use Coulomb branch indices of Argyres-Douglas theories on S 1 × L( k, 1) to quantize moduli spaces M_H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" — the graded dimensions of the Hilbert spaces from quantization — for four infinite families of M_H , giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in M_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform ST k S in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.

Quantization of noncompact coverings and its physical applications

NASA Astrophysics Data System (ADS)

Ivankov, Petr

2018-02-01

A rigorous algebraic definition of noncommutative coverings is developed. In the case of commutative algebras this definition is equivalent to the classical definition of topological coverings of locally compact spaces. The theory has following nontrivial applications: • Coverings of continuous trace algebras, • Coverings of noncommutative tori, • Coverings of the quantum SU(2) group, • Coverings of foliations, • Coverings of isospectral deformations of Spin - manifolds. The theory supplies the rigorous definition of noncommutative Wilson lines.

Entropy of black holes in N=2 supergravity

NASA Astrophysics Data System (ADS)

Chatterjee, A.

2018-07-01

Using the formalism of isolated horizons, we construct space of solutions of asymptotically flat extremal black holes in N=2 pure supergravity in 4 dimensions. We prove that the laws of black hole mechanics hold for these black holes. Further, restricting to constant area phase space, we show that the spherical horizons admit a Chern-Simons theory. Standard way of quantizing this topological theory and counting states confirms that entropy is indeed proportional to the area of horizon.

Implications of Einstein-Weyl Causality on Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bendaniel, David

A fundamental physical principle that has consequences for the topology of space-time is the principle of Einstein-Weyl causality. This also has quantum mechanical manifestations. Borchers and Sen have rigorously investigated the mathematical implications of Einstein-Weyl causality and shown the denumerable space-time Q2 would be implied. They were left with important philosophical paradoxes regarding the nature of the physical real line E, e.g., whether E = R, the real line of mathematics. In order to remove these paradoxes an investigation into a constructible foundation is suggested. We have pursued such a program and find it indeed provides a dense, denumerable space-time and, moreover, an interesting connection with quantum mechanics. We first show that this constructible theory contains polynomial functions which are locally homeomorphic with a dense, denumerable metric space R* and are inherently quantized. Eigenfunctions governing fields can then be effectively obtained by computational iteration. Postulating a Lagrangian for fields in a compactified space-time, we get a general description of which the Schrodinger equation is a special case. From these results we can then also show that this denumerable space-time is relational (in the sense that space is not infinitesimally small if and only if it contains a quantized field) and, since Q2 is imbedded in R*2, it directly fulfills the strict topological requirements for Einstein-Weyl causality. Therefore, the theory predicts that E = R*.

Segmentation of magnetic resonance images using fuzzy algorithms for learning vector quantization.

PubMed

Karayiannis, N B; Pai, P I

1999-02-01

This paper evaluates a segmentation technique for magnetic resonance (MR) images of the brain based on fuzzy algorithms for learning vector quantization (FALVQ). These algorithms perform vector quantization by updating all prototypes of a competitive network through an unsupervised learning process. Segmentation of MR images is formulated as an unsupervised vector quantization process, where the local values of different relaxation parameters form the feature vectors which are represented by a relatively small set of prototypes. The experiments evaluate a variety of FALVQ algorithms in terms of their ability to identify different tissues and discriminate between normal tissues and abnormalities.

Topological Frequency Conversion in Strongly Driven Quantum Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martin, Ivar; Refael, Gil; Halperin, Bertrand

When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of irrationally-related drive frequencies, and the evolution occurs in response to a built-in effective \\electric" field, whose components are proportional to the corresponding drive frequencies. The mapping allows to engineer and study temporal analogs of many real-space phenomena. Here we focus on the specifc example of a two-level system under two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence ofmore » such construction is quantized pumping of energy between the sources with frequencies w 1 and w 2. Finally, when the system is initialized into a Floquet band with the Chern number C, the pumping occurs at the rate P 12 = – P 21 = ( C/2π)hw 1w 2, an exact counterpart of the transverse current in a conventional topological insulator.« less

MBE growth of Topological Isolators based on strained semi-metallic HgCdTe layers

NASA Astrophysics Data System (ADS)

Grendysa, J.; Tomaka, G.; Sliz, P.; Becker, C. R.; Trzyna, M.; Wojnarowska-Nowak, R.; Bobko, E.; Sheregii, E. M.

2017-12-01

Particularities of Molecular Beam Epitaxial (MBE) technology for the growth of Topological Insulators (TI) based on the semi-metal Hg1-xCdx Te are presented. A series of strained layers grown on GaAs substrates with a composition close to the 3D Dirac point were studied. The composition of the layers was verified by means of the position of the E1 maximum in optical reflectivity in the visible region. The surface morphology was determined via atomic force and electron microscopy. Magneto-transport measurements show quantized Hall resistance curves and Shubnikov de Hass oscillations (up to 50 K). It has been demonstrated that a well-developed MBE technology enables one to grow strained Hg1-xCdx Te layers on GaAs/CdTe substrates with a well-defined composition near the 3D Dirac point and consequently allows one to produce a 3D topological Dirac semimetal - 3D analogy of graphene - for future applications.

Ballistic edge states in Bismuth nanowires revealed by SQUID interferometry.

PubMed

Murani, Anil; Kasumov, Alik; Sengupta, Shamashis; Kasumov, Yu A; Volkov, V T; Khodos, I I; Brisset, F; Delagrange, Raphaëlle; Chepelianskii, Alexei; Deblock, Richard; Bouchiat, Hélène; Guéron, Sophie

2017-07-05

The protection against backscattering provided by topology is a striking property. In two-dimensional insulators, a consequence of this topological protection is the ballistic nature of the one-dimensional helical edge states. One demonstration of ballisticity is the quantized Hall conductance. Here we provide another demonstration of ballistic transport, in the way the edge states carry a supercurrent. The system we have investigated is a micrometre-long monocrystalline bismuth nanowire with topological surfaces, that we connect to two superconducting electrodes. We have measured the relation between the Josephson current flowing through the nanowire and the superconducting phase difference at its ends, the current-phase relation. The sharp sawtooth-shaped phase-modulated current-phase relation we find demonstrates that transport occurs selectively along two ballistic edges of the nanowire. In addition, we show that a magnetic field induces 0-π transitions and ϕ 0 -junction behaviour, providing a way to manipulate the phase of the supercurrent-carrying edge states and generate spin supercurrents.

Ballistic edge states in Bismuth nanowires revealed by SQUID interferometry

PubMed Central

Murani, Anil; Kasumov, Alik; Sengupta, Shamashis; Kasumov, Yu A.; Volkov, V. T.; Khodos, I. I.; Brisset, F.; Delagrange, Raphaëlle; Chepelianskii, Alexei; Deblock, Richard; Bouchiat, Hélène; Guéron, Sophie

2017-01-01

The protection against backscattering provided by topology is a striking property. In two-dimensional insulators, a consequence of this topological protection is the ballistic nature of the one-dimensional helical edge states. One demonstration of ballisticity is the quantized Hall conductance. Here we provide another demonstration of ballistic transport, in the way the edge states carry a supercurrent. The system we have investigated is a micrometre-long monocrystalline bismuth nanowire with topological surfaces, that we connect to two superconducting electrodes. We have measured the relation between the Josephson current flowing through the nanowire and the superconducting phase difference at its ends, the current–phase relation. The sharp sawtooth-shaped phase-modulated current–phase relation we find demonstrates that transport occurs selectively along two ballistic edges of the nanowire. In addition, we show that a magnetic field induces 0–π transitions and φ0-junction behaviour, providing a way to manipulate the phase of the supercurrent-carrying edge states and generate spin supercurrents. PMID:28677681

Topological Frequency Conversion in Strongly Driven Quantum Systems

DOE PAGES

Martin, Ivar; Refael, Gil; Halperin, Bertrand

2017-10-16

When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of irrationally-related drive frequencies, and the evolution occurs in response to a built-in effective \\electric" field, whose components are proportional to the corresponding drive frequencies. The mapping allows to engineer and study temporal analogs of many real-space phenomena. Here we focus on the specifc example of a two-level system under two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence ofmore » such construction is quantized pumping of energy between the sources with frequencies w 1 and w 2. Finally, when the system is initialized into a Floquet band with the Chern number C, the pumping occurs at the rate P 12 = – P 21 = ( C/2π)hw 1w 2, an exact counterpart of the transverse current in a conventional topological insulator.« less

Quantized conductance doubling and hard gap in a two-dimensional semiconductor-superconductor heterostructure.

PubMed

Kjaergaard, M; Nichele, F; Suominen, H J; Nowak, M P; Wimmer, M; Akhmerov, A R; Folk, J A; Flensberg, K; Shabani, J; Palmstrøm, C J; Marcus, C M

2016-09-29

Coupling a two-dimensional (2D) semiconductor heterostructure to a superconductor opens new research and technology opportunities, including fundamental problems in mesoscopic superconductivity, scalable superconducting electronics, and new topological states of matter. One route towards topological matter is by coupling a 2D electron gas with strong spin-orbit interaction to an s-wave superconductor. Previous efforts along these lines have been adversely affected by interface disorder and unstable gating. Here we show measurements on a gateable InGaAs/InAs 2DEG with patterned epitaxial Al, yielding devices with atomically pristine interfaces between semiconductor and superconductor. Using surface gates to form a quantum point contact (QPC), we find a hard superconducting gap in the tunnelling regime. When the QPC is in the open regime, we observe a first conductance plateau at 4e 2 /h, consistent with theory. The hard-gap semiconductor-superconductor system demonstrated here is amenable to top-down processing and provides a new avenue towards low-dissipation electronics and topological quantum systems.

Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators

NASA Astrophysics Data System (ADS)

Chang, Cui-Zu; Li, Mingda

2016-03-01

The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity {σyx}=\\frac{{{e}2}}{h} without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies.

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

NASA Astrophysics Data System (ADS)

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.

Quantized conductance doubling and hard gap in a two-dimensional semiconductor–superconductor heterostructure

PubMed Central

Kjaergaard, M.; Nichele, F.; Suominen, H. J.; Nowak, M. P.; Wimmer, M.; Akhmerov, A. R.; Folk, J. A.; Flensberg, K.; Shabani, J.; Palmstrøm, C. J.; Marcus, C. M.

2016-01-01

Coupling a two-dimensional (2D) semiconductor heterostructure to a superconductor opens new research and technology opportunities, including fundamental problems in mesoscopic superconductivity, scalable superconducting electronics, and new topological states of matter. One route towards topological matter is by coupling a 2D electron gas with strong spin–orbit interaction to an s-wave superconductor. Previous efforts along these lines have been adversely affected by interface disorder and unstable gating. Here we show measurements on a gateable InGaAs/InAs 2DEG with patterned epitaxial Al, yielding devices with atomically pristine interfaces between semiconductor and superconductor. Using surface gates to form a quantum point contact (QPC), we find a hard superconducting gap in the tunnelling regime. When the QPC is in the open regime, we observe a first conductance plateau at 4e2/h, consistent with theory. The hard-gap semiconductor–superconductor system demonstrated here is amenable to top-down processing and provides a new avenue towards low-dissipation electronics and topological quantum systems. PMID:27682268

Topological magnetoelectric pump in three dimensions

NASA Astrophysics Data System (ADS)

Fukui, Takahiro; Fujiwara, Takanori

2017-11-01

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

Topological magnetic phase in LaMnO3 (111) bilayer

NASA Astrophysics Data System (ADS)

Weng, Yakui; Huang, Xin; Yao, Yugui; Dong, Shuai

2015-11-01

Candidates for correlated topological insulators, originated from the spin-orbit coupling as well as the Hubbard-type correlation, are expected in the (111) bilayer of perovskite-structural transition-metal oxides. Based on the first-principles calculation and tight-binding model, the electronic structure of a LaMnO3 (111) bilayer sandwiched in LaScO3 barriers has been investigated. For the ideal undistorted perovskite structure, the Fermi energy of LaMnO3 (111) bilayer just stays at the Dirac point, rendering a semimetal (graphenelike) which is also a half metal [different from graphene or the previously studied LaNiO3 (111) bilayer]. The Dirac cone can be opened by the spin-orbit coupling, giving rise to nontrivial topological bands corresponding to the (quantized) anomalous Hall effect. For the realistic orthorhombic distorted lattice, the Dirac point moves with increasing Hubbard repulsion (or equivalent Jahn-Teller distortion). Finally, a Mott gap opens, establishing a phase boundary between the Mott insulator and topological magnetic insulator. Our calculation finds that the gap opened by spin-orbit coupling is much smaller in the orthorhombic distorted lattice (˜1.7 meV) than the undistorted one (˜11 meV). Therefore, to suppress the lattice distortion can be helpful to enhance the robustness of the topological phase in perovskite (111) bilayers.

Role of helical edge modes in the chiral quantum anomalous Hall state.

PubMed

Mani, Arjun; Benjamin, Colin

2018-01-22

Although indications are that a single chiral quantum anomalous Hall(QAH) edge mode might have been experimentally detected. There have been very many recent experiments which conjecture that a chiral QAH edge mode always materializes along with a pair of quasi-helical quantum spin Hall (QSH) edge modes. In this work we deal with a substantial 'What If?' question- in case the QSH edge modes, from which these QAH edge modes evolve, are not topologically-protected then the QAH edge modes wont be topologically-protected too and thus unfit for use in any applications. Further, as a corollary one can also ask if the topological-protection of QSH edge modes does not carry over during the evolution process to QAH edge modes then again our 'What if?' scenario becomes apparent. The 'how' of the resolution of this 'What if?' conundrum is the main objective of our work. We show in similar set-ups affected by disorder and inelastic scattering, transport via trivial QAH edge mode leads to quantization of Hall resistance and not that via topological QAH edge modes. This perhaps begs a substantial reinterpretation of those experiments which purported to find signatures of chiral(topological) QAH edge modes albeit in conjunction with quasi helical QSH edge modes.

Classification and characterization of topological insulators and superconductors

NASA Astrophysics Data System (ADS)

Mong, Roger

Topological insulators (TIs) are a new class of materials which, until recently, have been overlooked despite decades of study in band insulators. Like semiconductors and ordinary insulators, TIs have a bulk gap, but feature robust surfaces excitations which are protected from disorder and interactions which do not close the bulk gap. TIs are distinguished from ordinary insulators not by the symmetries they possess (or break), but by topological invariants characterizing their bulk band structures. These two pictures, the existence of gapless surface modes, and the nontrivial topology of the bulk states, yield two contrasting approaches to the study of TIs. At the heart of the subject, they are connected by the bulk-boundary correspondence, relating bulk and surface degrees of freedom. In this work, we study both aspects of topological insulators, at the same time providing an illumination to their mysterious connection. First, we present a systematic approach to the classification of bulk states of systems with inversion-like symmetries, deriving a complete set of topological invariants for such ensembles. We find that the topological invariants in all dimensions may be computed algebraically via exact sequences. In particular, systems with spatial inversion symmetries in one-, two-, and three-dimensions can be classified by, respectively, 2, 5, and 11 integer invariants. The values of these integers are related to physical observables such as polarization, Hall conductivity, and magnetoelectric coupling. We also find that, for systems with “antiferromagnetic symmetry,” there is a Z2 classification in three-dimensions, and hence a class of “antiferromagnetic topological insulators” (AFTIs) which are distinguished from ordinary antiferromagnets. From the perspective of the bulk, AFTI exhibits the quantized magnetoelectric effect, whereas on the surface, gapless one-dimensional chiral modes emerge at step-defects. Next, we study how the surface spectrum can be computed from bulk quantities. Specifically, we present an analytic prescription for computing the edge dispersion E(k) of a tight-binding Dirac Hamiltonian terminated at an abrupt crystalline edge, based on the bulk Hamiltonian. The result is presented as a geometric formula, relating the existence of surface states as well as their energy dispersion to properties of the bulk Hamiltonian. We further prove the bulk-boundary correspondence for this specific class of systems, connecting the Chern number and the chiral edge modes for quantum Hall systems given in terms of Dirac Hamiltonians. In similar spirit, we examine the existence of Majorana zero modes in superconducting doped-TIs. We find that Majorana zero modes indeed appear but only if the doped Fermi energy is below a critical chemical potential. The critical doping is associated with a topological phase transition of vortex lines, which supports gapless excitations spanning their length. For weak pairing, the critical point is dependent on the non-abelian Berry phase of the bulk Fermi surface. Finally, we investigate the transport properties on the surfaces of TIs. While the surfaces of “strong topological insulators” - TIs with an odd number of Dirac cones in their surface spectrum - have been well studied in literature, studies of their counterpart “weak topological insulators” (WTIs) are meager, with conflicting claims. Because WTIs have an even number of Dirac cones in their surface spectrum, they are thought to be unstable to disorder, which leads to an insulating surface. Here we argue that the presence of disorder alone will not localize the surface states, rather, presence of a time-reversal symmetric mass term is required for localization. Through numerical simulations, we show that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the case of a strong topological insulator surface. With the inclusion of the mass, the transport properties of the surface of a weak topological insulator follow a two-parameter scaling form, reminiscent of the quantum Hall phase transition.

Sustained propagation and control of topological excitations in polariton superfluid

NASA Astrophysics Data System (ADS)

Pigeon, Simon; Bramati, Alberto

2017-09-01

We present a simple method to compensate for losses in a polariton superfluid. Based on a weak support field, it allows for the extended propagation of a resonantly driven polariton superfluid with minimal energetic cost. Moreover, this setup is based on optical bistability and leads to the significant release of the phase constraint imposed by resonant driving. This release, together with macroscopic polariton propagation, offers a unique opportunity to study the hydrodynamics of the topological excitations of polariton superfluids such as quantized vortices and dark solitons. We numerically study how the coherent field supporting the superfluid flow interacts with the vortices and how it can be used to control them. Interestingly, we show that standard hydrodynamics does not apply for this driven-dissipative fluid and new types of behaviour are identified.

Gauged baby Skyrme model with a Chern-Simons term

NASA Astrophysics Data System (ADS)

Samoilenka, A.; Shnir, Ya.

2017-02-01

The properties of the multisoliton solutions of the (2 +1 )-dimensional Maxwell-Chern-Simons-Skyrme model are investigated numerically. Coupling to the Chern-Simons term allows for existence of the electrically charge solitons which may also carry magnetic fluxes. Two particular choices of the potential term is considered: (i) the weakly bounded potential and (ii) the double vacuum potential. In the absence of gauge interaction in the former case the individual constituents of the multisoliton configuration are well separated, while in the latter case the rotational invariance of the configuration remains unbroken. It is shown that coupling of the planar multi-Skyrmions to the electric and magnetic field strongly affects the pattern of interaction between the constituents. We analyze the dependency of the structure of the solutions, the energies, angular momenta, electric and magnetic fields of the configurations on the gauge coupling constant g , and the electric potential. It is found that, generically, the coupling to the Chern-Simons term strongly affects the usual pattern of interaction between the skyrmions, in particular the electric repulsion between the solitons may break the multisoliton configuration into partons. We show that as the gauge coupling becomes strong, both the magnetic flux and the electric charge of the solutions become quantized although they are not topological numbers.

An analogue of Weyl’s law for quantized irreducible generalized flag manifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matassa, Marco, E-mail: marco.matassa@gmail.com, E-mail: mmatassa@math.uio.no

2015-09-15

We prove an analogue of Weyl’s law for quantized irreducible generalized flag manifolds. This is formulated in terms of a zeta function which, similarly to the classical setting, satisfies the following two properties: as a functional on the quantized algebra it is proportional to the Haar state and its first singularity coincides with the classical dimension. The relevant formulas are given for the more general case of compact quantum groups.

Universal Relation among the Many-Body Chern Number, Rotation Symmetry, and Filling

NASA Astrophysics Data System (ADS)

Matsugatani, Akishi; Ishiguro, Yuri; Shiozaki, Ken; Watanabe, Haruki

2018-03-01

Understanding the interplay between the topological nature and the symmetry property of interacting systems has been a central matter of condensed matter physics in recent years. In this Letter, we establish nonperturbative constraints on the quantized Hall conductance of many-body systems with arbitrary interactions. Our results allow one to readily determine the many-body Chern number modulo a certain integer without performing any integrations, solely based on the rotation eigenvalues and the average particle density of the many-body ground state.

Quantum Turbulence ---Another da Vinci Code---

NASA Astrophysics Data System (ADS)

Tsubota, M.

Quantum turbulence comprises a tangle of quantized vorticeswhich are stable topological defects created by Bose-Einstein condensation, being realized in superfluid helium and atomic Bose-Einstein condensates. In recent years there has been a growing interest in quantum turbulence. One of the important motivations is to understand the relation between quantum and classical turbulence. Quantum turbulence is expected to be much simpler than usual classical turbulence and give a prototype of turbulence. This article reviews shortly the recent research developments on quantum turbulence.

Contact geometry and quantum mechanics

NASA Astrophysics Data System (ADS)

Herczeg, Gabriel; Waldron, Andrew

2018-06-01

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime". We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics.

Operators and higher genus mirror curves

NASA Astrophysics Data System (ADS)

Codesido, Santiago; Gu, Jie; Mariño, Marcos

2017-02-01

We perform further tests of the correspondence between spectral theory and topological strings, focusing on mirror curves of genus greater than one with nontrivial mass parameters. In particular, we analyze the geometry relevant to the SU(3) relativistic Toda lattice, and the resolved C{^3}/Z_6 orbifold. Furthermore, we give evidence that the correspondence holds for arbitrary values of the mass parameters, where the quantization problem leads to resonant states. We also explore the relation between this correspondence and cluster integrable systems.

Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices

NASA Astrophysics Data System (ADS)

Zhu, Yan-Qing; Zhang, Dan-Wei; Yan, Hui; Xing, Ding-Yu; Zhu, Shi-Liang

2017-09-01

The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal excitations could be realized with artificial systems. Here, we construct two- and three-dimensional tight-binding models realizable with cold fermionic atoms in optical lattices, where the low energy excitations are effectively described by the spin-1 Maxwell equations in the Hamiltonian form. These relativistic (linear dispersion) excitations with unconventional integer pseudospin, beyond the Dirac-Weyl-Majorana fermions, are an exotic kind of fermions named as Maxwell fermions. We demonstrate that the systems have rich topological features. For instance, the threefold degenerate points called Maxwell points may have quantized Berry phases and anomalous quantum Hall effects with spin-momentum locking may appear in topological Maxwell insulators in the two-dimensional lattices. In three dimensions, Maxwell points may have nontrivial monopole charges of ±2 with two Fermi arcs connecting them, and the merging of the Maxwell points leads to topological phase transitions. Finally, we propose realistic schemes for realizing the model Hamiltonians and detecting the topological properties of the emergent Maxwell quasiparticles in optical lattices.

Surface Andreev Bound States and Odd-Frequency Pairing in Topological Superconductor Junctions

NASA Astrophysics Data System (ADS)

Tanaka, Yukio; Tamura, Shun

2018-04-01

In this review, we summarize the achievement of the physics of surface Andreev bound states (SABS) up to now. The route of this activity has started from the physics of SABS of unconventional superconductors where the pair potential has a sign change on the Fermi surface. It has been established that SABS can be regarded as a topological edge state with topological invariant defined in the bulk Hamiltonian. On the other hand, SABS accompanies odd-frequency pairing like spin-triplet s-wave or spin-singlet p-wave. In a spin-triplet superconductor junction, induced odd-frequency pairing can penetrate into a diffusive normal metal (DN) attached to the superconductor. It causes so called anomalous proximity effect where the local density of states of quasiparticle in DN has a zero energy peak. When bulk pairing symmetry is spin-triplet px-wave, the anomalous proximity effect becomes prominent and the zero bias voltage conductance is always quantized independent of the resistance in DN and interface. Finally, we show that the present anomalous proximity effect is realized in an artificial topological superconducting system, where a nanowire with spin-orbit coupling and Zeeman field is put on the conventional spin-singlet s-wave superconductor.

Topological magnetic phase in LaMnO3 (111) bilayer

NASA Astrophysics Data System (ADS)

Weng, Yakui; Huang, Xin; Yao, Yugui; Dong, Shuai

Candidates for correlated topological insulators, originated from the spin-orbit coupling as well as Hubbard type correlation, are expected in the (111) bilayer of perovskite-structural transition-metal oxides. Based on the first-principles calculation and tight-binding model, the electronic structure of a LaMnO3 (111) bilayer sandwiched in LaScO3 barriers has been investigated. For the ideal undistorted perovskite structure, the Fermi energy of LaMnO3 (111) bilayer just stays at the Dirac point, rendering a semi-metal (graphene-like) which is also a half-metal (different from graphene nor previous studied LaNiO3 (111) bilayer). The Dirac cone can be opened by the spin-orbit coupling, giving rise to nontrivial topological bands corresponding to the (quantized) anomalous Hall effect. For the realistic orthorhombic distorted lattice, the Dirac point moves with increasing Hubbard repulsion (or equivalent Jahn-Teller distortion). Finally, a Mott gap opens, establishing a phase boundary between the Mott insulator and topological magnetic insulator. Our calculation finds that the gap opened by spin-orbit coupling is much smaller in the orthorhombic distorted lattice (~ 1 . 7 meV) than the undistorted one (~11 meV).

Revealing the Topology of Fermi-Surface Wave Functions from Magnetic Quantum Oscillations

NASA Astrophysics Data System (ADS)

Alexandradinata, A.; Wang, Chong; Duan, Wenhui; Glazman, Leonid

2018-01-01

The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase (λ ) that is subleading in powers of the field; λ is measurable in the phase offset of the de Haas-van Alphen oscillation, as well as of fixed-bias oscillations of the differential conductance in tunneling spectroscopy. In some solids and for certain field orientations, λ /π are robustly integer valued, owing to the symmetry of the extremal orbit; i.e., they are the topological invariants of magnetotransport. Our comprehensive symmetry analysis identifies solids in any (magnetic) space group for which λ is a topological invariant, as well as the symmetry-enforced degeneracy of Landau levels. The analysis is simplified by our formulation of ten (and only ten) symmetry classes for closed, Fermi-surface orbits. Case studies are discussed for graphene, transition metal dichalcogenides, 3D Weyl and Dirac metals, and crystalline and Z2 topological insulators. In particular, we point out that a π phase offset in the fundamental oscillation should not be viewed as a smoking gun for a 3D Dirac metal.

Direct comparison of fractional and integer quantized Hall resistance

NASA Astrophysics Data System (ADS)

Ahlers, Franz J.; Götz, Martin; Pierz, Klaus

2017-08-01

We present precision measurements of the fractional quantized Hall effect, where the quantized resistance {{R}≤ft[ 1/3 \\right]} in the fractional quantum Hall state at filling factor 1/3 was compared with a quantized resistance {{R}[2]} , represented by an integer quantum Hall state at filling factor 2. A cryogenic current comparator bridge capable of currents down to the nanoampere range was used to directly compare two resistance values of two GaAs-based devices located in two cryostats. A value of 1-(5.3  ±  6.3) 10-8 (95% confidence level) was obtained for the ratio ({{R}≤ft[ 1/3 \\right]}/6{{R}[2]} ). This constitutes the most precise comparison of integer resistance quantization (in terms of h/e 2) in single-particle systems and of fractional quantization in fractionally charged quasi-particle systems. While not relevant for practical metrology, such a test of the validity of the underlying physics is of significance in the context of the upcoming revision of the SI.

Surface and 3D Quantum Hall Effects from Engineering of Exceptional Points in Nodal-Line Semimetals

NASA Astrophysics Data System (ADS)

Molina, Rafael A.; González, José

2018-04-01

We show that, under a strong magnetic field, a 3D nodal-line semimetal is driven into a topological insulating phase in which the electronic transport takes place at the surface of the material. When the magnetic field is perpendicular to the nodal ring, the surface states of the semimetal are transmuted into Landau states which correspond to exceptional points, i.e., branch points in the spectrum of a non-Hermitian Hamiltonian which arise upon the extension to complex values of the momentum. The complex structure of the spectrum then allows us to express the number of zero-energy flat bands in terms of a new topological invariant counting the number of exceptional points. When the magnetic field is parallel to the nodal ring, we find that the bulk states are built from the pairing of surfacelike evanescent waves, giving rise to a 3D quantum Hall effect with a flat level of Landau states residing in parallel 2D slices of the 3D material. The Hall conductance is quantized in either case in units of e2/h , leading in the 3D Hall effect to a number of channels growing linearly with the section of the surface and opening the possibility to observe a macroscopic chiral current at the surface of the material.

Topology-induced bifurcations for the nonlinear Schrödinger equation on the tadpole graph.

PubMed

Cacciapuoti, Claudio; Finco, Domenico; Noja, Diego

2015-01-01

In this paper we give the complete classification of solitons for a cubic nonlinear Schrödinger equation on the simplest network with a nontrivial topology: the tadpole graph, i.e., a ring with a half line attached to it and free boundary conditions at the junction. This is a step toward the modelization of condensate propagation and confinement in quasi-one-dimensional traps. The model, although simple, exhibits a surprisingly rich behavior and in particular we show that it admits: (i) a denumerable family of continuous branches of embedded solitons vanishing on the half line and bifurcating from linear eigenstates and threshold resonances of the system; (ii) a continuous branch of edge solitons bifurcating from the previous families at the threshold of the continuous spectrum with a pitchfork bifurcation; and (iii) a finite family of continuous branches of solitons without linear analog. All the solutions are explicitly constructed in terms of elliptic Jacobian functions. Moreover we show that families of nonlinear bound states of the above kind continue to exist in the presence of a uniform magnetic field orthogonal to the plane of the ring when a well definite flux quantization condition holds true. In this sense the magnetic field acts as a control parameter. Finally we highlight the role of resonances in the linearization as a signature of the occurrence of bifurcations of solitons from the continuous spectrum.

Argyres–Douglas theories, S 1 reductions, and topological symmetries

DOE PAGES

Buican, Matthew; Nishinaka, Takahiro

2015-12-21

In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A(1), A(2n-3)) and(A(1), D-2n) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S-1 regime of these indices. As expected on general grounds, our study reproduces the S-3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases-with the exception of the reduction of the (A(1), D-4) SCFTcertain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as Rmore » symmetry mixing with the topological symmetries of the direct S-1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional N = 2 superconformal U(1)(R) symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the fourdimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general N = 2 SCFTs.« less

Argyres–Douglas theories, S 1 reductions, and topological symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buican, Matthew; Nishinaka, Takahiro

In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A(1), A(2n-3)) and(A(1), D-2n) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S-1 regime of these indices. As expected on general grounds, our study reproduces the S-3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases-with the exception of the reduction of the (A(1), D-4) SCFTcertain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as Rmore » symmetry mixing with the topological symmetries of the direct S-1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional N = 2 superconformal U(1)(R) symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the fourdimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general N = 2 SCFTs.« less

Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors

DTIC Science & Technology

2011-04-15

funded by Mitsubishi Electric Research Laboratories. †ICTEAM Institute, ELEN Department, Université catholique de Louvain (UCL), B-1348 Louvain-la-Neuve...reduced to a simple comparator that tests for values above or below zero, enabling extremely simple, efficient, and fast quantization. A 1-bit quantizer is...these two terms appears to be significantly different, according to the previously discussed experiments. To test the hypothesis that this term is the key

Magnetic Dirac Fermions and Chern Insulator Supported on Pristine Silicon Surface

NASA Astrophysics Data System (ADS)

Fu, Huixia; Liu, Zheng; Sun, Jia-Tao; Meng, Sheng

Emergence of ferromagnetism in non-magnetic semiconductors is strongly desirable, especially in topological materials thanks to the possibility to achieve quantum anomalous Hall effect. Based on first principles calculations, we propose that for Si thin film grown on metal substrate, the pristine Si(111)-r3xr3 surface with a spontaneous weak reconstruction has a strong tendency of ferromagnetism and nontrivial topological properties, characterized by spin polarized Dirac-fermion surface states. In contrast to conventional routes relying on introduction of alien charge carriers or specially patterned substrates, the spontaneous magnetic order and spin-orbit coupling on the pristine silicon surface together gives rise to quantized anomalous Hall effect with a finite Chern number C = -1. This work suggests exciting opportunities in silicon-based spintronics and quantum computing free from alien dopants or proximity effects.

Large discrete jumps observed in the transition between Chern states in a ferromagnetic topological insulator

PubMed Central

Liu, Minhao; Wang, Wudi; Richardella, Anthony R.; Kandala, Abhinav; Li, Jian; Yazdani, Ali; Samarth, Nitin; Ong, N. Phuan

2016-01-01

A striking prediction in topological insulators is the appearance of the quantized Hall resistance when the surface states are magnetized. The surface Dirac states become gapped everywhere on the surface, but chiral edge states remain on the edges. In an applied current, the edge states produce a quantized Hall resistance that equals the Chern number C = ±1 (in natural units), even in zero magnetic field. This quantum anomalous Hall effect was observed by Chang et al. With reversal of the magnetic field, the system is trapped in a metastable state because of magnetic anisotropy. We investigate how the system escapes the metastable state at low temperatures (10 to 200 mK). When the dissipation (measured by the longitudinal resistance) is ultralow, we find that the system escapes by making a few very rapid transitions, as detected by large jumps in the Hall and longitudinal resistances. Using the field at which the initial jump occurs to estimate the escape rate, we find that raising the temperature strongly suppresses the rate. From a detailed map of the resistance versus gate voltage and temperature, we show that dissipation strongly affects the escape rate. We compare the observations with dissipative quantum tunneling predictions. In the ultralow dissipation regime, two temperature scales (T1 ~ 70 mK and T2 ~ 145 mK) exist, between which jumps can be observed. The jumps display a spatial correlation that extends over a large fraction of the sample. PMID:27482539

2D layered transport properties from topological insulator Bi2Se3 single crystals and micro flakes

PubMed Central

Chiatti, Olivio; Riha, Christian; Lawrenz, Dominic; Busch, Marco; Dusari, Srujana; Sánchez-Barriga, Jaime; Mogilatenko, Anna; Yashina, Lada V.; Valencia, Sergio; Ünal, Akin A.; Rader, Oliver; Fischer, Saskia F.

2016-01-01

Low-field magnetotransport measurements of topological insulators such as Bi2Se3 are important for revealing the nature of topological surface states by quantum corrections to the conductivity, such as weak-antilocalization. Recently, a rich variety of high-field magnetotransport properties in the regime of high electron densities (∼1019 cm−3) were reported, which can be related to additional two-dimensional layered conductivity, hampering the identification of the topological surface states. Here, we report that quantum corrections to the electronic conduction are dominated by the surface states for a semiconducting case, which can be analyzed by the Hikami-Larkin-Nagaoka model for two coupled surfaces in the case of strong spin-orbit interaction. However, in the metallic-like case this analysis fails and additional two-dimensional contributions need to be accounted for. Shubnikov-de Haas oscillations and quantized Hall resistance prove as strong indications for the two-dimensional layered metallic behavior. Temperature-dependent magnetotransport properties of high-quality Bi2Se3 single crystalline exfoliated macro and micro flakes are combined with high resolution transmission electron microscopy and energy-dispersive x-ray spectroscopy, confirming the structure and stoichiometry. Angle-resolved photoemission spectroscopy proves a single-Dirac-cone surface state and a well-defined bulk band gap in topological insulating state. Spatially resolved core-level photoelectron microscopy demonstrates the surface stability. PMID:27270569

Dynamically stable multiply quantized vortices in dilute Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huhtamaeki, J. A. M.; Virtanen, S. M. M.; Moettoenen, M.

2006-12-15

Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry andmore » condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.« less

Lattices for fractional Chern insulators

NASA Astrophysics Data System (ADS)

Repellin, Cécile; Regnault, Nicolas

2018-04-01

Individual electrons are elementary particles, but in some solid-state systems, electrons can act collectively as though they had a fraction of an electron's charge. This emergent behavior is spectacularly observed in two-dimensional (2D) electron gases as the fractional quantum Hall (FQH) effect in the form of a fractional quantized transverse (or Hall) conductivity and in shot-noise experiments. These experiments require low temperatures and very large magnetic fields in order to create strong electron interactions. This latter condition now appears not to be as essential as originally thought. On page 62 of this issue, Spanton et al. (1) report on an experimental platform based on bilayer graphene that forms a moiré pattern with an encapsulating hexagonal boron nitride layer. They observed incompressible phases with a fractional filling of the band structure with a nonzero Chern number (it has quantized properties robust to local perturbations, or topologically invariant). Some of which have no analog in traditional FQH systems (see the figure).

Chern Numbers Hiding in Time of Flight Images

NASA Astrophysics Data System (ADS)

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.

Symplectic Quantization of a Reducible Theory

NASA Astrophysics Data System (ADS)

Barcelos-Neto, J.; Silva, M. B. D.

We use the symplectic formalism to quantize the Abelian antisymmetric tensor gauge field. It is related to a reducible theory in the sense that all of its constraints are not independent. A procedure like ghost-of-ghost of the BFV method has to be used, but in terms of Lagrange multipliers.

Robust fault tolerant control based on sliding mode method for uncertain linear systems with quantization.

PubMed

Hao, Li-Ying; Yang, Guang-Hong

2013-09-01

This paper is concerned with the problem of robust fault-tolerant compensation control problem for uncertain linear systems subject to both state and input signal quantization. By incorporating novel matrix full-rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under a special actuator redundancy assumption. In order to compensate for quantization errors, an adjustment range of quantization sensitivity for a dynamic uniform quantizer is given through the flexible choices of design parameters. Comparing with the existing results, the derived inequality condition leads to the fault tolerance ability stronger and much wider scope of applicability. With a static adjustment policy of quantization sensitivity, an adaptive sliding mode controller is then designed to maintain the sliding mode, where the gain of the nonlinear unit vector term is updated automatically to compensate for the effects of actuator faults, quantization errors, exogenous disturbances and parameter uncertainties without the need for a fault detection and isolation (FDI) mechanism. Finally, the effectiveness of the proposed design method is illustrated via a model of a rocket fairing structural-acoustic. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Quantized kernel least mean square algorithm.

PubMed

Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C

2012-01-01

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

Topological Phases in the Real World

NASA Astrophysics Data System (ADS)

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 enhance the T c of the existing leading candidate Sr2RuO 4 and to propose new material candidates for topological superconductors. First, by carrying out perturbative renormalization group (RG) analysis, we predicted that straining the ruthenate films will maximize the T c for triplet pairing channel when the Fermi surface is close to van Hove singularities without tuning on to the singularity. Then with a similar RG approach and a self-consistent calculation for the gap equations, we investigated the repulsion-mediated intrinsic and proximity-induced superconductivity in a family of lightly hole-doped noncentrosymmetric semiconductors, monolayer transition metal dichalcogenides (TMDs). We found that thanks to the spin-valley locking in lightly hole-doped TMDs, two distinct topological pairing states are favored for the intrinsically superconducting case: an interpocket paired state with Chern number 2 and an intrapocket paired state with finite pair momentum. Moreover, nematic odd-parity pairing with a possibly high Tc can be induced when proximitized by a cuprate. A confirmation of our predictions will open up possibilities for manipulating unconventional and topological superconductivity at a higher temperature on the device-friendly platform of strained ruthenate films and monolayer TMDs. In the second part, I will discuss our studies on the stability of the Dirac surface states in 3D TIs in the presence of bulk states and in TI-ferromagnetic metal heterostructures. We constructed simple microscopic models with Fano-type couplings between localized and extended states for each situation. Then with ab initio calculations we investigated the fate of the Dirac surface states in terms of the spectrum, the spatial profile and the spin-texture. Based on our results, we proposed explanations for existing experimental spectroscopic and spin-torque results.

Treatment of constraints in the stochastic quantization method and covariantized Langevin equation

NASA Astrophysics Data System (ADS)

Ikegami, Kenji; Kimura, Tadahiko; Mochizuki, Riuji

1993-04-01

We study the treatment of the constraints in the stochastic quantization method. We improve the treatment of the stochastic consistency condition proposed by Namiki et al. by suitably taking into account the Ito calculus. Then we obtain an improved Langevi equation and the Fokker-Planck equation which naturally leads to the correct path integral quantization of the constrained system as the stochastic equilibrium state. This treatment is applied to an O( N) non-linear α model and it is shown that singular terms appearing in the improved Langevin equation cancel out the σ n(O) divergences in one loop order. We also ascertain that the above Langevin equation, rewritten in terms of idependent variables, is actually equivalent to the one in the general-coordinate transformation covariant and vielbein-rotation invariant formalish.

Chern-Simons Term: Theory and Applications.

NASA Astrophysics Data System (ADS)

Gupta, Kumar Sankar

1992-01-01

We investigate the quantization and applications of Chern-Simons theories to several systems of interest. Elementary canonical methods are employed for the quantization of abelian and nonabelian Chern-Simons actions using ideas from gauge theories and quantum gravity. When the spatial slice is a disc, it yields quantum states at the edge of the disc carrying a representation of the Kac-Moody algebra. We next include sources in this model and their quantum states are shown to be those of a conformal family. Vertex operators for both abelian and nonabelian sources are constructed. The regularized abelian Wilson line is proved to be a vertex operator. The spin-statistics theorem is established for Chern-Simons dynamics using purely geometrical techniques. Chern-Simons action is associated with exotic spin and statistics in 2 + 1 dimensions. We study several systems in which the Chern-Simons action affects the spin and statistics. The first class of systems we study consist of G/H models. The solitons of these models are shown to obey anyonic statistics in the presence of a Chern-Simons term. The second system deals with the effect of the Chern -Simons term in a model for high temperature superconductivity. The coefficient of the Chern-Simons term is shown to be quantized, one of its possible values giving fermionic statistics to the solitons of this model. Finally, we study a system of spinning particles interacting with 2 + 1 gravity, the latter being described by an ISO(2,1) Chern-Simons term. An effective action for the particles is obtained by integrating out the gauge fields. Next we construct operators which exchange the particles. They are shown to satisfy the braid relations. There are ambiguities in the quantization of this system which can be exploited to give anyonic statistics to the particles. We also point out that at the level of the first quantized theory, the usual spin-statistics relation need not apply to these particles.

Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes

NASA Astrophysics Data System (ADS)

Escalante, Alberto; Medel-Portugal, C.

2018-04-01

The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev-Jackiw context. The Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the Faddeev-Jackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions.

Google in a Quantum Network

PubMed Central

Paparo, G. D.; Martin-Delgado, M. A.

2012-01-01

We introduce the characterization of a class of quantum PageRank algorithms in a scenario in which some kind of quantum network is realizable out of the current classical internet web, but no quantum computer is yet available. This class represents a quantization of the PageRank protocol currently employed to list web pages according to their importance. We have found an instance of this class of quantum protocols that outperforms its classical counterpart and may break the classical hierarchy of web pages depending on the topology of the web. PMID:22685626

Quantum Hall effect in dual gated BiSbTeSe2 topological insulator

NASA Astrophysics Data System (ADS)

Chong, Su Kong; Han, Kyu Bum; Nagaoka, Akira; Harmer, Jared; Tsuchikawa, Ryuichi; Sparks, Taylor D.; Deshpande, Vikram V.

The discovery of topological insulators (TIs) has expanded the family of Dirac materials and enables the probing of exotic matter such as Majorana fermions and magnetic monopoles. Different from conventional 2D electron gas, 3D TIs exhibit a gapped insulating bulk and gapless topological surface states as a result of the strong spin-orbit coupling. BiSbTeSe2 is also known to be a 3D TI with a large intrinsic bulk gap of about 0.3 eV and a single Dirac cone surface state. The highly bulk insulating BiSbTeSe2 permits surface dominated conduction, which is an ideal system for the study of quantum Hall effect (QHE). Due to the spin-momentum locking, the Dirac fermions at the topological surface states have a degeneracy of one. In the QH regime, the Hall conductance is quantized to (n + 1 / 2) e2 / h , where n is an integer and the factor of half is related to Berry curvature. In this work, we study the QHE 3D TI using a dual gated BiSbTeSe2 device. By tuning the chemical potentials on top and bottom surfaces, integer QHE with Landau filling factors, ν = 0, +/-1, and +/-2 are observed.

Quantization and Superselection Sectors I:. Transformation Group C*-ALGEBRAS

NASA Astrophysics Data System (ADS)

Landsman, N. P.

Quantization is defined as the act of assigning an appropriate C*-algebra { A} to a given configuration space Q, along with a prescription mapping self-adjoint elements of { A} into physically interpretable observables. This procedure is adopted to solve the problem of quantizing a particle moving on a homogeneous locally compact configuration space Q=G/H. Here { A} is chosen to be the transformation group C*-algebra corresponding to the canonical action of G on Q. The structure of these algebras and their representations are examined in some detail. Inequivalent quantizations are identified with inequivalent irreducible representations of the C*-algebra corresponding to the system, hence with its superselection sectors. Introducing the concept of a pre-Hamiltonian, we construct a large class of G-invariant time-evolutions on these algebras, and find the Hamiltonians implementing these time-evolutions in each irreducible representation of { A}. “Topological” terms in the Hamiltonian (or the corresponding action) turn out to be representation-dependent, and are automatically induced by the quantization procedure. Known “topological” charge quantization or periodicity conditions are then identically satisfied as a consequence of the representation theory of { A}.

Dissipation and quantization for composite systems

NASA Astrophysics Data System (ADS)

Blasone, Massimo; Jizba, Petr; Scardigli, Fabio; Vitiello, Giuseppe

2009-11-01

In the framework of 't Hooft's quantization proposal, we show how to obtain from the composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region one can describe the system in terms of two irreducible elementary subsystems which correspond to two independent quantum harmonic oscillators.

't Hooft Quantization for Interacting Systems

NASA Astrophysics Data System (ADS)

Jizba, Petr; Scardigli, Fabio; Blasone, Massimo; Vitiello, Giuseppe

2012-02-01

In the framework of 't Hooft's "deterministic quantization" proposal, we show how to obtain from a composite system of two classical Bateman's oscillators a quantum isotonic oscillator. In a specific range of parameters, such a system can be also interpreted as a particle in an effective magnetic field, interacting through a spin-orbit interaction term. In the limit of a large separation from the interaction region, the system can be described in terms of two irreducible elementary subsystems, corresponding to two independent quantum harmonic oscillators.

Radical chiral Floquet phases in a periodically driven Kitaev model and beyond

NASA Astrophysics Data System (ADS)

Po, Hoi Chun; Fidkowski, Lukasz; Vishwanath, Ashvin; Potter, Andrew C.

2017-12-01

We theoretically discover a family of nonequilibrium fractional topological phases in which time-periodic driving of a 2D system produces excitations with fractional statistics, and produces chiral quantum channels that propagate a quantized fractional number of qubits along the sample edge during each driving period. These phases share some common features with fractional quantum Hall states, but are sharply distinct dynamical phenomena. Unlike the integer-valued invariant characterizing the equilibrium quantum Hall conductance, these phases are characterized by a dynamical topological invariant that is a square root of a rational number, inspiring the label: radical chiral Floquet phases. We construct solvable models of driven and interacting spin systems with these properties, and identify an unusual bulk-boundary correspondence between the chiral edge dynamics and bulk "anyon time-crystal" order characterized by dynamical transmutation of electric-charge into magnetic-flux excitations in the bulk.

Ballistic superconductivity in semiconductor nanowires.

PubMed

Zhang, Hao; Gül, Önder; Conesa-Boj, Sonia; Nowak, Michał P; Wimmer, Michael; Zuo, Kun; Mourik, Vincent; de Vries, Folkert K; van Veen, Jasper; de Moor, Michiel W A; Bommer, Jouri D S; van Woerkom, David J; Car, Diana; Plissard, Sébastien R; Bakkers, Erik P A M; Quintero-Pérez, Marina; Cassidy, Maja C; Koelling, Sebastian; Goswami, Srijit; Watanabe, Kenji; Taniguchi, Takashi; Kouwenhoven, Leo P

2017-07-06

Semiconductor nanowires have opened new research avenues in quantum transport owing to their confined geometry and electrostatic tunability. They have offered an exceptional testbed for superconductivity, leading to the realization of hybrid systems combining the macroscopic quantum properties of superconductors with the possibility to control charges down to a single electron. These advances brought semiconductor nanowires to the forefront of efforts to realize topological superconductivity and Majorana modes. A prime challenge to benefit from the topological properties of Majoranas is to reduce the disorder in hybrid nanowire devices. Here we show ballistic superconductivity in InSb semiconductor nanowires. Our structural and chemical analyses demonstrate a high-quality interface between the nanowire and a NbTiN superconductor that enables ballistic transport. This is manifested by a quantized conductance for normal carriers, a strongly enhanced conductance for Andreev-reflecting carriers, and an induced hard gap with a significantly reduced density of states. These results pave the way for disorder-free Majorana devices.

Two-dimensional Fermi surfaces in Kondo insulating SmB6

NASA Astrophysics Data System (ADS)

Li, Gang

There has been renewed interest in Samarium Hexaboride, which is a strongly correlated heavy Fermion material. Hybridization between itinerant electrons and localized orbitals lead to an opening of charge gap at low temperature. However, the resistivity of SmB6 does not diverge at low temperature. Former studies suggested that this residual conductance is contributed by various origins. Recent theoretical developments suggest that the particular symmetry of energy bands of SmB6 may host a topologically non-trivial surface state, i.e., a topological Kondo insulator. To probe the Fermiology of the possible metallic surface state, we use sensitive torque magnetometry to detect the de Haas van Alphen (dHvA) effect due to Landau level quantization on flux-grown crystals, down to He-3 temperature and up to 45 Tesla. Our angular and temperature dependent data suggest two-dimensional Fermi Surfaces lie in both crystalline (001) and (101) surface planes of SmB6.

Magnetic skyrmions on a two-lane racetrack

NASA Astrophysics Data System (ADS)

Müller, Jan

2017-02-01

Magnetic skyrmions are particle-like textures in magnetization, characterized by a topological winding number. Nanometer-scale skyrmions have been observed at room temperature in magnetic multilayer structures. The combination of their small size, topological quantization and their efficient electric manipulation makes them interesting candidates for information carriers in high-performance memory devices. A skyrmion racetrack memory has been suggested, in which information is encoded in the distance between skyrmions moving in a one-dimensional nanostrip. Here, I propose an alternative design where skyrmions move in two (or more) parallel lanes and the information is stored in the lane number of each skyrmion. Such a multilane track can be constructed by controlling the height profile of the nanostrip. Repulsive skyrmion-skyrmion interactions in narrow nanostrips guarantee that skyrmions on different lanes cannot pass each other. Current pulses can be used to induce a lane change, and combining these elements provides a robust, efficient design for skyrmion-based storage devices.

Geometrical Description of fractional quantum Hall quasiparticles

NASA Astrophysics Data System (ADS)

Park, Yeje; Yang, Bo; Haldane, F. D. M.

2012-02-01

We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.

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

NASA Astrophysics Data System (ADS)

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.

Generalized noise terms for the quantized fluctuational electrodynamics

NASA Astrophysics Data System (ADS)

Partanen, Mikko; Häyrynen, Teppo; Tulkki, Jukka; Oksanen, Jani

2017-03-01

The quantization of optical fields in vacuum has been known for decades, but extending the field quantization to lossy and dispersive media in nonequilibrium conditions has proven to be complicated due to the position-dependent electric and magnetic responses of the media. In fact, consistent position-dependent quantum models for the photon number in resonant structures have only been formulated very recently and only for dielectric media. Here we present a general position-dependent quantized fluctuational electrodynamics (QFED) formalism that extends the consistent field quantization to describe the photon number also in the presence of magnetic field-matter interactions. It is shown that the magnetic fluctuations provide an additional degree of freedom in media where the magnetic coupling to the field is prominent. Therefore, the field quantization requires an additional independent noise operator that is commuting with the conventional bosonic noise operator describing the polarization current fluctuations in dielectric media. In addition to allowing the detailed description of field fluctuations, our methods provide practical tools for modeling optical energy transfer and the formation of thermal balance in general dielectric and magnetic nanodevices. We use QFED to investigate the magnetic properties of microcavity systems to demonstrate an example geometry in which it is possible to probe fields arising from the electric and magnetic source terms. We show that, as a consequence of the magnetic Purcell effect, the tuning of the position of an emitter layer placed inside a vacuum cavity can make the emissivity of a magnetic emitter to exceed the emissivity of a corresponding electric emitter.

Nonperturbative light-front Hamiltonian methods

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2016-09-01

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

A Low Power Digital Accumulation Technique for Digital-Domain CMOS TDI Image Sensor.

PubMed

Yu, Changwei; Nie, Kaiming; Xu, Jiangtao; Gao, Jing

2016-09-23

In this paper, an accumulation technique suitable for digital domain CMOS time delay integration (TDI) image sensors is proposed to reduce power consumption without degrading the rate of imaging. In terms of the slight variations of quantization codes among different pixel exposures towards the same object, the pixel array is divided into two groups: one is for coarse quantization of high bits only, and the other one is for fine quantization of low bits. Then, the complete quantization codes are composed of both results from the coarse-and-fine quantization. The equivalent operation comparably reduces the total required bit numbers of the quantization. In the 0.18 µm CMOS process, two versions of 16-stage digital domain CMOS TDI image sensor chains based on a 10-bit successive approximate register (SAR) analog-to-digital converter (ADC), with and without the proposed technique, are designed. The simulation results show that the average power consumption of slices of the two versions are 6 . 47 × 10 - 8 J/line and 7 . 4 × 10 - 8 J/line, respectively. Meanwhile, the linearity of the two versions are 99.74% and 99.99%, respectively.

Speech coding at low to medium bit rates

NASA Astrophysics Data System (ADS)

Leblanc, Wilfred Paul

1992-09-01

Improved search techniques coupled with improved codebook design methodologies are proposed to improve the performance of conventional code-excited linear predictive coders for speech. Improved methods for quantizing the short term filter are developed by employing a tree search algorithm and joint codebook design to multistage vector quantization. Joint codebook design procedures are developed to design locally optimal multistage codebooks. Weighting during centroid computation is introduced to improve the outlier performance of the multistage vector quantizer. Multistage vector quantization is shown to be both robust against input characteristics and in the presence of channel errors. Spectral distortions of about 1 dB are obtained at rates of 22-28 bits/frame. Structured codebook design procedures for excitation in code-excited linear predictive coders are compared to general codebook design procedures. Little is lost using significant structure in the excitation codebooks while greatly reducing the search complexity. Sparse multistage configurations are proposed for reducing computational complexity and memory size. Improved search procedures are applied to code-excited linear prediction which attempt joint optimization of the short term filter, the adaptive codebook, and the excitation. Improvements in signal to noise ratio of 1-2 dB are realized in practice.

Valley-symmetric quasi-1D transport in ballistic graphene

NASA Astrophysics Data System (ADS)

Lee, Hu-Jong

We present our recent studies on gate-defined valley-symmetric one-dimensional (1D) carrier guiding in ballistic monolayer graphene and valley-symmetry-protected topological 1D transport in ballistic bilayer graphene. Successful carrier guiding was realized in ballistic monolayer graphene even in the absence of a band gap by inducing a high distinction ( more than two orders of magnitude) in the carrier density between the region of a quasi-1D channel and the rest of the top-gated regions. Conductance of a channel shows quantized values in units of 4e2/ h, suggesting that the valley symmetry is preserved. For the latter, the topological 1D conduction was realized between two closely arranged insulating regions with inverted band gaps, induced under a pair of split dual gating with polarities opposite to each other. The maximum conductance along the boundary channel showed 4e2/ h, again with the preserved valley symmetry. The 1D topological carrier guiding demonstrated in this study affords a promising route to robust valleytronic applications and sophisticated valley-associated functionalities based on 2D materials. This work was funded by the National Research Foundation of Korea.

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Qing Lin; Pan, Lei; Stern, Alexander L.

Majorana fermion is a hypothetical particle that is its own antiparticle. We report transport measurements that suggest the existence of one-dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. As the external magnetic field is swept, half-integer quantized conductance plateaus are observed at the locations of magnetization reversals, giving a distinct signature of the Majorana fermion modes. This transport signature is reproducible over many magnetic field sweeps and appears at different temperatures. This finding may open up an avenue to control Majorana fermions for implementing robust topological quantummore » computing.« less

Refined geometric transition and qq-characters

NASA Astrophysics Data System (ADS)

Kimura, Taro; Mori, Hironori; Sugimoto, Yuji

2018-01-01

We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe qq-characters from the string theory point of view. Though the suggested way to operate the refined geometric transition has passed through several checks, it is additionally found in this paper that the presence of the preferred direction brings a nontrivial effect. We provide the modified formula involving this point. We then apply our prescription of the refined geometric transition to proposing the stringy description of doubly quantized Seiberg-Witten curves called qq-characters in certain cases.

Equivariant branes and equivariant homological mirror symmetry

NASA Astrophysics Data System (ADS)

Ashwinkumar, Meer; Tan, Meng-Chwan

2018-03-01

We describe supersymmetric A-branes and B-branes in open N =(2 ,2 ) dynamically gauged nonlinear sigma models (GNLSM), placing emphasis on toric manifold target spaces. For a subset of toric manifolds, these equivariant branes have a mirror description as branes in gauged Landau-Ginzburg models with neutral matter. We then study correlation functions in the topological A-twisted version of the GNLSM and identify their values with open Hamiltonian Gromov-Witten invariants. Supersymmetry breaking can occur in the A-twisted GNLSM due to nonperturbative open symplectic vortices, and we canonically Becchi-Rouet-Stora-Tyutin quantize the mirror theory to analyze this phenomenon.

Quantized visual awareness.

PubMed

Escobar, W A

2013-01-01

The proposed model holds that, at its most fundamental level, visual awareness is quantized. That is to say that visual awareness arises as individual bits of awareness through the action of neural circuits with hundreds to thousands of neurons in at least the human striate cortex. Circuits with specific topologies will reproducibly result in visual awareness that correspond to basic aspects of vision like color, motion, and depth. These quanta of awareness (qualia) are produced by the feedforward sweep that occurs through the geniculocortical pathway but are not integrated into a conscious experience until recurrent processing from centers like V4 or V5 select the appropriate qualia being produced in V1 to create a percept. The model proposed here has the potential to shift the focus of the search for visual awareness to the level of microcircuits and these likely exist across the kingdom Animalia. Thus establishing qualia as the fundamental nature of visual awareness will not only provide a deeper understanding of awareness, but also allow for a more quantitative understanding of the evolution of visual awareness throughout the animal kingdom.

Quantum quench in a p+ip superfluid: Winding numbers and topological states far from equilibrium

NASA Astrophysics Data System (ADS)

Foster, Matthew S.; Dzero, Maxim; Gurarie, Victor; Yuzbashyan, Emil A.

2013-09-01

We study the nonadiabatic dynamics of a two-dimensional p+ip superfluid following an instantaneous quantum quench of the BCS coupling constant. The model describes a topological superconductor with a nontrivial BCS (trivial BEC) phase appearing at weak- (strong-) coupling strengths. We extract the exact long-time asymptotics of the order parameter Δ(t) by exploiting the integrability of the classical p-wave Hamiltonian, which we establish via a Lax construction. Three different types of asymptotic behavior can occur depending upon the strength and direction of the interaction quench. We refer to these as the nonequilibrium phases {I, II, III}, characterized as follows. In phase I, the order parameter asymptotes to zero due to dephasing. In phase II, Δ→Δ∞, a nonzero constant. Phase III is characterized by persistent oscillations of Δ(t). For quenches within phases I and II, we determine the topological character of the asymptotic states. We show that two different formulations of the bulk topological winding number, although equivalent in the BCS or BEC ground states, must be regarded as independent out of equilibrium. The first winding number Q characterizes the Anderson pseudospin texture of the initial state; we show that Q is generically conserved. For Q≠0, this leads to the prediction of a “gapless topological” state when Δ asymptotes to zero. The presence or absence of Majorana edge modes in a sample with a boundary is encoded in the second winding number W, which is formulated in terms of the retarded Green's function. We establish that W can change following a quench across the quantum critical point. When the order parameter asymptotes to a nonzero constant, the final value of W is well defined and quantized. We discuss the implications for the (dis)appearance of Majorana edge modes. Finally, we show that the parity of zeros in the bulk out-of-equilibrium Cooper-pair distribution function constitutes a Z2-valued quantum number, which is nonzero whenever W≠Q. The pair distribution can in principle be measured using rf spectroscopy in an ultracold-atom realization, allowing direct experimental detection of the Z2 number. This has the following interesting implication: topological information that is experimentally inaccessible in the bulk ground state can be transferred to an observable distribution function when the system is driven far from equilibrium.

Event-Triggered Distributed Average Consensus Over Directed Digital Networks With Limited Communication Bandwidth.

PubMed

Li, Huaqing; Chen, Guo; Huang, Tingwen; Dong, Zhaoyang; Zhu, Wei; Gao, Lan

2016-12-01

In this paper, we consider the event-triggered distributed average-consensus of discrete-time first-order multiagent systems with limited communication data rate and general directed network topology. In the framework of digital communication network, each agent has a real-valued state but can only exchange finite-bit binary symbolic data sequence with its neighborhood agents at each time step due to the digital communication channels with energy constraints. Novel event-triggered dynamic encoder and decoder for each agent are designed, based on which a distributed control algorithm is proposed. A scheme that selects the number of channel quantization level (number of bits) at each time step is developed, under which all the quantizers in the network are never saturated. The convergence rate of consensus is explicitly characterized, which is related to the scale of network, the maximum degree of nodes, the network structure, the scaling function, the quantization interval, the initial states of agents, the control gain and the event gain. It is also found that under the designed event-triggered protocol, by selecting suitable parameters, for any directed digital network containing a spanning tree, the distributed average consensus can be always achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. Two simulation examples are provided to illustrate the feasibility of presented protocol and the correctness of the theoretical results.

Self-dual phase space for (3 +1 )-dimensional lattice Yang-Mills theory

NASA Astrophysics Data System (ADS)

Riello, Aldo

2018-01-01

I propose a self-dual deformation of the classical phase space of lattice Yang-Mills theory, in which both the electric and magnetic fluxes take value in the compact gauge Lie group. A local construction of the deformed phase space requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which is reviewed here. The results is a full-fledged finite-dimensional and gauge-invariant phase space, the self-duality properties of which are largely enhanced in (3 +1 ) spacetime dimensions. This enhancement is due to a correspondence with the moduli space of an auxiliary noncommutative flat connection living on a Riemann surface defined from the lattice itself, which in turn equips the duality between electric and magnetic fluxes with a neat geometrical interpretation in terms of a Heegaard splitting of the space manifold. Finally, I discuss the consequences of the proposed deformation on the quantization of the phase space, its quantum gravitational interpretation, as well as its relevance for the construction of (3 +1 )-dimensional topological field theories with defects.

More on quantum groups from the quantization point of view

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1994-12-01

Star products on the classical double group of a simple Lie group and on corresponding symplectic groupoids are given so that the quantum double and the “quantized tangent bundle” are obtained in the deformation description. “Complex” quantum groups and bicovariant quantum Lie algebras are discussed from this point of view. Further we discuss the quantization of the Poisson structure on the symmetric algebra S(g) leading to the quantized enveloping algebra U h (g) as an example of biquantization in the sense of Turaev. Description of U h (g) in terms of the generators of the bicovariant differential calculus on F(G q ) is very convenient for this purpose. Finaly we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact Lie groups. An analogue of the classical Kirillov's universal character formula is given for the unitary irreducble representation in the compact case.

Event-triggered H∞ state estimation for semi-Markov jumping discrete-time neural networks with quantization.

PubMed

Rakkiyappan, R; Maheswari, K; Velmurugan, G; Park, Ju H

2018-05-17

This paper investigates H ∞ state estimation problem for a class of semi-Markovian jumping discrete-time neural networks model with event-triggered scheme and quantization. First, a new event-triggered communication scheme is introduced to determine whether or not the current sampled sensor data should be broad-casted and transmitted to the quantizer, which can save the limited communication resource. Second, a novel communication framework is employed by the logarithmic quantizer that quantifies and reduces the data transmission rate in the network, which apparently improves the communication efficiency of networks. Third, a stabilization criterion is derived based on the sufficient condition which guarantees a prescribed H ∞ performance level in the estimation error system in terms of the linear matrix inequalities. Finally, numerical simulations are given to illustrate the correctness of the proposed scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

Sub-Selective Quantization for Learning Binary Codes in Large-Scale Image Search.

PubMed

Li, Yeqing; Liu, Wei; Huang, Junzhou

2018-06-01

Recently with the explosive growth of visual content on the Internet, large-scale image search has attracted intensive attention. It has been shown that mapping high-dimensional image descriptors to compact binary codes can lead to considerable efficiency gains in both storage and performing similarity computation of images. However, most existing methods still suffer from expensive training devoted to large-scale binary code learning. To address this issue, we propose a sub-selection based matrix manipulation algorithm, which can significantly reduce the computational cost of code learning. As case studies, we apply the sub-selection algorithm to several popular quantization techniques including cases using linear and nonlinear mappings. Crucially, we can justify the resulting sub-selective quantization by proving its theoretic properties. Extensive experiments are carried out on three image benchmarks with up to one million samples, corroborating the efficacy of the sub-selective quantization method in terms of image retrieval.

Chromium-induced ferromagnetism with perpendicular anisotropy in topological crystalline insulator SnTe (111) thin films

NASA Astrophysics Data System (ADS)

Wang, Fei; Zhang, Hongrui; Jiang, Jue; Zhao, Yi-Fan; Yu, Jia; Liu, Wei; Li, Da; Chan, Moses H. W.; Sun, Jirong; Zhang, Zhidong; Chang, Cui-Zu

2018-03-01

Topological crystalline insulator is a recently discovered topological phase of matter. It possesses multiple Dirac surface states, which are protected by the crystal symmetry. This is in contrast to the time-reversal symmetry that is operative in the well-known topological insulators. In the presence of a Zeeman field and/or strain, the multiple Dirac surface states are gapped. The high-Chern-number quantum anomalous Hall (QAH) state is predicted to emerge if the chemical potential resides in all the Zeeman gaps. Here, we use molecular-beam epitaxy to grow 12 double-layer (DL) pure and Cr-doped SnTe (111) thin film on heat-treated SrTi O3 (111) substrate using a quintuple layer of insulating (Bi0.2Sb0.8 ) 2T e3 topological insulator as a buffer film. The Hall traces of Cr-doped SnTe film at low temperatures display square hysteresis loops indicating long-range ferromagnetic order with perpendicular anisotropy. The Curie temperature of the 12 DL S n0.9C r0.1Te film is ˜110 K. Due to the chemical potential crossing the bulk valence bands, the anomalous Hall resistance of 12 DL S n0.9C r0.1Te film is substantially lower than the predicted quantized value (˜1 /4 h /e2 ). It is possible that with systematic tuning the chemical potential via chemical doping and electrical gating, the high-Chern-number QAH state can be realized in the Cr-doped SnTe (111) thin film.

Observation of conductance doubling in an Andreev quantum point contact

NASA Astrophysics Data System (ADS)

Kjaergaard, M.; Nichele, F.; Suominen, H.; Nowak, M.; Wimmer, M.; Akhmerov, A.; Folk, J.; Flensberg, K.; Shabani, J.; Palmstrom, C.; Marcus, C.

One route to study the non-Abelian nature of excitations in topological superconductors is to realise gateable two dimensional (2D) semiconducting systems, with spin-orbit coupling in proximity to an s-wave superconductor. Previous work on coupling 2D electron gases (2DEG) with superconductors has been hindered by a non-ideal interface and unstable gateability. We report measurements on a gateable 2DEG coupled to superconductors through a pristine interface, and use aluminum grown in situ epitaxially on an InGaAs/InAs electron gas. We demonstrate quantization in units of 4e2 / h in a quantum point contact (QPC) in such hybrid systems. Operating the QPC as a tunnel probe, we observe a hard superconducting gap, overcoming the soft-gap problem in 2D superconductor/semiconductor systems. Our work paves way for a new and highly scalable system in which to pursue topological quantum information processing. Research supported by Microsoft Project Q and the Danish National Research Foundation.

Ballistic superconductivity in semiconductor nanowires

PubMed Central

Zhang, Hao; Gül, Önder; Conesa-Boj, Sonia; Nowak, Michał P.; Wimmer, Michael; Zuo, Kun; Mourik, Vincent; de Vries, Folkert K.; van Veen, Jasper; de Moor, Michiel W. A.; Bommer, Jouri D. S.; van Woerkom, David J.; Car, Diana; Plissard, Sébastien R; Bakkers, Erik P.A.M.; Quintero-Pérez, Marina; Cassidy, Maja C.; Koelling, Sebastian; Goswami, Srijit; Watanabe, Kenji; Taniguchi, Takashi; Kouwenhoven, Leo P.

2017-01-01

Semiconductor nanowires have opened new research avenues in quantum transport owing to their confined geometry and electrostatic tunability. They have offered an exceptional testbed for superconductivity, leading to the realization of hybrid systems combining the macroscopic quantum properties of superconductors with the possibility to control charges down to a single electron. These advances brought semiconductor nanowires to the forefront of efforts to realize topological superconductivity and Majorana modes. A prime challenge to benefit from the topological properties of Majoranas is to reduce the disorder in hybrid nanowire devices. Here we show ballistic superconductivity in InSb semiconductor nanowires. Our structural and chemical analyses demonstrate a high-quality interface between the nanowire and a NbTiN superconductor that enables ballistic transport. This is manifested by a quantized conductance for normal carriers, a strongly enhanced conductance for Andreev-reflecting carriers, and an induced hard gap with a significantly reduced density of states. These results pave the way for disorder-free Majorana devices. PMID:28681843

Quantum spin Hall state in monolayer 1T '-WTe 2

DOE PAGES

Tang, Shujie; Zhang, Chaofan; Wong, Dillon; ...

2017-06-26

A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin–orbit coupling. By investigating the electronic structure of epitaxially grown monolayer 1T '-WTe 2 using angle-resolved photoemission (ARPES) and first-principles calculations, we observe clear signatures of topological band inversion and bandgap opening, which are the hallmarks of a QSH state. Scanning tunnelling microscopy measurements further confirm the correct crystal structure and the existence of a bulkmore » bandgap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Our results establish monolayer 1T '-WTe 2 as a new class of QSH insulator with large band gap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).« less

Quantum spin Hall state in monolayer 1T '-WTe 2

DOE PAGES

Tang, Shujie; Zhang, Chaofan; Wong, Dillon; ...

2017-06-26

A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin–orbit coupling. By investigating the electronic structure of epitaxially grown monolayer 1T '-WTe 2 using angle-resolved photoemission (ARPES) and first-principles calculations, we observe clear signatures of topological band inversion and bandgap opening, which are the hallmarks of a QSH state. Scanning tunnelling microscopy measurements further confirm the correct crystal structure and the existence of a bulkmore » bandgap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Finally, our results establish monolayer 1T '-WTe 2 as a new class of QSH insulator with large band gap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).« less

Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects

NASA Astrophysics Data System (ADS)

Otrokov, M. M.; Menshchikova, T. V.; Vergniory, M. G.; Rusinov, I. P.; Vyazovskaya, A. Yu; Koroteev, Yu M.; Bihlmayer, G.; Ernst, A.; Echenique, P. M.; Arnau, A.; Chulkov, E. V.

2017-06-01

An interplay of spin-orbit coupling and intrinsic magnetism is known to give rise to the quantum anomalous Hall and topological magnetoelectric effects under certain conditions. Their realization could open access to low power consumption electronics as well as many fundamental phenomena like image magnetic monopoles, Majorana fermions and others. Unfortunately, being realized very recently, these effects are only accessible at extremely low temperatures and the lack of appropriate materials that would enable the temperature increase is a most severe challenge. Here, we propose a novel material platform with unique combination of properties making it perfectly suitable for the realization of both effects at elevated temperatures. The key element of the computational material design is an extension of a topological insulator (TI) surface by a thin film of ferromagnetic insulator, which is both structurally and compositionally compatible with the TI. Following this proposal we suggest a variety of specific systems and discuss their numerous advantages, in particular wide band gaps with the Fermi level located in the gap.

Hierarchically clustered adaptive quantization CMAC and its learning convergence.

PubMed

Teddy, S D; Lai, E M K; Quek, C

2007-11-01

The cerebellar model articulation controller (CMAC) neural network (NN) is a well-established computational model of the human cerebellum. Nevertheless, there are two major drawbacks associated with the uniform quantization scheme of the CMAC network. They are the following: (1) a constant output resolution associated with the entire input space and (2) the generalization-accuracy dilemma. Moreover, the size of the CMAC network is an exponential function of the number of inputs. Depending on the characteristics of the training data, only a small percentage of the entire set of CMAC memory cells is utilized. Therefore, the efficient utilization of the CMAC memory is a crucial issue. One approach is to quantize the input space nonuniformly. For existing nonuniformly quantized CMAC systems, there is a tradeoff between memory efficiency and computational complexity. Inspired by the underlying organizational mechanism of the human brain, this paper presents a novel CMAC architecture named hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC). HCAQ-CMAC employs hierarchical clustering for the nonuniform quantization of the input space to identify significant input segments and subsequently allocating more memory cells to these regions. The stability of the HCAQ-CMAC network is theoretically guaranteed by the proof of its learning convergence. The performance of the proposed network is subsequently benchmarked against the original CMAC network, as well as two other existing CMAC variants on two real-life applications, namely, automated control of car maneuver and modeling of the human blood glucose dynamics. The experimental results have demonstrated that the HCAQ-CMAC network offers an efficient memory allocation scheme and improves the generalization and accuracy of the network output to achieve better or comparable performances with smaller memory usages. Index Terms-Cerebellar model articulation controller (CMAC), hierarchical clustering, hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC), learning convergence, nonuniform quantization.

Geometric Defects in Quantum Hall States

NASA Astrophysics Data System (ADS)

Gromov, Andrey

I will describe a geometric analogue of Laughlin quasiholes in fractional quantum Hall (FQH) states. These ``quasiholes'' are generated by an insertion of quantized fluxes of curvature - which can be modeled by branch points of a certain Riemann surface - and, consequently, are related to genons. Unlike quasiholes, the genons are not excitations, but extrinsic defects. Fusion of genons describes the response of an FQH state to a process that changes (effective) topology of the physical space. These defects are abelian for IQH states and non-abelian for FQH states. I will explain how to calculate an electric charge, geometric spin and adiabatic mutual statistics of the these defects. Leo Kadanoff Fellowship.

Collective coordinates and constrained hamiltonian systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dayi, O.F.

1992-07-01

A general method of incorporating collective coordinates (transformation of fields into an overcomplete basis) with constrained hamiltonian systems is given where the original phase space variables and collective coordinates can be bosonic or/and fermionic. This method is illustrated by applying it to the SU(2) Yang-Mills-Higgs theory and its BFV-BRST quantization is discussed. Moreover, this formalism is used to give a systematic way of converting second class constraints into effectively first class ones, by considering second class constraints as first class constraints and gauge fixing conditions. This approach is applied to the massive superparticle. Proca lagrangian, and some topological quantum fieldmore » theories.« less

Classical BV Theories on Manifolds with Boundary

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai

2014-12-01

In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the BF theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing.

Analytical theory and possible detection of the ac quantum spin Hall effect

DOE PAGES

Deng, W. Y.; Ren, Y. J.; Lin, Z. X.; ...

2017-07-11

Here, we develop an analytical theory of the low-frequency ac quantum spin Hall (QSH) effect based upon the scattering matrix formalism. It is shown that the ac QSH effect can be interpreted as a bulk quantum pumping effect. When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. Furthermore, a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological ac spin current by electrical means.

Quantization of a U(1) gauged chiral boson in the Batalin-Fradkin-Vilkovisky scheme

NASA Astrophysics Data System (ADS)

Ghosh, Subir

1994-03-01

The scheme developed by Batalin, Fradkin, and Vilkovisky (BFV) to convert a second-class constrained system to a first-class one (having gauge invariance) is used in the Floreanini-Jackiw formulation of the chiral boson interacting with a U(1) gauge field. Explicit expressions of the BRST charge, the unitarizing Hamiltonian, and the BRST invariant effective action are provided and the full quantization is carried through. The spectra in both cases have been analyzed to show the presence of the proper chiral components explicitly. In the gauged model, Wess-Zumino terms in terms of the Batalin-Fradkin fields are identified.

Quantization of a U(1) gauged chiral boson in the Batalin-Fradkin-Vilkovisky scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, S.

1994-03-15

The scheme developed by Batalin, Fradkin, and Vilkovisky (BFV) to convert a second-class constrained system to a first-class one (having gauge invariance) is used in the Floreanini-Jackiw formulation of the chiral boson interacting with a U(1) gauge field. Explicit expressions of the BRST charge, the unitarizing Hamiltonian, and the BRST invariant effective action are provided and the full quantization is carried through. The spectra in both cases have been analyzed to show the presence of the proper chiral components explicitly. In the gauged model, Wess-Zumino terms in terms of the Batalin-Fradkin fields are identified.

The Casalbuoni-Brink-Schwarz superparticle with covariant, reducible constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dayi, O.F.

1992-04-30

This paper discusses the fermionic constraints of the massless Casalbuoni-Brink-Schwarz superparticle in d = 10 which are separated covariantly as first- and second-class constraints which are infinitely reducible. Although the reducibility conditions of the second-class constraints include the first-class ones a consistent quantization is possible. The ghost structure of the system for quantizing it in terms of the BFV-BRST methods is given and unitarity is shown.

Superfield Hamiltonian quantization in terms of quantum antibrackets

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.

2016-04-01

We develop a new version of the superfield Hamiltonian quantization. The main new feature is that the BRST-BFV charge and the gauge fixing Fermion are introduced on equal footing within the sigma model approach, which provides for the actual use of the quantum/derived antibrackets. We study in detail the generating equations for the quantum antibrackets and their primed counterparts. We discuss the finite quantum anticanonical transformations generated by the quantum antibracket.

Topological insulator nanowires and nanowire hetero-junctions

NASA Astrophysics Data System (ADS)

Deng, Haiming; Zhao, Lukas; Wade, Travis; Konczykowski, Marcin; Krusin-Elbaum, Lia

2014-03-01

The existing topological insulator materials (TIs) continue to present a number of challenges to complete understanding of the physics of topological spin-helical Dirac surface conduction channels, owing to a relatively large charge conduction in the bulk. One way to reduce the bulk contribution and to increase surface-to-volume ratio is by nanostructuring. Here we report on the synthesis and characterization of Sb2Te3, Bi2Te3 nanowires and nanotubes and Sb2Te3/Bi2Te3 heterojunctions electrochemically grown in porous anodic aluminum oxide (AAO) membranes with varied (from 50 to 150 nm) pore diameters. Stoichiometric rigid polycrystalline nanowires with controllable cross-sections were obtained using cell voltages in the 30 - 150 mV range. Transport measurements in up to 14 T magnetic fields applied along the nanowires show Aharonov-Bohm (A-B) quantum oscillations with periods corresponding to the nanowire diameters. All nanowires were found to exhibit sharp weak anti-localization (WAL) cusps, a characteristic signature of TIs. In addition to A-B oscillations, new quantization plateaus in magnetoresistance (MR) at low fields (< 0 . 7T) were observed. The analysis of MR as well as I - V characteristics of heterojunctions will be presented. Supported in part by NSF-DMR-1122594, NSF-DMR-1312483-MWN, and DOD-W911NF-13-1-0159.

Superfield quantization

NASA Astrophysics Data System (ADS)

Batalin, I. A.; Bering, K.; Damgaard, P. H.

1998-03-01

We present a superfield formulation of the quantization program for theories with first-class constraints. An exact operator formulation is given, and we show how to set up a phase-space path integral entirely in terms of superfields. BRST transformations and canonical transformations enter on equal footing, and they allow us to establish a superspace analog of the BFV theorem. We also present a formal derivation of the Lagrangian superfield analogue of the field-antifield formalism by an integration over half of the phase-space variables.

Quantum geometry of resurgent perturbative/nonperturbative relations

NASA Astrophysics Data System (ADS)

Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat

2017-05-01

For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain \\mathcal{N} = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and `special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.

Tunable multifunctional topological insulators in ternary Heusler and related compounds

NASA Astrophysics Data System (ADS)

Felser, Claudia

2011-03-01

Recently the quantum spin Hall effect was theoretically predicted and experimentally realized in quantum wells based on the binary semiconductor HgTe. The quantum spin Hall state and topological insulators are new states of quantum matter interesting for both fundamental condensed-matter physics and material science. Many Heusler compounds with C1b structure are ternary semiconductors that are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the bandgap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by the lattice parameter) and magnitude of spin--orbit coupling (by the atomic charge). Based on first-principle calculations we demonstrate that around 50 Heusler compounds show band inversion similar to that of HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantumwell structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare-earth element Ln, which can realize additional properties ranging from superconductivity (for example LaPtBi) to magnetism (for example GdPtBi) and heavy fermion behaviour (for example YbPtBi). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors. Heusler compounds are similar to a stuffed diamond, correspondingly, it should be possible to find the ``high Z'' equivalent of graphene in a graphite-like structure with 18 valence electrons and with inverted bands. Indeed the ternary compounds, such as LiAuSe and KHgSb with a honeycomb structure of their Au-Se and Hg-Sb layers feature band inversion very similar to HgTe which is a strong precondition for existence of the topological surface states. These materials have a gap at the Fermi energy and are therefore candidates for 3D-topological insulators. Additionally they are centro-symmetric, therefore, it is possible to determine the parity of their wave functions, and hence, their topological character. Surprisingly, the compound KHgSb with the strong SOC is topologically trivial, whereas LiAuSe is found to be a topological non-trivial insulator.

Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure

DOE PAGES

He, Qing Lin; Pan, Lei; Stern, Alexander L.; ...

2017-07-21

Majorana fermion is a hypothetical particle that is its own antiparticle. We report transport measurements that suggest the existence of one-dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. As the external magnetic field is swept, half-integer quantized conductance plateaus are observed at the locations of magnetization reversals, giving a distinct signature of the Majorana fermion modes. This transport signature is reproducible over many magnetic field sweeps and appears at different temperatures. This finding may open up an avenue to control Majorana fermions for implementing robust topological quantummore » computing.« less

Transport signatures of topology protected quantum criticality in Majorana islands

NASA Astrophysics Data System (ADS)

Papaj, Michal; Zhu, Zheng; Fu, Liang

Using numerical renormalization group we study a topological superconductor island coupled to three metallic leads in the vicinity of the charge degeneracy point. We show that the system flows to a non-Fermi liquid fixed point at low temperatures with fractional quantized DC conductance of 2 / 3e2 / h . Our proposal is experimentally feasible due to a much larger crossover temperature than in the previously studied cases and the robustness of the setup against the channel coupling anisotropy and charge degeneracy detuning. Including Majorana hybridization drives the system into a Fermi liquid phase at very low temperatures. The two proposed experimental signatures of multi-terminal electron teleportation include nonmonotonic temperature dependence of DC conductance and emergence of a plateau at 2 / 3e2 / h in tunnel coupling dependence of DC conductance. This work is funded by the DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award de-sc0010526 (ZZ and LF) and the NSF STC ''Center for Integrated Quantum Materials'' under Cooperative Agreement No. DMR-1231319 (MP).

Influence of topological transitions in a quantizing magnetic field and anisotropy of current carrier scattering by acoustic phonons on the longitudinal electrical conductivity of layered crystals with open fermi surfaces

NASA Astrophysics Data System (ADS)

Gorskii, P. V.

2011-03-01

It is demonstrated that the dependence of Fermi's energy on the magnetic field causes a set of the Shubnikov - de Haas (SDH) oscillation frequencies to change, and their relative contribution to the total longitudinal conductivity of layered crystals depends on whether the scattering of current carriers is isotropic or anisotropic. Owing to the topological transition in a strong magnetic field, Fermi's surface (FS) is transformed from open into closed one and is compressed in the magnetic field direction. Therefore, in an ultraquantum limit, disregarding the Dingle factor, the longitudinal electrical conductivity of the layered crystal tends to zero as a reciprocal square of the magnetic field for the isotropic scattering and as a reciprocal cube of the magnetic field for the anisotropic scattering. All calculations are performed in the approximation of relaxation time considered to be constant versus the quantum numbers for the isotropic scattering and proportional to the longitudinal velocity of current carriers for the anisotropic scattering.

Interband coherence induced correction to Thouless pumping: possible observation in cold-atom systems

NASA Astrophysics Data System (ADS)

Raghava, Gudapati Naresh; Zhou, Longwen; Gong, Jiangbin

2017-08-01

In Thouless pump, the charge transport in a one-dimensional insulator over an adiabatic cycle is topologically quantized. For nonequilibrium initial states, however, interband coherence will induce a previously unknown contribution to Thouless pumping. Though not geometric in nature, this contribution is independent of the time scale of the pumping protocol. In this work, we perform a detailed analysis of our previous finding [H.L. Wang et al., Phys. Rev. B 91, 085420 (2015)] in an already available cold-atom setup. We show that initial states with interband coherence can be obtained via a quench of the system's Hamiltonian. Adiabatic pumping in the post-quench system are then examined both theoretically and numerically, in which the interband coherence is shown to play an important role and can hence be observed experimentally. By choosing adiabatic protocols with different switching-on rates, we also show that the contribution of interband coherence to adiabatic pumping can be tuned. It is further proposed that the interband coherence induced correction to Thouless pumping may be useful in capturing a topological phase transition point. All our results have direct experimental interests.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guedes, Carlos; Oriti, Daniele; Raasakka, Matti

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-productmore » carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.« less

Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plyushchay, Mikhail S., E-mail: mikhail.plyushchay@usach.cl

A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metamorphosis that associates quantum systems with the first-order supersymmetry to the systems with the second-order supercharges.

Effects of Rashba spin-orbit coupling, Zeeman splitting and gyrotropy in two-dimensional cavity polaritons under the influence of the Landau quantization

NASA Astrophysics Data System (ADS)

Moskalenko, Sveatoslav A.; Podlesny, Igor V.; Dumanov, Evgheni V.; Liberman, Michael A.

2015-09-01

We consider the energy spectrum of the two-dimensional cavity polaritons under the influence of a strong magnetic and electric fields perpendicular to the surface of the GaAs-type quantum wells (QWs) with p-type valence band embedded into the resonators. As the first step in this direction the Landau quantization (LQ) of the electrons and heavy-holes (hh) was investigated taking into account the Rashba spin-orbit coupling (RSOC) with third-order chirality terms for hh and with nonparabolicity terms in their dispersion low including as well the Zeeman splitting (ZS) effects. The nonparabolicity term is proportional to the strength of the electric field and was introduced to avoid the collapse of the semiconductor energy gap under the influence of the third order chirality terms. The exact solutions for the eigenfunctions and eigenenergies were obtained using the Rashba method [E.I. Rashba, Fiz. Tverd. Tela 2, 1224 (1960) [Sov. Phys. Solid State 2, 1109 (1960)

Approaching the Planck scale from a generally relativistic point of view: A philosophical appraisal of loop quantum gravity

NASA Astrophysics Data System (ADS)

Wuthrich, Christian

My dissertation studies the foundations of loop quantum gravity (LQG), a candidate for a quantum theory of gravity based on classical general relativity. At the outset, I discuss two---and I claim separate---questions: first, do we need a quantum theory of gravity at all; and second, if we do, does it follow that gravity should or even must be quantized? My evaluation of different arguments either way suggests that while no argument can be considered conclusive, there are strong indications that gravity should be quantized. LQG attempts a canonical quantization of general relativity and thereby provokes a foundational interest as it must take a stance on many technical issues tightly linked to the interpretation of general relativity. Most importantly, it codifies general relativity's main innovation, the so-called background independence, in a formalism suitable for quantization. This codification pulls asunder what has been joined together in general relativity: space and time. It is thus a central issue whether or not general relativity's four-dimensional structure can be retrieved in the alternative formalism and how it fares through the quantization process. I argue that the rightful four-dimensional spacetime structure can only be partially retrieved at the classical level. What happens at the quantum level is an entirely open issue. Known examples of classically singular behaviour which gets regularized by quantization evoke an admittedly pious hope that the singularities which notoriously plague the classical theory may be washed away by quantization. This work scrutinizes pronouncements claiming that the initial singularity of classical cosmological models vanishes in quantum cosmology based on LQG and concludes that these claims must be severely qualified. In particular, I explicate why casting the quantum cosmological models in terms of a deterministic temporal evolution fails to capture the concepts at work adequately. Finally, a scheme is developed of how the re-emergence of the smooth spacetime from the underlying discrete quantum structure could be understood.

Polymer quantization, stability and higher-order time derivative terms

NASA Astrophysics Data System (ADS)

Cumsille, Patricio; Reyes, Carlos M.; Ossandon, Sebastian; Reyes, Camilo

2016-03-01

The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais-Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.

Effect of lead-aircraft ground-speed on self-spacing performance using a cockpit display of traffic information

NASA Technical Reports Server (NTRS)

Kelly, J. R.

1983-01-01

A simulator investigation was conducted to determine the effect of the lead-aircraft ground-speed quantization level on self-spacing performance using a Cockpit Display of Traffic Information (CDTI). The study utilized a simulator employing cathode-ray tubes for the primary flight and navigation displays and highly augmented flight control modes. The pilot's task was to follow, and self-space on, a lead aircraft which was performing an idle-thrust profile descent to an instrument landing system (ILS) approach and landing. The spacing requirement was specified in terms of both a minimum distance and a time interval. The results indicate that the ground-speed quantization level, lead-aircraft scenario, and pilot technique had a significant effect on self-spacing performance. However, the ground-speed quantization level only had a significant effect on the performance when the lead aircraft flew a fast final approach.

Quantized Lax Equations and Their Solutions

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schlieker, M.

Integrable systems on quantum groups are investigated. The Heisenberg equations possessing the Lax form are solved in terms of the solution to the factorization problem on the corresponding quantum group.

Nucleation of Quantized Vortices from Rotating Superfluid Drops

NASA Technical Reports Server (NTRS)

Donnelly, Russell J.

2001-01-01

The long-term goal of this project is to study the nucleation of quantized vortices in helium II by investigating the behavior of rotating droplets of helium II in a reduced gravity environment. The objective of this ground-based research grant was to develop new experimental techniques to aid in accomplishing that goal. The development of an electrostatic levitator for superfluid helium, described below, and the successful suspension of charged superfluid drops in modest electric fields was the primary focus of this work. Other key technologies of general low temperature use were developed and are also discussed.

Classical analogous of quantum cosmological perfect fluid models

NASA Astrophysics Data System (ADS)

Batista, A. B.; Fabris, J. C.; Gonçalves, S. V. B.; Tossa, J.

2001-05-01

Quantization in the minisuperspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state pQ= ρQ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.

Quantization of Spontaneously Broken Gauge Theory Based on the Bft-Bfv Formalism

NASA Astrophysics Data System (ADS)

Kim, Yong-Wan; Park, Young-Jai

We quantize the spontaneously broken Abelian U(1) Higgs model by using the improved BFT and BFV formalisms. We construct the BFT physical fields and obtain the firstclass observables including the Hamiltonian in terms of these fields. We also explicitly show that there are exact form invariances between the second-class and first-class quantities. Then, according to the BFV formalism, we derive the corresponding Lagrangian having U(1) gauge symmetry. We also discuss at the classical level how one easily gets the first-class Lagrangian from the symmetry-broken second-class Lagrangian.

Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams

NASA Astrophysics Data System (ADS)

Dennis, M. R.; Alonso, M. A.

2017-02-01

The connection between Poincaré spheres for polarization and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic two-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian modes, the Hermite-Gaussian, Laguerre-Gaussian and generalized Hermite-Laguerre-Gaussian modes as eigenfunctions of operators corresponding to the classical constants of motion of the two-dimensional oscillator, which acquire an extra significance as families of classical ellipses upon semiclassical quantization. This article is part of the themed issue 'Optical orbital angular momentum'.

Quantum geometry of resurgent perturbative/nonperturbative relations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Basar, Gokce; Dunne, Gerald V.; Unsal, Mithat

For a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential.more » These are related to the Chebyshev potentials, which are in turn related to certain N = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and ‘special geometry’. These systems inherit a natural modular structure corresponding to Ramanujan’s theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Lastly, our approach is very elementary, using basic classical geometry combined with all-orders WKB.« less

Quantum geometry of resurgent perturbative/nonperturbative relations

DOE PAGES

Basar, Gokce; Dunne, Gerald V.; Unsal, Mithat

2017-05-16

For a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential.more » These are related to the Chebyshev potentials, which are in turn related to certain N = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and ‘special geometry’. These systems inherit a natural modular structure corresponding to Ramanujan’s theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Lastly, our approach is very elementary, using basic classical geometry combined with all-orders WKB.« less

Topological Proximity Effect: A Gauge Influence from Distant Fields on Planar Quantum-Coherent Systems

NASA Astrophysics Data System (ADS)

Moulopoulos, K.

2015-06-01

A quantum system that lies nearby a magnetic or time-varying electric field region, and that is under periodic boundary conditions parallel to the interface, is shown to exhibit a "hidden" Aharonov-Bohm effect (magnetic or electric), caused by fluxes that are not enclosed by, but are merely neighboring to our system - its origin being the absence of magnetic monopoles in 3D space (with corresponding spacetime generalizations). Novel possibilities then arise, where a field-free system can be dramatically affected by manipulating fields in an adjacent or even distant land, provided that these nearby fluxes are not quantized (i.e. they are fractional or irrational parts of the flux quantum). Topological effects (such as Quantum Hall types of behaviors) can therefore be induced from outside our system (that is always field-free and can even reside in simply-connected space). Potential novel applications are outlined, and exotic consequences in solid state physics are pointed out (i.e. the possibility of field-free quantum periodic systems that violate Bloch's theorem), while formal analogies with certain high energy physics phenomena and with some rather under-explored areas in mechanics and thermodynamics are noted.

Quantum many-body adiabaticity, topological Thouless pump and driven impurity in a one-dimensional quantum fluid

NASA Astrophysics Data System (ADS)

Lychkovskiy, Oleg; Gamayun, Oleksandr; Cheianov, Vadim

2018-02-01

The quantum adiabatic theorem states that a driven system can be kept arbitrarily close to the instantaneous eigenstate of its Hamiltonian if the latter varies in time slowly enough. When it comes to applying the adiabatic theorem in practice, the key question to be answered is how slow slowly enough is. This question can be an intricate one, especially for many-body systems, where the limits of slow driving and large system size may not commute. Recently we have shown how the quantum adiabaticity in many-body systems is related to the generalized orthogonality catastrophe [arXiv 1611.00663, to appear in Phys. Rev. Lett.]. We have proven a rigorous inequality relating these two phenomena and applied it to establish conditions for the quantized transport in the topological Thouless pump. In the present contribution we (i) review these developments and (ii) apply the inequality to establish the conditions for adiabaticity in a one-dimensional system consisting of a quantum fluid and an impurity particle pulled through the fluid by an external force. The latter analysis is vital for the correct quantitative description of the phenomenon of quasi-Bloch oscillations in a one-dimensional translation invariant impurity-fluid system.

Semiclassical theory of the self-consistent vibration-rotation fields and its application to the bending-rotation interaction in the H{sub 2}O molecule

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skalozub, A.S.; Tsaune, A.Ya.

1994-12-01

A new approach for analyzing the highly excited vibration-rotation (VR) states of nonrigid molecules is suggested. It is based on the separation of the vibrational and rotational terms in the molecular VR Hamiltonian by introducing periodic auxiliary fields. These fields transfer different interactions within a molecule and are treated in terms of the mean-field approximation. As a result, the solution of the stationary Schroedinger equation with the VR Hamiltonian amounts to a quantization of the Berry phase in a problem of the molecular angular-momentum motion in a certain periodic VR field (rotational problem). The quantization procedure takes into account themore » motion of the collective vibrational variables in the appropriate VR potentials (vibrational problem). The quantization rules, the mean-field configurations of auxiliary interactions, and the solutions to the Schrodinger equations for the vibrational and rotational problems are self-consistently connected with one another. The potentialities of the theory are demonstrated by the bending-rotation interaction modeled by the Bunker-Landsberg potential function in the H{sub 2} molecule. The calculations are compared with both the results of the exact computations and those of other approximate methods. 32 refs., 4 tabs.« less

Effective field theories for topological insulators by functional bosonization

NASA Astrophysics Data System (ADS)

Chan, AtMa; Hughes, Taylor L.; Ryu, Shinsei; Fradkin, Eduardo

2013-02-01

Effective field theories that describe the dynamics of a conserved U(1) current in terms of “hydrodynamic” degrees of freedom of topological phases in condensed matter are discussed in general dimension D=d+1 using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII), and in the “primary series” of topological insulators, in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ (when D is even) terms. For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative “fractional” topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.

Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies

NASA Astrophysics Data System (ADS)

Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura

2018-05-01

Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the nonlinear kinetic term. Recently, for maximally symmetric spaces, simplified path integrals have been developed: they allow to trade the nonlinear kinetic term with a purely quadratic kinetic term (linear sigma model). This happens at the expense of introducing a suitable effective scalar potential, which contains the information on the curvature of the space. The simplified path integral provides a sensible gain in the efficiency of perturbative calculations. Here we extend the construction to models with N = 1 supersymmetry on the worldline, which are applicable to the first quantized description of a Dirac fermion. As an application we use the simplified worldline path integral to compute the type-A trace anomaly of a Dirac fermion in d dimensions up to d = 16.

Spectrum of Quantized Energy for a Lengthening Pendulum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Jeong Ryeol; Song, Ji Nny; Hong, Seong Ju

We considered a quantum system of simple pendulum whose length of string is increasing at a steady rate. Since the string length is represented as a time function, this system is described by a time-dependent Hamiltonian. The invariant operator method is very useful in solving the quantum solutions of time-dependent Hamiltonian systems like this. The invariant operator of the system is represented in terms of the lowering operator a(t) and the raising operator a{sup {dagger}}(t). The Schroedinger solutions {psi}{sub n}({theta}, t) whose spectrum is discrete are obtained by means of the invariant operator. The expectation value of the Hamiltonian inmore » the {psi}{sub n}({theta}, t) state is the same as the quantum energy. At first, we considered only {theta}{sup 2} term in the Hamiltonian in order to evaluate the quantized energy. The numerical study for quantum energy correction is also made by considering the angle variable not only up to {theta}{sup 4} term but also up to {theta}{sup 6} term in the Hamiltonian, using the perturbation theory.« less

Memory-efficient decoding of LDPC codes

NASA Technical Reports Server (NTRS)

Kwok-San Lee, Jason; Thorpe, Jeremy; Hawkins, Jon

2005-01-01

We present a low-complexity quantization scheme for the implementation of regular (3,6) LDPC codes. The quantization parameters are optimized to maximize the mutual information between the source and the quantized messages. Using this non-uniform quantized belief propagation algorithm, we have simulated that an optimized 3-bit quantizer operates with 0.2dB implementation loss relative to a floating point decoder, and an optimized 4-bit quantizer operates less than 0.1dB quantization loss.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid

PubMed Central

Dominici, Lorenzo; Dagvadorj, Galbadrakh; Fellows, Jonathan M.; Ballarini, Dario; De Giorgi, Milena; Marchetti, Francesca M.; Piccirillo, Bruno; Marrucci, Lorenzo; Bramati, Alberto; Gigli, Giuseppe; Szymańska, Marzena H.; Sanvitto, Daniele

2015-01-01

Vortices are archetypal objects that recur in the universe across the scale of complexity, from subatomic particles to galaxies and black holes. Their appearance is connected with spontaneous symmetry breaking and phase transitions. In Bose-Einstein condensates and superfluids, vortices are both point-like and quantized quasiparticles. We use a two-dimensional (2D) fluid of polaritons, bosonic particles constituted by hybrid photonic and electronic oscillations, to study quantum vortex dynamics. Polaritons benefit from easiness of wave function phase detection, a spinor nature sustaining half-integer vorticity, strong nonlinearity, and tuning of the background disorder. We can directly generate by resonant pulsed excitations a polariton condensate carrying either a full or half-integer vortex as initial condition and follow their coherent evolution using ultrafast imaging on the picosecond scale. The observations highlight a rich phenomenology, such as the spiraling of the half-vortex and the joint path of the twin charges of a full vortex, until the moment of their splitting. Furthermore, we observe the ordered branching into newly generated secondary couples, associated with the breaking of radial and azimuthal symmetries. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the vortex dynamics. In addition, our observations suggest that phase singularities may be seen as fundamental particles whose quantized events span from pair creation and recombination to 2D+t topological vortex strings. PMID:26665174

Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid.

PubMed

Dominici, Lorenzo; Dagvadorj, Galbadrakh; Fellows, Jonathan M; Ballarini, Dario; De Giorgi, Milena; Marchetti, Francesca M; Piccirillo, Bruno; Marrucci, Lorenzo; Bramati, Alberto; Gigli, Giuseppe; Szymańska, Marzena H; Sanvitto, Daniele

2015-12-01

Vortices are archetypal objects that recur in the universe across the scale of complexity, from subatomic particles to galaxies and black holes. Their appearance is connected with spontaneous symmetry breaking and phase transitions. In Bose-Einstein condensates and superfluids, vortices are both point-like and quantized quasiparticles. We use a two-dimensional (2D) fluid of polaritons, bosonic particles constituted by hybrid photonic and electronic oscillations, to study quantum vortex dynamics. Polaritons benefit from easiness of wave function phase detection, a spinor nature sustaining half-integer vorticity, strong nonlinearity, and tuning of the background disorder. We can directly generate by resonant pulsed excitations a polariton condensate carrying either a full or half-integer vortex as initial condition and follow their coherent evolution using ultrafast imaging on the picosecond scale. The observations highlight a rich phenomenology, such as the spiraling of the half-vortex and the joint path of the twin charges of a full vortex, until the moment of their splitting. Furthermore, we observe the ordered branching into newly generated secondary couples, associated with the breaking of radial and azimuthal symmetries. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the vortex dynamics. In addition, our observations suggest that phase singularities may be seen as fundamental particles whose quantized events span from pair creation and recombination to 2D+t topological vortex strings.

Noise-Coupled Image Rejection Architecture of Complex Bandpass ΔΣAD Modulator

NASA Astrophysics Data System (ADS)

San, Hao; Kobayashi, Haruo

This paper proposes a new realization technique of image rejection function by noise-coupling architecture, which is used for a complex bandpass ΔΣAD modulator. The complex bandpass ΔΣAD modulator processes just input I and Q signals, not image signals, and the AD conversion can be realized with low power dissipation. It realizes an asymmetric noise-shaped spectra, which is desirable for such low-IF receiver applications. However, the performance of the complex bandpass ΔΣAD modulator suffers from the mismatch between internal analog I and Q paths. I/Q path mismatch causes an image signal, and the quantization noise of the mirror image band aliases into the desired signal band, which degrades the SQNDR (Signal to Quantization Noise and Distortion Ratio) of the modulator. In our proposed modulator architecture, an extra notch for image rejection is realized by noise-coupled topology. We just add some passive capacitors and switches to the modulator; the additional integrator circuit composed of an operational amplifier in the conventional image rejection realization is not necessary. Therefore, the performance of the complex modulator can be effectively raised without additional power dissipation. We have performed simulation with MATLAB to confirm the validity of the proposed architecture. The simulation results show that the proposed architecture can achieve the realization of image-rejection effectively, and improve the SQNDR of the complex bandpass ΔΣAD modulator.

Casimir force phase transitions in the graphene family

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.

The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. We found that the expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. Here, we discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. Particularly, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences onmore » characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.« less

Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems

NASA Astrophysics Data System (ADS)

Qiao, Zhenhua; Han, Yulei; Zhang, Lei; Wang, Ke; Deng, Xinzhou; Jiang, Hua; Yang, Shengyuan A.; Wang, Jian; Niu, Qian

2016-07-01

We theoretically investigate the localization mechanism of the quantum anomalous Hall effect (QAHE) in the presence of spin-flip disorders. We show that the QAHE stays quantized at weak disorders, then enters a Berry-curvature mediated metallic phase at moderate disorders, and finally goes into the Anderson insulating phase at strong disorders. From the phase diagram, we find that at the charge neutrality point although the QAHE is most robust against disorders, the corresponding metallic phase is much easier to be localized into the Anderson insulating phase due to the interchange of Berry curvatures carried, respectively, by the conduction and valence bands. In the end, we provide a phenomenological picture related to the topological charges to better understand the underlying physical origin of the QAHE Anderson localization.

Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems

NASA Astrophysics Data System (ADS)

Han, Yulei; Qiao, Zhenhua

In this talk, we theoretically investigate the localization mechanism of the quantum anomalous Hall effect (QAHE) in the presence of spin-flip disorders. We show that the QAHE stays quantized at weak disorders, then enters a Berry-curvature mediated metallic phase at moderate disorders, and finally goes into the Anderson insulating phase at strong disorders. From the phase diagram, we find that at the charge neutrality point although the QAHE is most robust against disorders, the corresponding metallic phase is much easier to be localized into the Anderson insulating phase due to the interchange of Berry curvatures carried, respectively, by the conduction and valence bands. In the end, we provide a phenomenological picture related to the topological charges to better understand the underlying physical origin of the QAHE Anderson localization.

Casimir force phase transitions in the graphene family

DOE PAGES

Rodriguez-Lopez, Pablo; Kort-Kamp, Wilton J. M.; Dalvit, Diego A. R.; ...

2017-03-15

The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. We found that the expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. Here, we discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. Particularly, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences onmore » characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.« less

Operator Ordering and Classical Soliton Path in Two-Dimensional N = 2 Supersymmetry with KÄHLER Potential

NASA Astrophysics Data System (ADS)

Motoyui, Nobuyuki; Yamada, Mitsuru

We investigate a two-dimensional N = 2 supersymmetric model which consists of n chiral superfields with Kähler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super-Poincaré algebra by carrying out the canonical Dirac bracket quantization. This is shown to be also true when the supersymmetry algebra has a central extension by the presence of topological soliton. It is also shown that the path of soliton is a straight line in the complex plane of superpotential W and triangular mass inequality holds. One half of supersymmetry is broken by the presence of soliton.

Chiral Majorana fermion modes in a quantum anomalous Hall insulator-superconductor structure.

PubMed

He, Qing Lin; Pan, Lei; Stern, Alexander L; Burks, Edward C; Che, Xiaoyu; Yin, Gen; Wang, Jing; Lian, Biao; Zhou, Quan; Choi, Eun Sang; Murata, Koichi; Kou, Xufeng; Chen, Zhijie; Nie, Tianxiao; Shao, Qiming; Fan, Yabin; Zhang, Shou-Cheng; Liu, Kai; Xia, Jing; Wang, Kang L

2017-07-21

Majorana fermion is a hypothetical particle that is its own antiparticle. We report transport measurements that suggest the existence of one-dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. As the external magnetic field is swept, half-integer quantized conductance plateaus are observed at the locations of magnetization reversals, giving a distinct signature of the Majorana fermion modes. This transport signature is reproducible over many magnetic field sweeps and appears at different temperatures. This finding may open up an avenue to control Majorana fermions for implementing robust topological quantum computing. Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.

Iterative quantization: a Procrustean approach to learning binary codes for large-scale image retrieval.

PubMed

Gong, Yunchao; Lazebnik, Svetlana; Gordo, Albert; Perronnin, Florent

2013-12-01

This paper addresses the problem of learning similarity-preserving binary codes for efficient similarity search in large-scale image collections. We formulate this problem in terms of finding a rotation of zero-centered data so as to minimize the quantization error of mapping this data to the vertices of a zero-centered binary hypercube, and propose a simple and efficient alternating minimization algorithm to accomplish this task. This algorithm, dubbed iterative quantization (ITQ), has connections to multiclass spectral clustering and to the orthogonal Procrustes problem, and it can be used both with unsupervised data embeddings such as PCA and supervised embeddings such as canonical correlation analysis (CCA). The resulting binary codes significantly outperform several other state-of-the-art methods. We also show that further performance improvements can result from transforming the data with a nonlinear kernel mapping prior to PCA or CCA. Finally, we demonstrate an application of ITQ to learning binary attributes or "classemes" on the ImageNet data set.

A short essay on quantum black holes and underlying noncommutative quantized space-time

NASA Astrophysics Data System (ADS)

Tanaka, Sho

2017-01-01

We emphasize the importance of noncommutative geometry or Lorenz-covariant quantized space-time towards the ultimate theory of quantum gravity and Planck scale physics. We focus our attention on the statistical and substantial understanding of the Bekenstein-Hawking area-entropy law of black holes in terms of the kinematical holographic relation (KHR). KHR manifestly holds in Yang’s quantized space-time as the result of kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry, and plays an important role in our approach without any recourse to the familiar hypothesis, so-called holographic principle. In the present paper, we find a unified form of KHR applicable to the whole region ranging from macroscopic to microscopic scales in spatial dimension d  =  3. We notice a possibility of nontrivial modification of area-entropy law of black holes which becomes most remarkable in the extremely microscopic system close to Planck scale.

Quantization-Based Adaptive Actor-Critic Tracking Control With Tracking Error Constraints.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong; Ye, Dan

2018-04-01

In this paper, the problem of adaptive actor-critic (AC) tracking control is investigated for a class of continuous-time nonlinear systems with unknown nonlinearities and quantized inputs. Different from the existing results based on reinforcement learning, the tracking error constraints are considered and new critic functions are constructed to improve the performance further. To ensure that the tracking errors keep within the predefined time-varying boundaries, a tracking error transformation technique is used to constitute an augmented error system. Specific critic functions, rather than the long-term cost function, are introduced to supervise the tracking performance and tune the weights of the AC neural networks (NNs). A novel adaptive controller with a special structure is designed to reduce the effect of the NN reconstruction errors, input quantization, and disturbances. Based on the Lyapunov stability theory, the boundedness of the closed-loop signals and the desired tracking performance can be guaranteed. Finally, simulations on two connected inverted pendulums are given to illustrate the effectiveness of the proposed method.

A neural net based architecture for the segmentation of mixed gray-level and binary pictures

NASA Technical Reports Server (NTRS)

Tabatabai, Ali; Troudet, Terry P.

1991-01-01

A neural-net-based architecture is proposed to perform segmentation in real time for mixed gray-level and binary pictures. In this approach, the composite picture is divided into 16 x 16 pixel blocks, which are identified as character blocks or image blocks on the basis of a dichotomy measure computed by an adaptive 16 x 16 neural net. For compression purposes, each image block is further divided into 4 x 4 subblocks; a one-bit nonparametric quantizer is used to encode 16 x 16 character and 4 x 4 image blocks; and the binary map and quantizer levels are obtained through a neural net segmentor over each block. The efficiency of the neural segmentation in terms of computational speed, data compression, and quality of the compressed picture is demonstrated. The effect of weight quantization is also discussed. VLSI implementations of such adaptive neural nets in CMOS technology are described and simulated in real time for a maximum block size of 256 pixels.

Enhancing speech recognition using improved particle swarm optimization based hidden Markov model.

PubMed

Selvaraj, Lokesh; Ganesan, Balakrishnan

2014-01-01

Enhancing speech recognition is the primary intention of this work. In this paper a novel speech recognition method based on vector quantization and improved particle swarm optimization (IPSO) is suggested. The suggested methodology contains four stages, namely, (i) denoising, (ii) feature mining (iii), vector quantization, and (iv) IPSO based hidden Markov model (HMM) technique (IP-HMM). At first, the speech signals are denoised using median filter. Next, characteristics such as peak, pitch spectrum, Mel frequency Cepstral coefficients (MFCC), mean, standard deviation, and minimum and maximum of the signal are extorted from the denoised signal. Following that, to accomplish the training process, the extracted characteristics are given to genetic algorithm based codebook generation in vector quantization. The initial populations are created by selecting random code vectors from the training set for the codebooks for the genetic algorithm process and IP-HMM helps in doing the recognition. At this point the creativeness will be done in terms of one of the genetic operation crossovers. The proposed speech recognition technique offers 97.14% accuracy.

The quantization of the chiral Schwinger model based on the BFT-BFV formalism II

NASA Astrophysics Data System (ADS)

Park, Mu-In; Park, Young-Jai; Yoon, Sean J.

1998-12-01

We apply an improved version of Batalin-Fradkin-Tyutin Hamiltonian method to the a = 1 chiral Schwinger model, which is much more nontrivial than the a>1 one. Furthermore, through the path integral quantization, we newly resolve the problem of the nontrivial 0954-3899/24/12/002/img6-function as well as that of the unwanted Fourier parameter 0954-3899/24/12/002/img7 in the measure. As a result, we explicitly obtain the fully gauge invariant partition function, which includes a new type of Wess-Zumino term irrelevant to the gauge symmetry as well as the usual WZ action.

Stripes and honeycomb lattice of quantized vortices in rotating two-component Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Kasamatsu, Kenichi; Sakashita, Kouhei

2018-05-01

We study numerically the structure of a vortex lattice in rotating two-component Bose-Einstein condensates with equal atomic masses and equal intra- and intercomponent coupling strengths. The numerical simulations of the Gross-Pitaevskii equation show that the quantized vortices in this situation form lattice configuration accompanying vortex stripes, honeycomb lattices, and their complexes. This is a result of the degeneracy of the system for the SU(2) symmetric operation, which causes a continuous transformation between the above structures. In terms of the pseudospin representation, the complex lattice structures are identified as a hexagonal lattice of doubly winding half skyrmions.

Optical memory based on quantized atomic center-of-mass motion.

PubMed

Lopez, J P; de Almeida, A J F; Felinto, D; Tabosa, J W R

2017-11-01

We report a new type of optical memory using a pure two-level system of cesium atoms cooled by the magnetically assisted Sisyphus effect. The optical information of a probe field is stored in the coherence between quantized vibrational levels of the atoms in the potential wells of a 1-D optical lattice. The retrieved pulse shows Rabi oscillations with a frequency determined by the reading beam intensity and are qualitatively understood in terms of a simple theoretical model. The exploration of the external degrees of freedom of an atom may add another capability in the design of quantum-information protocols using light.

Is the Wheeler-DeWitt equation more fundamental than the Schrödinger equation?

NASA Astrophysics Data System (ADS)

Shestakova, Tatyana P.

The Wheeler-DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature, the opinion that the Wheeler-DeWitt equation is even more fundamental than the basic equation of quantum theory, the Schrödinger equation. We still should remember that we are in the situation when no observational data can confirm or reject the fundamental status of the Wheeler-DeWitt equation, so we can give just indirect arguments in favor of or against it, grounded on mathematical consistency and physical relevance. I shall present the analysis of the situation and comparison of the standard Wheeler-DeWitt approach with the extended phase space approach to quantization of gravity. In my analysis, I suppose, first, that a future quantum theory of gravity must be applicable to all phenomena from the early universe to quantum effects in strong gravitational fields, in the latter case, the state of the observer (the choice of a reference frame) may appear to be significant. Second, I suppose that the equation for the wave function of the universe must not be postulated but derived by means of a mathematically consistent procedure, which exists in path integral quantization. When applying this procedure to any gravitating system, one should take into account features of gravity, namely, nontrivial spacetime topology and possible absence of asymptotic states. The Schrödinger equation has been derived early for cosmological models with a finite number of degrees of freedom, and just recently it has been found for the spherically symmetric model which is a simplest model with an infinite number of degrees of freedom. The structure of the Schrödinger equation and its general solution appears to be very similar in these cases. The obtained results give grounds to say that the Schrödinger equation retains its fundamental meaning in constructing quantum theory of gravity.

New adaptive color quantization method based on self-organizing maps.

PubMed

Chang, Chip-Hong; Xu, Pengfei; Xiao, Rui; Srikanthan, Thambipillai

2005-01-01

Color quantization (CQ) is an image processing task popularly used to convert true color images to palletized images for limited color display devices. To minimize the contouring artifacts introduced by the reduction of colors, a new competitive learning (CL) based scheme called the frequency sensitive self-organizing maps (FS-SOMs) is proposed to optimize the color palette design for CQ. FS-SOM harmonically blends the neighborhood adaptation of the well-known self-organizing maps (SOMs) with the neuron dependent frequency sensitive learning model, the global butterfly permutation sequence for input randomization, and the reinitialization of dead neurons to harness effective utilization of neurons. The net effect is an improvement in adaptation, a well-ordered color palette, and the alleviation of underutilization problem, which is the main cause of visually perceivable artifacts of CQ. Extensive simulations have been performed to analyze and compare the learning behavior and performance of FS-SOM against other vector quantization (VQ) algorithms. The results show that the proposed FS-SOM outperforms classical CL, Linde, Buzo, and Gray (LBG), and SOM algorithms. More importantly, FS-SOM achieves its superiority in reconstruction quality and topological ordering with a much greater robustness against variations in network parameters than the current art SOM algorithm for CQ. A most significant bit (MSB) biased encoding scheme is also introduced to reduce the number of parallel processing units. By mapping the pixel values as sign-magnitude numbers and biasing the magnitudes according to their sign bits, eight lattice points in the color space are condensed into one common point density function. Consequently, the same processing element can be used to map several color clusters and the entire FS-SOM network can be substantially scaled down without severely scarifying the quality of the displayed image. The drawback of this encoding scheme is the additional storage overhead, which can be cut down by leveraging on existing encoder in an overall lossy compression scheme.

Automatic detection of voice impairments by means of short-term cepstral parameters and neural network based detectors.

PubMed

Godino-Llorente, J I; Gómez-Vilda, P

2004-02-01

It is well known that vocal and voice diseases do not necessarily cause perceptible changes in the acoustic voice signal. Acoustic analysis is a useful tool to diagnose voice diseases being a complementary technique to other methods based on direct observation of the vocal folds by laryngoscopy. Through the present paper two neural-network based classification approaches applied to the automatic detection of voice disorders will be studied. Structures studied are multilayer perceptron and learning vector quantization fed using short-term vectors calculated accordingly to the well-known Mel Frequency Coefficient cepstral parameterization. The paper shows that these architectures allow the detection of voice disorders--including glottic cancer--under highly reliable conditions. Within this context, the Learning Vector quantization methodology demonstrated to be more reliable than the multilayer perceptron architecture yielding 96% frame accuracy under similar working conditions.

Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames

NASA Astrophysics Data System (ADS)

Wacks, Daniel; Konstantinou, Ilias; Chakraborty, Nilanjan

2018-04-01

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar-turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable.

Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames

PubMed Central

Konstantinou, Ilias; Chakraborty, Nilanjan

2018-01-01

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar--turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable. PMID:29740257

Quarks, Symmetries and Strings - a Symposium in Honor of Bunji Sakita's 60th Birthday

NASA Astrophysics Data System (ADS)

Kaku, M.; Jevicki, A.; Kikkawa, K.

1991-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Evening Banquet Speech * I. Quarks and Phenomenology * From the SU(6) Model to Uniqueness in the Standard Model * A Model for Higgs Mechanism in the Standard Model * Quark Mass Generation in QCD * Neutrino Masses in the Standard Model * Solar Neutrino Puzzle, Horizontal Symmetry of Electroweak Interactions and Fermion Mass Hierarchies * State of Chiral Symmetry Breaking at High Temperatures * Approximate |ΔI| = 1/2 Rule from a Perspective of Light-Cone Frame Physics * Positronium (and Some Other Systems) in a Strong Magnetic Field * Bosonic Technicolor and the Flavor Problem * II. Strings * Supersymmetry in String Theory * Collective Field Theory and Schwinger-Dyson Equations in Matrix Models * Non-Perturbative String Theory * The Structure of Non-Perturbative Quantum Gravity in One and Two Dimensions * Noncritical Virasoro Algebra of d < 1 Matrix Model and Quantized String Field * Chaos in Matrix Models ? * On the Non-Commutative Symmetry of Quantum Gravity in Two Dimensions * Matrix Model Formulation of String Field Theory in One Dimension * Geometry of the N = 2 String Theory * Modular Invariance form Gauge Invariance in the Non-Polynomial String Field Theory * Stringy Symmetry and Off-Shell Ward Identities * q-Virasoro Algebra and q-Strings * Self-Tuning Fields and Resonant Correlations in 2d-Gravity * III. Field Theory Methods * Linear Momentum and Angular Momentum in Quaternionic Quantum Mechanics * Some Comments on Real Clifford Algebras * On the Quantum Group p-adics Connection * Gravitational Instantons Revisited * A Generalized BBGKY Hierarchy from the Classical Path-Integral * A Quantum Generated Symmetry: Group-Level Duality in Conformal and Topological Field Theory * Gauge Symmetries in Extended Objects * Hidden BRST Symmetry and Collective Coordinates * Towards Stochastically Quantizing Topological Actions * IV. Statistical Methods * A Brief Summary of the s-Channel Theory of Superconductivity * Neural Networks and Models for the Brain * Relativistic One-Body Equations for Planar Particles with Arbitrary Spin * Chiral Property of Quarks and Hadron Spectrum in Lattice QCD * Scalar Lattice QCD * Semi-Superconductivity of a Charged Anyon Gas * Two-Fermion Theory of Strongly Correlated Electrons and Charge-Spin Separation * Statistical Mechanics and Error-Correcting Codes * Quantum Statistics

Knots in electromagnetism

NASA Astrophysics Data System (ADS)

Arrayás, M.; Bouwmeester, D.; Trueba, J. L.

2017-01-01

Maxwell equations in vacuum allow for solutions with a non-trivial topology in the electric and magnetic field line configurations at any given moment in time. One example is a space filling congruence of electric and magnetic field lines forming circles lying on the surfaces of nested tori. In this example the electric, magnetic and Poynting vector fields are orthogonal everywhere. As time evolves the electric and magnetic fields expand and deform without changing the topology and energy, while the Poynting vector structure remains unchanged while propagating with the speed of light. The topology is characterized by the concept of helicity of the field configuration. Helicity is an important fundamental concept and for massless fields it is a conserved quantity under conformal transformations. We will review several methods by which linked and knotted electromagnetic (spin-1) fields can be derived. A first method, introduced by A. Rañada, uses the formulation of the Maxwell equations in terms of differential forms combined with the Hopf map from the three-sphere S3 to the two-sphere S2. A second method is based on spinor and twistor theory developed by R. Penrose in which elementary twistor functions correspond to the family of electromagnetic torus knots. A third method uses the Bateman construction of generating null solutions from complex Euler potentials. And a fourth method uses special conformal transformations, in particular conformal inversion, to generate new linked and knotted field configurations from existing ones. This fourth method is often accompanied by shifting singularities in the field to complex space-time points. Of course the various methods must be closely related to one another although they have been developed largely independently and they suggest different directions in which to expand the study of topologically non-trivial field configurations. It will be shown how the twistor formulation allows for a direct extension to massless fields of other spin values, such as spin-2 fields satisfying the linearized Einstein vacuum equation, and how the formulation by A. Rañada can be extended to fields for which the electric and magnetic fields are not orthogonal everywhere. Underlying the various methods is the fact that electric and magnetic field lines can be described as the level curves of complex functions. Compactification of R3 naturally leads to finite energy solutions because the fields at infinity in all directions should all converge towards zero. An intriguing question that is raised by the finite energy is whether there is a connection to the quantization of the classical electromagnetic field. We will review some issues related to this question. Another interesting question is why the general formulation of topologically non-trivial solutions uses the electric and magnetic fields instead of the electromagnetic vector potentials. This leads to a discussion of the Clebsch representation of the electromagnetic field strength 2-form. Finally, a topic of great interest is the possibility of experimentally generating and investigating linked and knotted field configurations. Since the non-trivial topological field solutions exploit the special conformal symmetry of the underlying vacuum wave-equations it will only be possible to approximate the solutions in an experiment, which necessarily introduces material objects that will break the special conformal symmetry. We will review the research on plasma configurations in which the magnetic field-line configuration approximates plasma torus knots leading to the prediction of topological solitons in plasma.

Integrable generalizations of non-linear multiple three-wave interaction models

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-07-01

Integrable generalizations of multiple three-wave interaction models in terms of r-matrix formulation are investigated. The Lax representations, complete sets of first integrals in involution are constructed, the quantization leading to Gaudin's models is discussed.

BRST quantization of cosmological perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Armendariz-Picon, Cristian; Şengör, Gizem

2016-11-08

BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structuremore » of the propagators, whereas Dirac quantization, which amounts to quantization in synchronous gauge, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.« less

Deformation of second and third quantization

NASA Astrophysics Data System (ADS)

Faizal, Mir

2015-03-01

In this paper, we will deform the second and third quantized theories by deforming the canonical commutation relations in such a way that they become consistent with the generalized uncertainty principle. Thus, we will first deform the second quantized commutator and obtain a deformed version of the Wheeler-DeWitt equation. Then we will further deform the third quantized theory by deforming the third quantized canonical commutation relation. This way we will obtain a deformed version of the third quantized theory for the multiverse.

N =2 super Yang-Mills theory in projective superspace

NASA Astrophysics Data System (ADS)

Davgadorj, Ariunzul; von Unge, Rikard

2018-05-01

We find a formulation of N =2 supersymmetric Yang-Mills theory in projective superspace. In particular we find an expression for the field strength in terms of an unconstrained prepotential which is desirable when quantizing the theory. We use this to write the action in terms of the prepotential and show that it reduces to the known result in the Abelian limit.

Two-terminal charge tunneling: Disentangling Majorana zero modes from partially separated Andreev bound states in semiconductor-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Moore, Christopher; Stanescu, Tudor D.; Tewari, Sumanta

2018-04-01

We show that a pair of overlapping Majorana bound states (MBSs) forming a partially separated Andreev bound state (ps-ABS) represents a generic low-energy feature in spin-orbit-coupled semiconductor-superconductor (SM-SC) hybrid nanowire in the presence of a Zeeman field. The ps-ABS interpolates continuously between the "garden variety" ABS, which consists of two MBSs sitting on top of each other, and the topologically protected Majorana zero modes (MZMs), which are separated by a distance given by the length of the wire. The really problematic ps-ABSs consist of component MBSs separated by a distance of the order of the characteristic Majorana decay length ξ , and have nearly zero energy in a significant range of control parameters, such as the Zeeman field and chemical potential, within the topologically trivial phase. Despite being topologically trivial, such ps-ABSs can generate signatures identical to MZMs in local charge tunneling experiments. In particular, the height of the zero-bias conductance peak (ZBCP) generated by ps-ABSs has the quantized value 2 e2/h , and it can remain unchanged in an extended range of experimental parameters, such as Zeeman field and the tunnel barrier height. We illustrate the formation of such low-energy robust ps-ABSs in two experimentally relevant situations: a hybrid SM-SC system consisting of a proximitized nanowire coupled to a quantum dot and the SM-SC system in the presence of a spatially varying inhomogeneous potential. We then show that, unlike local measurements, a two-terminal experiment involving charge tunneling at both ends of the wire is capable of distinguishing between the generic ps-ABSs and the non-Abelian MZMs. While the MZMs localized at the opposite ends of the wire generate correlated differential conduction spectra, including correlations in energy splittings and critical Zeeman fields associated with the emergence of the ZBCPs, such correlations are absent if the ZBCPs are due to ps-ABSs emerging in the topologically trivial phase. Measuring such correlations is the clearest and most straightforward test of topological MZMs in SM-SC heterostructures that can be done in a currently accessible experimental setup.

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors

NASA Astrophysics Data System (ADS)

Chiu, Ching-Kai; Schnyder, Andreas P.

2014-11-01

While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superconductor), (ii) whether the mirror symmetry commutes or anticommutes with the nonspatial symmetries, and (iii) how the Fermi surfaces (nodal lines or points) transform under the mirror reflection and nonspatial symmetries. The classification is derived by examining all possible symmetry-allowed mass terms that can be added to the Bloch or Bogoliubov-de Gennes Hamiltonian in a given symmetry class and by explicitly deriving topological invariants. We discuss several examples of reflection-symmetry-protected topological semimetals and nodal superconductors, including topological crystalline semimetals with mirror Z2 numbers and topological crystalline nodal superconductors with mirror winding numbers.

Quantization of the Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Kozlowski, K.; Sklyanin, E. K.; Torrielli, A.

2017-08-01

We propose a quantization of the Kadomtsev-Petviashvili equation on a cylinder equivalent to an infinite system of nonrelativistic one-dimensional bosons with the masses m = 1, 2,.... The Hamiltonian is Galilei-invariant and includes the split and merge terms Ψ _{{m_1}}^\\dag Ψ _{{m_2}}^\\dag {Ψ _{{m_1} + {m_2}}} and Ψ _{{m_1} + {m_2}}^\\dag {Ψ _{{m_1}}}{Ψ _{{m_2}}} for all combinations of particles with masses m 1, m 2, and m 1 + m 2 for a special choice of coupling constants. We construct the Bethe eigenfunctions for the model and verify the consistency of the coordinate Bethe ansatz and hence the quantum integrability of the model up to the mass M=8 sector.

Relativistic top: An application of the BFV quantization procedure for systems with degenerate constraints

NASA Astrophysics Data System (ADS)

Nielsen, N. K.; Quaade, U. J.

1995-07-01

The physical phase space of the relativistic top, as defined by Hansson and Regge, is expressed in terms of canonical coordinates of the Poincaré group manifold. The system is described in the Hamiltonian formalism by the mass-shell condition and constraints that reduce the number of spin degrees of freedom. The constraints are second class and are modified into a set of first class constraints by adding combinations of gauge-fixing functions. The Batalin-Fradkin-Vilkovisky method is then applied to quantize the system in the path integral formalism in Hamiltonian form. It is finally shown that different gauge choices produce different equivalent forms of the constraints.

Stochastic quantization and holographic Wilsonian renormalization group of free massive fermion

NASA Astrophysics Data System (ADS)

Moon, Sung Pil

2018-06-01

We examine a suggested relation between stochastic quantization and the holographic Wilsonian renormalization group in the massive fermion case on Euclidean AdS space. The original suggestion about the general relation between the two theories is posted in arXiv:1209.2242. In the previous researches, it is already verified that scalar fields, U(1) gauge fields, and massless fermions are consistent with the relation. In this paper, we examine the relation in the massive fermion case. Contrary to the other case, in the massive fermion case, the action needs particular boundary terms to satisfy boundary conditions. We finally confirm that the proposed suggestion is also valid in the massive fermion case.

Quasinormal modes and quantization of area/entropy for noncommutative BTZ black hole

NASA Astrophysics Data System (ADS)

Huang, Lu; Chen, Juhua; Wang, Yongjiu

2018-04-01

We investigate the quasinormal modes and area/entropy spectrum for the noncommutative BTZ black hole. The exact expressions for QNM frequencies are presented by expanding the noncommutative parameter in horizon radius. We find that the noncommutativity does not affect conformal weights (hL, hR), but it influences the thermal equilibrium. The intuitive expressions of the area/entropy spectrum are calculated in terms of Bohr-Sommerfeld quantization, and our results show that the noncommutativity leads to a nonuniform area/entropy spectrum. We also find that the coupling constant ξ , which is the coupling between the scalar and the gravitational fields, shifts the QNM frequencies but not influences the structure of area/entorpy spectrum.

New fast DCT algorithms based on Loeffler's factorization

NASA Astrophysics Data System (ADS)

Hong, Yoon Mi; Kim, Il-Koo; Lee, Tammy; Cheon, Min-Su; Alshina, Elena; Han, Woo-Jin; Park, Jeong-Hoon

2012-10-01

This paper proposes a new 32-point fast discrete cosine transform (DCT) algorithm based on the Loeffler's 16-point transform. Fast integer realizations of 16-point and 32-point transforms are also provided based on the proposed transform. For the recent development of High Efficiency Video Coding (HEVC), simplified quanti-zation and de-quantization process are proposed. Three different forms of implementation with the essentially same performance, namely matrix multiplication, partial butterfly, and full factorization can be chosen accord-ing to the given platform. In terms of the number of multiplications required for the realization, our proposed full-factorization is 3~4 times faster than a partial butterfly, and about 10 times faster than direct matrix multiplication.

Disrupted topology of hippocampal connectivity is associated with short-term antidepressant response in major depressive disorder.

PubMed

Gong, Liang; Hou, Zhenghua; Wang, Zan; He, Cancan; Yin, Yingying; Yuan, Yonggui; Zhang, Haisan; Lv, Luxian; Zhang, Hongxing; Xie, Chunming; Zhang, Zhijun

2018-01-01

Graph theoretical analyses have identified disrupted functional topological organization across the brain in patients with major depressive disorder (MDD). However, the relationship between brain topology and short-term treatment responses in patients with MDD remains unknown. Sixty-eight patients with MDD and 63 cognitively normal (CN) subjects were recruited at baseline and underwent resting-state functional magnetic resonance imaging scans. Graph theory analysis was used to examine group differences in the whole-brain functional topological properties. The association between altered brain topology and the early antidepressant response was examined. Patients with MDD showed lower normalized clustering coefficients, lower small-worldness scalars and increased nodal efficiencies in the default mode network and decreased nodal efficiencies in basal ganglia and hippocampal networks. In addition, the decreased nodal efficiency in left hippocampus was negatively correlated with depressive severity at baseline and positively correlated with changes in the depressive scores after two weeks of antidepressant treatment. The patients in the present study received different medications. These findings indicated that the altered brain functional topological organization in patients with MDD is associated with the treatment response in the early phase of medication. Therefore, brain topology assessments might be considered a useful and convenient predictor of short-term antidepressant responses. Copyright © 2017 Elsevier B.V. All rights reserved.

A discrete mechanics approach to dislocation dynamics in BCC crystals

NASA Astrophysics Data System (ADS)

Ramasubramaniam, A.; Ariza, M. P.; Ortiz, M.

2007-03-01

A discrete mechanics approach to modeling the dynamics of dislocations in BCC single crystals is presented. Ideas are borrowed from discrete differential calculus and algebraic topology and suitably adapted to crystal lattices. In particular, the extension of a crystal lattice to a CW complex allows for convenient manipulation of forms and fields defined over the crystal. Dislocations are treated within the theory as energy-minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory eliminates the need for regularization of the core singularity and inherently allows for dislocation reactions and complicated topological transitions. The quantization of slip to integer multiples of the Burgers' vector leads to a large integer optimization problem. A novel approach to solving this NP-hard problem based on considerations of metastability is proposed. A numerical example that applies the method to study the emanation of dislocation loops from a point source of dilatation in a large BCC crystal is presented. The structure and energetics of BCC screw dislocation cores, as obtained via the present formulation, are also considered and shown to be in good agreement with available atomistic studies. The method thus provides a realistic avenue for mesoscale simulations of dislocation based crystal plasticity with fully atomistic resolution.

Spin-foam models and the physical scalar product

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alesci, Emanuele; Centre de Physique Theorique de Luminy, Universite de la Mediterranee, F-13288 Marseille; Noui, Karim

2008-11-15

This paper aims at clarifying the link between loop quantum gravity and spin-foam models in four dimensions. Starting from the canonical framework, we construct an operator P acting on the space of cylindrical functions Cyl({gamma}), where {gamma} is the four-simplex graph, such that its matrix elements are, up to some normalization factors, the vertex amplitude of spin-foam models. The spin-foam models we are considering are the topological model, the Barrett-Crane model, and the Engle-Pereira-Rovelli model. If one of these spin-foam models provides a covariant quantization of gravity, then the associated operator P should be the so-called ''projector'' into physical statesmore » and its matrix elements should give the physical scalar product. We discuss the possibility to extend the action of P to any cylindrical functions on the space manifold.« less

Intrinsic quantum anomalous hall effect in a two-dimensional anilato-based lattice.

PubMed

Ni, Xiaojuan; Jiang, Wei; Huang, Huaqing; Jin, Kyung-Hwan; Liu, Feng

2018-06-13

Using first-principles calculations, we predict an intrinsic quantum anomalous Hall (QAH) state in a monolayer anilato-based metal-organic framework M2(C6O4X2)3 (M = Mn and Tc, X = F, Cl, Br and I). The spin-orbit coupling of M d orbitals opens a nontrivial band gap up to 18 meV at the Dirac point. The electron counting rule is used to explain the intrinsic nature of the QAH state. The calculated nonzero Chern number, gapless edge states and quantized Hall conductance all confirm the nontrivial topological properties in the anilato-based lattice. Our findings provide an organic materials platform for the realization of the QAH effect without the need for magnetic and charge doping, which are highly desirable for the development of low-energy-consumption spintronic devices.

Coherent transmutation of electrons into fractionalized anyons.

PubMed

Barkeshli, Maissam; Berg, Erez; Kivelson, Steven

2014-11-07

Electrons have three quantized properties-charge, spin, and Fermi statistics-that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron as it enters a certain exotic state of matter known as a quantum spin liquid (QSL). In a QSL, electron spins collectively form a highly entangled quantum state that gives rise to the fractionalization of spin, charge, and statistics. We show that certain QSLs host distinct, topologically robust boundary types, some of which allow the electron to coherently enter the QSL as a fractionalized quasi-particle, leaving its spin, charge, or statistics behind. We use these ideas to propose a number of universal, conclusive experimental signatures that would establish fractionalization in QSLs. Copyright © 2014, American Association for the Advancement of Science.

Universal Faraday Rotation in HgTe Wells with Critical Thickness.

PubMed

Shuvaev, A; Dziom, V; Kvon, Z D; Mikhailov, N N; Pimenov, A

2016-09-09

The universal value of the Faraday rotation angle close to the fine structure constant (α≈1/137) is experimentally observed in thin HgTe quantum wells with a thickness on the border between trivial insulating and the topologically nontrivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the holelike carriers extracted from the analysis of the transmission data shows a theoretically predicted universal value of σ_{xy}=e^{2}/h, which is consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage, the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electronlike part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorier, Matthieu; Mubarak, Misbah; Ross, Rob

Two-tiered direct network topologies such as Dragonflies have been proposed for future post-petascale and exascale machines, since they provide a high-radix, low-diameter, fast interconnection network. Such topologies call for redesigning MPI collective communication algorithms in order to attain the best performance. Yet as increasingly more applications share a machine, it is not clear how these topology-aware algorithms will react to interference with concurrent jobs accessing the same network. In this paper, we study three topology-aware broadcast algorithms, including one designed by ourselves. We evaluate their performance through event-driven simulation for small- and large-sized broadcasts (in terms of both data sizemore » and number of processes). We study the effect of different routing mechanisms on the topology-aware collective algorithms, as well as their sensitivity to network contention with other jobs. Our results show that while topology-aware algorithms dramatically reduce link utilization, their advantage in terms of latency is more limited.« less

On the relationship between topological and geometric defects.

PubMed

Griffin, Sinéad M; Spaldin, Nicola A

2017-08-31

The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding skyrmionic lattices. Each of these systems possess a property that is 'protected' in a symmetry sense, and is defined rigorously using a branch of mathematics known as topology. In this article we review the formal definition of topological defects as they are classified in terms of homotopy theory, and discuss the precise symmetry-breaking conditions that lead to their formation. We distinguish topological defects from defects that arise from the details of the stacking or structure of the material but are not protected by symmetry, and we propose the term 'geometric defects' to describe the latter. We provide simple material examples of both topological and geometric defect types, and discuss the implications of the classification on the resulting material properties.

Full Spectrum Conversion Using Traveling Pulse Wave Quantization

DTIC Science & Technology

2017-03-01

Full Spectrum Conversion Using Traveling Pulse Wave Quantization Michael S. Kappes Mikko E. Waltari IQ-Analog Corporation San Diego, California...temporal-domain quantization technique called Traveling Pulse Wave Quantization (TPWQ). Full spectrum conversion is defined as the complete...pulse width measurements that are continuously generated hence the name “traveling” pulse wave quantization. Our TPWQ-based ADC is composed of a

Topological BF field theory description of topological insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cho, Gil Young; Moore, Joel E., E-mail: jemoore@berkeley.edu; Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

2011-06-15

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

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd₃As₂.

PubMed

Jeon, Sangjun; Zhou, Brian B; Gyenis, Andras; Feldman, Benjamin E; Kimchi, Itamar; Potter, Andrew C; Gibson, Quinn D; Cava, Robert J; Vishwanath, Ashvin; Yazdani, Ali

2014-09-01

Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

BFV-BRST quantization of two-dimensional supergravity

NASA Astrophysics Data System (ADS)

Fujiwara, T.; Igarashi, Y.; Kuriki, R.; Tabei, T.

1996-01-01

Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in the most general class of gauges. A local effective action constructed in the configuration space contains two super-Liouville actions; one is a noncovariant but local functional written only in terms of two-dimensional supergravity fields, and the other contains the super-Liouville fields canceling the super-Weyl anomaly. Auxiliary fields for the Liouville and the gravity supermultiplets are introduced to make the BRST algebra close off-shell. Inclusion of them turns out to be essentially important especially in the super-light-cone gauge fixing, where the supercurvature equations (∂3-g++=∂2-χ++=0) are obtained as a result of BRST invariance of the theory. Our approach reveals the origin of the OSp(1,2) current algebra symmetry in a transparent manner.

Physical realization of the Glauber quantum oscillator.

PubMed

Gentilini, Silvia; Braidotti, Maria Chiara; Marcucci, Giulia; DelRe, Eugenio; Conti, Claudio

2015-11-02

More than thirty years ago Glauber suggested that the link between the reversible microscopic and the irreversible macroscopic world can be formulated in physical terms through an inverted harmonic oscillator describing quantum amplifiers. Further theoretical studies have shown that the paradigm for irreversibility is indeed the reversed harmonic oscillator. As outlined by Glauber, providing experimental evidence of these idealized physical systems could open the way to a variety of fundamental studies, for example to simulate irreversible quantum dynamics and explain the arrow of time. However, supporting experimental evidence of reversed quantized oscillators is lacking. We report the direct observation of exploding n = 0 and n = 2 discrete states and Γ0 and Γ2 quantized decay rates of a reversed harmonic oscillator generated by an optical photothermal nonlinearity. Our results give experimental validation to the main prediction of irreversible quantum mechanics, that is, the existence of states with quantized decay rates. Our results also provide a novel perspective to optical shock-waves, potentially useful for applications as lasers, optical amplifiers, white-light and X-ray generation.

Vector quantization for efficient coding of upper subbands

NASA Technical Reports Server (NTRS)

Zeng, W. J.; Huang, Y. F.

1994-01-01

This paper examines the application of vector quantization (VQ) to exploit both intra-band and inter-band redundancy in subband coding. The focus here is on the exploitation of inter-band dependency. It is shown that VQ is particularly suitable and effective for coding the upper subbands. Three subband decomposition-based VQ coding schemes are proposed here to exploit the inter-band dependency by making full use of the extra flexibility of VQ approach over scalar quantization. A quadtree-based variable rate VQ (VRVQ) scheme which takes full advantage of the intra-band and inter-band redundancy is first proposed. Then, a more easily implementable alternative based on an efficient block-based edge estimation technique is employed to overcome the implementational barriers of the first scheme. Finally, a predictive VQ scheme formulated in the context of finite state VQ is proposed to further exploit the dependency among different subbands. A VRVQ scheme proposed elsewhere is extended to provide an efficient bit allocation procedure. Simulation results show that these three hybrid techniques have advantages, in terms of peak signal-to-noise ratio (PSNR) and complexity, over other existing subband-VQ approaches.

Quantizing and sampling considerations in digital phased-locked loops

NASA Technical Reports Server (NTRS)

Hurst, G. T.; Gupta, S. C.

1974-01-01

The quantizer problem is first considered. The conditions under which the uniform white sequence model for the quantizer error is valid are established independent of the sampling rate. An equivalent spectral density is defined for the quantizer error resulting in an effective SNR value. This effective SNR may be used to determine quantized performance from infinitely fine quantized results. Attention is given to sampling rate considerations. Sampling rate characteristics of the digital phase-locked loop (DPLL) structure are investigated for the infinitely fine quantized system. The predicted phase error variance equation is examined as a function of the sampling rate. Simulation results are presented and a method is described which enables the minimum required sampling rate to be determined from the predicted phase error variance equations.

Modeling and analysis of energy quantization effects on single electron inverter performance

NASA Astrophysics Data System (ADS)

Dan, Surya Shankar; Mahapatra, Santanu

2009-08-01

In this paper, for the first time, the effects of energy quantization on single electron transistor (SET) inverter performance are analyzed through analytical modeling and Monte Carlo simulations. It is shown that energy quantization mainly changes the Coulomb blockade region and drain current of SET devices and thus affects the noise margin, power dissipation, and the propagation delay of SET inverter. A new analytical model for the noise margin of SET inverter is proposed which includes the energy quantization effects. Using the noise margin as a metric, the robustness of SET inverter is studied against the effects of energy quantization. A compact expression is developed for a novel parameter quantization threshold which is introduced for the first time in this paper. Quantization threshold explicitly defines the maximum energy quantization that an SET inverter logic circuit can withstand before its noise margin falls below a specified tolerance level. It is found that SET inverter designed with CT:CG=1/3 (where CT and CG are tunnel junction and gate capacitances, respectively) offers maximum robustness against energy quantization.

Berezin-Toeplitz quantization and naturally defined star products for Kähler manifolds

NASA Astrophysics Data System (ADS)

Schlichenmaier, Martin

2018-04-01

For compact quantizable Kähler manifolds the Berezin-Toeplitz quantization schemes, both operator and deformation quantization (star product) are reviewed. The treatment includes Berezin's covariant symbols and the Berezin transform. The general compact quantizable case was done by Bordemann-Meinrenken-Schlichenmaier, Schlichenmaier, and Karabegov-Schlichenmaier. For star products on Kähler manifolds, separation of variables, or equivalently star product of (anti-) Wick type, is a crucial property. As canonically defined star products the Berezin-Toeplitz, Berezin, and the geometric quantization are treated. It turns out that all three are equivalent, but different.

Symmetries for Light-Front Quantization of Yukawa Model with Renormalization

NASA Astrophysics Data System (ADS)

Żochowski, Jan; Przeszowski, Jerzy A.

2017-12-01

In this work we discuss the Yukawa model with the extra term of self-interacting scalar field in D=1+3 dimensions. We present the method of derivation the light-front commutators and anti-commutators from the Heisenberg equations induced by the kinematical generating operator of the translation P+. Mentioned Heisenberg equations are the starting point for obtaining this algebra of the (anti-) commutators. Some discrepancies between existing and proposed method of quantization are revealed. The Lorentz and the CPT symmetry, together with some features of the quantum theory were applied to obtain the two-point Wightman function for the free fermions. Moreover, these Wightman functions were computed especially without referring to the Fock expansion. The Gaussian effective potential for the Yukawa model was found in the terms of the Wightman functions. It was regularized by the space-like point-splitting method. The coupling constants within the model were redefined. The optimum mass parameters remained regularization independent. Finally, the Gaussian effective potential was renormalized.

A visual detection model for DCT coefficient quantization

NASA Technical Reports Server (NTRS)

Ahumada, Albert J., Jr.; Watson, Andrew B.

1994-01-01

The discrete cosine transform (DCT) is widely used in image compression and is part of the JPEG and MPEG compression standards. The degree of compression and the amount of distortion in the decompressed image are controlled by the quantization of the transform coefficients. The standards do not specify how the DCT coefficients should be quantized. One approach is to set the quantization level for each coefficient so that the quantization error is near the threshold of visibility. Results from previous work are combined to form the current best detection model for DCT coefficient quantization noise. This model predicts sensitivity as a function of display parameters, enabling quantization matrices to be designed for display situations varying in luminance, veiling light, and spatial frequency related conditions (pixel size, viewing distance, and aspect ratio). It also allows arbitrary color space directions for the representation of color. A model-based method of optimizing the quantization matrix for an individual image was developed. The model described above provides visual thresholds for each DCT frequency. These thresholds are adjusted within each block for visual light adaptation and contrast masking. For given quantization matrix, the DCT quantization errors are scaled by the adjusted thresholds to yield perceptual errors. These errors are pooled nonlinearly over the image to yield total perceptual error. With this model one may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. Custom matrices for a number of images show clear improvement over image-independent matrices. Custom matrices are compatible with the JPEG standard, which requires transmission of the quantization matrix.

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

NASA Astrophysics Data System (ADS)

Göschl, Daniel

2018-03-01

We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition function is a sum over fermion loops, fermion dimers and plaquette-occupation numbers. We explore strategies to update the fermion loops coupled to the gauge degrees of freedom and check our results with conventional simulations (without topological term and at zero chemical potential), as well as with exact summation on small volumes. Some physical implications of the results are discussed.

Pbte Nanostructures for Spin Filtering and Detecting

NASA Astrophysics Data System (ADS)

Grabecki, G.

2005-08-01

An uniqueness of lead telluride PbTe relies on combination of excellent semiconducting properties, like high electron mobility and tunable carrier concentration, with paraelectric behavior leading to huge dielectric constant at low temperatures. The present article is a review of our experimental works performed on PbTe nanostructures. The main result is observation of one-dimensional quantization of the electron motion at much impure conditions than in any other system studied so far. We explain this in terms of dielectric screening of Coulomb potentials produced by charged defects. Furthermore, in an external magnetic field, the conductance quantization steps show very pronounced spin splitting, already visible at several kilogauss. This indicates that PbTe nanostructures have a potential as local spin filtering devices.

Magnetic monopole in noncommutative space-time and Wu-Yang singularity-free gauge transformations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laangvik, Miklos; Salminen, Tapio; Tureanu, Anca

2011-04-15

We investigate the validity of the Dirac quantization condition for magnetic monopoles in noncommutative space-time. We use an approach which is based on an extension of the method introduced by Wu and Yang. To study the effects of noncommutativity of space-time, we consider the gauge transformations of U{sub *}(1) gauge fields and use the corresponding deformed Maxwell's equations. Using a perturbation expansion in the noncommutativity parameter {theta}, we show that the Dirac quantization condition remains unmodified up to the first order in the expansion parameter. The result is obtained for a class of noncommutative source terms, which reduce to themore » Dirac delta function in the commutative limit.« less

Image coding using entropy-constrained residual vector quantization

NASA Technical Reports Server (NTRS)

Kossentini, Faouzi; Smith, Mark J. T.; Barnes, Christopher F.

1993-01-01

The residual vector quantization (RVQ) structure is exploited to produce a variable length codeword RVQ. Necessary conditions for the optimality of this RVQ are presented, and a new entropy-constrained RVQ (ECRVQ) design algorithm is shown to be very effective in designing RVQ codebooks over a wide range of bit rates and vector sizes. The new EC-RVQ has several important advantages. It can outperform entropy-constrained VQ (ECVQ) in terms of peak signal-to-noise ratio (PSNR), memory, and computation requirements. It can also be used to design high rate codebooks and codebooks with relatively large vector sizes. Experimental results indicate that when the new EC-RVQ is applied to image coding, very high quality is achieved at relatively low bit rates.

Video data compression using artificial neural network differential vector quantization

NASA Technical Reports Server (NTRS)

Krishnamurthy, Ashok K.; Bibyk, Steven B.; Ahalt, Stanley C.

1991-01-01

An artificial neural network vector quantizer is developed for use in data compression applications such as Digital Video. Differential Vector Quantization is used to preserve edge features, and a new adaptive algorithm, known as Frequency-Sensitive Competitive Learning, is used to develop the vector quantizer codebook. To develop real time performance, a custom Very Large Scale Integration Application Specific Integrated Circuit (VLSI ASIC) is being developed to realize the associative memory functions needed in the vector quantization algorithm. By using vector quantization, the need for Huffman coding can be eliminated, resulting in superior performance against channel bit errors than methods that use variable length codes.

Topology-function conservation in protein-protein interaction networks.

PubMed

Davis, Darren; Yaveroğlu, Ömer Nebil; Malod-Dognin, Noël; Stojmirovic, Aleksandar; Pržulj, Nataša

2015-05-15

Proteins underlay the functioning of a cell and the wiring of proteins in protein-protein interaction network (PIN) relates to their biological functions. Proteins with similar wiring in the PIN (topology around them) have been shown to have similar functions. This property has been successfully exploited for predicting protein functions. Topological similarity is also used to guide network alignment algorithms that find similarly wired proteins between PINs of different species; these similarities are used to transfer annotation across PINs, e.g. from model organisms to human. To refine these functional predictions and annotation transfers, we need to gain insight into the variability of the topology-function relationships. For example, a function may be significantly associated with specific topologies, while another function may be weakly associated with several different topologies. Also, the topology-function relationships may differ between different species. To improve our understanding of topology-function relationships and of their conservation among species, we develop a statistical framework that is built upon canonical correlation analysis. Using the graphlet degrees to represent the wiring around proteins in PINs and gene ontology (GO) annotations to describe their functions, our framework: (i) characterizes statistically significant topology-function relationships in a given species, and (ii) uncovers the functions that have conserved topology in PINs of different species, which we term topologically orthologous functions. We apply our framework to PINs of yeast and human, identifying seven biological process and two cellular component GO terms to be topologically orthologous for the two organisms. © The Author 2015. Published by Oxford University Press.

Optimal Quantization Scheme for Data-Efficient Target Tracking via UWSNs Using Quantized Measurements.

PubMed

Zhang, Senlin; Chen, Huayan; Liu, Meiqin; Zhang, Qunfei

2017-11-07

Target tracking is one of the broad applications of underwater wireless sensor networks (UWSNs). However, as a result of the temporal and spatial variability of acoustic channels, underwater acoustic communications suffer from an extremely limited bandwidth. In order to reduce network congestion, it is important to shorten the length of the data transmitted from local sensors to the fusion center by quantization. Although quantization can reduce bandwidth cost, it also brings about bad tracking performance as a result of information loss after quantization. To solve this problem, this paper proposes an optimal quantization-based target tracking scheme. It improves the tracking performance of low-bit quantized measurements by minimizing the additional covariance caused by quantization. The simulation demonstrates that our scheme performs much better than the conventional uniform quantization-based target tracking scheme and the increment of the data length affects our scheme only a little. Its tracking performance improves by only 4.4% from 2- to 3-bit, which means our scheme weakly depends on the number of data bits. Moreover, our scheme also weakly depends on the number of participate sensors, and it can work well in sparse sensor networks. In a 6 × 6 × 6 sensor network, compared with 4 × 4 × 4 sensor networks, the number of participant sensors increases by 334.92%, while the tracking accuracy using 1-bit quantized measurements improves by only 50.77%. Overall, our optimal quantization-based target tracking scheme can achieve the pursuit of data-efficiency, which fits the requirements of low-bandwidth UWSNs.

High-Resolution Faraday Rotation and Electron-Phonon Coupling in Surface States of the Bulk-Insulating Topological Insulator Cu_{0.02}Bi_{2}Se_{3}.

PubMed

Wu, Liang; Tse, Wang-Kong; Brahlek, M; Morris, C M; Aguilar, R Valdés; Koirala, N; Oh, S; Armitage, N P

2015-11-20

We have utilized time-domain magnetoterahertz spectroscopy to investigate the low-frequency optical response of the topological insulator Cu_{0.02}Bi_{2}Se_{3} and Bi_{2}Se_{3} films. With both field and frequency dependence, such experiments give sufficient information to measure the mobility and carrier density of multiple conduction channels simultaneously. We observe sharp cyclotron resonances (CRs) in both materials. The small amount of Cu incorporated into the Cu_{0.02}Bi_{2}Se_{3} induces a true bulk insulator with only a single type of conduction with a total sheet carrier density of ~4.9×10^{12}/cm^{2} and mobility as high as 4000 cm^{2}/V·s. This is consistent with conduction from two virtually identical topological surface states (TSSs) on the top and bottom of the film with a chemical potential ~145 meV above the Dirac point and in the bulk gap. The CR broadens at high fields, an effect that we attribute to an electron-phonon interaction. This assignment is supported by an extended Drude model analysis of the zero-field Drude conductance. In contrast, in normal Bi_{2}Se_{3} films, two conduction channels were observed, and we developed a self-consistent analysis method to distinguish the dominant TSSs and coexisting trivial bulk or two-dimensional electron gas states. Our high-resolution Faraday rotation spectroscopy on Cu_{0.02}Bi_{2}Se_{3} paves the way for the observation of quantized Faraday rotation under experimentally achievable conditions to push the chemical potential in the lowest Landau level.

Perceptual Optimization of DCT Color Quantization Matrices

NASA Technical Reports Server (NTRS)

Watson, Andrew B.; Statler, Irving C. (Technical Monitor)

1994-01-01

Many image compression schemes employ a block Discrete Cosine Transform (DCT) and uniform quantization. Acceptable rate/distortion performance depends upon proper design of the quantization matrix. In previous work, we showed how to use a model of the visibility of DCT basis functions to design quantization matrices for arbitrary display resolutions and color spaces. Subsequently, we showed how to optimize greyscale quantization matrices for individual images, for optimal rate/perceptual distortion performance. Here we describe extensions of this optimization algorithm to color images.

Coexistence of type-II Dirac point and weak topological phase in Pt 3 Sn

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Minsung; Wang, Cai -Zhuang; Ho, Kai -Ming

Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while topological Dirac/Weyl semimetals show “relativistic” linear band crossings. Here, we report an unusual topological state of Pt 3Sn, where the two topological features appear simultaneously. Based on first-principles calculations, we show that Pt 3Sn is a three-dimensional weak topological semimetal with topologically nontrivial band inversion between the valence and conduction bands, where the band structure also possesses type-II Dirac points at the boundary of two electron pockets. The formation of the Dirac points can be understood in terms of the representationsmore » of relevant symmetry groups and the compatibility relations. The topological surface states appear in accordance with the nontrivial bulk band topology. As a result, the unique coexistence of the two distinct topological features in Pt 3Sn enlarges the material scope in topological physics, and is potentially useful for spintronics.« less

Coexistence of type-II Dirac point and weak topological phase in Pt 3 Sn

DOE PAGES

Kim, Minsung; Wang, Cai -Zhuang; Ho, Kai -Ming

2017-11-06

Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while topological Dirac/Weyl semimetals show “relativistic” linear band crossings. Here, we report an unusual topological state of Pt 3Sn, where the two topological features appear simultaneously. Based on first-principles calculations, we show that Pt 3Sn is a three-dimensional weak topological semimetal with topologically nontrivial band inversion between the valence and conduction bands, where the band structure also possesses type-II Dirac points at the boundary of two electron pockets. The formation of the Dirac points can be understood in terms of the representationsmore » of relevant symmetry groups and the compatibility relations. The topological surface states appear in accordance with the nontrivial bulk band topology. As a result, the unique coexistence of the two distinct topological features in Pt 3Sn enlarges the material scope in topological physics, and is potentially useful for spintronics.« less

Crystallized and amorphous vortices in rotating atomic-molecular Bose-Einstein condensates

PubMed Central

Liu, Chao-Fei; Fan, Heng; Gou, Shih-Chuan; Liu, Wu-Ming

2014-01-01

Vortex is a topological defect with a quantized winding number of the phase in superfluids and superconductors. Here, we investigate the crystallized (triangular, square, honeycomb) and amorphous vortices in rotating atomic-molecular Bose-Einstein condensates (BECs) by using the damped projected Gross-Pitaevskii equation. The amorphous vortices are the result of the considerable deviation induced by the interaction of atomic-molecular vortices. By changing the atom-molecule interaction from attractive to repulsive, the configuration of vortices can change from an overlapped atomic-molecular vortices to carbon-dioxide-type ones, then to atomic vortices with interstitial molecular vortices, and finally into independent separated ones. The Raman detuning can tune the ratio of the atomic vortex to the molecular vortex. We provide a phase diagram of vortices in rotating atomic-molecular BECs as a function of Raman detuning and the strength of atom-molecule interaction. PMID:24573303

Loop quantum corrected Einstein Yang-Mills black holes

NASA Astrophysics Data System (ADS)

Protter, Mason; DeBenedictis, Andrew

2018-05-01

In this paper, we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian, along with the restriction to homogeneity, allows for an anomaly-free effective quantization. In particular, we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fields in the quantum corrected interior, which possesses topology R ×S2 . Beyond the bounce, the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever-expanding R sector even though the two-sphere volume is asymptotically constant. The results are similar with and without Wilson loop corrections on the Yang-Mills potential.

Three-body unitarity in the finite volume

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mai, M.; Döring, M.

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

Universal Faraday Rotation in HgTe Wells with Critical Thickness

NASA Astrophysics Data System (ADS)

Shuvaev, A.; Dziom, V.; Kvon, Z. D.; Mikhailov, N. N.; Pimenov, A.

2016-09-01

The universal value of the Faraday rotation angle close to the fine structure constant (α ≈1 /137 ) is experimentally observed in thin HgTe quantum wells with a thickness on the border between trivial insulating and the topologically nontrivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the holelike carriers extracted from the analysis of the transmission data shows a theoretically predicted universal value of σx y=e2/h , which is consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage, the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electronlike part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model.

Three-body unitarity in the finite volume

DOE PAGES

Mai, M.; Döring, M.

2017-12-18

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

A visual detection model for DCT coefficient quantization

NASA Technical Reports Server (NTRS)

Ahumada, Albert J., Jr.; Peterson, Heidi A.

1993-01-01

The discrete cosine transform (DCT) is widely used in image compression, and is part of the JPEG and MPEG compression standards. The degree of compression, and the amount of distortion in the decompressed image are determined by the quantization of the transform coefficients. The standards do not specify how the DCT coefficients should be quantized. Our approach is to set the quantization level for each coefficient so that the quantization error is at the threshold of visibility. Here we combine results from our previous work to form our current best detection model for DCT coefficient quantization noise. This model predicts sensitivity as a function of display parameters, enabling quantization matrices to be designed for display situations varying in luminance, veiling light, and spatial frequency related conditions (pixel size, viewing distance, and aspect ratio). It also allows arbitrary color space directions for the representation of color.

Simultaneous Conduction and Valence Band Quantization in Ultrashallow High-Density Doping Profiles in Semiconductors

NASA Astrophysics Data System (ADS)

Mazzola, F.; Wells, J. W.; Pakpour-Tabrizi, A. C.; Jackman, R. B.; Thiagarajan, B.; Hofmann, Ph.; Miwa, J. A.

2018-01-01

We demonstrate simultaneous quantization of conduction band (CB) and valence band (VB) states in silicon using ultrashallow, high-density, phosphorus doping profiles (so-called Si:P δ layers). We show that, in addition to the well-known quantization of CB states within the dopant plane, the confinement of VB-derived states between the subsurface P dopant layer and the Si surface gives rise to a simultaneous quantization of VB states in this narrow region. We also show that the VB quantization can be explained using a simple particle-in-a-box model, and that the number and energy separation of the quantized VB states depend on the depth of the P dopant layer beneath the Si surface. Since the quantized CB states do not show a strong dependence on the dopant depth (but rather on the dopant density), it is straightforward to exhibit control over the properties of the quantized CB and VB states independently of each other by choosing the dopant density and depth accordingly, thus offering new possibilities for engineering quantum matter.

The architecture of dynamic reservoir in the echo state network

NASA Astrophysics Data System (ADS)

Cui, Hongyan; Liu, Xiang; Li, Lixiang

2012-09-01

Echo state network (ESN) has recently attracted increasing interests because of its superior capability in modeling nonlinear dynamic systems. In the conventional echo state network model, its dynamic reservoir (DR) has a random and sparse topology, which is far from the real biological neural networks from both structural and functional perspectives. We hereby propose three novel types of echo state networks with new dynamic reservoir topologies based on complex network theory, i.e., with a small-world topology, a scale-free topology, and a mixture of small-world and scale-free topologies, respectively. We then analyze the relationship between the dynamic reservoir structure and its prediction capability. We utilize two commonly used time series to evaluate the prediction performance of the three proposed echo state networks and compare them to the conventional model. We also use independent and identically distributed time series to analyze the short-term memory and prediction precision of these echo state networks. Furthermore, we study the ratio of scale-free topology and the small-world topology in the mixed-topology network, and examine its influence on the performance of the echo state networks. Our simulation results show that the proposed echo state network models have better prediction capabilities, a wider spectral radius, but retain almost the same short-term memory capacity as compared to the conventional echo state network model. We also find that the smaller the ratio of the scale-free topology over the small-world topology, the better the memory capacities.

Hg-Based Epitaxial Materials for Topological Insulators

DTIC Science & Technology

2014-07-01

Research Laboratory for investigation of properties. 15. SUBJECT TERMS EOARD, topological insulator , diluted magnetic ...topological superconductors and spintronics to quantum computation (e.g. see C.L.Kane and J.E.Moore "Topological Insulators " Physics World (2011) 24...tetradymite semiconductors Bi2Te3, Bi2Se3, and Sb2Te3 which form magnetically ordered insulators when doped with transition metal elements Cr or Fe (Rui Yu et

Topology versus Anderson localization: Nonperturbative solutions in one dimension

NASA Astrophysics Data System (ADS)

Altland, Alexander; Bagrets, Dmitry; Kamenev, Alex

2015-02-01

We present an analytic theory of quantum criticality in quasi-one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters (g ,χ ) representing localization and topological properties, respectively. Certain critical values of χ (half-integer for Z classes, or zero for Z2 classes) define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two-parameter flow of the integer quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given in terms of the transfer-matrix solution of corresponding supersymmetric nonlinear sigma models. In Z2 classes we uncover a hidden supersymmetry, present at the quantum critical point.

An adaptive vector quantization scheme

NASA Technical Reports Server (NTRS)

Cheung, K.-M.

1990-01-01

Vector quantization is known to be an effective compression scheme to achieve a low bit rate so as to minimize communication channel bandwidth and also to reduce digital memory storage while maintaining the necessary fidelity of the data. However, the large number of computations required in vector quantizers has been a handicap in using vector quantization for low-rate source coding. An adaptive vector quantization algorithm is introduced that is inherently suitable for simple hardware implementation because it has a simple architecture. It allows fast encoding and decoding because it requires only addition and subtraction operations.

Multipurpose image watermarking algorithm based on multistage vector quantization.

PubMed

Lu, Zhe-Ming; Xu, Dian-Guo; Sun, Sheng-He

2005-06-01

The rapid growth of digital multimedia and Internet technologies has made copyright protection, copy protection, and integrity verification three important issues in the digital world. To solve these problems, the digital watermarking technique has been presented and widely researched. Traditional watermarking algorithms are mostly based on discrete transform domains, such as the discrete cosine transform, discrete Fourier transform (DFT), and discrete wavelet transform (DWT). Most of these algorithms are good for only one purpose. Recently, some multipurpose digital watermarking methods have been presented, which can achieve the goal of content authentication and copyright protection simultaneously. However, they are based on DWT or DFT. Lately, several robust watermarking schemes based on vector quantization (VQ) have been presented, but they can only be used for copyright protection. In this paper, we present a novel multipurpose digital image watermarking method based on the multistage vector quantizer structure, which can be applied to image authentication and copyright protection. In the proposed method, the semi-fragile watermark and the robust watermark are embedded in different VQ stages using different techniques, and both of them can be extracted without the original image. Simulation results demonstrate the effectiveness of our algorithm in terms of robustness and fragility.

BFV-BRST quantization of two-dimensional supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujiwara, T.; Igarashi, Y.; Kuriki, R.

1996-01-01

Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in the most general class of gauges. A local effective action constructed in the configuration space contains two super-Liouville actions; one is a noncovariant but local functional written only in terms of two-dimensional supergravity fields, and the other contains the super-Liouville fields canceling the super-Weyl anomaly. Auxiliary fields for the Liouville and the gravity supermultiplets aremore » introduced to make the BRST algebra close off-shell. Inclusion of them turns out to be essentially important especially in the super-light-cone gauge fixing, where the supercurvature equations ({partial_derivative}{sup 3}{sub {minus}}{ital g}{sub +}{sub +}={partial_derivative}{sup 2}{sub {minus}}{chi}{sub +}{sub +}=0) are obtained as a result of BRST invariance of the theory. Our approach reveals the origin of the OSp(1,2) current algebra symmetry in a transparent manner. {copyright} {ital 1996 The American Physical Society.}« less

Radiation and matter: Electrodynamics postulates and Lorenz gauge

NASA Astrophysics Data System (ADS)

Bobrov, V. B.; Trigger, S. A.; van Heijst, G. J.; Schram, P. P.

2016-11-01

In general terms, we have considered matter as the system of charged particles and quantized electromagnetic field. For consistent description of the thermodynamic properties of matter, especially in an extreme state, the problem of quantization of the longitudinal and scalar potentials should be solved. In this connection, we pay attention that the traditional postulates of electrodynamics, which claim that only electric and magnetic fields are observable, is resolved by denial of the statement about validity of the Maxwell equations for microscopic fields. The Maxwell equations, as the generalization of experimental data, are valid only for averaged values. We show that microscopic electrodynamics may be based on postulation of the d'Alembert equations for four-vector of the electromagnetic field potential. The Lorenz gauge is valid for the averages potentials (and provides the implementation of the Maxwell equations for averages). The suggested concept overcomes difficulties under the electromagnetic field quantization procedure being in accordance with the results of quantum electrodynamics. As a result, longitudinal and scalar photons become real rather than virtual and may be observed in principle. The longitudinal and scalar photons provide not only the Coulomb interaction of charged particles, but also allow the electrical Aharonov-Bohm effect.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ovchinnikov, Igor V.

Here, a scenario is proposed, according to which a generic self-organized critical (SOC) system can be looked upon as a Witten-type topological field theory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST) symmetry. One of the conditions for the SOC is the slow driving noise, which unambiguously suggests Stratonovich interpretation of the corresponding stochastic differential equation (SDE). This, in turn, necessitates the use of Parisi-Sourlas-Wu stochastic quantization procedure, which straightforwardly leads to a model with BRST-exact action, i.e., to a W-TFT. In the parameter space of the SDE, there must exist full-dimensional regions where the BRST symmetry is spontaneously broken by instantons,more » which in the context of SOC are essentially avalanches. In these regions, the avalanche-type SOC dynamics is liberated from overwise a rightful dynamics-less W-TFT, and a Goldstone mode of Fadeev-Popov ghosts exists. Goldstinos represent moduli of instantons (avalanches) and being gapless are responsible for the critical avalanche distribution in the low-energy, long-wavelength limit. The above arguments are robust against moderate variations of the SDE's parameters and the criticality is 'self-tuned'. The proposition of this paper suggests that the machinery of W-TFTs may find its applications in many different areas of modern science studying various physical realizations of SOC. It also suggests that there may in principle exist a connection between some SOC's and the concept of topological quantum computing.« less

Thermoelectric Transport Signatures of Dirac Composite Fermions in the Half-Filled Landau Level

NASA Astrophysics Data System (ADS)

Potter, Andrew C.; Serbyn, Maksym; Vishwanath, Ashvin

2016-07-01

The half-filled Landau level is expected to be approximately particle-hole symmetric, which requires an extension of the Halperin-Lee-Read (HLR) theory of the compressible state observed at this filling. Recent work indicates that, when particle-hole symmetry is preserved, the composite fermions experience a quantized π -Berry phase upon winding around the composite Fermi surface, analogous to Dirac fermions at the surface of a 3D topological insulator. In contrast, the effective low-energy theory of the composite fermion liquid originally proposed by HLR lacks particle-hole symmetry and has vanishing Berry phase. In this paper, we explain how thermoelectric transport measurements can be used to test the Dirac nature of the composite fermions by quantitatively extracting this Berry phase. First, we point out that longitudinal thermopower (Seebeck effect) is nonvanishing because of the unusual nature of particle-hole symmetry in this context and is not sensitive to the Berry phase. In contrast, we find that off-diagonal thermopower (Nernst effect) is directly related to the topological structure of the composite Fermi surface, vanishing for zero Berry phase and taking its maximal value for π Berry phase. In contrast, in purely electrical transport signatures, the Berry phase contributions appear as small corrections to a large background signal, making the Nernst effect a promising diagnostic of the Dirac nature of composite fermions.

Three-body spectrum in a finite volume: The role of cubic symmetry

DOE PAGES

Doring, M.; Hammer, H. -W.; Mai, M.; ...

2018-06-15

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge

NASA Astrophysics Data System (ADS)

Lee, Taejin

2018-01-01

We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field theory. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be promoted to the second quantized closed string theory. We explicitly calculate the scattering amplitudes of three gravitons by using the closed string field theory in the proper-time gauge.

Three-body spectrum in a finite volume: The role of cubic symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doring, M.; Hammer, H. -W.; Mai, M.

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

The Quantized Geometry of Visual Space: The Coherent Computation of Depth, Form, and Lightness. Revised Version.

DTIC Science & Technology

1982-08-01

of sensitivity with background luminance, and the finitE capacity of visual short term memory are discussed in terms of a small set of ...binocular rivalry, reflectance rivalry, Fechner’s paradox, decrease of threshold contrast with increased number of cycles in a grating pattern, hysteresis...adaptation level tuning, Weber law modulation, shift of sensitivity with background luminance, and the finite capacity of visual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Serwer, Philip, E-mail: serwer@uthscsa.edu; Wright, Elena T.; Liu, Zheng

DNA packaging of phages phi29, T3 and T7 sometimes produces incompletely packaged DNA with quantized lengths, based on gel electrophoretic band formation. We discover here a packaging ATPase-free, in vitro model for packaged DNA length quantization. We use directed evolution to isolate a five-site T3 point mutant that hyper-produces tail-free capsids with mature DNA (heads). Three tail gene mutations, but no head gene mutations, are present. A variable-length DNA segment leaks from some mutant heads, based on DNase I-protection assay and electron microscopy. The protected DNA segment has quantized lengths, based on restriction endonuclease analysis: six sharp bands of DNAmore » missing 3.7–12.3% of the last end packaged. Native gel electrophoresis confirms quantized DNA expulsion and, after removal of external DNA, provides evidence that capsid radius is the quantization-ruler. Capsid-based DNA length quantization possibly evolved via selection for stalling that provides time for feedback control during DNA packaging and injection. - Graphical abstract: Highlights: • We implement directed evolution- and DNA-sequencing-based phage assembly genetics. • We purify stable, mutant phage heads with a partially leaked mature DNA molecule. • Native gels and DNase-protection show leaked DNA segments to have quantized lengths. • Native gels after DNase I-removal of leaked DNA reveal the capsids to vary in radius. • Thus, we hypothesize leaked DNA quantization via variably quantized capsid radius.« less

Dimensional quantization effects in the thermodynamics of conductive filaments

NASA Astrophysics Data System (ADS)

Niraula, D.; Grice, C. R.; Karpov, V. G.

2018-06-01

We consider the physical effects of dimensional quantization in conductive filaments that underlie operations of some modern electronic devices. We show that, as a result of quantization, a sufficiently thin filament acquires a positive charge. Several applications of this finding include the host material polarization, the stability of filament constrictions, the equilibrium filament radius, polarity in device switching, and quantization of conductance.

Nearly associative deformation quantization

NASA Astrophysics Data System (ADS)

Vassilevich, Dmitri; Oliveira, Fernando Martins Costa

2018-04-01

We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation quantization algebras require the Jacobi identities on the Poisson bracket and, under very general assumptions, are associative. At the same time, flexible deformation quantization algebras exist for any Poisson bracket.

Dimensional quantization effects in the thermodynamics of conductive filaments.

PubMed

Niraula, D; Grice, C R; Karpov, V G

2018-06-29

We consider the physical effects of dimensional quantization in conductive filaments that underlie operations of some modern electronic devices. We show that, as a result of quantization, a sufficiently thin filament acquires a positive charge. Several applications of this finding include the host material polarization, the stability of filament constrictions, the equilibrium filament radius, polarity in device switching, and quantization of conductance.

Nonperturbative quantization of the electroweak model's electrodynamic sector

NASA Astrophysics Data System (ADS)

Fry, M. P.

2015-04-01

Consider the Euclidean functional integral representation of any physical process in the electroweak model. Integrating out the fermion degrees of freedom introduces 24 fermion determinants. These multiply the Gaussian functional measures of the Maxwell, Z , W , and Higgs fields to give an effective functional measure. Suppose the functional integral over the Maxwell field is attempted first. This paper is concerned with the large amplitude behavior of the Maxwell effective measure. It is assumed that the large amplitude variation of this measure is insensitive to the presence of the Z , W , and H fields; they are assumed to be a subdominant perturbation of the large amplitude Maxwell sector. Accordingly, we need only examine the large amplitude variation of a single QED fermion determinant. To facilitate this the Schwinger proper time representation of this determinant is decomposed into a sum of three terms. The advantage of this is that the separate terms can be nonperturbatively estimated for a measurable class of large amplitude random fields in four dimensions. It is found that the QED fermion determinant grows faster than exp [c e2∫d4x Fμν 2] , c >0 , in the absence of zero mode supporting random background potentials. This raises doubt on whether the QED fermion determinant is integrable with any Gaussian measure whose support does not include zero mode supporting potentials. Including zero mode supporting background potentials can result in a decaying exponential growth of the fermion determinant. This is prima facie evidence that Maxwellian zero modes are necessary for the nonperturbative quantization of QED and, by implication, for the nonperturbative quantization of the electroweak model.

Poisson traces, D-modules, and symplectic resolutions

NASA Astrophysics Data System (ADS)

Etingof, Pavel; Schedler, Travis

2018-03-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Poisson traces, D-modules, and symplectic resolutions.

PubMed

Etingof, Pavel; Schedler, Travis

2018-01-01

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein-Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require.

Black holes in quasi-topological gravity and conformal couplings

NASA Astrophysics Data System (ADS)

Chernicoff, Mariano; Fierro, Octavio; Giribet, Gaston; Oliva, Julio

2017-02-01

Lovelock theory of gravity provides a tractable model to investigate the effects of higher-curvature terms in the context of AdS/CFT. Yielding second order, ghost-free field equations, this theory represents a minimal setup in which higher-order gravitational couplings in asymptotically Anti-de Sitter (AdS) spaces, including black holes, can be solved analytically. This however has an obvious limitation as in dimensions lower than seven, the contribution from cubic or higher curvature terms is merely topological. Therefore, in order to go beyond quadratic order and study higher terms in AdS5 analytically, one is compelled to look for other toy models. One such model is the so-called quasi-topological gravity, which, despite being a higher-derivative theory, provides a tractable setup with R 3 and R 4 terms. In this paper, we investigate AdS5 black holes in quasi-topological gravity. We consider the theory conformally coupled to matter and in presence of Abelian gauge fields. We show that charged black holes in AdS5 which, in addition, exhibit a backreaction of the matter fields on the geometry can be found explicitly in this theory. These solutions generalize the black hole solution of quasi-topological gravity and exist in a region of the parameter spaces consistent with the constraints coming from causality and other consistency conditions. They have finite conserved charges and exhibit non-trivial thermodynamical properties.

A New Cross-By-Pass-Torus Architecture Based on CBP-Mesh and Torus Interconnection for On-Chip Communication.

PubMed

Gulzari, Usman Ali; Sajid, Muhammad; Anjum, Sheraz; Agha, Shahrukh; Torres, Frank Sill

2016-01-01

A Mesh topology is one of the most promising architecture due to its regular and simple structure for on-chip communication. Performance of mesh topology degraded greatly by increasing the network size due to small bisection width and large network diameter. In order to overcome this limitation, many researchers presented modified Mesh design by adding some extra links to improve its performance in terms of network latency and power consumption. The Cross-By-Pass-Mesh was presented by us as an improved version of Mesh topology by intelligent addition of extra links. This paper presents an efficient topology named Cross-By-Pass-Torus for further increase in the performance of the Cross-By-Pass-Mesh topology. The proposed design merges the best features of the Cross-By-Pass-Mesh and Torus, to reduce the network diameter, minimize the average number of hops between nodes, increase the bisection width and to enhance the overall performance of the network. In this paper, the architectural design of the topology is presented and analyzed against similar kind of 2D topologies in terms of average latency, throughput and power consumption. In order to certify the actual behavior of proposed topology, the synthetic traffic trace and five different real embedded application workloads are applied to the proposed as well as other competitor network topologies. The simulation results indicate that Cross-By-Pass-Torus is an efficient candidate among its predecessor's and competitor topologies due to its less average latency and increased throughput at a slight cost in network power and energy for on-chip communication.

The topological Anderson insulator phase in the Kane-Mele model

NASA Astrophysics Data System (ADS)

Orth, Christoph P.; Sekera, Tibor; Bruder, Christoph; Schmidt, Thomas L.

2016-04-01

It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.

The Topological Panorama Camera: A New Tool for Teaching Concepts Related to Space and Time.

ERIC Educational Resources Information Center

Gelphman, Janet L.; And Others

1992-01-01

Included are the description, operating characteristics, uses, and future plans for the Topological Panorama Camera, which is an experimental, robotic photographic device capable of producing visual renderings of the mathematical characteristics of an equation in terms of position changes of an object or in terms of the shape of the space…

On the Dequantization of Fedosov's Deformation Quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2003-08-01

To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of the cotangent bundle to M to the formal neighborhood of the diagonal of the product M x M~, where M~ is a copy of M with the opposite Poisson structure. We call it dequantization of the natural deformation quantization. Then we "dequantize" Fedosov's quantization.

Topological insulating phases from two-dimensional nodal loop semimetals

NASA Astrophysics Data System (ADS)

Li, Linhu; Araújo, Miguel A. N.

2016-10-01

Starting from a minimal model for a two-dimensional nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase-winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases, and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak- and strong-field regimes, as well as the edge states in a ribbon geometry.

Quantum gravity from noncommutative spacetime

NASA Astrophysics Data System (ADS)

Lee, Jungjai; Yang, Hyun Seok

2014-12-01

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative ★-algebra) of quantum gravity.

Effective Lagrangians and Current Algebra in Three Dimensions

NASA Astrophysics Data System (ADS)

Ferretti, Gabriele

In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.

Effects of Structural and Electronic Disorder in Topological Insulator Sb2Te3 Thin Films

NASA Astrophysics Data System (ADS)

Korzhovska, Inna

Topological quantum matter is a unique and potentially transformative protectorate against disorder-induced backscattering. The ultimate disorder limits to the topological state, however, are still not known - understanding these limits is critical to potential applications in the fields of spintronics and information processing. In topological insulators spin-orbit interaction and time-reversal-symmetry invariance guarantees - at least up to a certain disorder strength - that charge transport through 2D gapless Dirac surface states is robust against backscattering by non-magnetic disorder. Strong disorder may destroy topological protection and gap out Dirac surface states, although recent theories predict that under severe electronic disorder a quantized topological conductance might yet reemerge. Very strong electronic disorder, however, is not trivial to install and quantify, and topological matter under such conditions thus far has not been experimentally tested. This thesis addresses the behavior of three-dimensional (3D) topological insulator (TI) films in a wide range of structural and electronic disorder. We establish strong positional disorder in thin (20-50 nm) Sb2Te 3 films, free of extrinsic magnetic dopants. Sb 2Te3 is a known 2nd generation topological insulator in the low-disorder crystalline state. It is also a known phase-change material that undergoes insulator-to-metal transition with the concurrent orders of magnitude resistive drop, where a huge range of disorder could be controllably explored. In this work we show that even in the absence of magnetic dopants, disorder may induce spin correlations detrimental to the topological state. Chapter 1 contains a brief introduction to the topological matter and describes the role played by disorder. This is followed by theory considerations and a survey of prior experimental work. Next we describe the motivation for our experiments and explain the choice of the material. Chapter 2 describes deposition techniques used for material growth, including the parameters significance and effects on the material properties. Chapter 3 describes structural and electrical characterization techniques employed in the work. In Chapter 4-5 we discuss the experimental results. Sb2Te 3 films at extreme disorder, where spin correlations dominate the transport of charge, are discussed in Chapter 4. We employ transport measurements as our main tool to explore disorder-induced changes in the Sb2Te 3. In addition we directly detect disorder-induced spin response in thin Sb2Te3 films free of extrinsic magnetic dopants; it onsets at a surprisingly high temperature ( 200 K) and vanishes when disorder is reduced. Localized spins control the hopping (tunneling) transport through spin memory induced by the non-equilibrium charge currents. The observed spin-memory phenomenon emerges as negative magnetoresistance distinct from orbital quantum interference effects. The hopping mechanism and spin correlations dominate transport over an extensive disorder range. Spin correlations are eventually suppressed by the restoration of positional order in the (bulk) crystalline state, implying a disorder threshold to the topological state. As disorder is reduced the material undergoes structural and electronic transitions, which are discussed in Chapter 5. We obtain a number of characteristic attributes that change sharply at the structural and electronic transitions: localization length, dimensionality, and the nature of conductance. Structural transition is clearly seen in the changes in lattice vibrations tracked by Raman spectroscopy, which we use here as a metric of disorder. The significance of the disorder-induced localization transition is discussed. Next we investigate the effects of structural and electronic disorder on the bulk and surfaces in the crystalline state of Sb2Te3. The nontrivial topology of this strongly spin-orbit coupled material comes from the band inversion in the bulk. One of the key transport signatures of topological surfaces is weak antilocalization (WAL) correction to conductivity; it is associated with the topological pi Berry phase and should display a two-dimensional (2D) character. In our work, we establish the disorder level at which 2D WAL appears. The conduction at this threshold is one conduction quantum G0; it corresponds to the topological quantum channel. Finally, we summarize our key findings and discuss open questions and next steps toward the understanding of disorder-induced correlations in the spin and charge channels that can alter the emergent behaviors of the topological states.

(Dis)Orientation and Spatial Sense: Topological Thinking in the Middle Grades

ERIC Educational Resources Information Center

de Freitas, Elizabeth; McCarthy, MaryJean

2014-01-01

In this paper, we focus on topological approaches to space and we argue that experiences with topology allow middle school students to develop a more robust understanding of orientation and dimension. We frame our argument in terms of the phenomenological literature on perception and corporeal space. We discuss findings from a quasi-experimental…

Quantum Computing and Second Quantization

DOE PAGES

Makaruk, Hanna Ewa

2017-02-10

Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

Quantum Computing and Second Quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makaruk, Hanna Ewa

Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

BSIFT: toward data-independent codebook for large scale image search.

PubMed

Zhou, Wengang; Li, Houqiang; Hong, Richang; Lu, Yijuan; Tian, Qi

2015-03-01

Bag-of-Words (BoWs) model based on Scale Invariant Feature Transform (SIFT) has been widely used in large-scale image retrieval applications. Feature quantization by vector quantization plays a crucial role in BoW model, which generates visual words from the high- dimensional SIFT features, so as to adapt to the inverted file structure for the scalable retrieval. Traditional feature quantization approaches suffer several issues, such as necessity of visual codebook training, limited reliability, and update inefficiency. To avoid the above problems, in this paper, a novel feature quantization scheme is proposed to efficiently quantize each SIFT descriptor to a descriptive and discriminative bit-vector, which is called binary SIFT (BSIFT). Our quantizer is independent of image collections. In addition, by taking the first 32 bits out from BSIFT as code word, the generated BSIFT naturally lends itself to adapt to the classic inverted file structure for image indexing. Moreover, the quantization error is reduced by feature filtering, code word expansion, and query sensitive mask shielding. Without any explicit codebook for quantization, our approach can be readily applied in image search in some resource-limited scenarios. We evaluate the proposed algorithm for large scale image search on two public image data sets. Experimental results demonstrate the index efficiency and retrieval accuracy of our approach.

Density-Dependent Quantized Least Squares Support Vector Machine for Large Data Sets.

PubMed

Nan, Shengyu; Sun, Lei; Chen, Badong; Lin, Zhiping; Toh, Kar-Ann

2017-01-01

Based on the knowledge that input data distribution is important for learning, a data density-dependent quantization scheme (DQS) is proposed for sparse input data representation. The usefulness of the representation scheme is demonstrated by using it as a data preprocessing unit attached to the well-known least squares support vector machine (LS-SVM) for application on big data sets. Essentially, the proposed DQS adopts a single shrinkage threshold to obtain a simple quantization scheme, which adapts its outputs to input data density. With this quantization scheme, a large data set is quantized to a small subset where considerable sample size reduction is generally obtained. In particular, the sample size reduction can save significant computational cost when using the quantized subset for feature approximation via the Nyström method. Based on the quantized subset, the approximated features are incorporated into LS-SVM to develop a data density-dependent quantized LS-SVM (DQLS-SVM), where an analytic solution is obtained in the primal solution space. The developed DQLS-SVM is evaluated on synthetic and benchmark data with particular emphasis on large data sets. Extensive experimental results show that the learning machine incorporating DQS attains not only high computational efficiency but also good generalization performance.

Image-adapted visually weighted quantization matrices for digital image compression

NASA Technical Reports Server (NTRS)

Watson, Andrew B. (Inventor)

1994-01-01

A method for performing image compression that eliminates redundant and invisible image components is presented. The image compression uses a Discrete Cosine Transform (DCT) and each DCT coefficient yielded by the transform is quantized by an entry in a quantization matrix which determines the perceived image quality and the bit rate of the image being compressed. The present invention adapts or customizes the quantization matrix to the image being compressed. The quantization matrix comprises visual masking by luminance and contrast techniques and by an error pooling technique all resulting in a minimum perceptual error for any given bit rate, or minimum bit rate for a given perceptual error.

Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes

NASA Astrophysics Data System (ADS)

Saini, Sahil; Singh, Parampreet

2018-03-01

We study the generic resolution of strong singularities in loop quantized effective Bianchi-IX spacetime in two different quantizations—the connection operator based ‘A’ quantization and the extrinsic curvature based ‘K’ quantization. We show that in the effective spacetime description with arbitrary matter content, it is necessary to include inverse triad corrections to resolve all the strong singularities in the ‘A’ quantization. Whereas in the ‘K’ quantization these results can be obtained without including inverse triad corrections. Under these conditions, the energy density, expansion and shear scalars for both of the quantization prescriptions are bounded. Notably, both the quantizations can result in potentially curvature divergent events if matter content allows divergences in the partial derivatives of the energy density with respect to the triad variables at a finite energy density. Such events are found to be weak curvature singularities beyond which geodesics can be extended in the effective spacetime. Our results show that all potential strong curvature singularities of the classical theory are forbidden in Bianchi-IX spacetime in loop quantum cosmology and geodesic evolution never breaks down for such events.

Color confinement from fluctuating topology

DOE PAGES

Kharzeev, Dmitri E.

2016-10-19

QCD possesses a compact gauge group, and this implies a non-trivial topological structure of the vacuum. In this contribution to the Gribov-85 Memorial volume, we first discuss the origin of Gribov copies and their interpretation in terms of fluctuating topology in the QCD vacuum. We then describe the recent work with E. Levin that links the confinement of gluons and color screening to the fluctuating topology, and discuss implications for spin physics, high energy scattering, and the physics of quark-gluon plasma.

Pseudo-Kähler Quantization on Flag Manifolds

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kähler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant symbols.

Dynamical Properties of a Living Nematic

NASA Astrophysics Data System (ADS)

Genkin, Mikhail

The systems, which are made of a large number or interacting particles, or agents that convert the energy stored in the environment into mechanical motion, are called active systems, or active matter. The examples of active matter include both living and synthetic systems. The size of agents varies significantly: bird flocks and fish schools represent macroscopic active systems, while suspensions of living organisms or artificial colloidal particles are examples of microscopic ones. In this work, I studied one of the simplest realization of active matter termed living (or active) nematics, that can be conceived by mixing swimming bacteria and nematic liquid crystal. Using modeling, numerical simulations and experiments I studied various dynamical properties of active nematics. This work hints into new methods of control and manipulation of active matter. Active nematic exhibits complex spatiotemporal behavior manifested by formation, proliferation, and annihilation of topological defects. A new computational 2D model coupling nematic liquid crystal and swimming bacteria dynamics have been proposed. We investigated the developed system of partial differential equations analytically and integrated it numerically using the highly efficient parallel GPU code. The integration results are in a very good agreement with other theoretical and experimental studies. In addition, our model revealed a number of testable phenomena. The major model prediction (bacteria accumulation in positive and depletion in negative topological defects) was tested by a dedicated experiment. We extended our model to study active nematics in a biphasic state, where nematic and isotropic phases coexist. Typically this coexistence is manifested by formation of tactoids - isotropic elongated regions surrounded by nematic phase, or nematic regions surrounded by isotropic phase. Using numerical integration, we revealed fundamental properties of such systems. Our main model outcome - spontaneous negative charging of isotropic-nematic interfaces - was confirmed by the experiment. The provided modeling and experimental results are in a very good qualitative and quantitative agreement. At last, we studied living nematics experimentally. We worked with swimming bacteria Bacillus subtilis suspended in disodium cromoglycate (DSCG) liquid crystal. Using cylindrical confinement, we were able to observe quantization of nematics' bending instability. Our experimental results revealed a complex interplay between bacteria self-propulsion and nematics' elasticity in the presence of cylindrical confinements of different sizes.

Instant-Form and Light-Front Quantization of Field Theories

NASA Astrophysics Data System (ADS)

Kulshreshtha, Usha; Kulshreshtha, Daya Shankar; Vary, James

2018-05-01

In this work we consider the instant-form and light-front quantization of some field theories. As an example, we consider a class of gauged non-linear sigma models with different regularizations. In particular, we present the path integral quantization of the gauged non-linear sigma model in the Faddeevian regularization. We also make a comparision of the possible differences in the instant-form and light-front quantization at appropriate places.

Quantization improves stabilization of dynamical systems with delayed feedback

NASA Astrophysics Data System (ADS)

Stepan, Gabor; Milton, John G.; Insperger, Tamas

2017-11-01

We show that an unstable scalar dynamical system with time-delayed feedback can be stabilized by quantizing the feedback. The discrete time model corresponds to a previously unrecognized case of the microchaotic map in which the fixed point is both locally and globally repelling. In the continuous-time model, stabilization by quantization is possible when the fixed point in the absence of feedback is an unstable node, and in the presence of feedback, it is an unstable focus (spiral). The results are illustrated with numerical simulation of the unstable Hayes equation. The solutions of the quantized Hayes equation take the form of oscillations in which the amplitude is a function of the size of the quantization step. If the quantization step is sufficiently small, the amplitude of the oscillations can be small enough to practically approximate the dynamics around a stable fixed point.

Perceptual compression of magnitude-detected synthetic aperture radar imagery

NASA Technical Reports Server (NTRS)

Gorman, John D.; Werness, Susan A.

1994-01-01

A perceptually-based approach for compressing synthetic aperture radar (SAR) imagery is presented. Key components of the approach are a multiresolution wavelet transform, a bit allocation mask based on an empirical human visual system (HVS) model, and hybrid scalar/vector quantization. Specifically, wavelet shrinkage techniques are used to segregate wavelet transform coefficients into three components: local means, edges, and texture. Each of these three components is then quantized separately according to a perceptually-based bit allocation scheme. Wavelet coefficients associated with local means and edges are quantized using high-rate scalar quantization while texture information is quantized using low-rate vector quantization. The impact of the perceptually-based multiresolution compression algorithm on visual image quality, impulse response, and texture properties is assessed for fine-resolution magnitude-detected SAR imagery; excellent image quality is found at bit rates at or above 1 bpp along with graceful performance degradation at rates below 1 bpp.

Strapdown system performance optimization test evaluations (SPOT), volume 1

NASA Technical Reports Server (NTRS)

Blaha, R. J.; Gilmore, J. P.

1973-01-01

A three axis inertial system was packaged in an Apollo gimbal fixture for fine grain evaluation of strapdown system performance in dynamic environments. These evaluations have provided information to assess the effectiveness of real-time compensation techniques and to study system performance tradeoffs to factors such as quantization and iteration rate. The strapdown performance and tradeoff studies conducted include: (1) Compensation models and techniques for the inertial instrument first-order error terms were developed and compensation effectivity was demonstrated in four basic environments; single and multi-axis slew, and single and multi-axis oscillatory. (2) The theoretical coning bandwidth for the first-order quaternion algorithm expansion was verified. (3) Gyro loop quantization was identified to affect proportionally the system attitude uncertainty. (4) Land navigation evaluations identified the requirement for accurate initialization alignment in order to pursue fine grain navigation evaluations.

Viterbi decoding for satellite and space communication.

NASA Technical Reports Server (NTRS)

Heller, J. A.; Jacobs, I. M.

1971-01-01

Convolutional coding and Viterbi decoding, along with binary phase-shift keyed modulation, is presented as an efficient system for reliable communication on power limited satellite and space channels. Performance results, obtained theoretically and through computer simulation, are given for optimum short constraint length codes for a range of code constraint lengths and code rates. System efficiency is compared for hard receiver quantization and 4 and 8 level soft quantization. The effects on performance of varying of certain parameters relevant to decoder complexity and cost are examined. Quantitative performance degradation due to imperfect carrier phase coherence is evaluated and compared to that of an uncoded system. As an example of decoder performance versus complexity, a recently implemented 2-Mbit/sec constraint length 7 Viterbi decoder is discussed. Finally a comparison is made between Viterbi and sequential decoding in terms of suitability to various system requirements.

Analysis on the urban street network of Korea: Connections between topology and meta-information

NASA Astrophysics Data System (ADS)

Lee, Byoung-Hwa; Jung, Woo-Sung

2018-05-01

Cities consist of infrastructure that enables transportation, which can be considered as topology in abstract terms. Once cities are physically organized in terms of infrastructure, people interact with each other to form the values, which can be regarded as the meta-information of the cities. The topology and meta-information coevolve together as the cities are developed. In this study, we investigate the relationship between the topology and meta-information for a street network, which has aspects of both a complex network and planar graph. The degree of organization of a street structure determines the efficiency and productivity of the city in that they act as blood vessels to transport people, goods, and information. We analyze the topological aspect of a street network using centralities including the betweenness, closeness, straightness, and information. We classify the cities into several groups that share common meta-information based on the centrality, indicating that the topological factor of the street structure is closely related to meta-information through coevolution. We also obtain the coevolution in the planned cities using the regularity. Another footprint is the relation between the street segment length and the population, which shows the sublinear scaling.

Assessment of the instantaneous unit hydrograph derived from the theory of topologically random networks

USGS Publications Warehouse

Karlinger, M.R.; Troutman, B.M.

1985-01-01

An instantaneous unit hydrograph (iuh) based on the theory of topologically random networks (topological iuh) is evaluated in terms of sets of basin characteristics and hydraulic parameters. Hydrographs were computed using two linear routing methods for each of two drainage basins in the southeastern United States and are the basis of comparison for the topological iuh's. Elements in the sets of basin characteristics for the topological iuh's are the number of first-order streams only, (N), or the nuber of sources together with the number of channel links in the topological diameter (N, D); the hydraulic parameters are values of the celerity and diffusivity constant. Sensitivity analyses indicate that the mean celerity of the internal links in the network is the critical hydraulic parameter for determining the shape of the topological iuh, while the diffusivity constant has minimal effect on the topological iuh. Asymptotic results (source-only) indicate the number of sources need not be large to approximate the topological iuh with the Weibull probability density function.

Interframe vector wavelet coding technique

NASA Astrophysics Data System (ADS)

Wus, John P.; Li, Weiping

1997-01-01

Wavelet coding is often used to divide an image into multi- resolution wavelet coefficients which are quantized and coded. By 'vectorizing' scalar wavelet coding and combining this with vector quantization (VQ), vector wavelet coding (VWC) can be implemented. Using a finite number of states, finite-state vector quantization (FSVQ) takes advantage of the similarity between frames by incorporating memory into the video coding system. Lattice VQ eliminates the potential mismatch that could occur using pre-trained VQ codebooks. It also eliminates the need for codebook storage in the VQ process, thereby creating a more robust coding system. Therefore, by using the VWC coding method in conjunction with the FSVQ system and lattice VQ, the formulation of a high quality very low bit rate coding systems is proposed. A coding system using a simple FSVQ system where the current state is determined by the previous channel symbol only is developed. To achieve a higher degree of compression, a tree-like FSVQ system is implemented. The groupings are done in this tree-like structure from the lower subbands to the higher subbands in order to exploit the nature of subband analysis in terms of the parent-child relationship. Class A and Class B video sequences from the MPEG-IV testing evaluations are used in the evaluation of this coding method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ballesteros, Ángel, E-mail: angelb@ubu.es; Enciso, Alberto, E-mail: aenciso@icmat.es; Herranz, Francisco J., E-mail: fjherranz@ubu.es

In this paper we quantize the N-dimensional classical Hamiltonian system H=(|q|)/(2(η+|q|)) p{sup 2}−k/(η+|q|) , that can be regarded as a deformation of the Coulomb problem with coupling constant k, that it is smoothly recovered in the limit η→0. Moreover, the kinetic energy term in H is just the one corresponding to an N-dimensional Taub–NUT space, a fact that makes this system relevant from a geometric viewpoint. Since the Hamiltonian H is known to be maximally superintegrable, we propose a quantization prescription that preserves such superintegrability in the quantum mechanical setting. We show that, to this end, one must choose asmore » the kinetic part of the Hamiltonian the conformal Laplacian of the underlying Riemannian manifold, which combines the usual Laplace–Beltrami operator on the Taub–NUT manifold and a multiple of its scalar curvature. As a consequence, we obtain a novel exactly solvable deformation of the quantum Coulomb problem, whose spectrum is computed in closed form for positive values of η and k, and showing that the well-known maximal degeneracy of the flat system is preserved in the deformed case. Several interesting algebraic and physical features of this new exactly solvable quantum system are analyzed, and the quantization problem for negative values of η and/or k is also sketched.« less

Accelerating simulation for the multiple-point statistics algorithm using vector quantization

NASA Astrophysics Data System (ADS)

Zuo, Chen; Pan, Zhibin; Liang, Hao

2018-03-01

Multiple-point statistics (MPS) is a prominent algorithm to simulate categorical variables based on a sequential simulation procedure. Assuming training images (TIs) as prior conceptual models, MPS extracts patterns from TIs using a template and records their occurrences in a database. However, complex patterns increase the size of the database and require considerable time to retrieve the desired elements. In order to speed up simulation and improve simulation quality over state-of-the-art MPS methods, we propose an accelerating simulation for MPS using vector quantization (VQ), called VQ-MPS. First, a variable representation is presented to make categorical variables applicable for vector quantization. Second, we adopt a tree-structured VQ to compress the database so that stationary simulations are realized. Finally, a transformed template and classified VQ are used to address nonstationarity. A two-dimensional (2D) stationary channelized reservoir image is used to validate the proposed VQ-MPS. In comparison with several existing MPS programs, our method exhibits significantly better performance in terms of computational time, pattern reproductions, and spatial uncertainty. Further demonstrations consist of a 2D four facies simulation, two 2D nonstationary channel simulations, and a three-dimensional (3D) rock simulation. The results reveal that our proposed method is also capable of solving multifacies, nonstationarity, and 3D simulations based on 2D TIs.

Topological Rényi Entropy after a Quantum Quench

NASA Astrophysics Data System (ADS)

Halász, Gábor B.; Hamma, Alioscia

2013-04-01

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

Topological Rényi entropy after a quantum quench.

PubMed

Halász, Gábor B; Hamma, Alioscia

2013-04-26

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

Quantized discrete space oscillators

NASA Technical Reports Server (NTRS)

Uzes, C. A.; Kapuscik, Edward

1993-01-01

A quasi-canonical sequence of finite dimensional quantizations was found which has canonical quantization as its limit. In order to demonstrate its practical utility and its numerical convergence, this formalism is applied to the eigenvalue and 'eigenfunction' problem of several harmonic and anharmonic oscillators.

Complete theory of symmetry-based indicators of band topology.

PubMed

Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki

2017-06-30

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

Topological strings in d < 1

NASA Astrophysics Data System (ADS)

Dijkgraaf, Robbert; Verlinde, Herman; Verlinde, Erik

1991-03-01

We calculate correlation functions in minimal topological field theories. These twisted versions of N = 2 minimal models have recently been proposed to describe d < 1 matrix models, once coupled to topological gravity. In our calculation we make use of the Landau-Ginzburg formulation of the N = 2 models, and we find a direct relation between the Landau-Ginzburg superpotential and the KdV differential operator. Using this correspondence we show that the minimal topological models are in perfect agreement with the matrix models as solved in terms of the KdV hierarchy. This proves the equivalence at tree-level of topological and ordinary string thoery in d < 1.

Circuit topology of proteins and nucleic acids.

PubMed

Mashaghi, Alireza; van Wijk, Roeland J; Tans, Sander J

2014-09-02

Folded biomolecules display a bewildering structural complexity and diversity. They have therefore been analyzed in terms of generic topological features. For instance, folded proteins may be knotted, have beta-strands arranged into a Greek-key motif, or display high contact order. In this perspective, we present a method to formally describe the topology of all folded linear chains and hence provide a general classification and analysis framework for a range of biomolecules. Moreover, by identifying the fundamental rules that intrachain contacts must obey, the method establishes the topological constraints of folded linear chains. We also briefly illustrate how this circuit topology notion can be applied to study the equivalence of folded chains, the engineering of artificial RNA structures and DNA origami, the topological structure of genomes, and the role of topology in protein folding. Copyright © 2014 Elsevier Ltd. All rights reserved.

Dielectric response properties of parabolically-confined nanostructures in a quantizing magnetic field

NASA Astrophysics Data System (ADS)

Sabeeh, Kashif

This thesis presents theoretical studies of dielectric response properties of parabolically-confined nanostructures in a magnetic field. We have determined the retarded Schrodinger Green's function for an electron in such a parabolically confined system in the presence of a time dependent electric field and an ambient magnetic field. Following an operator equation of motion approach developed by Schwinger, we calculate the result in closed form in terms of elementary functions in direct-time representation. From the retarded Schrodinger Green's function we construct the closed-form thermodynamic Green's function for a parabolically confined quantum-dot in a magnetic field to determine its plasmon spectrum. Due to confinement and Landau quantization this system is fully quantized, with an infinite number of collective modes. The RPA integral equation for the inverse dielectric function is solved using Fredholm theory in the nondegenerate and quantum limit to determine the frequencies with which the plasmons participate in response to excitation by an external potential. We exhibit results for the variation of plasmon frequency as a function of magnetic field strength and of confinement frequency. A calculation of the van der Waals interaction energy between two harmonically confined quantum dots is discussed in terms of the dipole-dipole correlation function. The results are presented as a function of confinement strength and distance between the dots. We also rederive a result of Fertig & Halperin [32] for the tunneling-scattering of an electron through a saddle potential which is also known as a quantum point contact (QPC), in the presence of a magnetic field. Using the retarded Green's function we confirm the result for the transmission coefficient and analyze it.

Visibility of wavelet quantization noise

NASA Technical Reports Server (NTRS)

Watson, A. B.; Yang, G. Y.; Solomon, J. A.; Villasenor, J.

1997-01-01

The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

A recursive technique for adaptive vector quantization

NASA Technical Reports Server (NTRS)

Lindsay, Robert A.

1989-01-01

Vector Quantization (VQ) is fast becoming an accepted, if not preferred method for image compression. The VQ performs well when compressing all types of imagery including Video, Electro-Optical (EO), Infrared (IR), Synthetic Aperture Radar (SAR), Multi-Spectral (MS), and digital map data. The only requirement is to change the codebook to switch the compressor from one image sensor to another. There are several approaches for designing codebooks for a vector quantizer. Adaptive Vector Quantization is a procedure that simultaneously designs codebooks as the data is being encoded or quantized. This is done by computing the centroid as a recursive moving average where the centroids move after every vector is encoded. When computing the centroid of a fixed set of vectors the resultant centroid is identical to the previous centroid calculation. This method of centroid calculation can be easily combined with VQ encoding techniques. The defined quantizer changes after every encoded vector by recursively updating the centroid of minimum distance which is the selected by the encoder. Since the quantizer is changing definition or states after every encoded vector, the decoder must now receive updates to the codebook. This is done as side information by multiplexing bits into the compressed source data.

Thermal field theory and generalized light front quantization

NASA Astrophysics Data System (ADS)

Weldon, H. Arthur

2003-04-01

The dependence of thermal field theory on the surface of quantization and on the velocity of the heat bath is investigated by working in general coordinates that are arbitrary linear combinations of the Minkowski coordinates. In the general coordinates the metric tensor gμν¯ is nondiagonal. The Kubo-Martin-Schwinger condition requires periodicity in thermal correlation functions when the temporal variable changes by an amount -i/(T(g00¯)). Light-front quantization fails since g00¯=0; however, various related quantizations are possible.

SATA II - Stochastic Algebraic Topology and Applications

DTIC Science & Technology

2017-01-30

AFRL-AFOSR-UK-TR-2017-0018 SATA II - Stochastic Algebraic Topology and Applications 150032 Robert Adler TECHNION ISRAEL INSTITUTE OF TECHNOLOGY Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Dec 2014 to 14 Dec 2016 4. TITLE AND SUBTITLE SATA II - Stochastic Algebraic Topology and Applications ...has recently been submitted to AFOSR. 15. SUBJECT TERMS Network Theory, Sensor Technology, Mathematical Modeling, EOARD 16. SECURITY CLASSIFICATION OF

Generalized radiation-field quantization method and the Petermann excess-noise factor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheng, Y.-J.; Siegman, A.E.; E.L. Ginzton Laboratory, Stanford University, Stanford, California 94305

2003-10-01

We propose a generalized radiation-field quantization formalism, where quantization does not have to be referenced to a set of power-orthogonal eigenmodes as conventionally required. This formalism can be used to directly quantize the true system eigenmodes, which can be non-power-orthogonal due to the open nature of the system or the gain/loss medium involved in the system. We apply this generalized field quantization to the laser linewidth problem, in particular, lasers with non-power-orthogonal oscillation modes, and derive the excess-noise factor in a fully quantum-mechanical framework. We also show that, despite the excess-noise factor for oscillating modes, the total spatially averaged decaymore » rate for the laser atoms remains unchanged.« less

Simultaneous fault detection and control design for switched systems with two quantized signals.

PubMed

Li, Jian; Park, Ju H; Ye, Dan

2017-01-01

The problem of simultaneous fault detection and control design for switched systems with two quantized signals is presented in this paper. Dynamic quantizers are employed, respectively, before the output is passed to fault detector, and before the control input is transmitted to the switched system. Taking the quantized errors into account, the robust performance for this kind of system is given. Furthermore, sufficient conditions for the existence of fault detector/controller are presented in the framework of linear matrix inequalities, and fault detector/controller gains and the supremum of quantizer range are derived by a convex optimized method. Finally, two illustrative examples demonstrate the effectiveness of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Deformation quantization of fermi fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Galaviz, I.; Garcia-Compean, H.; Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, P.O. Box 14-740, 07000 Mexico, D.F.

2008-04-15

Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal *-product and the Wigner functional are obtained by extending the formalism proposed recently in [I. Galaviz, H. Garcia-Compean, M. Przanowski, F.J. Turrubiates, Weyl-Wigner-Moyal Formalism for Fermi Classical Systems, arXiv:hep-th/0612245] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal *-product, the Wigner functional, the normal ordering operator, and finally,more » the Dirac propagator have been found with the use of these variables.« less

Polymer-Fourier quantization of the scalar field revisited

NASA Astrophysics Data System (ADS)

Garcia-Chung, Angel; Vergara, J. David

2016-10-01

The polymer quantization of the Fourier modes of the real scalar field is studied within algebraic scheme. We replace the positive linear functional of the standard Poincaré invariant quantization by a singular one. This singular positive linear functional is constructed as mimicking the singular limit of the complex structure of the Poincaré invariant Fock quantization. The resulting symmetry group of such polymer quantization is the subgroup SDiff(ℝ4) which is a subgroup of Diff(ℝ4) formed by spatial volume preserving diffeomorphisms. In consequence, this yields an entirely different irreducible representation of the canonical commutation relations, nonunitary equivalent to the standard Fock representation. We also compared the Poincaré invariant Fock vacuum with the polymer Fourier vacuum.

A CU-Level Rate and Distortion Estimation Scheme for RDO of Hardware-Friendly HEVC Encoders Using Low-Complexity Integer DCTs.

PubMed

Lee, Bumshik; Kim, Munchurl

2016-08-01

In this paper, a low complexity coding unit (CU)-level rate and distortion estimation scheme is proposed for High Efficiency Video Coding (HEVC) hardware-friendly implementation where a Walsh-Hadamard transform (WHT)-based low-complexity integer discrete cosine transform (DCT) is employed for distortion estimation. Since HEVC adopts quadtree structures of coding blocks with hierarchical coding depths, it becomes more difficult to estimate accurate rate and distortion values without actually performing transform, quantization, inverse transform, de-quantization, and entropy coding. Furthermore, DCT for rate-distortion optimization (RDO) is computationally high, because it requires a number of multiplication and addition operations for various transform block sizes of 4-, 8-, 16-, and 32-orders and requires recursive computations to decide the optimal depths of CU or transform unit. Therefore, full RDO-based encoding is highly complex, especially for low-power implementation of HEVC encoders. In this paper, a rate and distortion estimation scheme is proposed in CU levels based on a low-complexity integer DCT that can be computed in terms of WHT whose coefficients are produced in prediction stages. For rate and distortion estimation in CU levels, two orthogonal matrices of 4×4 and 8×8 , which are applied to WHT that are newly designed in a butterfly structure only with addition and shift operations. By applying the integer DCT based on the WHT and newly designed transforms in each CU block, the texture rate can precisely be estimated after quantization using the number of non-zero quantized coefficients and the distortion can also be precisely estimated in transform domain without de-quantization and inverse transform required. In addition, a non-texture rate estimation is proposed by using a pseudoentropy code to obtain accurate total rate estimates. The proposed rate and the distortion estimation scheme can effectively be used for HW-friendly implementation of HEVC encoders with 9.8% loss over HEVC full RDO, which much less than 20.3% and 30.2% loss of a conventional approach and Hadamard-only scheme, respectively.

Investigation of another approach in topology optimization

NASA Astrophysics Data System (ADS)

Krotkikh, A. A.; Maximov, P. V.

2018-05-01

The paper presents investigation of another approach in topology optimization. The authors realized the method of topology optimization with using ideas of the SIMP method which was created by Martin P. Bends0e. There are many ways in objective function formulation of topology optimization methods. In terms of elasticity theory, the objective function of the SIMP method is a compliance of an object which should be minimized. The main idea of this paper was avoiding the filtering procedure in the SIMP method. Reformulation of the statement of the problem in terms of function minimization allows us to solve this by big variety of methods. The authors decided to use the interior point method which was realized in Wolfram Mathematica. This way can generate side effects which should be investigated for preventing their appearing in future. Results comparison of the SIMP method and the suggested method are presented in paper and analyzed.

On the dual equivalence of the self-dual and topologically massive /p-form models

NASA Astrophysics Data System (ADS)

Menezes, R.; Nascimento, J. R. S.; Ribeiro, R. F.; Wotzasek, C.

2003-07-01

We study the duality symmetry in p-form models containing a generalized Bq∧Fp+1 term in spacetime manifolds of arbitrary dimensions. The equivalence between the Bq∧Fp+1 self-dual (SDB∧F) and the Bq∧Fp+1 topologically massive (TMB∧F) models is established using a gauge embedding procedure, including the minimal coupling to conserved charged matter current. The minimal coupling adopted for both tensor fields in the self-dual representation is transformed into a non-minimal magnetic like coupling in the topologically massive representation but with the currents swapped. It is known that to establish this equivalence a current-current interaction term is needed to render the matter sector unchanged. We show that both terms arise naturally from the embedding adopted. Comparison with Higgs/Julia-Toulouse duality is established.

Instabilities caused by floating-point arithmetic quantization.

NASA Technical Reports Server (NTRS)

Phillips, C. L.

1972-01-01

It is shown that an otherwise stable digital control system can be made unstable by signal quantization when the controller operates on floating-point arithmetic. Sufficient conditions of instability are determined, and an example of loss of stability is treated when only one quantizer is operated.

Dynamic State Estimation of Power Systems With Quantization Effects: A Recursive Filter Approach.

PubMed

Hu, Liang; Wang, Zidong; Liu, Xiaohui

2016-08-01

In this paper, a recursive filter algorithm is developed to deal with the state estimation problem for power systems with quantized nonlinear measurements. The measurements from both the remote terminal units and the phasor measurement unit are subject to quantizations described by a logarithmic quantizer. Attention is focused on the design of a recursive filter such that, in the simultaneous presence of nonlinear measurements and quantization effects, an upper bound for the estimation error covariance is guaranteed and subsequently minimized. Instead of using the traditional approximation methods in nonlinear estimation that simply ignore the linearization errors, we treat both the linearization and quantization errors as norm-bounded uncertainties in the algorithm development so as to improve the performance of the estimator. For the power system with such kind of introduced uncertainties, a filter is designed in the framework of robust recursive estimation, and the developed filter algorithm is tested on the IEEE benchmark power system to demonstrate its effectiveness.

Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Błaszak, Maciej, E-mail: blaszakm@amu.edu.pl; Domański, Ziemowit, E-mail: ziemowit@amu.edu.pl

In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed. -- Highlights: •An invariant quantization procedure of classical mechanics on the phase space over flat configuration space is presented. •The passage tomore » an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. •Explicit form of position and momentum operators and their appropriate ordering in curvilinear coordinates is shown. •The invariant form of Hamiltonian operators quadratic and cubic in momenta is derived. •The extension of presented formalism onto non-flat case and related ambiguities of the quantization process are discussed.« less

Quantization noise in digital speech. M.S. Thesis- Houston Univ.

NASA Technical Reports Server (NTRS)

Schmidt, O. L.

1972-01-01

The amount of quantization noise generated in a digital-to-analog converter is dependent on the number of bits or quantization levels used to digitize the analog signal in the analog-to-digital converter. The minimum number of quantization levels and the minimum sample rate were derived for a digital voice channel. A sample rate of 6000 samples per second and lowpass filters with a 3 db cutoff of 2400 Hz are required for 100 percent sentence intelligibility. Consonant sounds are the first speech components to be degraded by quantization noise. A compression amplifier can be used to increase the weighting of the consonant sound amplitudes in the analog-to-digital converter. An expansion network must be installed at the output of the digital-to-analog converter to restore the original weighting of the consonant sounds. This technique results in 100 percent sentence intelligibility for a sample rate of 5000 samples per second, eight quantization levels, and lowpass filters with a 3 db cutoff of 2000 Hz.

Superconductivity and ferromagnetism in topological insulators

NASA Astrophysics Data System (ADS)

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 exist when topological insulators are interfaced with superconductors. The observation of Majorana fermions would not only be fundamentally important, but would also lead to applications in fault-tolerant topological quantum computation. By interfacing topological insulator nanoribbons with superconducting electrodes, we observe distinct signatures of proximity-induced superconductivity, which is found to be present in devices with channel lengths that are much longer than the normal transport characteristic lengths. This might suggest preferential coupling of the proximity effect to a ballistic surface channel of the topological insulator. In addition, when the electrodes are in the superconducting state, we observe periodic magnetoresistance oscillations which suggest the formation of vortices in the proximity-induced region of the nanoribbons. Our results demonstrate that proximity-induced superconductivity and vortices can be realized in our nanoribbon geometry, which accomplishes a first important step towards the search for Majorana fermions in condensed matter. In Chapter 5, I will discuss experiments on a magnetically-doped topological insulator (Mn-doped Bi2Se3) to induce a surface state gap. The metallic Dirac cone surface states of a topological insulator are expected to be protected against small perturbations by time-reversal symmetry. However, these surface states can be dramatically modified and a finite energy gap can be opened at the Dirac point by breaking the time-reversal symmetry via magnetic doping. The interplay between magnetism and topological surface states is predicted to yield novel phenomena of fundamental interest such as a topological magneto-electric effect, a quantized anomalous Hall effect, and the induction of magnetic monopoles. Our systematic measurements reveal a close correlation between the onset of ferromagnetism and quantum corrections to diffusive transport, which crosses over from the symplectic (weak anti-localization) to the unitary (weak localization) class. A comprehensive interpretation of data obtained from electrical transport, angle-resolved photoemission spectroscopy, superconducting quantum interference device magnetometry, and scanning tunneling microscopy indicates that the ferromagnetism responsible for modifications in the surface states occurs in nanoscale regions on the surface where magnetic atoms segregate during sample growth. This suggests that some aspects of the observed magnetoconductance may indeed originate from surface transport despite the non-ideal nature of the samples. These observations are consistent with the prediction of a time-reversal symmetry breaking gap, which is further supported by angle-resolved photoemission spectroscopy measurements.

Topology preserving non-rigid image registration using time-varying elasticity model for MRI brain volumes.

PubMed

Ahmad, Sahar; Khan, Muhammad Faisal

2015-12-01

In this paper, we present a new non-rigid image registration method that imposes a topology preservation constraint on the deformation. We propose to incorporate the time varying elasticity model into the deformable image matching procedure and constrain the Jacobian determinant of the transformation over the entire image domain. The motion of elastic bodies is governed by a hyperbolic partial differential equation, generally termed as elastodynamics wave equation, which we propose to use as a deformation model. We carried out clinical image registration experiments on 3D magnetic resonance brain scans from IBSR database. The results of the proposed registration approach in terms of Kappa index and relative overlap computed over the subcortical structures were compared against the existing topology preserving non-rigid image registration methods and non topology preserving variant of our proposed registration scheme. The Jacobian determinant maps obtained with our proposed registration method were qualitatively and quantitatively analyzed. The results demonstrated that the proposed scheme provides good registration accuracy with smooth transformations, thereby guaranteeing the preservation of topology. Copyright © 2015 Elsevier Ltd. All rights reserved.

Characterization of the geometry and topology of DNA pictured as a discrete collection of atoms

PubMed Central

Olson, Wilma K.

2014-01-01

The structural and physical properties of DNA are closely related to its geometry and topology. The classical mathematical treatment of DNA geometry and topology in terms of ideal smooth space curves was not designed to characterize the spatial arrangements of atoms found in high-resolution and simulated double-helical structures. We present here new and rigorous numerical methods for the rapid and accurate assessment of the geometry and topology of double-helical DNA structures in terms of the constituent atoms. These methods are well designed for large DNA datasets obtained in detailed numerical simulations or determined experimentally at high-resolution. We illustrate the usefulness of our methodology by applying it to the analysis of three canonical double-helical DNA chains, a 65-bp minicircle obtained in recent molecular dynamics simulations, and a crystallographic array of protein-bound DNA duplexes. Although we focus on fully base-paired DNA structures, our methods can be extended to treat the geometry and topology of melted DNA structures as well as to characterize the folding of arbitrary molecules such as RNA and cyclic peptides. PMID:24791158

Exotic dark spinor fields

NASA Astrophysics Data System (ADS)

Da Rocha, Roldão; Bernardini, Alex E.; da Silva, J. M. Hoff

2011-04-01

Exotic dark spinor fields are introduced and investigated in the context of inequivalent spin structures on arbitrary curved spacetimes, which induces an additional term on the associated Dirac operator, related to a Čech cohomology class. For the most kinds of spinor fields, any exotic term in the Dirac operator can be absorbed and encoded as a shift of the electromagnetic vector potential representing an element of the cohomology group {H^1}( {M,{{Z}_2}} ) . The possibility of concealing such an exotic term does not exist in case of dark (ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the full topological analysis must be evaluated. Since exotic dark spinor fields also satisfy Klein-Gordon propagators, the dynamical constraints related to the exotic term in the Dirac equation can be explicitly calculated. It forthwith implies that the non-trivial topology associated to the spacetime can drastically engender — from the dynamics of dark spinor fields — constraints in the spacetime metric structure. Meanwhile, such constraints may be alleviated, at the cost of constraining the exotic spacetime topology. Besides being prime candidates to the dark matter problem, dark spinor fields are shown to be potential candidates to probe non-trivial topologies in spacetime, as well as probe the spacetime metric structure.

Coherent state quantization of quaternions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muraleetharan, B., E-mail: bbmuraleetharan@jfn.ac.lk, E-mail: santhar@gmail.com; Thirulogasanthar, K., E-mail: bbmuraleetharan@jfn.ac.lk, E-mail: santhar@gmail.com

Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols, and related quantities are analyzed. Quaternionic version of the harmonic oscillator and Weyl-Heisenberg algebra are also obtained.

Magnonic quantum spin Hall state in the zigzag and stripe phases of the antiferromagnetic honeycomb lattice

NASA Astrophysics Data System (ADS)

Lee, Ki Hoon; Chung, Suk Bum; Park, Kisoo; Park, Je-Geun

2018-05-01

We investigated the topological property of magnon bands in the collinear magnetic orders of zigzag and stripe phases for the antiferromagnetic honeycomb lattice and identified Berry curvature and symmetry constraints on the magnon band structure. Different symmetries of both zigzag and stripe phases lead to different topological properties, in particular, the magnon bands of the stripe phase being disentangled with a finite Dzyaloshinskii-Moriya (DM) term with nonzero spin Chern number. This is corroborated by calculating the spin Nernst effect. Our study establishes the existence of a nontrivial magnon band topology for all observed collinear antiferromagnetic honeycomb lattices in the presence of the DM term.

Random multispace quantization as an analytic mechanism for BioHashing of biometric and random identity inputs.

PubMed

Teoh, Andrew B J; Goh, Alwyn; Ngo, David C L

2006-12-01

Biometric analysis for identity verification is becoming a widespread reality. Such implementations necessitate large-scale capture and storage of biometric data, which raises serious issues in terms of data privacy and (if such data is compromised) identity theft. These problems stem from the essential permanence of biometric data, which (unlike secret passwords or physical tokens) cannot be refreshed or reissued if compromised. Our previously presented biometric-hash framework prescribes the integration of external (password or token-derived) randomness with user-specific biometrics, resulting in bitstring outputs with security characteristics (i.e., noninvertibility) comparable to cryptographic ciphers or hashes. The resultant BioHashes are hence cancellable, i.e., straightforwardly revoked and reissued (via refreshed password or reissued token) if compromised. BioHashing furthermore enhances recognition effectiveness, which is explained in this paper as arising from the Random Multispace Quantization (RMQ) of biometric and external random inputs.

Chern-Simons theory with Wilson lines and boundary in the BV-BFV formalism

NASA Astrophysics Data System (ADS)

Alekseev, Anton; Barmaz, Yves; Mnev, Pavel

2013-05-01

We consider the Chern-Simons theory with Wilson lines in 3D and in 1D in the BV-BFV formalism of Cattaneo-Mnev-Reshetikhin. In particular, we allow for Wilson lines to end on the boundary of the space-time manifold. In the toy model of 1D Chern-Simons theory, the quantized BFV boundary action coincides with the Kostant cubic Dirac operator which plays an important role in representation theory. In the case of 3D Chern-Simons theory, the boundary action turns out to be the odd (degree 1) version of the BF model with source terms for the B field at the points where the Wilson lines meet the boundary. The boundary space of states arising as the cohomology of the quantized BFV action coincides with the space of conformal blocks of the corresponding WZW model.

Face recognition: a convolutional neural-network approach.

PubMed

Lawrence, S; Giles, C L; Tsoi, A C; Back, A D

1997-01-01

We present a hybrid neural-network for human face recognition which compares favourably with other methods. The system combines local image sampling, a self-organizing map (SOM) neural network, and a convolutional neural network. The SOM provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space, thereby providing dimensionality reduction and invariance to minor changes in the image sample, and the convolutional neural network provides partial invariance to translation, rotation, scale, and deformation. The convolutional network extracts successively larger features in a hierarchical set of layers. We present results using the Karhunen-Loeve transform in place of the SOM, and a multilayer perceptron (MLP) in place of the convolutional network for comparison. We use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression, pose, and facial details. We analyze the computational complexity and discuss how new classes could be added to the trained recognizer.

Untangling the mechanics versus topology of overhand knots

NASA Astrophysics Data System (ADS)

Reis, Pedro; Jawed, Mohammad; Dieleman, Peter; Audoly, Basile

2015-03-01

We study the interplay between mechanics and topology of overhand knots in slender elastic rods. We perform precision desktop experiments of overhand knots with increasing values for the crossing number (our measure of topology) and characterize their mechanical response through tension-displacement tests. The tensile force required to tighten the knot is governed by an intricate balance between topology, bending, friction, and contact forces. Digital imaging is employed to characterize the configuration of the contact braid as a function of crossing number. A robust scaling law is found for the pulling force in terms of the geometric and topological parameters of the knot. A reduced theory is developed, which predictively rationalizes the process.

Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator

NASA Astrophysics Data System (ADS)

Pillay, Jason C.; McCulloch, Ian P.

2018-05-01

The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.

Educational Information Quantization for Improving Content Quality in Learning Management Systems

ERIC Educational Resources Information Center

Rybanov, Alexander Aleksandrovich

2014-01-01

The article offers the educational information quantization method for improving content quality in Learning Management Systems. The paper considers questions concerning analysis of quality of quantized presentation of educational information, based on quantitative text parameters: average frequencies of parts of speech, used in the text; formal…

BFV quantization on hermitian symmetric spaces

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1995-02-01

Gauge-invariant BFV approach to geometric quantization is applied to the case of hermitian symmetric spaces G/ H. In particular, gauge invariant quantization on the Lobachevski plane and sphere is carried out. Due to the presence of symmetry, master equations for the first-class constraints, quantum observables and physical quantum states are exactly solvable. BFV-BRST operator defines a flat G-connection in the Fock bundle over G/ H. Physical quantum states are covariantly constant sections with respect to this connection and are shown to coincide with the generalized coherent states for the group G. Vacuum expectation values of the quantum observables commuting with the quantum first-class constraints reduce to the covariant symbols of Berezin. The gauge-invariant approach to quantization on symplectic manifolds synthesizes geometric, deformation and Berezin quantization approaches.

Topological Materials: Weyl Semimetals

NASA Astrophysics Data System (ADS)

Yan, Binghai; Felser, Claudia

2017-03-01

Topological insulators and topological semimetals are both new classes of quantum materials, which are characterized by surface states induced by the topology of the bulk band structure. Topological Dirac or Weyl semimetals show linear dispersion around nodes, termed the Dirac or Weyl points, as the three-dimensional analog of graphene. We review the basic concepts and compare these topological states of matter from the materials perspective with a special focus on Weyl semimetals. The TaAs family is the ideal materials class to introduce the signatures of Weyl points in a pedagogical way, from Fermi arcs to the chiral magnetotransport properties, followed by hunting for the type-II Weyl semimetals in WTe2, MoTe2, and related compounds. Many materials are members of big families, and topological properties can be tuned. As one example, we introduce the multifunctional topological materials, Heusler compounds, in which both topological insulators and magnetic Weyl semimetals can be found. Instead of a comprehensive review, this article is expected to serve as a helpful introduction and summary by taking a snapshot of the quickly expanding field.

A Algebraic Approach to the Quantization of Constrained Systems: Finite Dimensional Examples.

NASA Astrophysics Data System (ADS)

Tate, Ranjeet Shekhar

1992-01-01

General relativity has two features in particular, which make it difficult to apply to it existing schemes for the quantization of constrained systems. First, there is no background structure in the theory, which could be used, e.g., to regularize constraint operators, to identify a "time" or to define an inner product on physical states. Second, in the Ashtekar formulation of general relativity, which is a promising avenue to quantum gravity, the natural variables for quantization are not canonical; and, classically, there are algebraic identities between them. Existing schemes are usually not concerned with such identities. Thus, from the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a general prescription to find the physical inner product, and is flexible enough to accommodate non -canonical variables. In this dissertation I present an algebraic formulation of the Dirac approach to the quantization of constrained systems. The Dirac quantization program is augmented by a general principle to find the inner product on physical states. Essentially, the Hermiticity conditions on physical operators determine this inner product. I also clarify the role in quantum theory of possible algebraic identities between the elementary variables. I use this approach to quantize various finite dimensional systems. Some of these models test the new aspects of the algebraic framework. Others bear qualitative similarities to general relativity, and may give some insight into the pitfalls lurking in quantum gravity. The previous quantizations of one such model had many surprising features. When this model is quantized using the algebraic program, there is no longer any unexpected behaviour. I also construct the complete quantum theory for a previously unsolved relativistic cosmology. All these models indicate that the algebraic formulation provides powerful new tools for quantization. In (spatially compact) general relativity, the Hamiltonian is constrained to vanish. I present various approaches one can take to obtain an interpretation of the quantum theory of such "dynamically constrained" systems. I apply some of these ideas to the Bianchi I cosmology, and analyze the issue of the initial singularity in quantum theory.

Characterization of Lifshitz transitions in topological nodal line semimetals

NASA Astrophysics Data System (ADS)

Jiang, Hui; Li, Linhu; Gong, Jiangbin; Chen, Shu

2018-04-01

We introduce a two-band model of three-dimensional nodal line semimetals (NLSMs), the Fermi surface of which at half-filling may form various one-dimensional configurations of different topology. We study the symmetries and "drumhead" surface states of the model, and find that the transitions between different configurations, namely, the Lifshitz transitions, can be identified solely by the number of gap-closing points on some high-symmetry planes in the Brillouin zone. A global phase diagram of this model is also obtained accordingly. We then investigate the effect of some extra terms analogous to a two-dimensional Rashba-type spin-orbit coupling. The introduced extra terms open a gap for the NLSMs and can be useful in engineering different topological insulating phases. We demonstrate that the behavior of surface Dirac cones in the resulting insulating system has a clear correspondence with the different configurations of the original nodal lines in the absence of the gap terms.

Emergent gauge fields and their nonperturbative effects in correlated electrons

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Tanaka, Akihiro

2015-06-01

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner’s and Anderson’s physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high Tc superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner’s description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner’s paradigm. In this review paper, we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high Tc cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one-dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Emergent Gauge Fields and Their Nonperturbative Effects in Correlated Electrons

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Tanaka, Akihiro

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner's and Anderson's physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high Tc superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner's description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner's paradigm. In this review article we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high Tc cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Quasi-topological Ricci polynomial gravities

NASA Astrophysics Data System (ADS)

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.

Quantization Distortion in Block Transform-Compressed Data

NASA Technical Reports Server (NTRS)

Boden, A. F.

1995-01-01

The popular JPEG image compression standard is an example of a block transform-based compression scheme; the image is systematically subdivided into block that are individually transformed, quantized, and encoded. The compression is achieved by quantizing the transformed data, reducing the data entropy and thus facilitating efficient encoding. A generic block transform model is introduced.

Quantized impedance dealing with the damping behavior of the one-dimensional oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Jinghao; Zhang, Jing; Li, Yuan

2015-11-15

A quantized impedance is proposed to theoretically establish the relationship between the atomic eigenfrequency and the intrinsic frequency of the one-dimensional oscillator in this paper. The classical oscillator is modified by the idea that the electron transition is treated as a charge-discharge process of a suggested capacitor with the capacitive energy equal to the energy level difference of the jumping electron. The quantized capacitance of the impedance interacting with the jumping electron can lead the resonant frequency of the oscillator to the same as the atomic eigenfrequency. The quantized resistance reflects that the damping coefficient of the oscillator is themore » mean collision frequency of the transition electron. In addition, the first and third order electric susceptibilities based on the oscillator are accordingly quantized. Our simulation of the hydrogen atom emission spectrum based on the proposed method agrees well with the experimental one. Our results exhibits that the one-dimensional oscillator with the quantized impedance may become useful in the estimations of the refractive index and one- or multi-photon absorption coefficients of some nonmagnetic media composed of hydrogen-like atoms.« less

Low-rate image coding using vector quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makur, A.

1990-01-01

This thesis deals with the development and analysis of a computationally simple vector quantization image compression system for coding monochrome images at low bit rate. Vector quantization has been known to be an effective compression scheme when a low bit rate is desirable, but the intensive computation required in a vector quantization encoder has been a handicap in using it for low rate image coding. The present work shows that, without substantially increasing the coder complexity, it is indeed possible to achieve acceptable picture quality while attaining a high compression ratio. Several modifications to the conventional vector quantization coder aremore » proposed in the thesis. These modifications are shown to offer better subjective quality when compared to the basic coder. Distributed blocks are used instead of spatial blocks to construct the input vectors. A class of input-dependent weighted distortion functions is used to incorporate psychovisual characteristics in the distortion measure. Computationally simple filtering techniques are applied to further improve the decoded image quality. Finally, unique designs of the vector quantization coder using electronic neural networks are described, so that the coding delay is reduced considerably.« less

Quantized impedance dealing with the damping behavior of the one-dimensional oscillator

NASA Astrophysics Data System (ADS)

Zhu, Jinghao; Zhang, Jing; Li, Yuan; Zhang, Yong; Fang, Zhengji; Zhao, Peide; Li, Erping

2015-11-01

A quantized impedance is proposed to theoretically establish the relationship between the atomic eigenfrequency and the intrinsic frequency of the one-dimensional oscillator in this paper. The classical oscillator is modified by the idea that the electron transition is treated as a charge-discharge process of a suggested capacitor with the capacitive energy equal to the energy level difference of the jumping electron. The quantized capacitance of the impedance interacting with the jumping electron can lead the resonant frequency of the oscillator to the same as the atomic eigenfrequency. The quantized resistance reflects that the damping coefficient of the oscillator is the mean collision frequency of the transition electron. In addition, the first and third order electric susceptibilities based on the oscillator are accordingly quantized. Our simulation of the hydrogen atom emission spectrum based on the proposed method agrees well with the experimental one. Our results exhibits that the one-dimensional oscillator with the quantized impedance may become useful in the estimations of the refractive index and one- or multi-photon absorption coefficients of some nonmagnetic media composed of hydrogen-like atoms.

Probabilistic distance-based quantizer design for distributed estimation

NASA Astrophysics Data System (ADS)

Kim, Yoon Hak

2016-12-01

We consider an iterative design of independently operating local quantizers at nodes that should cooperate without interaction to achieve application objectives for distributed estimation systems. We suggest as a new cost function a probabilistic distance between the posterior distribution and its quantized one expressed as the Kullback Leibler (KL) divergence. We first present the analysis that minimizing the KL divergence in the cyclic generalized Lloyd design framework is equivalent to maximizing the logarithmic quantized posterior distribution on the average which can be further computationally reduced in our iterative design. We propose an iterative design algorithm that seeks to maximize the simplified version of the posterior quantized distribution and discuss that our algorithm converges to a global optimum due to the convexity of the cost function and generates the most informative quantized measurements. We also provide an independent encoding technique that enables minimization of the cost function and can be efficiently simplified for a practical use of power-constrained nodes. We finally demonstrate through extensive experiments an obvious advantage of improved estimation performance as compared with the typical designs and the novel design techniques previously published.

Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

NASA Astrophysics Data System (ADS)

Georgiev, Lachezar S.

2006-12-01

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma , in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the π/8 gate, are also explicitly implemented by quasihole braidings. Instead of the π/8 gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled- Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g3 .

Light-cone quantization of two dimensional field theory in the path integral approach

NASA Astrophysics Data System (ADS)

Cortés, J. L.; Gamboa, J.

1999-05-01

A quantization condition due to the boundary conditions and the compatification of the light cone space-time coordinate x- is identified at the level of the classical equations for the right-handed fermionic field in two dimensions. A detailed analysis of the implications of the implementation of this quantization condition at the quantum level is presented. In the case of the Thirring model one has selection rules on the excitations as a function of the coupling and in the case of the Schwinger model a double integer structure of the vacuum is derived in the light-cone frame. Two different quantized chiral Schwinger models are found, one of them without a θ-vacuum structure. A generalization of the quantization condition to theories with several fermionic fields and to higher dimensions is presented.

Relational symplectic groupoid quantization for constant poisson structures

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Moshayedi, Nima; Wernli, Konstantin

2017-09-01

As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of mixed boundary conditions and the globalization of results are also addressed. In particular, the paper includes an extension to space-times with boundary of some formal geometry considerations in the BV-BFV formalism, and specifically introduces into the BV-BFV framework a "differential" version of the classical and quantum master equations. The quantization constructed in this paper induces Kontsevich's deformation quantization on the underlying Poisson manifold, i.e., the Moyal product, which is known in full details. This allows focussing on the BV-BFV technology and testing it. For the inexperienced reader, this is also a practical and reasonably simple way to learn it.

A hybrid LBG/lattice vector quantizer for high quality image coding

NASA Technical Reports Server (NTRS)

Ramamoorthy, V.; Sayood, K.; Arikan, E. (Editor)

1991-01-01

It is well known that a vector quantizer is an efficient coder offering a good trade-off between quantization distortion and bit rate. The performance of a vector quantizer asymptotically approaches the optimum bound with increasing dimensionality. A vector quantized image suffers from the following types of degradations: (1) edge regions in the coded image contain staircase effects, (2) quasi-constant or slowly varying regions suffer from contouring effects, and (3) textured regions lose details and suffer from granular noise. All three of these degradations are due to the finite size of the code book, the distortion measures used in the design, and due to the finite training procedure involved in the construction of the code book. In this paper, we present an adaptive technique which attempts to ameliorate the edge distortion and contouring effects.

Nanoscale Device Properties of Tellurium-based Chalcogenide Compounds

NASA Astrophysics Data System (ADS)

Dahal, Bishnu R.

The great progress achieved in miniaturization of microelectronic devices has now reached a distinct bottleneck, as devices are starting to approach the fundamental fabrication and performance limit. Even if a major breakthrough is made in the fabrication process, these scaled down electronic devices will not function properly since the quantum effects can no longer be neglected in the nanoscale regime. Advances in nanotechnology and new materials are driving novel technologies for future device applications. Current microelectronic devices have the smallest feature size, around 10 nm, and the industry is planning to switch away from silicon technology in the near future. The new technology will be fundamentally different. There are several leading technologies based on spintronics, tunneling transistors, and the newly discovered 2-dimensional material systems. All of these technologies are at the research level, and are far from ready for use in making devices in large volumes. This dissertation will focus on a very promising material system, Te-based chalcogenides, which have potential applications in spintronics, thermoelectricity and topological insulators that can lead to low-power-consumption electronics. Very recently it was predicted and experimentally observed that the spin-orbit interaction in certain materials can lead to a new electronic state called topological insulating phase. The topological insulator, like an ordinary insulator, has a bulk energy gap separating the highest occupied electronic band from the lowest empty band. However, the surface states in the case of a three-dimensional or edge states in a two-dimensional topological insulator allow electrons to conduct at the surface, due to the topological character of the bulk wavefunctions. These conducting states are protected by time-reversal symmetry, and cannot be eliminated by defects or chemical passivation. The edge/surface states satisfy Dirac dispersion relations, and hence the physics of relativistic Dirac fermions becomes relevant. This results in peculiar quantum oscillations in transport measurements which make it possible to unambiguously identify surface Dirac fermions. In order to lead us towards a better understanding of topological insulators and their applications, it is, however, necessary to develop techniques that will enable high quality materials to be obtained in a routine and reliable way. However, this has been an enormous challenge so far. Since highly volatile components are involved in most topological insulators, whether in bulk single crystal or epitaxial thin films or chemical vapor deposition grown nanoribbons, maintaining near stoichiometry has proven to be very difficult. Observing the predicted transport properties of these systems, particularly surface carriers of high mobility whilst maintaining bulk insulating states, is seriously impeded by the unintentional doping of bulk carriers. Moreover, in thin films and hetrostructures, at the all-important thickness range of a few nanometers, the additional limitation of the film-substrate lattice mismatch and the resulting strain in films is a major concern. In this thesis, we have developed a synthesis technique to obtain high quality SnTe nanoribbons, which is a topological crystalline insulator and its surface states are topologically protected by mirror symmetry of the lattice. The obtained ribbons are nearly stoichiometric and show strong semiconducting behavior with a bandgap of 240 meV. This is the first time high quality SnTe nanoribbons have been synthesized. High quality SnTe nanoribbons form a potential platform to understand the magnetic topological insulating behavior. In this thesis, it is also shown that magnetic behavior can be introduced in SnTe nanoribbons by means of chromium doping. Magnetically doped topological insulators, possessing an energy gap created at the Dirac point are predicted to exhibit exotic phenomena including the quantized anomalous Hall Effect and a dissipationless transport, which facilitate the development of low-power-consumption devices using electron spins. In addition, this thesis also discusses the growth and transport properties of another Te-based chalcogenide system, CoTe with ferrimagnetic and semiconducting behavior. We have shown that the structural, electrical and magnetic properties can be tuned by controlling the amount of cobalt in the system.

Landau quantization in the spinning cosmic string spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muniz, C.R., E-mail: celiomuniz@yahoo.com; Bezerra, V.B.; Cunha, M.S.

2014-11-15

We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schrödinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, suchmore » that makes sense to apply the Schrödinger equation in a curved background whose metric has an off diagonal term which involves time and space. It is also assumed that the particle orbits sufficiently far from the boundary of the region of closed timelike curves which exist around this topological defect. Finally, we find the Landau levels of the particle in the presence of a spinning cosmic string endowed with internal structure, i.e., having a finite width and uniformly filled with both material and vacuum energies. - Highlights: • Solution of the wave equation characterizing the problem. • Energy levels of the particle in spacetime of the structureless string. • Expression for an analogous of the quadratic Zeeman effect. • Energy levels of the particle in spacetime of the string with internal structure. • Evidence of the string structure by the internal existence of the vacuum energy.« less

Single-user MIMO versus multi-user MIMO in distributed antenna systems with limited feedback

NASA Astrophysics Data System (ADS)

Schwarz, Stefan; Heath, Robert W.; Rupp, Markus

2013-12-01

This article investigates the performance of cellular networks employing distributed antennas in addition to the central antennas of the base station. Distributed antennas are likely to be implemented using remote radio units, which is enabled by a low latency and high bandwidth dedicated link to the base station. This facilitates coherent transmission from potentially all available antennas at the same time. Such distributed antenna system (DAS) is an effective way to deal with path loss and large-scale fading in cellular systems. DAS can apply precoding across multiple transmission points to implement single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) transmission. The throughput performance of various SU-MIMO and MU-MIMO transmission strategies is investigated in this article, employing a Long-Term evolution (LTE) standard compliant simulation framework. The previously theoretically established cell-capacity improvement of MU-MIMO in comparison to SU-MIMO in DASs is confirmed under the practical constraints imposed by the LTE standard, even under the assumption of imperfect channel state information (CSI) at the base station. Because practical systems will use quantized feedback, the performance of different CSI feedback algorithms for DASs is investigated. It is shown that significant gains in the CSI quantization accuracy and in the throughput of especially MU-MIMO systems can be achieved with relatively simple quantization codebook constructions that exploit the available temporal correlation and channel gain differences.

On the dual equivalence of the self-dual and topologically massive /B∧F models coupled to dynamical fermionic matter

NASA Astrophysics Data System (ADS)

Menezes, R.; Nascimento, J. R. S.; Ribeiro, R. F.; Wotzasek, C.

2002-06-01

We study the equivalence between the /B∧F self-dual (SDB∧F) and the /B∧F topologically massive (TMB∧F) models including the coupling to dynamical, U(1) charged fermionic matter. This is done through an iterative procedure of gauge embedding that produces the dual mapping. In the interactive cases, the minimal coupling adopted for both vector and tensor fields in the self-dual representation is transformed into a non-minimal magnetic like coupling in the topologically massive representation but with the currents swapped. It is known that to establish this equivalence a current-current interaction term is needed to render the matter sector unchanged. We show that both terms arise naturally from the embedding procedure.

Universe creation from the third-quantized vacuum

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGuigan, M.

1989-04-15

Third quantization leads to a Hilbert space containing a third-quantized vacuum in which no universes are present as well as multiuniverse states. We consider the possibility of universe creation for the special case where the universe emerges in a no-particle state. The probability of such a creation is computed from both the path-integral and operator formalisms.

Universe creation from the third-quantized vacuum

NASA Astrophysics Data System (ADS)

McGuigan, Michael

1989-04-01

Third quantization leads to a Hilbert space containing a third-quantized vacuum in which no universes are present as well as multiuniverse states. We consider the possibility of universe creation for the special case where the universe emerges in a no-particle state. The probability of such a creation is computed from both the path-integral and operator formalisms.

4D Sommerfeld quantization of the complex extended charge

NASA Astrophysics Data System (ADS)

Bulyzhenkov, Igor E.

2017-12-01

Gravitational fields and accelerations cannot change quantized magnetic flux in closed line contours due to flat 3D section of curved 4D space-time-matter. The relativistic Bohr-Sommerfeld quantization of the imaginary charge reveals an electric analog of the Compton length, which can introduce quantitatively the fine structure constant and the Plank length.

Semiclassical electron transport at the edge of a two-dimensional topological insulator: Interplay of protected and unprotected modes

NASA Astrophysics Data System (ADS)

Khalaf, E.; Skvortsov, M. A.; Ostrovsky, P. M.

2016-03-01

We study electron transport at the edge of a generic disordered two-dimensional topological insulator, where some channels are topologically protected from backscattering. Assuming the total number of channels is large, we consider the edge as a quasi-one-dimensional quantum wire and describe it in terms of a nonlinear sigma model with a topological term. Neglecting localization effects, we calculate the average distribution function of transmission probabilities as a function of the sample length. We mainly focus on the two experimentally relevant cases: a junction between two quantum Hall (QH) states with different filling factors (unitary class) and a relatively thick quantum well exhibiting quantum spin Hall (QSH) effect (symplectic class). In a QH sample, the presence of topologically protected modes leads to a strong suppression of diffusion in the other channels already at scales much shorter than the localization length. On the semiclassical level, this is accompanied by the formation of a gap in the spectrum of transmission probabilities close to unit transmission, thereby suppressing shot noise and conductance fluctuations. In the case of a QSH system, there is at most one topologically protected edge channel leading to weaker transport effects. In order to describe `topological' suppression of nearly perfect transparencies, we develop an exact mapping of the semiclassical limit of the one-dimensional sigma model onto a zero-dimensional sigma model of a different symmetry class, allowing us to identify the distribution of transmission probabilities with the average spectral density of a certain random-matrix ensemble. We extend our results to other symmetry classes with topologically protected edges in two dimensions.

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

PubMed

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.

Quintessential quartic quasi-topological quartet

NASA Astrophysics Data System (ADS)

Ahmed, Jamil; Hennigar, Robie A.; Mann, Robert B.; Mir, Mozhgan

2017-05-01

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

Symmetric Topological Phases and Tensor Network States

NASA Astrophysics Data System (ADS)

Jiang, Shenghan

Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.

Reducing weight precision of convolutional neural networks towards large-scale on-chip image recognition

NASA Astrophysics Data System (ADS)

Ji, Zhengping; Ovsiannikov, Ilia; Wang, Yibing; Shi, Lilong; Zhang, Qiang

2015-05-01

In this paper, we develop a server-client quantization scheme to reduce bit resolution of deep learning architecture, i.e., Convolutional Neural Networks, for image recognition tasks. Low bit resolution is an important factor in bringing the deep learning neural network into hardware implementation, which directly determines the cost and power consumption. We aim to reduce the bit resolution of the network without sacrificing its performance. To this end, we design a new quantization algorithm called supervised iterative quantization to reduce the bit resolution of learned network weights. In the training stage, the supervised iterative quantization is conducted via two steps on server - apply k-means based adaptive quantization on learned network weights and retrain the network based on quantized weights. These two steps are alternated until the convergence criterion is met. In this testing stage, the network configuration and low-bit weights are loaded to the client hardware device to recognize coming input in real time, where optimized but expensive quantization becomes infeasible. Considering this, we adopt a uniform quantization for the inputs and internal network responses (called feature maps) to maintain low on-chip expenses. The Convolutional Neural Network with reduced weight and input/response precision is demonstrated in recognizing two types of images: one is hand-written digit images and the other is real-life images in office scenarios. Both results show that the new network is able to achieve the performance of the neural network with full bit resolution, even though in the new network the bit resolution of both weight and input are significantly reduced, e.g., from 64 bits to 4-5 bits.

The coordinate coherent states approach revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miao, Yan-Gang, E-mail: miaoyg@nankai.edu.cn; Zhang, Shao-Jun, E-mail: sjzhang@mail.nankai.edu.cn

2013-02-15

We revisit the coordinate coherent states approach through two different quantization procedures in the quantum field theory on the noncommutative Minkowski plane. The first procedure, which is based on the normal commutation relation between an annihilation and creation operators, deduces that a point mass can be described by a Gaussian function instead of the usual Dirac delta function. However, we argue this specific quantization by adopting the canonical one (based on the canonical commutation relation between a field and its conjugate momentum) and show that a point mass should still be described by the Dirac delta function, which implies thatmore » the concept of point particles is still valid when we deal with the noncommutativity by following the coordinate coherent states approach. In order to investigate the dependence on quantization procedures, we apply the two quantization procedures to the Unruh effect and Hawking radiation and find that they give rise to significantly different results. Under the first quantization procedure, the Unruh temperature and Unruh spectrum are not deformed by noncommutativity, but the Hawking temperature is deformed by noncommutativity while the radiation specturm is untack. However, under the second quantization procedure, the Unruh temperature and Hawking temperature are untack but the both spectra are modified by an effective greybody (deformed) factor. - Highlights: Black-Right-Pointing-Pointer Suggest a canonical quantization in the coordinate coherent states approach. Black-Right-Pointing-Pointer Prove the validity of the concept of point particles. Black-Right-Pointing-Pointer Apply the canonical quantization to the Unruh effect and Hawking radiation. Black-Right-Pointing-Pointer Find no deformations in the Unruh temperature and Hawking temperature. Black-Right-Pointing-Pointer Provide the modified spectra of the Unruh effect and Hawking radiation.« less

Topology optimization in acoustics and elasto-acoustics via a level-set method

NASA Astrophysics Data System (ADS)

Desai, J.; Faure, A.; Michailidis, G.; Parry, G.; Estevez, R.

2018-04-01

Optimizing the shape and topology (S&T) of structures to improve their acoustic performance is quite challenging. The exact position of the structural boundary is usually of critical importance, which dictates the use of geometric methods for topology optimization instead of standard density approaches. The goal of the present work is to investigate different possibilities for handling topology optimization problems in acoustics and elasto-acoustics via a level-set method. From a theoretical point of view, we detail two equivalent ways to perform the derivation of surface-dependent terms and propose a smoothing technique for treating problems of boundary conditions optimization. In the numerical part, we examine the importance of the surface-dependent term in the shape derivative, neglected in previous studies found in the literature, on the optimal designs. Moreover, we test different mesh adaptation choices, as well as technical details related to the implicit surface definition in the level-set approach. We present results in two and three-space dimensions.

Entropy-aware projected Landweber reconstruction for quantized block compressive sensing of aerial imagery

NASA Astrophysics Data System (ADS)

Liu, Hao; Li, Kangda; Wang, Bing; Tang, Hainie; Gong, Xiaohui

2017-01-01

A quantized block compressive sensing (QBCS) framework, which incorporates the universal measurement, quantization/inverse quantization, entropy coder/decoder, and iterative projected Landweber reconstruction, is summarized. Under the QBCS framework, this paper presents an improved reconstruction algorithm for aerial imagery, QBCS, with entropy-aware projected Landweber (QBCS-EPL), which leverages the full-image sparse transform without Wiener filter and an entropy-aware thresholding model for wavelet-domain image denoising. Through analyzing the functional relation between the soft-thresholding factors and entropy-based bitrates for different quantization methods, the proposed model can effectively remove wavelet-domain noise of bivariate shrinkage and achieve better image reconstruction quality. For the overall performance of QBCS reconstruction, experimental results demonstrate that the proposed QBCS-EPL algorithm significantly outperforms several existing algorithms. With the experiment-driven methodology, the QBCS-EPL algorithm can obtain better reconstruction quality at a relatively moderate computational cost, which makes it more desirable for aerial imagery applications.

Integral Sliding Mode Fault-Tolerant Control for Uncertain Linear Systems Over Networks With Signals Quantization.

PubMed

Hao, Li-Ying; Park, Ju H; Ye, Dan

2017-09-01

In this paper, a new robust fault-tolerant compensation control method for uncertain linear systems over networks is proposed, where only quantized signals are assumed to be available. This approach is based on the integral sliding mode (ISM) method where two kinds of integral sliding surfaces are constructed. One is the continuous-state-dependent surface with the aim of sliding mode stability analysis and the other is the quantization-state-dependent surface, which is used for ISM controller design. A scheme that combines the adaptive ISM controller and quantization parameter adjustment strategy is then proposed. Through utilizing H ∞ control analytical technique, once the system is in the sliding mode, the nature of performing disturbance attenuation and fault tolerance from the initial time can be found without requiring any fault information. Finally, the effectiveness of our proposed ISM control fault-tolerant schemes against quantization errors is demonstrated in the simulation.

Rate and power efficient image compressed sensing and transmission

NASA Astrophysics Data System (ADS)

Olanigan, Saheed; Cao, Lei; Viswanathan, Ramanarayanan

2016-01-01

This paper presents a suboptimal quantization and transmission scheme for multiscale block-based compressed sensing images over wireless channels. The proposed method includes two stages: dealing with quantization distortion and transmission errors. First, given the total transmission bit rate, the optimal number of quantization bits is assigned to the sensed measurements in different wavelet sub-bands so that the total quantization distortion is minimized. Second, given the total transmission power, the energy is allocated to different quantization bit layers based on their different error sensitivities. The method of Lagrange multipliers with Karush-Kuhn-Tucker conditions is used to solve both optimization problems, for which the first problem can be solved with relaxation and the second problem can be solved completely. The effectiveness of the scheme is illustrated through simulation results, which have shown up to 10 dB improvement over the method without the rate and power optimization in medium and low signal-to-noise ratio cases.

Strong and weak second-order topological insulators with hexagonal symmetry and ℤ3 index

NASA Astrophysics Data System (ADS)

Ezawa, Motohiko

2018-06-01

We propose second-order topological insulators (SOTIs) whose lattice structure has a hexagonal symmetry C6. We start with a three-dimensional weak topological insulator constructed on a stacked triangular lattice, which has only side topological surface states. We then introduce an additional mass term which gaps out the side surface states but preserves the hinge states. The resultant system is a three-dimensional SOTI. The bulk topological quantum number is shown to be the Z3 index protected by inversion time-reversal symmetry I T and rotoinversion symmetry I C6 . We obtain three phases: trivial, strong, and weak SOTI phases. We argue the origin of these two types of SOTIs. A hexagonal prism is a typical structure respecting these symmetries, where six topological hinge states emerge at the side. The building block is a hexagon in two dimensions, where topological corner states emerge at the six corners in the SOTI phase. Strong and weak SOTIs are obtained when the interlayer hopping interaction is strong and weak, respectively.

Entanglement entropy and entanglement spectrum of triplet topological superconductors.

PubMed

Oliveira, T P; Ribeiro, P; Sacramento, P D

2014-10-22

We analyze the entanglement entropy properties of a 2D p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and we find numerical evidence that for this model the derivative with respect to the magnetization provides a sensible signature of each topological phase. Following the area law for the entanglement entropy, we systematically analyze the contributions that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the finite subsystem. For this model, we show that even though the topological entanglement entropy vanishes, it signals the topological phase transitions in a finite system. We also observe a relationship between a topological contribution to the entanglement entropy in a half-cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state, as in other topological systems.

Sine-gordon type field in spacetime of arbitrary dimension. II: Stochastic quantization

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1995-11-01

Using the theory of Dirichlet forms, we prove the existence of a distribution-valued diffusion process such that the Nelson measure of a field with a bounded interaction density is its invariant probability measure. A Langevin equation in mathematically correct form is formulated which is satisfied by the process. The drift term of the equation is interpreted as a renormalized Euclidean current operator.

Development of Advanced Technologies for Complete Genomic and Proteomic Characterization of Quantized Human Tumor Cells

DTIC Science & Technology

2015-09-01

glioblastoma . We have successfully established several patient-derived cell lines from glioblastoma tumors and further established a number of...and single-cell technologies. Although the focus of this research is glioblastoma , the proposed tools are generally applicable to all cancer-based...studies. 15. SUBJECT TERMS Human cohorts, Glioblastoma , Genomic, Proteomic, Single-cell technologies, Hypothesis-driven, integrative systems approach

Bulk and interface quantum states of electrons in multi-layer heterostructures with topological materials

NASA Astrophysics Data System (ADS)

Nikolic, Aleksandar; Zhang, Kexin; Barnes, C. H. W.

2018-06-01

In this article we describe the bulk and interface quantum states of electrons in multi-layer heterostructures in one dimension, consisting of topological insulators (TIs) and topologically trivial materials. We use and extend an effective four-band continuum Hamiltonian by introducing position dependence to the eight material parameters of the Hamiltonian. We are able to demonstrate complete conduction-valence band mixing in the interface states. We find evidence for topological features of bulk states of multi-layer TI heterostructures, as well as demonstrating both complete and incomplete conduction-valence band inversion at different bulk state energies. We show that the linear k z terms in the low-energy Hamiltonian, arising from overlap of p z orbitals between different atomic layers in the case of chalcogenides, control the amount of tunneling from TIs to trivial insulators. Finally, we show that the same linear k z terms in the low-energy Hamiltonian affect the material’s ability to form the localised interface state, and we demonstrate that due to this effect the spin and probability density localisation in a thin film of Sb2Te3 is incomplete. We show that changing the parameter that controls the magnitude of the overlap of p z orbitals affects the transport characteristics of the topologically conducting states, with incomplete topological state localisation resulting in increased backscattering.

Bulk and interface quantum states of electrons in multi-layer heterostructures with topological materials.

PubMed

Nikolic, Aleksandar; Zhang, Kexin; Barnes, C H W

2018-06-13

In this article we describe the bulk and interface quantum states of electrons in multi-layer heterostructures in one dimension, consisting of topological insulators (TIs) and topologically trivial materials. We use and extend an effective four-band continuum Hamiltonian by introducing position dependence to the eight material parameters of the Hamiltonian. We are able to demonstrate complete conduction-valence band mixing in the interface states. We find evidence for topological features of bulk states of multi-layer TI heterostructures, as well as demonstrating both complete and incomplete conduction-valence band inversion at different bulk state energies. We show that the linear k z terms in the low-energy Hamiltonian, arising from overlap of p z orbitals between different atomic layers in the case of chalcogenides, control the amount of tunneling from TIs to trivial insulators. Finally, we show that the same linear k z terms in the low-energy Hamiltonian affect the material's ability to form the localised interface state, and we demonstrate that due to this effect the spin and probability density localisation in a thin film of Sb 2 Te 3 is incomplete. We show that changing the parameter that controls the magnitude of the overlap of p z orbitals affects the transport characteristics of the topologically conducting states, with incomplete topological state localisation resulting in increased backscattering.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions.

PubMed

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-04-22

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions

PubMed Central

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-01-01

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems. PMID:27102945

Vector quantization

NASA Technical Reports Server (NTRS)

Gray, Robert M.

1989-01-01

During the past ten years Vector Quantization (VQ) has developed from a theoretical possibility promised by Shannon's source coding theorems into a powerful and competitive technique for speech and image coding and compression at medium to low bit rates. In this survey, the basic ideas behind the design of vector quantizers are sketched and some comments made on the state-of-the-art and current research efforts.

Robust vector quantization for noisy channels

NASA Technical Reports Server (NTRS)

Demarca, J. R. B.; Farvardin, N.; Jayant, N. S.; Shoham, Y.

1988-01-01

The paper briefly discusses techniques for making vector quantizers more tolerant to tranmsission errors. Two algorithms are presented for obtaining an efficient binary word assignment to the vector quantizer codewords without increasing the transmission rate. It is shown that about 4.5 dB gain over random assignment can be achieved with these algorithms. It is also proposed to reduce the effects of error propagation in vector-predictive quantizers by appropriately constraining the response of the predictive loop. The constrained system is shown to have about 4 dB of SNR gain over an unconstrained system in a noisy channel, with a small loss of clean-channel performance.

Image data compression having minimum perceptual error

NASA Technical Reports Server (NTRS)

Watson, Andrew B. (Inventor)

1995-01-01

A method for performing image compression that eliminates redundant and invisible image components is described. The image compression uses a Discrete Cosine Transform (DCT) and each DCT coefficient yielded by the transform is quantized by an entry in a quantization matrix which determines the perceived image quality and the bit rate of the image being compressed. The present invention adapts or customizes the quantization matrix to the image being compressed. The quantization matrix comprises visual masking by luminance and contrast techniques and by an error pooling technique all resulting in a minimum perceptual error for any given bit rate, or minimum bit rate for a given perceptual error.

Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity

NASA Astrophysics Data System (ADS)

Veraguth, Olivier J.; Wang, Charles H.-T.

2017-10-01

Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field setting the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arbitrary group parameter that requires no further fixing as its present standard form does. Here, we find that this can be naturally realized via conformal frame transformations in scalar-tensor gravity. Such a theory generally incorporates a dynamical scalar gravitational field and reduces to general relativity when the scalar field becomes a pure gauge. In particular, we introduce a conformal Einstein frame in which loop quantization is implemented. We then discuss how different Immirzi parameters under this description may be related by conformal frame transformations and yet share the same quantization having, for example, the same area gaps, modulated by the scalar gravitational field.

Tribology of the lubricant quantized sliding state.

PubMed

Castelli, Ivano Eligio; Capozza, Rosario; Vanossi, Andrea; Santoro, Giuseppe E; Manini, Nicola; Tosatti, Erio

2009-11-07

In the framework of Langevin dynamics, we demonstrate clear evidence of the peculiar quantized sliding state, previously found in a simple one-dimensional boundary lubricated model [A. Vanossi et al., Phys. Rev. Lett. 97, 056101 (2006)], for a substantially less idealized two-dimensional description of a confined multilayer solid lubricant under shear. This dynamical state, marked by a nontrivial "quantized" ratio of the averaged lubricant center-of-mass velocity to the externally imposed sliding speed, is recovered, and shown to be robust against the effects of thermal fluctuations, quenched disorder in the confining substrates, and over a wide range of loading forces. The lubricant softness, setting the width of the propagating solitonic structures, is found to play a major role in promoting in-registry commensurate regions beneficial to this quantized sliding. By evaluating the force instantaneously exerted on the top plate, we find that this quantized sliding represents a dynamical "pinned" state, characterized by significantly low values of the kinetic friction. While the quantized sliding occurs due to solitons being driven gently, the transition to ordinary unpinned sliding regimes can involve lubricant melting due to large shear-induced Joule heating, for example at large speed.

Optimal Compression of Floating-Point Astronomical Images Without Significant Loss of Information

NASA Technical Reports Server (NTRS)

Pence, William D.; White, R. L.; Seaman, R.

2010-01-01

We describe a compression method for floating-point astronomical images that gives compression ratios of 6 - 10 while still preserving the scientifically important information in the image. The pixel values are first preprocessed by quantizing them into scaled integer intensity levels, which removes some of the uncompressible noise in the image. The integers are then losslessly compressed using the fast and efficient Rice algorithm and stored in a portable FITS format file. Quantizing an image more coarsely gives greater image compression, but it also increases the noise and degrades the precision of the photometric and astrometric measurements in the quantized image. Dithering the pixel values during the quantization process greatly improves the precision of measurements in the more coarsely quantized images. We perform a series of experiments on both synthetic and real astronomical CCD images to quantitatively demonstrate that the magnitudes and positions of stars in the quantized images can be measured with the predicted amount of precision. In order to encourage wider use of these image compression methods, we have made available a pair of general-purpose image compression programs, called fpack and funpack, which can be used to compress any FITS format image.

A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nikolaenko, S S

2014-02-28

The paper is concerned with the topological analysis of the Chaplygin integrable case in the dynamics of a rigid body in a fluid. A full list of the topological types of Chaplygin systems in their dependence on the energy level is compiled on the basis of the Fomenko-Zieschang theory. An effective description of the topology of the Liouville foliation in terms of natural coordinate variables is also presented, which opens a direct way to calculating topological invariants. It turns out that on all nonsingular energy levels Chaplygin systems are Liouville equivalent to the well-known Euler case in the dynamics of a rigid body withmore » fixed point. Bibliography: 23 titles.« less

Analysis of Fixed Duty Cycle Hysteretic Flyback Converter for Firing Set Applications.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Love, Thomas Michael

2017-05-01

This paper analyzes several performance aspects of the fixed-duty-cycle, hysteretic flyback converter topology typically used in firing sets. Topologies with and without active pulse-by-pulse current limiting are considered, and closed-form expressions in terms of basic operating parameters are derived.

Evaluation of NASA speech encoder

NASA Technical Reports Server (NTRS)

1976-01-01

Techniques developed by NASA for spaceflight instrumentation were used in the design of a quantizer for speech-decoding. Computer simulation of the actions of the quantizer was tested with synthesized and real speech signals. Results were evaluated by a phometician. Topics discussed include the relationship between the number of quantizer levels and the required sampling rate; reconstruction of signals; digital filtering; speech recording, sampling, and storage, and processing results.

Disclinations, dislocations, and continuous defects: A reappraisal

NASA Astrophysics Data System (ADS)

Kleman, M.; Friedel, J.

2008-01-01

Disclinations were first observed in mesomorphic phases. They were later found relevant to a number of ill-ordered condensed-matter media involving continuous symmetries or frustrated order. Disclinations also appear in polycrystals at the edges of grain boundaries; but they are of limited interest in solid single crystals, where they can move only by diffusion climb and, owing to their large elastic stresses, mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, and change of shape involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye’s dislocation densities, which are particularly well suited for consideration here. The notion of an extended Volterra process is introduced, which takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by a variety of applications in amorphous solids, mesomorphic phases, and frustrated media in their curved habit space. These often involve disclination networks with specific node conditions. The powerful topological theory of line defects considers only defects stable against any change of boundary conditions or relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, particularly suited for media of high plasticity or/and complex structures. It cannot analyze the dynamical properties of defects nor the elastic constants involved in their static properties; topological stability cannot guarantee energetic stability, and sometimes cannot distinguish finer details of the structure of defects.

Quantum games of opinion formation based on the Marinatto-Weber quantum game scheme

NASA Astrophysics Data System (ADS)

Deng, Xinyang; Deng, Yong; Liu, Qi; Shi, Lei; Wang, Zhen

2016-06-01

Quantization has become a new way to investigate classical game theory since quantum strategies and quantum games were proposed. In the existing studies, many typical game models, such as the prisoner's dilemma, battle of the sexes, Hawk-Dove game, have been extensively explored by using quantization approach. Along a similar method, here several game models of opinion formations will be quantized on the basis of the Marinatto-Weber quantum game scheme, a frequently used scheme of converting classical games to quantum versions. Our results show that the quantization can fascinatingly change the properties of some classical opinion formation game models so as to generate win-win outcomes.

On Fock-space representations of quantized enveloping algebras related to noncommutative differential geometry

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schlieker, M.

1995-07-01

In this paper explicitly natural (from the geometrical point of view) Fock-space representations (contragradient Verma modules) of the quantized enveloping algebras are constructed. In order to do so, one starts from the Gauss decomposition of the quantum group and introduces the differential operators on the corresponding q-deformed flag manifold (assumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group are expressed as first-order differential operators on the q-deformed flag manifold.

Exploratory research session on the quantization of the gravitational field. At the Institute for Theoretical Physics, Copenhagen, Denmark, June-July 1957

NASA Astrophysics Data System (ADS)

DeWitt, Bryce S.

2017-06-01

During the period June-July 1957 six physicists met at the Institute for Theoretical Physics of the University of Copenhagen in Denmark to work together on problems connected with the quantization of the gravitational field. A large part of the discussion was devoted to exposition of the individual work of the various participants, but a number of new results were also obtained. The topics investigated by these physicists are outlined in this report and may be grouped under the following main headings: The theory of measurement. Topographical problems in general relativity. Feynman quantization. Canonical quantization. Approximation methods. Special problems.

2007 International Brain Mapping and Intraoperative Surgical Planning Society’s (IBMISPS) Annual World Congress

DTIC Science & Technology

2008-02-01

and Stroke Two Long Term Consequences of Penetrating Head Injuries : Exacerbated Decline and Post-Traumatic Stress Disorder Key Note speaker: Michael L...an intuitively obvious first principle that if modern medicine hopes to repair adult brains (damaged by war injuries , automobile accidents, stroke ...Imaging Animal Models of Brain Disease Background and Animal Model Quantization of Structure Cerebral Blood Flow Mini- Strokes Cancer Future

Quantized expected returns in terms of dividend yield at the money

NASA Astrophysics Data System (ADS)

Dieng, Lamine

2011-03-01

We use the Bachelier (additive model) and the Black-Scholes (multiplicative model) as our models for the stock price movement for an investor who has entered into an America call option contract. We assume the investor to pay certain dividend yield on the expected rate of returns from buying stocks. In this work, we also assume the stock price to be initially in the out of the money state and eventually will move up through at the money state to the deep in the money state where the expected future payoffs and returns are positive for the stock holder. We call a singularity point at the money because the expected payoff vanishes at this point. Then, using martingale, supermartingale and Markov theories we obtain the Bachelier-type of the Black-Scholes and the Black-Scholes equations which we hedge in the limit where the change of the expected payoff of the call option is extremely small. Hence, by comparison we obtain the time-independent Schroedinger equation in Quantum Mechanics. We solve completely the time independent Schroedinger equation for both models to obtain the expected rate of returns and the expected payoffs for the stock holder at the money. We find the expected rate of returns to be quantized in terms of the dividend yield.

Magnetic resonance image compression using scalar-vector quantization

NASA Astrophysics Data System (ADS)

Mohsenian, Nader; Shahri, Homayoun

1995-12-01

A new coding scheme based on the scalar-vector quantizer (SVQ) is developed for compression of medical images. SVQ is a fixed-rate encoder and its rate-distortion performance is close to that of optimal entropy-constrained scalar quantizers (ECSQs) for memoryless sources. The use of a fixed-rate quantizer is expected to eliminate some of the complexity issues of using variable-length scalar quantizers. When transmission of images over noisy channels is considered, our coding scheme does not suffer from error propagation which is typical of coding schemes which use variable-length codes. For a set of magnetic resonance (MR) images, coding results obtained from SVQ and ECSQ at low bit-rates are indistinguishable. Furthermore, our encoded images are perceptually indistinguishable from the original, when displayed on a monitor. This makes our SVQ based coder an attractive compression scheme for picture archiving and communication systems (PACS), currently under consideration for an all digital radiology environment in hospitals, where reliable transmission, storage, and high fidelity reconstruction of images are desired.

2-Step scalar deadzone quantization for bitplane image coding.

PubMed

Auli-Llinas, Francesc

2013-12-01

Modern lossy image coding systems generate a quality progressive codestream that, truncated at increasing rates, produces an image with decreasing distortion. Quality progressivity is commonly provided by an embedded quantizer that employs uniform scalar deadzone quantization (USDQ) together with a bitplane coding strategy. This paper introduces a 2-step scalar deadzone quantization (2SDQ) scheme that achieves same coding performance as that of USDQ while reducing the coding passes and the emitted symbols of the bitplane coding engine. This serves to reduce the computational costs of the codec and/or to code high dynamic range images. The main insights behind 2SDQ are the use of two quantization step sizes that approximate wavelet coefficients with more or less precision depending on their density, and a rate-distortion optimization technique that adjusts the distortion decreases produced when coding 2SDQ indexes. The integration of 2SDQ in current codecs is straightforward. The applicability and efficiency of 2SDQ are demonstrated within the framework of JPEG2000.

Fast large-scale object retrieval with binary quantization

NASA Astrophysics Data System (ADS)

Zhou, Shifu; Zeng, Dan; Shen, Wei; Zhang, Zhijiang; Tian, Qi

2015-11-01

The objective of large-scale object retrieval systems is to search for images that contain the target object in an image database. Where state-of-the-art approaches rely on global image representations to conduct searches, we consider many boxes per image as candidates to search locally in a picture. In this paper, a feature quantization algorithm called binary quantization is proposed. In binary quantization, a scale-invariant feature transform (SIFT) feature is quantized into a descriptive and discriminative bit-vector, which allows itself to adapt to the classic inverted file structure for box indexing. The inverted file, which stores the bit-vector and box ID where the SIFT feature is located inside, is compact and can be loaded into the main memory for efficient box indexing. We evaluate our approach on available object retrieval datasets. Experimental results demonstrate that the proposed approach is fast and achieves excellent search quality. Therefore, the proposed approach is an improvement over state-of-the-art approaches for object retrieval.

Performance of coded MFSK in a Rician fading channel. [Multiple Frequency Shift Keyed modulation

NASA Technical Reports Server (NTRS)

Modestino, J. W.; Mui, S. Y.

1975-01-01

The performance of convolutional codes in conjunction with noncoherent multiple frequency shift-keyed (MFSK) modulation and Viterbi maximum likelihood decoding on a Rician fading channel is examined in detail. While the primary motivation underlying this work has been concerned with system performance on the planetary entry channel, it is expected that the results are of considerably wider interest. Particular attention is given to modeling the channel in terms of a few meaningful parameters which can be correlated closely with the results of theoretical propagation studies. Fairly general upper bounds on bit error probability performance in the presence of fading are derived and compared with simulation results using both unquantized and quantized receiver outputs. The effects of receiver quantization and channel memory are investigated and it is concluded that the coded noncoherent MFSK system offers an attractive alternative to coherent BPSK in providing reliable low data rate communications in fading channels typical of planetary entry missions.

Image segmentation using hidden Markov Gauss mixture models.

PubMed

Pyun, Kyungsuk; Lim, Johan; Won, Chee Sun; Gray, Robert M

2007-07-01

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

Analog-to-digital conversion as a source of drifts in displacements derived from digital recordings of ground acceleration

USGS Publications Warehouse

Boore, D.M.

2003-01-01

Displacements obtained from double integration of digitally recorded ground accelerations often show drifts much larger than those expected for the true ground displacements. These drifts might be due to many things, including dynamic elastic ground tilt, inelastic ground deformation, hysteresis in the instruments, and cross feed due to misalignment of nominally orthogonal sensors. This article shows that even if those effects were not present, the analog-to-digital conversion (ADC) process can produce apparent "pulses" and offsets in the acceleration baseline if the ground motion is slowly varying compared with the quantization level of the digitization. Such slowly varying signals can be produced by constant offsets that do not coincide with a quantization level and by near- and intermediate-field terms in the wave field radiated from earthquakes. Double integration of these apparent pulses and offsets leads to drifts in the displacements similar to those found in processing real recordings. These effects decrease in importance as the resolution of the ADC process increases.

Perturbative Quantum Gravity and its Relation to Gauge Theory.

PubMed

Bern, Zvi

2002-01-01

In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D -dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.

Tissue Variability and Antennas for Power Transfer to Wireless Implantable Medical Devices.

PubMed

Bocan, Kara N; Mickle, Marlin H; Sejdic, Ervin

2017-01-01

The design of effective transcutaneous systems demands the consideration of inevitable variations in tissue characteristics, which vary across body areas, among individuals, and over time. The purpose of this paper was to design and evaluate several printed antenna topologies for ultrahigh frequency (UHF) transcutaneous power transfer to implantable medical devices, and to investigate the effects of variations in tissue properties on dipole and loop topologies. Here, we show that a loop antenna topology provides the greatest achievable gain with the smallest implanted antenna, while a dipole system provides higher impedance for conjugate matching and the ability to increase gain with a larger external antenna. In comparison to the dipole system, the loop system exhibits greater sensitivity to changes in tissue structure and properties in terms of power gain, but provides higher gain when the separation is on the order of the smaller antenna dimension. The dipole system was shown to provide higher gain than the loop system at greater implant depths for the same implanted antenna area, and was less sensitive to variations in tissue properties and structure in terms of power gain at all investigated implant depths. The results show the potential of easily-fabricated, low-cost printed antenna topologies for UHF transcutaneous power, and the importance of environmental considerations in choosing the antenna topology.

Tissue Variability and Antennas for Power Transfer to Wireless Implantable Medical Devices

PubMed Central

Bocan, Kara N.; Mickle, Marlin H.

2017-01-01

The design of effective transcutaneous systems demands the consideration of inevitable variations in tissue characteristics, which vary across body areas, among individuals, and over time. The purpose of this paper was to design and evaluate several printed antenna topologies for ultrahigh frequency (UHF) transcutaneous power transfer to implantable medical devices, and to investigate the effects of variations in tissue properties on dipole and loop topologies. Here, we show that a loop antenna topology provides the greatest achievable gain with the smallest implanted antenna, while a dipole system provides higher impedance for conjugate matching and the ability to increase gain with a larger external antenna. In comparison to the dipole system, the loop system exhibits greater sensitivity to changes in tissue structure and properties in terms of power gain, but provides higher gain when the separation is on the order of the smaller antenna dimension. The dipole system was shown to provide higher gain than the loop system at greater implant depths for the same implanted antenna area, and was less sensitive to variations in tissue properties and structure in terms of power gain at all investigated implant depths. The results show the potential of easily-fabricated, low-cost printed antenna topologies for UHF transcutaneous power, and the importance of environmental considerations in choosing the antenna topology. PMID:29018637

An improved fault-tolerant control scheme for PWM inverter-fed induction motor-based EVs.

PubMed

Tabbache, Bekheïra; Benbouzid, Mohamed; Kheloui, Abdelaziz; Bourgeot, Jean-Matthieu; Mamoune, Abdeslam

2013-11-01

This paper proposes an improved fault-tolerant control scheme for PWM inverter-fed induction motor-based electric vehicles. The proposed strategy deals with power switch (IGBTs) failures mitigation within a reconfigurable induction motor control. To increase the vehicle powertrain reliability regarding IGBT open-circuit failures, 4-wire and 4-leg PWM inverter topologies are investigated and their performances discussed in a vehicle context. The proposed fault-tolerant topologies require only minimum hardware modifications to the conventional off-the-shelf six-switch three-phase drive, mitigating the IGBTs failures by specific inverter control. Indeed, the two topologies exploit the induction motor neutral accessibility for fault-tolerant purposes. The 4-wire topology uses then classical hysteresis controllers to account for the IGBT failures. The 4-leg topology, meanwhile, uses a specific 3D space vector PWM to handle vehicle requirements in terms of size (DC bus capacitors) and cost (IGBTs number). Experiments on an induction motor drive and simulations on an electric vehicle are carried-out using a European urban driving cycle to show that the proposed fault-tolerant control approach is effective and provides a simple configuration with high performance in terms of speed and torque responses. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Haralick texture features from apparent diffusion coefficient (ADC) MRI images depend on imaging and pre-processing parameters.

PubMed

Brynolfsson, Patrik; Nilsson, David; Torheim, Turid; Asklund, Thomas; Karlsson, Camilla Thellenberg; Trygg, Johan; Nyholm, Tufve; Garpebring, Anders

2017-06-22

In recent years, texture analysis of medical images has become increasingly popular in studies investigating diagnosis, classification and treatment response assessment of cancerous disease. Despite numerous applications in oncology and medical imaging in general, there is no consensus regarding texture analysis workflow, or reporting of parameter settings crucial for replication of results. The aim of this study was to assess how sensitive Haralick texture features of apparent diffusion coefficient (ADC) MR images are to changes in five parameters related to image acquisition and pre-processing: noise, resolution, how the ADC map is constructed, the choice of quantization method, and the number of gray levels in the quantized image. We found that noise, resolution, choice of quantization method and the number of gray levels in the quantized images had a significant influence on most texture features, and that the effect size varied between different features. Different methods for constructing the ADC maps did not have an impact on any texture feature. Based on our results, we recommend using images with similar resolutions and noise levels, using one quantization method, and the same number of gray levels in all quantized images, to make meaningful comparisons of texture feature results between different subjects.

From black holes to white holes: a quantum gravitational, symmetric bounce

NASA Astrophysics Data System (ADS)

Olmedo, Javier; Saini, Sahil; Singh, Parampreet

2017-11-01

Recently, a consistent non-perturbative quantization of the Schwarzschild interior resulting in a bounce from black hole to white hole geometry has been obtained by loop quantizing the Kantowski-Sachs vacuum spacetime. As in other spacetimes where the singularity is dominated by the Weyl part of the spacetime curvature, the structure of the singularity is highly anisotropic in the Kantowski-Sachs vacuum spacetime. As a result, the bounce turns out to be in general asymmetric, creating a large mass difference between the parent black hole and the child white hole. In this manuscript, we investigate under what circumstances a symmetric bounce scenario can be constructed in the above quantization. Using the setting of Dirac observables and geometric clocks, we obtain a symmetric bounce condition which can be satisfied by a slight modification in the construction of loops over which holonomies are considered in the quantization procedure. These modifications can be viewed as quantization ambiguities, and are demonstrated in three different flavors, all of which lead to a non-singular black to white hole transition with identical masses. Our results show that quantization ambiguities can mitigate or even qualitatively change some key features of the physics of singularity resolution. Further, these results are potentially helpful in motivating and constructing symmetric black to white hole transition scenarios.

Rate-distortion analysis of dead-zone plus uniform threshold scalar quantization and its application--part II: two-pass VBR coding for H.264/AVC.

PubMed

Sun, Jun; Duan, Yizhou; Li, Jiangtao; Liu, Jiaying; Guo, Zongming

2013-01-01

In the first part of this paper, we derive a source model describing the relationship between the rate, distortion, and quantization steps of the dead-zone plus uniform threshold scalar quantizers with nearly uniform reconstruction quantizers for generalized Gaussian distribution. This source model consists of rate-quantization, distortion-quantization (D-Q), and distortion-rate (D-R) models. In this part, we first rigorously confirm the accuracy of the proposed source model by comparing the calculated results with the coding data of JM 16.0. Efficient parameter estimation strategies are then developed to better employ this source model in our two-pass rate control method for H.264 variable bit rate coding. Based on our D-Q and D-R models, the proposed method is of high stability, low complexity and is easy to implement. Extensive experiments demonstrate that the proposed method achieves: 1) average peak signal-to-noise ratio variance of only 0.0658 dB, compared to 1.8758 dB of JM 16.0's method, with an average rate control error of 1.95% and 2) significant improvement in smoothing the video quality compared with the latest two-pass rate control method.

Glass transition temperature and topological constraints of sodium borophosphate glass-forming liquids.

PubMed

Jiang, Qi; Zeng, Huidan; Liu, Zhao; Ren, Jing; Chen, Guorong; Wang, Zhaofeng; Sun, Luyi; Zhao, Donghui

2013-09-28

Sodium borophosphate glasses exhibit intriguing mixed network former effect, with the nonlinear compositional dependence of their glass transition temperature as one of the most typical examples. In this paper, we establish the widely applicable topological constraint model of sodium borophosphate mixed network former glasses to explain the relationship between the internal structure and nonlinear changes of glass transition temperature. The application of glass topology network was discussed in detail in terms of the unified methodology for the quantitative distribution of each coordinated boron and phosphorus units and glass transition temperature dependence of atomic constraints. An accurate prediction of composition scaling of the glass transition temperature was obtained based on topological constraint model.

New displacement-based methods for optimal truss topology design

NASA Technical Reports Server (NTRS)

Bendsoe, Martin P.; Ben-Tal, Aharon; Haftka, Raphael T.

1991-01-01

Two alternate methods for maximum stiffness truss topology design are presented. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, nonconvex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained, and convex problem in the displacements only can be formulated, and this problem can be solved by a nonsmooth, steepest descent algorithm. In both methods, the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix are circumvented. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.

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

NASA Astrophysics Data System (ADS)

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.