A heat kernel proof of the index theorem for deformation quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander

2017-11-01

We give a heat kernel proof of the algebraic index theorem for deformation quantization with separation of variables on a pseudo-Kähler manifold. We use normalizations of the canonical trace density of a star product and of the characteristic classes involved in the index formula for which this formula contains no extra constant factors.

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.

Equivalence of Einstein and Jordan frames in quantized anisotropic cosmological models

NASA Astrophysics Data System (ADS)

Pandey, Sachin; Pal, Sridip; Banerjee, Narayan

2018-06-01

The present work shows that the mathematical equivalence of the Jordan frame and its conformally transformed version, the Einstein frame, so as far as Brans-Dicke theory is concerned, survives a quantization of cosmological models, arising as solutions to the Brans-Dicke theory. We work with the Wheeler-deWitt quantization scheme and take up quite a few anisotropic cosmological models as examples. We effectively show that the transformation from the Jordan to the Einstein frame is a canonical one and hence two frames furnish equivalent description of same physical scenario.

Gauge fixing and BFV quantization

NASA Astrophysics Data System (ADS)

Rogers, Alice

2000-01-01

Non-singularity conditions are established for the Batalin-Fradkin-Vilkovisky (BFV) gauge-fixing fermion which are sufficient for it to lead to the correct path integral for a theory with constraints canonically quantized in the BFV approach. The conditions ensure that the anticommutator of this fermion with the BRST charge regularizes the path integral by regularizing the trace over non-physical states in each ghost sector. The results are applied to the quantization of a system which has a Gribov problem, using a non-standard form of the gauge-fixing fermion.

Covariant spinor representation of iosp(d,2/2) and quantization of the spinning relativistic particle

NASA Astrophysics Data System (ADS)

Jarvis, P. D.; Corney, S. P.; Tsohantjis, I.

1999-12-01

A covariant spinor representation of iosp(d,2/2) is constructed for the quantization of the spinning relativistic particle. It is found that, with appropriately defined wavefunctions, this representation can be identified with the state space arising from the canonical extended BFV-BRST quantization of the spinning particle with admissible gauge fixing conditions after a contraction procedure. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the iosp(d,2/2) algebra.

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.

Covariant scalar representation of ? and quantization of the scalar relativistic particle

NASA Astrophysics Data System (ADS)

Jarvis, P. D.; Tsohantjis, I.

1996-03-01

A covariant scalar representation of iosp(d,2/2) is constructed and analysed in comparison with existing BFV-BRST methods for the quantization of the scalar relativistic particle. It is found that, with appropriately defined wavefunctions, this iosp(d,2/2) produced representation can be identified with the state space arising from the canonical BFV-BRST quantization of the modular-invariant, unoriented scalar particle (or antiparticle) with admissible gauge-fixing conditions. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the iosp(d,2/2) algebra.

Quantization of Non-Lagrangian Systems

NASA Astrophysics Data System (ADS)

Kochan, Denis

A novel method for quantization of non-Lagrangian (open) systems is proposed. It is argued that the essential object, which provides both classical and quantum evolution, is a certain canonical two-form defined in extended velocity space. In this setting classical dynamics is recovered from the stringy-type variational principle, which employs umbilical surfaces instead of histories of the system. Quantization is then accomplished in accordance with the introduced variational principle. The path integral for the transition probability amplitude (propagator) is rearranged to a surface functional integral. In the standard case of closed (Lagrangian) systems the presented method reduces to the standard Feynman's approach. The inverse problem of the calculus of variation, the problem of quantization ambiguity and the quantum mechanics in the presence of friction are analyzed in detail.

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).

New vertices and canonical quantization

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

Alexandrov, Sergei

2010-07-15

We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the Engle-Pereira-Rovelli-Livine model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer to loop quantum gravity. Second, we however argue that the quantization procedure used to derive the new models is inconsistent since it relies on the symplectic structure of the unconstrained BF theory.

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

Paul Weiss and the genesis of canonical quantization

NASA Astrophysics Data System (ADS)

Rickles, Dean; Blum, Alexander

2015-12-01

This paper describes the life and work of a figure who, we argue, was of primary importance during the early years of field quantisation and (albeit more indirectly) quantum gravity. A student of Dirac and Born, he was interned in Canada during the second world war as an enemy alien and after his release never seemed to regain a good foothold in physics, identifying thereafter as a mathematician. He developed a general method of quantizing (linear and non-linear) field theories based on the parameters labelling an arbitrary hypersurface. This method (the `parameter formalism' often attributed to Dirac), though later discarded, was employed (and viewed at the time as an extremely important tool) by the leading figures associated with canonical quantum gravity: Dirac, Pirani and Schild, Bergmann, DeWitt, and others. We argue that he deserves wider recognition for this and other innovations.

BOOK REVIEW: Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity

NASA Astrophysics Data System (ADS)

Husain, Viqar

2012-03-01

Research on quantum gravity from a non-perturbative 'quantization of geometry' perspective has been the focus of much research in the past two decades, due to the Ashtekar-Barbero Hamiltonian formulation of general relativity. This approach provides an SU(2) gauge field as the canonical configuration variable; the analogy with Yang-Mills theory at the kinematical level opened up some research space to reformulate the old Wheeler-DeWitt program into what is now known as loop quantum gravity (LQG). The author is known for his work in the LQG approach to cosmology, which was the first application of this formalism that provided the possibility of exploring physical questions. Therefore the flavour of the book is naturally informed by this history. The book is based on a set of graduate-level lectures designed to impart a working knowledge of the canonical approach to gravitation. It is more of a textbook than a treatise, unlike three other recent books in this area by Kiefer [1], Rovelli [2] and Thiemann [3]. The style and choice of topics of these authors are quite different; Kiefer's book provides a broad overview of the path integral and canonical quantization methods from a historical perspective, whereas Rovelli's book focuses on philosophical and formalistic aspects of the problems of time and observables, and gives a development of spin-foam ideas. Thiemann's is much more a mathematical physics book, focusing entirely on the theory of representing constraint operators on a Hilbert space and charting a mathematical trajectory toward a physical Hilbert space for quantum gravity. The significant difference from these books is that Bojowald covers mainly classical topics until the very last chapter, which contains the only discussion of quantization. In its coverage of classical gravity, the book has some content overlap with Poisson's book [4], and with Ryan and Shepley's older work on relativistic cosmology [5]; for instance the contents of chapter five of the book are also covered in detail, and with more worked examples, in the former book, and the entire focus of the latter is Bianchi models. After a brief introduction outlining the aim of the book, the second chapter provides the canonical theory of homogeneous isotropic cosmology with scalar matter; this covers the basics and linear perturbation theory, and is meant as a first taste of what is to come. The next chapter is a thorough introduction of the canonical formulation of general relativity in both the ADM and Ashtekar-Barbero variables. This chapter contains details useful for graduate students which are either scattered or missing in the literature. Applications of the canonical formalism are in the following chapter. These cover standard material and techniques for obtaining mini(midi)-superspace models, including the Bianchi and Gowdy cosmologies, and spherically symmetric reductions. There is also a brief discussion of the two-dimensional dilaton gravity. The spherically symmetric reduction is presented in detail also in the connection-triad variables. The chapter on global and asymptotic properties gives introductions to geodesic and null congruences, trapped surfaces, a survey of singularity theorems, horizons and asymptotic properties. The chapter ends with a discussion of junction conditions and the Vaidya solution. As already mentioned, this material is covered in detail in Poisson's book. The final chapter on quantization describes and contrasts the Dirac and reduced phase space methods. It also gives an introduction to background independent quantization using the holonomy-flux operators, which forms the basis of the LQG program. The application of this method to cosmology and its affect on the Friedmann equation is covered next, followed by a brief introduction to the effective constraint method, which is another area developed by the author. I think this book is a useful addition to the literature for graduate students, and potentially also for researchers in other areas who wish to learn about the canonical approach to gravity. However, given the brief chapter on quantization, the book would go well with a review paper, or parts of the other three quantum gravity books cited above. References [1] Kiefer C 2006 Quantum Gravity 2nd ed. (Oxford University Press) [2] Rovelli C 2007 Quantum Gravity (Cambridge University Press) [3] Thiemann T 2008 Modern Canonical Quantum Gravity (Cambridge University Press) [4] Posson E 2004 A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics (Cambridge University Press) [5] Ryan M P and Shepley L C 1975 Homogeneous Relativistic Cosmology (Princeton University Press)

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.

How quantizable matter gravitates: A practitioner's guide

NASA Astrophysics Data System (ADS)

Schuller, Frederic P.; Witte, Christof

2014-05-01

We present the practical step-by-step procedure for constructing canonical gravitational dynamics and kinematics directly from any previously specified quantizable classical matter dynamics, and then illustrate the application of this recipe by way of two completely worked case studies. Following the same procedure, any phenomenological proposal for fundamental matter dynamics must be supplemented with a suitable gravity theory providing the coefficients and kinematical interpretation of the matter theory, before any of the two theories can be meaningfully compared to experimental data.

Consistency of certain constitutive relations with quantum electromagnetism

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

Horsley, S. A. R.

2011-12-15

Recent work by Philbin [New J. Phys. 12, 123008 (2010)] has provided a Lagrangian theory that establishes a general method for the canonical quantization of the electromagnetic field in any dispersive, lossy, linear dielectric. Working from this theory, we extend the Lagrangian description to reciprocal and nonreciprocal magnetoelectric (bianisotropic) media, showing that some versions of the constitutive relations are inconsistent with a real Lagrangian, and hence with quantization. This amounts to a restriction on the magnitude of the magnetoelectric coupling. Moreover, from the point of view of quantization, moving media are shown to be fundamentally different from stationary magnetoelectrics, despitemore » the formal similarity in the constitutive relations.« less

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}.

Topologies on quantum topoi induced by quantization

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

Nakayama, Kunji

2013-07-15

In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantummore » topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.« less

Electrical and thermal conductance quantization in nanostructures

NASA Astrophysics Data System (ADS)

Nawrocki, Waldemar

2008-10-01

In the paper problems of electron transport in mesoscopic structures and nanostructures are considered. The electrical conductance of nanowires was measured in a simple experimental system. Investigations have been performed in air at room temperature measuring the conductance between two vibrating metal wires with standard oscilloscope. Conductance quantization in units of G0 = 2e2/h = (12.9 kΩ)-1 up to five quanta of conductance has been observed for nanowires formed in many metals. The explanation of this universal phenomena is the formation of a nanometer-sized wire (nanowire) between macroscopic metallic contacts which induced, due to theory proposed by Landauer, the quantization of conductance. Thermal problems in nanowires are also discussed in the paper.

Thermal distributions of first, second and third quantization

NASA Astrophysics Data System (ADS)

McGuigan, Michael

1989-05-01

We treat first quantized string theory as two-dimensional gravity plus matter. This allows us to compute the two-dimensional density of one string states by the method of Darwin and Fowler. One can then use second quantized methods to form a grand microcanonical ensemble in which one can compute the density of multistring states of arbitrary momentum and mass. It is argued that modelling an elementary particle as a d-1-dimensional object whose internal degrees of freedom are described by a massless d-dimensional gas yields a density of internal states given by σ d(m)∼m -aexp((bm) {2(d-1)}/{d}) . This indicates that these objects cannot be in thermal equilibrium at any temperature unless d⩽2; that is for a string or a particle. Finally, we discuss the application of the above ideas to four-dimensional gravity and introduce an ensemble of multiuniverse states parameterized by second quantized canonical momenta and particle number.

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.

Macroscopic Quantum Phase-Locking Model for the Quantum Hall = Effect

NASA Astrophysics Data System (ADS)

Wang, Te-Chun; Gou, Yih-Shun

1997-08-01

A macroscopic model of nonlinear dissipative phase-locking between a Josephson-like frequency and a macroscopic electron wave frequency is proposed to explain the Quantum Hall Effect. It is well known that a r.f-biased Josephson junction displays a collective phase-locking behavior which can be described by a non-autonomous second order equation or an equivalent 2+1-dimensional dynamical system. Making a direct analogy between the QHE and the Josephson system, this report proposes a computer-solving nonlinear dynamical model for the quantization of the Hall resistance. In this model, the Hall voltage is assumed to be proportional to a Josephson-like frequency and the Hall current is assumed related to a coherent electron wave frequency. The Hall resistance is shown to be quantized in units of the fine structure constant as the ratio of these two frequencies are locked into a rational winding number. To explain the sample-width dependence of the critical current, the 2DEG under large applied current is further assumed to develop a Josephson-like junction array in which all Josephson-like frequencies are synchronized. Other remarkable features of the QHE such as the resistance fluctuation and the even-denominator states are also discussed within this picture.

Baryon number violation and novel canonical anti-commutation relations

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo; Tureanu, Anca

2018-02-01

The possible neutron-antineutron oscillation is described by an effective quadratic Lagrangian analogous to the BCS theory. It is shown that the conventional equal-time anti-commutation relations of the neutron variable n (t , x →) are modified by the baryon number violating terms. This is established by the Bjorken-Johnson-Low prescription and also by the canonical quantization combined with equations of motion. This novel canonical behavior can give rise to an important physical effect, which is illustrated by analyzing the Lagrangian that violates the baryon number but gives rise to the degenerate effective Majorana fermions and thus no neutron-antineutron oscillation. Technically, this model is neatly treated using a relativistic analogue of the Bogoliubov transformation.

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'.

Quantization of Simple Parametrized Systems

NASA Astrophysics Data System (ADS)

Ruffini, Giulio

1995-01-01

I study the canonical formulation and quantization of some simple parametrized systems using Dirac's formalism and the Becchi-Rouet-Stora-Tyutin (BRST) extended phase space method. These systems include the parametrized particle and minisuperspace. Using Dirac's formalism I first analyze for each case the construction of the classical reduced phase space. There are two separate features of these systems that may make this construction difficult: (a) Because of the boundary conditions used, the actions are not gauge invariant at the boundaries. (b) The constraints may have a disconnected solution space. The relativistic particle and minisuperspace have such complicated constraints, while the non-relativistic particle displays only the first feature. I first show that a change of gauge fixing is equivalent to a canonical transformation in the reduced phase space, thus resolving the problems associated with the first feature above. Then I consider the quantization of these systems using several approaches: Dirac's method, Dirac-Fock quantization, and the BRST formalism. In the cases of the relativistic particle and minisuperspace I consider first the quantization of one branch of the constraint at the time and then discuss the backgrounds in which it is possible to quantize simultaneously both branches. I motivate and define the inner product, and obtain, for example, the Klein-Gordon inner product for the relativistic case. Then I show how to construct phase space path integral representations for amplitudes in these approaches--the Batalin-Fradkin-Vilkovisky (BFV) and the Faddeev path integrals --from which one can then derive the path integrals in coordinate space--the Faddeev-Popov path integral and the geometric path integral. In particular I establish the connection between the Hilbert space representation and the range of the lapse in the path integrals. I also examine the class of paths that contribute in the path integrals and how they affect space-time covariance, concluding that it is consistent to take paths that move forward in time only when there is no electric field. The key elements in this analysis are the space-like paths and the behavior of the action under the non-trivial ( Z_2) element of the reparametrization group.

Fractional Quantization of the Hall Effect

DOE R&D Accomplishments Database

Laughlin, R. B.

1984-02-27

The Fractional Quantum Hall Effect is caused by the condensation of a two-dimensional electron gas in a strong magnetic field into a new type of macroscopic ground state, the elementary excitations of which are fermions of charge 1/m, where m is an odd integer. A mathematical description is presented.

Third quantization

NASA Astrophysics Data System (ADS)

Seligman, Thomas H.; Prosen, Tomaž

2010-12-01

The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a non-orthogonal basis, the latter requires the introduction of a dual set of spaces. In both cases an operator algebra closely resembling the canonical one is developed and used to define the dual sets of bases. We here concentrated on the bosonic case where the unboundedness of the operators requires the definitions of dual spaces to support the pair of bases. Some applications, mainly to non-equilibrium steady states, will be mentioned.

Third quantization

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

Seligman, Thomas H.; Centro Internacional de Ciencias, Cuernavaca, Morelos; Prosen, Tomaz

2010-12-23

The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a non-orthogonal basis, the latter requires the introduction of a dual set of spaces. In both cases an operator algebra closely resembling the canonical one is developed and used to define the dual sets of bases. We here concentrated on the bosonic case where the unboundedness of the operators requires the definitions of dual spaces to support the pair of bases. Somemore » applications, mainly to non-equilibrium steady states, will be mentioned.« less

Formal Symplectic Groupoid of a Deformation Quantization

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2005-08-01

We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique formal symplectic groupoid ‘with separation of variables’ over an arbitrary Kähler-Poisson manifold.

Quark and gluon production from a boost-invariantly expanding color electric field

NASA Astrophysics Data System (ADS)

Taya, Hidetoshi

2017-07-01

Particle production from an expanding classical color electromagnetic field is extensively studied, motivated by the early stage dynamics of ultrarelativistic heavy ion collisions. We develop a formalism at one-loop order to compute the particle spectra by canonically quantizing quark, gluon, and ghost fluctuations under the presence of such an expanding classical color background field; the canonical quantization is done in the τ -η coordinates in order to take into account manifestly the expanding geometry. As a demonstration, we model the expanding classical color background field by a boost-invariantly expanding homogeneous color electric field with lifetime T , for which we obtain analytically the quark and gluon production spectra by solving the equations of motion of QCD nonperturbatively with respect to the color electric field. In this paper we study (i) the finite lifetime effect, which is found to modify significantly the particle spectra from those expected from the Schwinger formula; (ii) the difference between the quark and gluon production; and (iii) the quark mass dependence of the production spectra. Implications of these results to ultrarelativistic heavy ion collisions are also discussed.

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

The canonical quantization of chaotic maps on the torus

NASA Astrophysics Data System (ADS)

Rubin, Ron Shai

In this thesis, a quantization method for classical maps on the torus is presented. The quantum algebra of observables is defined as the quantization of measurable functions on the torus with generators exp (2/pi ix) and exp (2/pi ip). The Hilbert space we use remains the infinite-dimensional L2/ (/IR, dx). The dynamics is given by a unitary quantum propagator such that as /hbar /to 0, the classical dynamics is returned. We construct such a quantization for the Kronecker map, the cat map, the baker's map, the kick map, and the Harper map. For the cat map, we find the same for the propagator on the plane the same integral kernel conjectured in (HB) using semiclassical methods. We also define a quantum 'integral over phase space' as a trace over the quantum algebra. Using this definition, we proceed to define quantum ergodicity and mixing for maps on the torus. We prove that the quantum cat map and Kronecker map are both ergodic, but only the cat map is mixing, true to its classical origins. For Planck's constant satisfying the integrality condition h = 1/N, with N/in doubz+, we construct an explicit isomorphism between L2/ (/IR, dx) and the Hilbert space of sections of an N-dimensional vector bundle over a θ-torus T2 of boundary conditions. The basis functions are distributions in L2/ (/IR, dx), given by an infinite comb of Dirac δ-functions. In Bargmann space these distributions take on the form of Jacobi ϑ-functions. Transformations from position to momentum representation can be implemented via a finite N-dimensional discrete Fourier transform. With the θ-torus, we provide a connection between the finite-dimensional quantum maps given in the physics literature and the canonical quantization presented here and found in the language of pseudo-differential operators elsewhere in mathematics circles. Specifically, at a fixed point of the dynamics on the θ-torus, we return a finite-dimensional matrix propagator. We present this connection explicitly for several examples.

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.

Quantization of the Szekeres system

NASA Astrophysics Data System (ADS)

Paliathanasis, A.; Zampeli, Adamantia; Christodoulakis, T.; Mustafa, M. T.

2018-06-01

We study the quantum corrections on the Szekeres system in the context of canonical quantization in the presence of symmetries. We start from an effective point-like Lagrangian with two integrals of motion, one corresponding to the Hamiltonian and the other to a second rank killing tensor. Imposing their quantum version on the wave function results to a solution which is then interpreted in the context of Bohmian mechanics. In this semiclassical approach, it is shown that there is no quantum corrections, thus the classical trajectories of the Szekeres system are not affected at this level. Finally, we define a probability function which shows that a stationary surface of the probability corresponds to a classical exact solution.

Mathematics of Quantization and Quantum Fields

NASA Astrophysics Data System (ADS)

Dereziński, Jan; Gérard, Christian

2013-03-01

Preface; 1. Vector spaces; 2. Operators in Hilbert spaces; 3. Tensor algebras; 4. Analysis in L2(Rd); 5. Measures; 6. Algebras; 7. Anti-symmetric calculus; 8. Canonical commutation relations; 9. CCR on Fock spaces; 10. Symplectic invariance of CCR in finite dimensions; 11. Symplectic invariance of the CCR on Fock spaces; 12. Canonical anti-commutation relations; 13. CAR on Fock spaces; 14. Orthogonal invariance of CAR algebras; 15. Clifford relations; 16. Orthogonal invariance of the CAR on Fock spaces; 17. Quasi-free states; 18. Dynamics of quantum fields; 19. Quantum fields on space-time; 20. Diagrammatics; 21. Euclidean approach for bosons; 22. Interacting bosonic fields; Subject index; Symbols index.

Quantization of spinor fields. III. Fermions on coherent (Bose) domains

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr

1983-02-01

A formulation of the c-number classics-quanta correspondence rule for spinor systems requires all elements of the quantum field algebra to be expanded into power series with respect to the generators of the canonical commutation relation (CCR) algebra. On the other hand, the asymptotic completeness demand would result in the (Haag) expansions with respect to the canonical anticommutation relation (CAR) generators. We establish the conditions under which the above correspondence rule can be reconciled with the existence of Haag expansions in terms of asymptotic free Fermi fields. Then, the CAR become represented on the state space of the Bose (CCR) system.

Generalized centripetal force law and quantization of motion constrained on 2D surfaces

NASA Astrophysics Data System (ADS)

Liu, Q. H.; Zhang, J.; Lian, D. K.; Hu, L. D.; Li, Z.

2017-03-01

For a particle of mass μ moves on a 2D surface f(x) = 0 embedded in 3D Euclidean space of coordinates x, there is an open and controversial problem whether the Dirac's canonical quantization scheme for the constrained motion allows for the geometric potential that has been experimentally confirmed. We note that the Dirac's scheme hypothesizes that the symmetries indicated by classical brackets among positions x and momenta p and Hamiltonian Hc remain in quantum mechanics, i.e., the following Dirac brackets [ x ,Hc ] D and [ p ,Hc ] D holds true after quantization, in addition to the fundamental ones [ x , x ] D, [ x , p ] D and [ p , p ] D. This set of hypotheses implies that the Hamiltonian operator is simultaneously determined during the quantization. The quantum mechanical relations corresponding to the classical mechanical ones p / μ =[ x ,Hc ] D directly give the geometric momenta. The time t derivative of the momenta p ˙ =[ p ,Hc ] D in classical mechanics is in fact the generalized centripetal force law for particle on the 2D surface, which in quantum mechanics permits both the geometric momenta and the geometric potential.

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.

Quantum self-gravitating collapsing matter in a quantum geometry

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge

2016-09-01

The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole.

Testing quantum mechanics against macroscopic realism using the output of {chi}{sup (2)} nonlinearity

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

Podoshvedov, Sergey A.; Kim, Jaewan

2006-09-15

We suggest an all-optical scheme to generate entangled superposition of a single photon with macroscopic entangled states for testing macroscopic realism. The scheme consists of source of single photons, a Mach-Zehnder interferometer in routes of which a system of coupled-down converters with type-I phase matching is inserted, and a beam splitter for the other auxiliary modes of the scheme. We use quantization of the pumping modes, depletion of the coherent states passing through the system, and interference effect in the pumping modes in the process of erasing which-path information of the single-photon on exit from the Mach-Zehnder interferometer. We showmore » the macroscopic fields of the output superposition are distinguishable states. This scheme generates macroscopic entangled state that violates Bell's inequality. Moreover, the detailed analysis concerning change of amplitudes of entangled superposition by means of repeating this process many times is accomplished. We show our scheme works without photon number resolving detection and it is robust to detector inefficiency.« less

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 and Quantum-Like Phenomena: A Number Amplitude Approach

NASA Astrophysics Data System (ADS)

Robinson, T. R.; Haven, E.

2015-12-01

Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.

Electron Transport In Nanowires - An Engineer'S View

NASA Astrophysics Data System (ADS)

Nawrocki, W.

In the paper technological problems connected to electron transport in mesoscopic- and nanostructures are considered. The electrical conductance of nanowires formed by metallic contacts in an experimental setup proposed by Costa-Kramer et al. The investigation has been performed in air at room temperature measuring the conductance between two vibrating metal wires with standard oscilloscope. Conductance quantization in units of G o = 2e /h = (12.9 kΩ)-1 up to five quanta of conductance has been observed for nanowires formed in many metals. The explanation of this universal phenomena is the formation of a nanometer-sized wire (nanowire) between macroscopic metallic contacts which induced, due to theory proposed by Landauer, the quantization of conductance. Thermal problems in nanowirese are also discussed in the paper.

Reduced Order Podolsky Model

NASA Astrophysics Data System (ADS)

Thibes, Ronaldo

2017-02-01

We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution, we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure to implement the second-class constraints and the Batalin-Fradkin-Vilkovisky path integral quantization scheme to deal with the symmetries generated by the first-class constraints. The physical interpretation of the results turns out to be simpler due to the reduced derivatives order permeating the equations of motion, Dirac brackets and effective action.

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

Constraining the loop quantum gravity parameter space from phenomenology

NASA Astrophysics Data System (ADS)

Brahma, Suddhasattwa; Ronco, Michele

2018-03-01

Development of quantum gravity theories rarely takes inputs from experimental physics. In this letter, we take a small step towards correcting this by establishing a paradigm for incorporating putative quantum corrections, arising from canonical quantum gravity (QG) theories, in deriving falsifiable modified dispersion relations (MDRs) for particles on a deformed Minkowski space-time. This allows us to differentiate and, hopefully, pick between several quantization choices via testable, state-of-the-art phenomenological predictions. Although a few explicit examples from loop quantum gravity (LQG) (such as the regularization scheme used or the representation of the gauge group) are shown here to establish the claim, our framework is more general and is capable of addressing other quantization ambiguities within LQG and also those arising from other similar QG approaches.

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.

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.

Relativistic Hamiltonian dynamics for N point particles

NASA Astrophysics Data System (ADS)

King, M. J.

1980-08-01

The theory is quantized canonically to give a relativistic quantum mechanics for N particles. The existence of such a theory has been in doubt since the proof of the No-interaction theorem. However, such a theory does exist and was generalized. This dynamics is expressed in terms of N + 1 pairs of canonical fourvectors (center-of-momentum variables or CMV). A gauge independent reduction due to N + 3 first class kinematic constraints leads to a 6N + 2 dimensional minimum kinematic phase space, K. The kinematics and dynamics of particles with intrinsic spin were also considered. To this end known constraint techniques were generalized to make use of graded Lie algebras. The (Poincare) invariant Hamiltonian is specified in terms of the gauge invarient variables of K. The covariant worldline variables of each particle were found to be gauge dependent. As such they will usually not satisfy a canonical algebra. An exception exists for free particles. The No-interaction theorem therefore is not violated.

Quantum motion on a torus as a submanifold problem in a generalized Dirac's theory of second-class constraints

NASA Astrophysics Data System (ADS)

Xun, D. M.; Liu, Q. H.; Zhu, X. M.

2013-11-01

A generalization of Dirac's canonical quantization scheme for a system with second-class constraints is proposed, in which the fundamental commutation relations are constituted by all commutators between positions, momenta and Hamiltonian, so they are simultaneously quantized in a self-consistent manner, rather than by those between merely positions and momenta which leads to ambiguous forms of the Hamiltonian and the momenta. The application of the generalized scheme to the quantum motion on a torus leads to a remarkable result: the quantum theory is inconsistent if built up in an intrinsic geometric manner, whereas it becomes consistent within an extrinsic examination of the torus as a submanifold in three dimensional flat space with the use of the Cartesian coordinate system. The geometric momentum and potential are then reasonably reproduced.

Quantization of systems with temporally varying discretization. II. Local evolution moves

NASA Astrophysics Data System (ADS)

Höhn, Philipp A.

2014-10-01

Several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves. Local evolution moves in variational discrete systems (1) are a generalization of the Pachner evolution moves of simplicial gravity models, (2) update only a small subset of the dynamical data, (3) change the number of kinematical and physical degrees of freedom, and (4) generate a dynamical (or canonical) coarse graining or refining of the underlying discretization. To systematically explore such local moves and their implications in the quantum theory, this article suitably expands the quantum formalism for global evolution moves, constructed in Paper I [P. A. Höhn, "Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces," J. Math. Phys. 55, 083508 (2014); e-print arXiv:1401.6062 [gr-qc

Complexity theory, time series analysis and Tsallis q-entropy principle part one: theoretical aspects

NASA Astrophysics Data System (ADS)

Pavlos, George P.

2017-12-01

In this study, we present the highlights of complexity theory (Part I) and significant experimental verifications (Part II) and we try to give a synoptic description of complexity theory both at the microscopic and at the macroscopic level of the physical reality. Also, we propose that the self-organization observed macroscopically is a phenomenon that reveals the strong unifying character of the complex dynamics which includes thermodynamical and dynamical characteristics in all levels of the physical reality. From this point of view, macroscopical deterministic and stochastic processes are closely related to the microscopical chaos and self-organization. The scientific work of scientists such as Wilson, Nicolis, Prigogine, Hooft, Nottale, El Naschie, Castro, Tsallis, Chang and others is used for the development of a unified physical comprehension of complex dynamics from the microscopic to the macroscopic level. Finally, we provide a comprehensive description of the novel concepts included in the complexity theory from microscopic to macroscopic level. Some of the modern concepts that can be used for a unified description of complex systems and for the understanding of modern complexity theory, as it is manifested at the macroscopic and the microscopic level, are the fractal geometry and fractal space-time, scale invariance and scale relativity, phase transition and self-organization, path integral amplitudes, renormalization group theory, stochastic and chaotic quantization and E-infinite theory, etc.

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.

The BRST complex of homological Poisson reduction

NASA Astrophysics Data System (ADS)

Müller-Lennert, Martin

2017-02-01

BRST complexes are differential graded Poisson algebras. They are associated with a coisotropic ideal J of a Poisson algebra P and provide a description of the Poisson algebra (P/J)^J as their cohomology in degree zero. Using the notion of stable equivalence introduced in Felder and Kazhdan (Contemporary Mathematics 610, Perspectives in representation theory, 2014), we prove that any two BRST complexes associated with the same coisotropic ideal are quasi-isomorphic in the case P = R[V] where V is a finite-dimensional symplectic vector space and the bracket on P is induced by the symplectic structure on V. As a corollary, the cohomology of the BRST complexes is canonically associated with the coisotropic ideal J in the symplectic case. We do not require any regularity assumptions on the constraints generating the ideal J. We finally quantize the BRST complex rigorously in the presence of infinitely many ghost variables and discuss the uniqueness of the quantization procedure.

Comment on 'Controversy concerning the definition of quark and gluon angular momentum' by Elliot Leader [PRD 83, 096012 (2011)

NASA Astrophysics Data System (ADS)

Lin, Huey-Wen; Liu, Keh-Fei

2012-03-01

It is argued by the author that the canonical form of the quark energy-momentum tensor with a partial derivative instead of the covariant derivative is the correct definition for the quark momentum and angular momentum fraction of the nucleon in covariant quantization. Although it is not manifestly gauge-invariant, its matrix elements in the nucleon will be nonvanishing and are gauge-invariant. We test this idea in the path-integral quantization by calculating correlation functions on the lattice with a gauge-invariant nucleon interpolation field and replacing the gauge link in the quark lattice momentum operator with unity, which corresponds to the partial derivative in the continuum. We find that the ratios of three-point to two-point functions are zero within errors for both the u and d quarks, contrary to the case without setting the gauge links to unity.

Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity

NASA Astrophysics Data System (ADS)

Ruz, Soumendranath; Mandal, Ranajit; Debnath, Subhra; Sanyal, Abhik Kumar

2016-07-01

The Hamiltonian constraint H_c = N{H} = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a branch function of momentum. Here we propose an extended theory of Lanczos-Lovelock gravity to construct a unique Hamiltonian in its minisuperspace version, which results in manifest diffeomorphic invariance and canonical quantization.

Vortices and antivortices in two-dimensional ultracold Fermi gases

PubMed Central

Bighin, G.; Salasnich, L.

2017-01-01

Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatures of macroscopic quantum phenomena. In two-dimensional superfluids quantized vortices play a key role in determining finite-temperature properties, as the superfluid phase and the normal state are separated by a vortex unbinding transition, the Berezinskii-Kosterlitz-Thouless transition. Very recent experiments with two-dimensional superfluid fermions motivate the present work: we present theoretical results based on the renormalization group showing that the universal jump of the superfluid density and the critical temperature crucially depend on the interaction strength, providing a strong benchmark for forthcoming investigations. PMID:28374762

Vortices and antivortices in two-dimensional ultracold Fermi gases

NASA Astrophysics Data System (ADS)

Bighin, G.; Salasnich, L.

2017-04-01

Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatures of macroscopic quantum phenomena. In two-dimensional superfluids quantized vortices play a key role in determining finite-temperature properties, as the superfluid phase and the normal state are separated by a vortex unbinding transition, the Berezinskii-Kosterlitz-Thouless transition. Very recent experiments with two-dimensional superfluid fermions motivate the present work: we present theoretical results based on the renormalization group showing that the universal jump of the superfluid density and the critical temperature crucially depend on the interaction strength, providing a strong benchmark for forthcoming investigations.

Connections between ’t Hooft’s beables and canonical descriptions of dissipative systems

NASA Astrophysics Data System (ADS)

Schuch, Dieter; Blasone, Massimo

2017-08-01

According to a proposal by ’t Hooft, information loss introduced by constraints in certain classical dissipative systems may lead to quantization. This scheme can be realized within the Bateman model of two coupled oscillators, one damped and one accelerated. In this paper we analyze the links of this approach to effective Hamiltonians where the environmental degrees of freedom do not appear explicitly but their effect leads to the same friction force appearing in the Bateman model. In particular, it is shown that by imposing constraints, the Bateman Hamiltonian can be transformed into an effective one expressed in expanding coordinates. This one can be transformed via a canonical transformation into Caldirola and Kanai’s effective Hamiltonian that can be linked to the conventional system-plus-reservoir approach, for example, in a form used by Caldeira and Leggett.

Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

NASA Astrophysics Data System (ADS)

Lempert, László; Szőke, Róbert

2014-04-01

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H s of Hilbert spaces, and the question arises if the spaces H s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787-902, 1991) and Hitchin (Commun. Math. Phys. 131:347-380, 1990) suggest viewing H s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle along a non-proper map . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Szőke (Bull. Lond. Math. Soc. 44:367-374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.

Thermal Equilibrium of a Macroscopic Quantum System in a Pure State.

PubMed

Goldstein, Sheldon; Huse, David A; Lebowitz, Joel L; Tumulka, Roderich

2015-09-04

We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (MITE). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between MITE and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and MITE. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but MITE fails to hold for any phase point.

Material parameter determination from scattering measurements

NASA Technical Reports Server (NTRS)

Dominek, A.; Park, A.; Peters, L., Jr.

1988-01-01

The electrical, macroscopic performance of isotropic material can generally be described through their constitutive scalar parameters, permittivity and permeability which are symbolically represented by epsilon and mu, respectively. These parameters relate the electric and magnetic flux densities to the electric and magnetic fields through the following relationships: (1) D=epsilonE; and (2) B=muH. It is through these parameters that the interaction of electromagnetic waves with material can be quantized in terms of reflection and transmission coefficients, and propagation and attenuation factors.

The Noncommutative Doplicher-Fredenhagen-Roberts-Amorim Space

NASA Astrophysics Data System (ADS)

Abreu, Everton M. C.; Mendes, Albert C. R.; Oliveira, Wilson; Zangirolami, Adriano O.

2010-10-01

This work is an effort in order to compose a pedestrian review of the recently elaborated Doplicher, Fredenhagen, Roberts and Amorim (DFRA) noncommutative (NC) space which is a minimal extension of the DFR space. In this DRFA space, the object of noncommutativity (θμν) is a variable of the NC system and has a canonical conjugate momentum. Namely, for instance, in NC quantum mechanics we will show that θij (i,j=1,2,3) is an operator in Hilbert space and we will explore the consequences of this so-called ''operationalization''. The DFRA formalism is constructed in an extended space-time with independent degrees of freedom associated with the object of noncommutativity θμν. We will study the symmetry properties of an extended x+θ space-time, given by the group P', which has the Poincaré group P as a subgroup. The Noether formalism adapted to such extended x+θ (D=4+6) space-time is depicted. A consistent algebra involving the enlarged set of canonical operators is described, which permits one to construct theories that are dynamically invariant under the action of the rotation group. In this framework it is also possible to give dynamics to the NC operator sector, resulting in new features. A consistent classical mechanics formulation is analyzed in such a way that, under quantization, it furnishes a NC quantum theory with interesting results. The Dirac formalism for constrained Hamiltonian systems is considered and the object of noncommutativity θij plays a fundamental role as an independent quantity. Next, we explain the dynamical spacetime symmetries in NC relativistic theories by using the DFRA algebra. It is also explained about the generalized Dirac equation issue, that the fermionic field depends not only on the ordinary coordinates but on θμν as well. The dynamical symmetry content of such fermionic theory is discussed, and we show that its action is invariant under P'. In the last part of this work we analyze the complex scalar fields using this new framework. As said above, in a first quantized formalism, θμν and its canonical momentum πμν are seen as operators living in some Hilbert space. In a second quantized formalism perspective, we show an explicit form for the extended Poincaré generators and the same algebra is generated via generalized Heisenberg relations. We also consider a source term and construct the general solution for the complex scalar fields using the Green function technique.

q-bosons and the q-analogue quantized field

NASA Technical Reports Server (NTRS)

Nelson, Charles A.

1995-01-01

The q-analogue coherent states are used to identify physical signatures for the presence of a 1-analogue quantized radiation field in the q-CS classical limits where the absolute value of z is large. In this quantum-optics-like limit, the fractional uncertainties of most physical quantities (momentum, position, amplitude, phase) which characterize the quantum field are O(1). They only vanish as O(1/absolute value of z) when q = 1. However, for the number operator, N, and the N-Hamiltonian for a free q-boson gas, H(sub N) = h(omega)(N + 1/2), the fractional uncertainties do still approach zero. A signature for q-boson counting statistics is that (Delta N)(exp 2)/ (N) approaches 0 as the absolute value of z approaches infinity. Except for its O(1) fractional uncertainty, the q-generalization of the Hermitian phase operator of Pegg and Barnett, phi(sub q), still exhibits normal classical behavior. The standard number-phase uncertainty-relation, Delta(N) Delta phi(sub q) = 1/2, and the approximate commutation relation, (N, phi(sub q)) = i, still hold for the single-mode q-analogue quantized field. So, N and phi(sub q) are almost canonically conjugate operators in the q-CS classical limit. The q-analogue CS's minimize this uncertainty relation for moderate (absolute value of z)(exp 2).

Connecting dissipation and noncommutativity: A Bateman system case study

NASA Astrophysics Data System (ADS)

Pal, Sayan Kumar; Nandi, Partha; Chakraborty, Biswajit

2018-06-01

We present an approach to the problem of quantization of the damped harmonic oscillator. To start with, we adopt the standard method of doubling the degrees of freedom of the system (Bateman form) and then, by introducing some new parameters, we get a generalized coupled set of equations from the Bateman form. Using the corresponding time-independent Lagrangian, quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) are analyzed by using both path integral and canonical quantization schemes within the framework of the Hilbert-Schmidt operator formulation. Our method is distinct from those existing in the literature and where the ambient space was taken to be commutative. Our quantization shows that we end up again with a Bateman system except that the damping factor undergoes renormalization. Strikingly, the corresponding expression shows that the renormalized damping factor can be nonzero even if "bare" one is zero to begin with. In other words, noncommutativity can act as a source of dissipation. Conversely, the noncommutative parameter θ , taken to be a free one now, can be fine tuned to get a vanishing renormalized damping factor. This indicates in some sense a "duality" between dissipation and noncommutativity. Our results match the existing results in the commutative limit.

Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum

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

Panahi, H., E-mail: t-panahi@guilan.ac.ir; Jahangiri, L., E-mail: laleh.jahangiry@yahoo.com

2016-09-15

In this work we apply the Dirac method in order to obtain the classical relations for a particle on an ellipsoid. We also determine the quantum mechanical form of these relations by using Dirac quantization. Then by considering the canonical commutation relations between the position and momentum operators in terms of curved coordinates, we try to propose the suitable representations for momentum operator that satisfy the obtained commutators between position and momentum in Euclidean space. We see that our representations for momentum operators are the same as geometric one.

Maslov indices, Poisson brackets, and singular differential forms

NASA Astrophysics Data System (ADS)

Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.

2014-06-01

Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.

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).

Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

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

Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx; Manuel-Cabrera, J., E-mail: jmanuel@ifuap.buap.mx

2015-10-15

A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. - Highlights: • A detailed Faddeev–Jackiw analysis for exotic action of gravity is performed.more » • We show that Dirac’s brackets and Generalized [FJ] brackets are equivalent. • Without fixing the gauge exotic action is a non-commutative theory. • The fundamental gauge transformations of the theory are found. • Dirac and Faddeev–Jackiw approaches are compared.« less

Quantization of wave equations and hermitian structures in partial differential varieties

PubMed Central

Paneitz, S. M.; Segal, I. E.

1980-01-01

Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation—e.g., of the form □ϕ + m2ϕ + gϕp = 0—admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments. PMID:16592923

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.

Quantum canonical ensemble: A projection operator approach

NASA Astrophysics Data System (ADS)

Magnus, Wim; Lemmens, Lucien; Brosens, Fons

2017-09-01

Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function ZN and the Helmholtz free energy FN as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 -FN, as illustrated for a two-dimensional fermion gas.

Diffeomorphisms as symplectomorphisms in history phase space: Bosonic string model

NASA Astrophysics Data System (ADS)

Kouletsis, I.; Kuchař, K. V.

2002-06-01

The structure of the history phase space G of a covariant field system and its history group (in the sense of Isham and Linden) is analyzed on an example of a bosonic string. The history space G includes the time map T from the spacetime manifold (the two-sheet) Y to a one-dimensional time manifold T as one of its configuration variables. A canonical history action is posited on G such that its restriction to the configuration history space yields the familiar Polyakov action. The standard Dirac-ADM action is shown to be identical with the canonical history action, the only difference being that the underlying action is expressed in two different coordinate charts on G. The canonical history action encompasses all individual Dirac-ADM actions corresponding to different choices T of foliating Y. The history Poisson brackets of spacetime fields on G induce the ordinary Poisson brackets of spatial fields in the instantaneous phase space G0 of the Dirac-ADM formalism. The canonical history action is manifestly invariant both under spacetime diffeomorphisms Diff Y and temporal diffeomorphisms Diff T. Both of these diffeomorphisms are explicitly represented by symplectomorphisms on the history phase space G. The resulting classical history phase space formalism is offered as a starting point for projection operator quantization and consistent histories interpretation of the bosonic string model.

From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

NASA Astrophysics Data System (ADS)

Bergeron, H.

2001-09-01

Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence principle). Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We also recover by this approach the semi-classical formalism developed by E. Prugovečki [Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)].

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.

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.

Synchronicity - The Link Between Physics and Psyche, from Pauli and Jung to Chopra

NASA Astrophysics Data System (ADS)

Teodorani, M.

2006-07-01

This book, which is entirely dedicated to the mystery of "synchronicity", is divided into three parts: a) the joint research between analytic psychologist Carl Gustav Jung and quantum physicist Wolfgang Pauli; b) synchronicity mechanisms occurring in the microscopic (canonical quantum entanglement), mesoscopic and macroscopic scales; c) research and philosophy concerning synchronicity by MD Deepak Chopra.

Stochastic space interval as a link between quantum randomness and macroscopic randomness?

NASA Astrophysics Data System (ADS)

Haug, Espen Gaarder; Hoff, Harald

2018-03-01

For many stochastic phenomena, we observe statistical distributions that have fat-tails and high-peaks compared to the Gaussian distribution. In this paper, we will explain how observable statistical distributions in the macroscopic world could be related to the randomness in the subatomic world. We show that fat-tailed (leptokurtic) phenomena in our everyday macroscopic world are ultimately rooted in Gaussian - or very close to Gaussian-distributed subatomic particle randomness, but they are not, in a strict sense, Gaussian distributions. By running a truly random experiment over a three and a half-year period, we observed a type of random behavior in trillions of photons. Combining our results with simple logic, we find that fat-tailed and high-peaked statistical distributions are exactly what we would expect to observe if the subatomic world is quantized and not continuously divisible. We extend our analysis to the fact that one typically observes fat-tails and high-peaks relative to the Gaussian distribution in stocks and commodity prices and many aspects of the natural world; these instances are all observable and documentable macro phenomena that strongly suggest that the ultimate building blocks of nature are discrete (e.g. they appear in quanta).

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

NASA Astrophysics Data System (ADS)

Majima, H.; Suzuki, A.

2011-12-01

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity ( -γẋ) and a time-dependent external force ( K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: ℒ=mẋẏ-U(x+{1}/{2}y)+U(x-{1}/{2}y)+{γ}/{2}(xẏ-yẋ)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x±y/2)={1}/{2}k( specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian ℋ. The Heisenberg equations of motion utilizing the quantized Hamiltonian ℋ̂ surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.

Constructive tensorial group field theory I: The {U(1)} -{T^4_3} model

NASA Astrophysics Data System (ADS)

Lahoche, Vincent

2018-05-01

The loop vertex expansion (LVE) is a constructive technique using canonical combinatorial tools. It works well for quantum field theories without renormalization, which is the case of the field theory studied in this paper. Tensorial group field theories (TGFTs) are a new class of field theories proposed to quantize gravity. This paper is devoted to a very simple TGFT for rank three tensors with U(1) group and quartic interactions, hence nicknamed -. It has no ultraviolet divergence, and we show, with the LVE, that it is Borel summable in its coupling constant.

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.

Do semiclassical zero temperature black holes exist?

PubMed

Anderson, P R; Hiscock, W A; Taylor, B E

2000-09-18

The semiclassical Einstein equations are solved to first order in epsilon = Planck's over 2pi/M2 for the case of a Reissner-Nordström black hole perturbed by the vacuum stress energy of quantized free fields. Massless and massive fields of spin 0, 1/2, and 1 are considered. We show that in all physically realistic cases, macroscopic zero temperature black hole solutions do not exist. Any static zero temperature semiclassical black hole solutions must then be microscopic and isolated in the space of solutions; they do not join smoothly onto the classical extreme Reissner-Nordström solution as epsilon-->0.

Casual Set Approach to a Minimal Invariant Length

NASA Astrophysics Data System (ADS)

Raut, Usha

2007-04-01

Any attempt to quantize gravity would necessarily introduce a minimal observable length scale of the order of the Planck length. This conclusion is based on several different studies and thought experiments and appears to be an inescapable feature of all quantum gravity theories, irrespective of the method used to quantize gravity. Over the last few years there has been growing concern that such a minimal length might lead to a contradiction with the basic postulates of special relativity, in particular the Lorentz-Fitzgerald contraction. A few years ago, Rovelli et.al, attempted to reconcile an invariant minimal length with Special Relativity, using the framework of loop quantum gravity. However, the inherently canonical formalism of the loop quantum approach is plagued by a variety of problems, many brought on by separation of space and time co-ordinates. In this paper we use a completely different approach. Using the framework of the causal set paradigm, along with a statistical measure of closeness between Lorentzian manifolds, we re-examine the issue of introducing a minimal observable length that is not at odds with Special Relativity postulates.

Tolerance in the Ramsey interference of a trapped nanodiamond

NASA Astrophysics Data System (ADS)

Wan, C.; Scala, M.; Bose, S.; Frangeskou, A. C.; Rahman, ATM A.; Morley, G. W.; Barker, P. F.; Kim, M. S.

2016-04-01

In the scheme recently proposed by M. Scala et al. [Phys. Rev. Lett. 111, 180403 (2013), 10.1103/PhysRevLett.111.180403], a gravity-dependent phase shift is induced on the spin of a nitrogen-vacancy (NV) center in a trapped nanodiamond by the interaction between its magnetic moment and the quantized motion of the particle. This provides a way to detect spatial quantum superpositions by means of only spin measurements. Here, the effect of unwanted coupling with other motional degrees of freedom is considered, and we show that it does not affect the validity of the scheme. Both this coupling and the additional error source due to misalignment between the quantization axis of the NV center spin and the trapping axis are shown not to change the qualitative behavior of the system, so that a proof-of-principle experiment can be neatly performed. Our analysis, which shows that the scheme retains the important features of not requiring ground-state cooling and of being resistant to thermal fluctuations, can be useful for several schemes which have been proposed recently for testing macroscopic superpositions in trapped microsystems.

Coherent states for the relativistic harmonic oscillator

NASA Technical Reports Server (NTRS)

Aldaya, Victor; Guerrero, J.

1995-01-01

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

Mixing properties of the one-atom maser

NASA Astrophysics Data System (ADS)

Bruneau, Laurent

2014-06-01

We study the relaxation properties of the quantized electromagnetic field in a cavity under repeated interactions with single two-level atoms, so-called one-atom maser. We improve the ergodic results obtained in Bruneau and Pillet (J Stat Phys 134(5-6):1071-1095, 2009) and prove that, whenever the atoms are initially distributed according to the canonical ensemble at temperature , all the invariant states are mixing. Under some non-resonance condition this invariant state is known to be thermal equilibirum at some renormalized temperature and we prove that the mixing is then arbitrarily slow, in other words that there is no lower bound on the relaxation speed.

On the phase form of a deformation quantization with separation of variables

NASA Astrophysics Data System (ADS)

Karabegov, Alexander

2016-06-01

Given a star product with separation of variables on a pseudo-Kähler manifold, we obtain a new formal (1, 1)-form from its classifying form and call it the phase form of the star product. The cohomology class of a star product with separation of variables equals the class of its phase form. We show that the phase forms can be arbitrary and they bijectively parametrize the star products with separation of variables. We also describe the action of a change of the formal parameter on a star product with separation of variables, its formal Berezin transform, classifying form, phase form, and canonical trace density.

Grand Canonical adaptive resolution simulation for molecules with electrons: A theoretical framework based on physical consistency

NASA Astrophysics Data System (ADS)

Delle Site, Luigi

2018-01-01

A theoretical scheme for the treatment of an open molecular system with electrons and nuclei is proposed. The idea is based on the Grand Canonical description of a quantum region embedded in a classical reservoir of molecules. Electronic properties of the quantum region are calculated at constant electronic chemical potential equal to that of the corresponding (large) bulk system treated at full quantum level. Instead, the exchange of molecules between the quantum region and the classical environment occurs at the chemical potential of the macroscopic thermodynamic conditions. The Grand Canonical Adaptive Resolution Scheme is proposed for the treatment of the classical environment; such an approach can treat the exchange of molecules according to first principles of statistical mechanics and thermodynamic. The overall scheme is build on the basis of physical consistency, with the corresponding definition of numerical criteria of control of the approximations implied by the coupling. Given the wide range of expertise required, this work has the intention of providing guiding principles for the construction of a well founded computational protocol for actual multiscale simulations from the electronic to the mesoscopic scale.

Canonical quantization of constrained systems and coadjoint orbits of Diff(S sup 1 )

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

Scherer, W.M.

It is shown that Dirac's treatment of constrained Hamiltonian systems and Schwinger's action principle quantization lead to identical commutations relations. An explicit relation between the Lagrange multipliers in the action principle approach and the additional terms in the Dirac bracket is derived. The equivalence of the two methods is demonstrated in the case of the non-linear sigma model. Dirac's method is extended to superspace and this extension is applied to the chiral superfield. The Dirac brackets of the massive interacting chiral superfluid are derived and shown to give the correct commutation relations for the component fields. The Hamiltonian of themore » theory is given and the Hamiltonian equations of motion are computed. They agree with the component field results. An infinite sequence of differential operators which are covariant under the coadjoint action of Diff(S{sup 1}) and analogues to Hill's operator is constructed. They map conformal fields of negative integer and half-integer weight to their dual space. Some properties of these operators are derived and possible applications are discussed. The Korteweg-de Vries equation is formulated as a coadjoint orbit of Diff(S{sup 1}).« less

On the Path Integral in Non-Commutative (nc) Qft

NASA Astrophysics Data System (ADS)

Dehne, Christoph

2008-09-01

As is generally known, different quantization schemes applied to field theory on NC spacetime lead to Feynman rules with different physical properties, if time does not commute with space. In particular, the Feynman rules that are derived from the path integral corresponding to the T*-product (the so-called naïve Feynman rules) violate the causal time ordering property. Within the Hamiltonian approach to quantum field theory, we show that we can (formally) modify the time ordering encoded in the above path integral. The resulting Feynman rules are identical to those obtained in the canonical approach via the Gell-Mann-Low formula (with T-ordering). They preserve thus unitarity and causal time ordering.

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

NASA Astrophysics Data System (ADS)

Kim, Won T.; Kim, Yong-Wan; Park, Mu-In; Park, Young-Jai; Yoon, Sean J.

1997-03-01

We apply the newly improved Batalin - Fradkin - Tyutin (BFT) Hamiltonian method to the chiral Schwinger model in the case of the regularization ambiguity a>1. We show that one can systematically construct the first class constraints by the BFT Hamiltonian method, and also show that the well-known Dirac brackets of the original phase space variables are exactly the Poisson brackets of the corresponding modified fields in the extended phase space. Furthermore, we show that the first class Hamiltonian is simply obtained by replacing the original fields in the canonical Hamiltonian by these modified fields. Performing the momentum integrations, we obtain the corresponding first class Lagrangian in the configuration space.

Numerical simulation of transmission coefficient using c-number Langevin equation

NASA Astrophysics Data System (ADS)

Barik, Debashis; Bag, Bidhan Chandra; Ray, Deb Shankar

2003-12-01

We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik et al., J. Chem. Phys. 119, 680 (2003); Banerjee et al., Phys. Rev. E 65, 021109 (2002)] to calculate transmission coefficient. The Kramers' turnover, the T2 enhancement of the rate at low temperatures and other related features of temporal behavior of the transmission coefficient over a range of temperature down to absolute zero, noise correlation, and friction are examined for a double well potential and compared with other known results. This simple method is based on canonical quantization and Wigner quasiclassical phase space function and takes care of quantum effects due to the system order by order.

Time-dependent variational approach in terms of squeezed coherent states: Implication to semi-classical approximation

NASA Technical Reports Server (NTRS)

Tsue, Yasuhiko

1994-01-01

A general framework for time-dependent variational approach in terms of squeezed coherent states is constructed with the aim of describing quantal systems by means of classical mechanics including higher order quantal effects with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. The Maslov phase occurring in a semi-classical quantization rule is investigated in this framework. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to the Berry phase. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation.

Quantum gravitational corrections from the Wheeler–DeWitt equation for scalar–tensor theories

NASA Astrophysics Data System (ADS)

Steinwachs, Christian F.; van der Wild, Matthijs L.

2018-07-01

We perform the canonical quantization of a general scalar–tensor theory and derive the first quantum gravitational corrections following from a semiclassical expansion of the Wheeler–DeWitt equation. The non-minimal coupling of the scalar field to gravity induces a derivative coupling between the scalar field and the gravitational degrees of freedom, which prevents a direct application of the expansion scheme. We address this technical difficulty by transforming the theory from the Jordan frame to the Einstein frame. We find that a large non-minimal coupling can have strong effects on the quantum gravitational correction terms. We briefly discuss these effects in the context of the specific model of Higgs inflation.

Quantum theory of structured monochromatic light

NASA Astrophysics Data System (ADS)

Punnoose, Alexander; Tu, J. J.

2017-08-01

Applications that envisage utilizing the orbital angular momentum (OAM) at the single photon level assume that the OAM degrees of freedom of the photons are orthogonal. To test this critical assumption, we quantize the beam-like solutions of the vector Helmholtz equation from first principles. We show that although the photon operators of a diffracting monochromatic beam do not in general satisfy the canonical commutation relations, implying that the photon states in Fock space are not orthogonal, the states are bona fide eigenstates of the number and Hamiltonian operators. As a result, the representation for the photon operators presented in this work form a natural basis to study structured monochromatic light at the single photon level.

Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media

NASA Astrophysics Data System (ADS)

Toptygin, I. N.

2017-12-01

Applying a quantum mechanical treatment to a high-frequency macroscopic electromagnetic field and radiative phenomena in a medium, we construct quantum operators for energy-momentum tensor components in dispersive media and find their eigenvalues, which are different in the Minkowski and Abraham representations. It is shown that the photon momentum in a medium resulting from the quantization of the vector potential differs from that defined from Abraham’s symmetric energy-momentum-tensor but is equal to the momentum defined from the Minkowski tensor. A similar result is obtained by calculating the intrinsic angular momentum (spin) of an electro-magnetic field in the medium. Only the Minkowski tensor leads to the experimentally confirmed spin values that are multiples of ħ, providing the grounds for choosing the Minkowski representation as the proper form for the momentum density of a transverse electromagnetic field in a transparent medium, in both classical and quantum descriptions of the field. The Abraham representation is unsuitable for this purpose and leads to contradictions. The conclusion drawn does not apply to quasistatic and static fields.

Second order perturbations of a macroscopic string: Covariant approach

NASA Astrophysics Data System (ADS)

Larsen, A. L.; Nicolaidis, A.

2001-06-01

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessary for a consistent computation of the energy. We also quantize the perturbations and derive the mass formula up to second order in perturbations for an observer using world-sheet time τ. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be nondiagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind.

Quantum time crystal by decoherence: Proposal with an incommensurate charge density wave ring

NASA Astrophysics Data System (ADS)

Nakatsugawa, K.; Fujii, T.; Tanda, S.

2017-09-01

We show that time translation symmetry of a ring system with a macroscopic quantum ground state is broken by decoherence. In particular, we consider a ring-shaped incommensurate charge density wave (ICDW ring) threaded by a fluctuating magnetic flux: the Caldeira-Leggett model is used to model the fluctuating flux as a bath of harmonic oscillators. We show that the charge density expectation value of a quantized ICDW ring coupled to its environment oscillates periodically. The Hamiltonians considered in this model are time independent unlike "Floquet time crystals" considered recently. Our model forms a metastable quantum time crystal with a finite length in space and in time.

Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

NASA Astrophysics Data System (ADS)

Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes

2018-03-01

We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.

Hamiltonian thermodynamics of three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.

2008-08-15

The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free {omega} parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcationmore » 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates (M,P{sub M}), M being the mass parameter and P{sub M} its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

Interferometric tests of Planckian quantum geometry models

DOE PAGES

Kwon, Ohkyung; Hogan, Craig J.

2016-04-19

The effect of Planck scale quantum geometrical effects on measurements with interferometers is estimated with standard physics, and with a variety of proposed extensions. It is shown that effects are negligible in standard field theory with canonically quantized gravity. Statistical noise levels are estimated in a variety of proposals for nonstandard metric fluctuations, and these alternatives are constrained using upper bounds on stochastic metric fluctuations from LIGO. Idealized models of several interferometer system architectures are used to predict signal noise spectra in a quantum geometry that cannot be described by a fluctuating metric, in which position noise arises from holographicmore » bounds on directional information. Lastly, predictions in this case are shown to be close to current and projected experimental bounds.« less

Quantum cluster algebras and quantum nilpotent algebras.

PubMed

Goodearl, Kenneth R; Yakimov, Milen T

2014-07-08

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein-Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405-455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337-397] for the case of symmetric Kac-Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1-52] associated with double Bruhat cells coincide with the corresponding cluster algebras.

New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis

NASA Astrophysics Data System (ADS)

Bodendorfer, N.; Thiemann, T.; Thurn, A.

2013-02-01

Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional supergravity loop quantizations at one’s disposal in order to compare these approaches. In this series of papers we take first steps toward this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG which does not require the time gauge and which generalizes to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauß, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1, D) or SO(D + 1) and the latter choice is preferred for purposes of quantization.

Relational particle models: I. Reconciliation with standard classical and quantum theory

NASA Astrophysics Data System (ADS)

Anderson, Edward

2006-04-01

This paper concerns the absolute versus relative motion debate. The Barbour and Bertotti (1982) work may be viewed as an indirectly set up relational formulation of a portion of Newtonian mechanics. I consider further direct formulations of this and argue that the portion in question—universes with zero total angular momentum that are conservative and with kinetic terms that are (homogeneous) quadratic in their velocities—is capable of accommodating a wide range of classical physics phenomena. Furthermore, as I develop in paper II, this relational particle model is a useful toy model for canonical general relativity. I consider what happens if one quantizes relational rather than absolute mechanics, indeed whether the latter is misleading. By exploiting Jacobi coordinates, I show how to access many examples of quantized relational particle models and then interpret these from a relational perspective. By these means, previous suggestions of bad semiclassicality for such models can be eluded. I show how small (particle number) universe relational particle model examples display eigenspectrum truncation, gaps, energy interlocking and counterbalanced total angular momentum. These features mean that these small universe models make interesting toy models for some aspects of closed-universe quantum cosmology. Meanwhile, these features do not compromise the recovery of reality as regards the practicalities of experimentation in a large universe such as our own.

Quantum cluster algebras and quantum nilpotent algebras

PubMed Central

Goodearl, Kenneth R.; Yakimov, Milen T.

2014-01-01

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

The actual content of quantum theoretical kinematics and mechanics

NASA Technical Reports Server (NTRS)

Heisenberg, W.

1983-01-01

First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantum mechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantum mechanics. Several imaginary experiments are discussed to elucidate the theory.

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.

Quantum-limited heat conduction over macroscopic distances

NASA Astrophysics Data System (ADS)

Partanen, Matti; Tan, Kuan Yen; Govenius, Joonas; Lake, Russell E.; Mäkelä, Miika K.; Tanttu, Tuomo; Möttönen, Mikko

2016-05-01

The emerging quantum technological apparatuses, such as the quantum computer, call for extreme performance in thermal engineering. Cold distant heat sinks are needed for the quantized electric degrees of freedom owing to the increasing packaging density and heat dissipation. Importantly, quantum mechanics sets a fundamental upper limit for the flow of information and heat, which is quantified by the quantum of thermal conductance. However, the short distance between the heat-exchanging bodies in the previous experiments hinders their applicability in quantum technology. Here, we present experimental observations of quantum-limited heat conduction over macroscopic distances extending to a metre. We achieved this improvement of four orders of magnitude in the distance by utilizing microwave photons travelling in superconducting transmission lines. Thus, it seems that quantum-limited heat conduction has no fundamental distance cutoff. This work establishes the integration of normal-metal components into the framework of circuit quantum electrodynamics, which provides a basis for the superconducting quantum computer. Especially, our results facilitate remote cooling of nanoelectronic devices using faraway in situ-tunable heat sinks. Furthermore, quantum-limited heat conduction is important in contemporary thermodynamics. Here, the long distance may lead to ultimately efficient mesoscopic heat engines with promising practical applications.

Semiclassical states on Lie algebras

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

Tsobanjan, Artur, E-mail: artur.tsobanjan@gmail.com

2015-03-15

The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following themore » methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.« 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.

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.

Cal Poly Pomona NUE Project: Implementing Microscale and Nanoscale Investigations Throughout the Undergraduate Curriculum

PubMed Central

Vandervoort, Kurt; Brelles-Mariño, Graciela

2013-01-01

NUE funded work at California State Polytechnic University involved development and implementation of nanotechnology modules for physics courses spanning all levels of the undergraduate curriculum, from freshman service courses to senior level laboratories and independent research projects. These modules demonstrate the application of fundamental physics at the nanoscale that complement macroscopic investigations. The introductory level and some of the advanced level modules have been described previously in journal papers and will be outlined briefly here. The main focus of this article, however, is to describe some newer work involving nanoscale experiments that have been developed for senior level laboratories and independent research. These experiments involve applications as diverse as tunneling diodes, gas discharge plasmas for biofilm inactivation, and quantized conductance in gold nanowires. PMID:24163716

Cal Poly Pomona NUE Project: Implementing Microscale and Nanoscale Investigations Throughout the Undergraduate Curriculum.

PubMed

Vandervoort, Kurt; Brelles-Mariño, Graciela

2013-06-01

NUE funded work at California State Polytechnic University involved development and implementation of nanotechnology modules for physics courses spanning all levels of the undergraduate curriculum, from freshman service courses to senior level laboratories and independent research projects. These modules demonstrate the application of fundamental physics at the nanoscale that complement macroscopic investigations. The introductory level and some of the advanced level modules have been described previously in journal papers and will be outlined briefly here. The main focus of this article, however, is to describe some newer work involving nanoscale experiments that have been developed for senior level laboratories and independent research. These experiments involve applications as diverse as tunneling diodes, gas discharge plasmas for biofilm inactivation, and quantized conductance in gold nanowires.

Electroweak standard model with very special relativity

NASA Astrophysics Data System (ADS)

Alfaro, Jorge; González, Pablo; Ávila, Ricardo

2015-05-01

The very special relativity electroweak Standard Model (VSR EW SM) is a theory with SU (2 )L×U (1 )R symmetry, with the same number of leptons and gauge fields as in the usual Weinberg-Salam model. No new particles are introduced. The model is renormalizable and unitarity is preserved. However, photons obtain mass and the massive bosons obtain different masses for different polarizations. Besides, neutrino masses are generated. A VSR-invariant term will produce neutrino oscillations and new processes are allowed. In particular, we compute the rate of the decays μ →e +γ . All these processes, which are forbidden in the electroweak Standard Model, put stringent bounds on the parameters of our model and measure the violation of Lorentz invariance. We investigate the canonical quantization of this nonlocal model. Second quantization is carried out, and we obtain a well-defined particle content. Additionally, we do a counting of the degrees of freedom associated with the gauge bosons involved in this work, after spontaneous symmetry breaking has been realized. Violations of Lorentz invariance have been predicted by several theories of quantum gravity [J. Alfaro, H. Morales-Tecotl, and L. F. Urrutia, Phys. Rev. Lett. 84, 2318 (2000); Phys. Rev. D 65, 103509 (2002)]. It is a remarkable possibility that the low-energy effects of Lorentz violation induced by quantum gravity could be contained in the nonlocal terms of the VSR EW SM.

Colliding holes in Riemann surfaces and quantum cluster algebras

NASA Astrophysics Data System (ADS)

Chekhov, Leonid; Mazzocco, Marta

2018-01-01

In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appears when colliding two holes or two sides of the same hole in an orientable Riemann surface with boundary (and possibly orbifold points). As a result of this surgery, bordered cusps appear on the boundary components of the Riemann surface. In Poincaré uniformization, these bordered cusps correspond to ideal triangles in the fundamental domain. We introduce the notion of bordered cusped Teichmüller space and endow it with a Poisson structure, quantization of which is achieved with a canonical quantum ordering. We give a complete combinatorial description of the bordered cusped Teichmüller space by introducing the notion of maximal cusped lamination, a lamination consisting of geodesic arcs between bordered cusps and closed geodesics homotopic to the boundaries such that it triangulates the Riemann surface. We show that each bordered cusp carries a natural decoration, i.e. a choice of a horocycle, so that the lengths of the arcs in the maximal cusped lamination are defined as λ-lengths in Thurston-Penner terminology. We compute the Goldman bracket explicitly in terms of these λ-lengths and show that the groupoid of flip morphisms acts as a generalized cluster algebra mutation. From the physical point of view, our construction provides an explicit coordinatization of moduli spaces of open/closed string worldsheets and their quantization.

Quantum particles in general spacetimes: A tangent bundle formalism

NASA Astrophysics Data System (ADS)

Wohlfarth, Mattias N. R.

2018-06-01

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new type of nonminimal coupling of the fields and is shown to admit a canonical quantization procedure. For the resulting quantum theory we demonstrate the emergence of a particle interpretation, fully consistent with general relativistic geometry. The path dependency of parallel transport forces each observer to carry their own quantum state; we find that the communication of the corresponding quantum information may generate extra particles on curved spacetimes. A speculative link between quantum information and spacetime curvature is discussed which might lead to novel explanations for quantum decoherence and vanishing interference in double-slit or interaction-free measurement scenarios, in the mere presence of additional observers.

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

Linear absorptive dielectrics

NASA Astrophysics Data System (ADS)

Tip, A.

1998-06-01

Starting from Maxwell's equations for a linear, nonconducting, absorptive, and dispersive medium, characterized by the constitutive equations D(x,t)=ɛ1(x)E(x,t)+∫t-∞dsχ(x,t-s)E(x,s) and H(x,t)=B(x,t), a unitary time evolution and canonical formalism is obtained. Given the complex, coordinate, and frequency-dependent, electric permeability ɛ(x,ω), no further assumptions are made. The procedure leads to a proper definition of band gaps in the periodic case and a new continuity equation for energy flow. An S-matrix formalism for scattering from lossy objects is presented in full detail. A quantized version of the formalism is derived and applied to the generation of Čerenkov and transition radiation as well as atomic decay. The last case suggests a useful generalization of the density of states to the absorptive situation.

Enhancement of macroscopic quantum tunneling in the higher-order phase switches of Bi2212 intrinsic Josephson junctions

NASA Astrophysics Data System (ADS)

Kitano, Haruhisa; Yamaguchi, Ayami; Takahashi, Yusaku; Umegai, Shunpei; Watabe, Yuji; Ohnuma, Haruka; Hosaka, Kazutaka; Kakehi, Daiki

2018-03-01

The macroscopic quantum tunneling (MQT) in the current-biased intrinsic Josephson junctions (IJJs) of high-T c cuprates has attracted much attention for decades. Although the MQT for the phase switches from the zero to the first voltage state (1st SW) in the multiple-branched I-V curves is well explained by the conventional theory, the occurrence of MQT for the higher order switches such as the switch from the 1st to 2nd voltage state (2nd SW) has been still debated. Here, we present an experimental study on the phase switches of small IJJs fabricated from underdoped Bi2Sr2(Ca,Y)Cu2Oy. We observed the single photon transition between quantized energy levels in the 3rd phase switches at 59.15 GHz and 2 K. The comparison with the previous studies on the nearly optimal-doped Bi2Sr2CaCu2Oy clearly suggests a possibility that the MQT rate for the higher-order phase switches is commonly enhanced by the effective suppression of the energy barrier for the higher-order phase escape due to the phase-running state after the 1st SW, in spite of the large difference in a critical current density and T c.

Long-range interacting systems in the unconstrained ensemble.

PubMed

Latella, Ivan; Pérez-Madrid, Agustín; Campa, Alessandro; Casetti, Lapo; Ruffo, Stefano

2017-01-01

Completely open systems can exchange heat, work, and matter with the environment. While energy, volume, and number of particles fluctuate under completely open conditions, the equilibrium states of the system, if they exist, can be specified using the temperature, pressure, and chemical potential as control parameters. The unconstrained ensemble is the statistical ensemble describing completely open systems and the replica energy is the appropriate free energy for these control parameters from which the thermodynamics must be derived. It turns out that macroscopic systems with short-range interactions cannot attain equilibrium configurations in the unconstrained ensemble, since temperature, pressure, and chemical potential cannot be taken as a set of independent variables in this case. In contrast, we show that systems with long-range interactions can reach states of thermodynamic equilibrium in the unconstrained ensemble. To illustrate this fact, we consider a modification of the Thirring model and compare the unconstrained ensemble with the canonical and grand-canonical ones: The more the ensemble is constrained by fixing the volume or number of particles, the larger the space of parameters defining the equilibrium configurations.

Macroscopic self-oscillations and aging transition in a network of synaptically coupled quadratic integrate-and-fire neurons.

PubMed

Ratas, Irmantas; Pyragas, Kestutis

2016-09-01

We analyze the dynamics of a large network of coupled quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rate and the mean membrane potential, which are exact in the infinite-size limit. The bifurcation analysis of the reduced equations reveals a rich scenario of asymptotic behavior, the most interesting of which is the macroscopic limit-cycle oscillations. It is shown that the finite width of synaptic pulses is a necessary condition for the existence of such oscillations. The robustness of the oscillations against aging damage, which transforms spiking neurons into nonspiking neurons, is analyzed. The validity of the reduced equations is confirmed by comparing their solutions with the solutions of microscopic equations for the finite-size networks.

Comment on "Peres experiment using photons: No test for hypercomplex (quaternionic) quantum theories"

NASA Astrophysics Data System (ADS)

Procopio, Lorenzo M.; Rozema, Lee A.; Dakić, Borivoje; Walther, Philip

2017-09-01

In his recent article [Phys. Rev. A 95, 060101(R) (2017), 10.1103/PhysRevA.95.060101], Adler questions the usefulness of the bound found in our experimental search for genuine effects of hypercomplex quantum mechanics [Nat. Commun. 8, 15044 (2017), 10.1038/ncomms15044]. Our experiment was performed using a black-box (instrumentalist) approach to generalized probabilistic theories; therefore, it does not assume a priori any particular underlying mechanism. From that point of view our experimental results do indeed place meaningful bounds on the possible effects of "postquantum theories," including quaternionic quantum mechanics. In his article, Adler compares our experiment to nonrelativistic and Möller formal scattering theories within quaternionic quantum mechanics. With a particular set of assumptions, he finds that quaternionic effects would likely not manifest themselves in general. Although these assumptions are justified in the nonrelativistic case, a proper calculation for relativistic particles is still missing. Here, we provide a concrete relativistic example of Klein-Gordon scattering wherein the quaternionic effects persist. We note that when the Klein-Gordon equation is formulated using a Hamiltonian formalism it displays a so-called "indefinite metric," a characteristic feature of relativistic quantum wave equations. In Adler's example this is directly forbidden by his assumptions, and therefore our present example is not in contradiction to his work. In complex quantum mechanics this problem of an indefinite metric is solved in a second quantization. Unfortunately, there is no known algorithm for canonical field quantization in quaternionic quantum mechanics.

Restoration of four-dimensional diffeomorphism covariance in canonical general relativity: An intrinsic Hamilton-Jacobi approach

NASA Astrophysics Data System (ADS)

Salisbury, Donald; Renn, Jürgen; Sundermeyer, Kurt

2016-02-01

Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord special privilege to any geometric structure. Intrinsic space-time curvature-based coordinates grant equal status to all geometric backgrounds. They play an essential role as a starting point for inequivalent semiclassical quantizations. The scheme calls into question Wheeler’s geometrodynamical approach and the associated Wheeler-DeWitt equation in which 3-metrics are featured geometrical objects. The formalism deals with variables that are manifestly invariant under the full diffeomorphism group. Yet, perhaps paradoxically, the liberty in selecting intrinsic coordinates is precisely as broad as is the original diffeomorphism freedom. We show how various ideas from the past five decades concerning the true degrees of freedom of general relativity can be interpreted in light of this new constrained Hamiltonian description. In particular, we show how the Kuchař multi-fingered time approach can be understood as a means of introducing full four-dimensional diffeomorphism invariants. Every choice of new phase space variables yields new Einstein-Hamilton-Jacobi constraining relations, and corresponding intrinsic Schrödinger equations. We show how to implement this freedom by canonical transformation of the intrinsic Hamiltonian. We also reinterpret and rectify significant work by Dittrich on the construction of “Dirac observables.”

BOOK REVIEW: Quantum Gravity (2nd edn)

NASA Astrophysics Data System (ADS)

Husain, Viqar

2008-06-01

There has been a flurry of books on quantum gravity in the past few years. The first edition of Kiefer's book appeared in 2004, about the same time as Carlo Rovelli's book with the same title. This was soon followed by Thomas Thiemann's 'Modern Canonical Quantum General Relativity'. Although the main focus of each of these books is non-perturbative and non-string approaches to the quantization of general relativity, they are quite orthogonal in temperament, style, subject matter and mathematical detail. Rovelli and Thiemann focus primarily on loop quantum gravity (LQG), whereas Kiefer attempts a broader introduction and review of the subject that includes chapters on string theory and decoherence. Kiefer's second edition attempts an even wider and somewhat ambitious sweep with 'new sections on asymptotic safety, dynamical triangulation, primordial black holes, the information-loss problem, loop quantum cosmology, and other topics'. The presentation of these current topics is necessarily brief given the size of the book, but effective in encapsulating the main ideas in some cases. For instance the few pages devoted to loop quantum cosmology describe how the mini-superspace reduction of the quantum Hamiltonian constraint of LQG becomes a difference equation, whereas the discussion of 'dynamical triangulations', an approach to defining a discretized Lorentzian path integral for quantum gravity, is less detailed. The first few chapters of the book provide, in a roughly historical sequence, the covariant and canonical metric variable approach to the subject developed in the 1960s and 70s. The problem(s) of time in quantum gravity are nicely summarized in the chapter on quantum geometrodynamics, followed by a detailed and effective introduction of the WKB approach and the semi-classical approximation. These topics form the traditional core of the subject. The next three chapters cover LQG, quantization of black holes, and quantum cosmology. Of these the chapter on LQG is the shortest at fourteen pages—a reflection perhaps of the fact that there are two books and a few long reviews of the subject available written by the main protagonists in the field. The chapters on black holes and cosmology provide a more or less standard introduction to black hole thermodynamics, Hawking and Unruh radiation, quantization of the Schwarzschild metric and mini-superspace collapse models, and the DeWitt, Hartle Hawking and Vilenkin wavefunctions. The chapter on string theory is an essay-like overview of its quantum gravitational aspects. It provides a nice introduction to selected ideas and a guide to the literature. Here a prescient student may be left wondering why there is no quantum cosmology in string theory, perhaps a deliberate omission to avoid the 'landscape' and its fauna. In summary, I think this book succeeds in its purpose of providing a broad introduction to quantum gravity, and nicely complements some of the other books on the subject.

Coherent states for quantum compact groups

NASA Astrophysics Data System (ADS)

Jurĉo, B.; Ŝťovíĉek, P.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l, Bl, Cl and D l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested.

Shape from sound: toward new tools for quantum gravity.

PubMed

Aasen, David; Bhamre, Tejal; Kempf, Achim

2013-03-22

To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at least in the case of the Euclidean signature, is the discipline of spectral geometry. It aims at describing curved manifolds in terms of the spectra of their canonical differential operators. As an immediate benefit, this would offer a clean gauge-independent identification of the metric's degrees of freedom in terms of invariants that should be ready to quantize. However, spectral geometry is itself hard and has been plagued by ambiguities. Here, we regularize and break up spectral geometry into small, finite-dimensional and therefore manageable steps. We constructively demonstrate that this strategy works at least in two dimensions. We can now calculate the shapes of two-dimensional objects from their vibrational spectra.

Quantum-limited heat conduction over macroscopic distances

PubMed Central

Partanen, Matti; Tan, Kuan Yen; Govenius, Joonas; Lake, Russell E.; Mäkelä, Miika K.; Tanttu, Tuomo; Möttönen, Mikko

2016-01-01

The emerging quantum technological apparatuses1, 2, such as the quantum computer3–6, call for extreme performance in thermal engineering7. Cold distant heat sinks are needed for the quantized electric degrees of freedom due to the increasing packaging density and heat dissipation. Importantly, quantum mechanics sets a fundamental upper limit for the flow of information and heat, which is quantified by the quantum of thermal conductance8–10. However, the short distance between the heat-exchanging bodies in the previous experiments11–14 hinders their applicability in quantum technology. Here, we present experimental observations of quantum-limited heat conduction over macroscopic distances extending to a metre. We achieved this improvement of four orders of magnitude in the distance by utilizing microwave photons travelling in superconducting transmission lines. Thus, it seems that quantum-limited heat conduction has no fundamental distance cutoff. This work establishes the integration of normal-metal components into the framework of circuit quantum electrodynamics15–17 which provides a basis for the superconducting quantum computer18–21. Especially, our results facilitate remote cooling of nanoelectronic devices using far-away in-situ-tunable heat sinks22, 23. Furthermore, quantum-limited heat conduction is important in contemporary thermodynamics24, 25. Here, the long distance may lead to ultimately efficient mesoscopic heat engines with promising practical applications26. PMID:27239219

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.

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.

Modified Bose-Einstein and Fermi-Dirac statistics if excitations are localized on an intermediate length scale: applications to non-Debye specific heat.

PubMed

Chamberlin, Ralph V; Davis, Bryce F

2013-10-01

Disordered systems show deviations from the standard Debye theory of specific heat at low temperatures. These deviations are often attributed to two-level systems of uncertain origin. We find that a source of excess specific heat comes from correlations between quanta of energy if excitations are localized on an intermediate length scale. We use simulations of a simplified Creutz model for a system of Ising-like spins coupled to a thermal bath of Einstein-like oscillators. One feature of this model is that energy is quantized in both the system and its bath, ensuring conservation of energy at every step. Another feature is that the exact entropies of both the system and its bath are known at every step, so that their temperatures can be determined independently. We find that there is a mismatch in canonical temperature between the system and its bath. In addition to the usual finite-size effects in the Bose-Einstein and Fermi-Dirac distributions, if excitations in the heat bath are localized on an intermediate length scale, this mismatch is independent of system size up to at least 10(6) particles. We use a model for correlations between quanta of energy to adjust the statistical distributions and yield a thermodynamically consistent temperature. The model includes a chemical potential for units of energy, as is often used for other types of particles that are quantized and conserved. Experimental evidence for this model comes from its ability to characterize the excess specific heat of imperfect crystals at low temperatures.

Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.; Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa

2008-10-15

The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free {omega} parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{+-}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3), all with a Maxwell term. The Hamiltonian formalismmore » is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P{sub M};Q,P{sub Q}), where M is the mass parameter, which for {omega}<-(3/2) and for {omega}={+-}{infinity} needs a careful renormalization, P{sub M} is the conjugate momenta of M, Q is the charge parameter, and P{sub Q} is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field {phi}. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

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.

Bose-Einstein condensation of light: general theory.

PubMed

Sob'yanin, Denis Nikolaevich

2013-08-01

A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.

Collisionless distribution function for the relativistic force-free Harris sheet

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

Stark, C. R.; Neukirch, T.

A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters ofmore » the distribution function and the macroscopic parameters such as the current sheet thickness is discussed.« less

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

Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid

NASA Astrophysics Data System (ADS)

Yu, Xiaoquan; Billam, Thomas P.; Nian, Jun; Reeves, Matthew T.; Bradley, Ashton S.

2016-08-01

Clustering of like-sign vortices in a planar bounded domain is known to occur at negative temperature, a phenomenon that Onsager demonstrated to be a consequence of bounded phase space. In a confined superfluid, quantized vortices can support such an ordered phase, provided they evolve as an almost isolated subsystem containing sufficient energy. A detailed theoretical understanding of the statistical mechanics of such states thus requires a microcanonical approach. Here we develop an analytical theory of the vortex clustering transition in a neutral system of quantum vortices confined to a two-dimensional disk geometry, within the microcanonical ensemble. The choice of ensemble is essential for identifying the correct thermodynamic limit of the system, enabling a rigorous description of clustering in the language of critical phenomena. As the system energy increases above a critical value, the system develops global order via the emergence of a macroscopic dipole structure from the homogeneous phase of vortices, spontaneously breaking the Z2 symmetry associated with invariance under vortex circulation exchange, and the rotational SO (2 ) symmetry due to the disk geometry. The dipole structure emerges characterized by the continuous growth of the macroscopic dipole moment which serves as a global order parameter, resembling a continuous phase transition. The critical temperature of the transition, and the critical exponent associated with the dipole moment, are obtained exactly within mean-field theory. The clustering transition is shown to be distinct from the final state reached at high energy, known as supercondensation. The dipole moment develops via two macroscopic vortex clusters and the cluster locations are found analytically, both near the clustering transition and in the supercondensation limit. The microcanonical theory shows excellent agreement with Monte Carlo simulations, and signatures of the transition are apparent even for a modest system of 100 vortices, accessible in current Bose-Einstein condensate experiments.

Group field theories for all loop quantum gravity

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Ryan, James P.; Thürigen, Johannes

2015-02-01

Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

Non-uniform cosine modulated filter banks using meta-heuristic algorithms in CSD space.

PubMed

Kalathil, Shaeen; Elias, Elizabeth

2015-11-01

This paper presents an efficient design of non-uniform cosine modulated filter banks (CMFB) using canonic signed digit (CSD) coefficients. CMFB has got an easy and efficient design approach. Non-uniform decomposition can be easily obtained by merging the appropriate filters of a uniform filter bank. Only the prototype filter needs to be designed and optimized. In this paper, the prototype filter is designed using window method, weighted Chebyshev approximation and weighted constrained least square approximation. The coefficients are quantized into CSD, using a look-up-table. The finite precision CSD rounding, deteriorates the filter bank performances. The performances of the filter bank are improved using suitably modified meta-heuristic algorithms. The different meta-heuristic algorithms which are modified and used in this paper are Artificial Bee Colony algorithm, Gravitational Search algorithm, Harmony Search algorithm and Genetic algorithm and they result in filter banks with less implementation complexity, power consumption and area requirements when compared with those of the conventional continuous coefficient non-uniform CMFB.

Non-uniform cosine modulated filter banks using meta-heuristic algorithms in CSD space

PubMed Central

Kalathil, Shaeen; Elias, Elizabeth

2014-01-01

This paper presents an efficient design of non-uniform cosine modulated filter banks (CMFB) using canonic signed digit (CSD) coefficients. CMFB has got an easy and efficient design approach. Non-uniform decomposition can be easily obtained by merging the appropriate filters of a uniform filter bank. Only the prototype filter needs to be designed and optimized. In this paper, the prototype filter is designed using window method, weighted Chebyshev approximation and weighted constrained least square approximation. The coefficients are quantized into CSD, using a look-up-table. The finite precision CSD rounding, deteriorates the filter bank performances. The performances of the filter bank are improved using suitably modified meta-heuristic algorithms. The different meta-heuristic algorithms which are modified and used in this paper are Artificial Bee Colony algorithm, Gravitational Search algorithm, Harmony Search algorithm and Genetic algorithm and they result in filter banks with less implementation complexity, power consumption and area requirements when compared with those of the conventional continuous coefficient non-uniform CMFB. PMID:26644921

Black holes in loop quantum gravity.

PubMed

Perez, Alejandro

2017-12-01

This is a review of results on black hole physics in the context of loop quantum gravity. The key feature underlying these results is the discreteness of geometric quantities at the Planck scale predicted by this approach to quantum gravity. Quantum discreteness follows directly from the canonical quantization prescription when applied to the action of general relativity that is suitable for the coupling of gravity with gauge fields, and especially with fermions. Planckian discreteness and causal considerations provide the basic structure for the understanding of the thermal properties of black holes close to equilibrium. Discreteness also provides a fresh new look at more (at the moment) speculative issues, such as those concerning the fate of information in black hole evaporation. The hypothesis of discreteness leads, also, to interesting phenomenology with possible observational consequences. The theory of loop quantum gravity is a developing program; this review reports its achievements and open questions in a pedagogical manner, with an emphasis on quantum aspects of black hole physics.

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.

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.

Ferroelectricity by Bose-Einstein condensation in a quantum magnet.

PubMed

Kimura, S; Kakihata, K; Sawada, Y; Watanabe, K; Matsumoto, M; Hagiwara, M; Tanaka, H

2016-09-26

The Bose-Einstein condensation is a fascinating phenomenon, which results from quantum statistics for identical particles with an integer spin. Surprising properties, such as superfluidity, vortex quantization or Josephson effect, appear owing to the macroscopic quantum coherence, which spontaneously develops in Bose-Einstein condensates. Realization of Bose-Einstein condensation is not restricted in fluids like liquid helium, a superconducting phase of paired electrons in a metal and laser-cooled dilute alkali atoms. Bosonic quasi-particles like exciton-polariton and magnon in solids-state systems can also undergo Bose-Einstein condensation in certain conditions. Here, we report that the quantum coherence in Bose-Einstein condensate of the magnon quasi particles yields spontaneous electric polarization in the quantum magnet TlCuCl 3 , leading to remarkable magnetoelectric effect. Very soft ferroelectricity is realized as a consequence of the O(2) symmetry breaking by magnon Bose-Einstein condensation. The finding of this ferroelectricity will open a new window to explore multi-functionality of quantum magnets.

From Discrete Breathers to Many Body Localization and Flatbands

NASA Astrophysics Data System (ADS)

Flach, Sergej

Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves. Also at New Zealand Institute of Advanced Study, Massey University, Auckland, New Zealand.

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

Laser cooling and control of excitations in superfluid helium

NASA Astrophysics Data System (ADS)

Harris, G. I.; McAuslan, D. L.; Sheridan, E.; Sachkou, Y.; Baker, C.; Bowen, W. P.

2016-08-01

Superfluidity is a quantum state of matter that exists macroscopically in helium at low temperatures. The elementary excitations in superfluid helium have been probed with great success using techniques such as neutron and light scattering. However, measurements of phonon excitations have so far been limited to average thermodynamic properties or the driven response far out of thermal equilibrium. Here, we use cavity optomechanics to probe the thermodynamics of phonon excitations in real time. Furthermore, strong light-matter interactions allow both laser cooling and amplification. This represents a new tool to observe and control superfluid excitations that may provide insight into phonon-phonon interactions, quantized vortices and two-dimensional phenomena such as the Berezinskii-Kosterlitz-Thouless transition. The third sound modes studied here also offer a pathway towards quantum optomechanics with thin superfluid films, including the prospect of femtogram masses, high mechanical quality factors, strong phonon-phonon and phonon-vortex interactions, and self-assembly into complex geometries with sub-nanometre feature size.

Observation of the quantum Hall effect in δ-doped SrTiO3

PubMed Central

Matsubara, Y.; Takahashi, K. S.; Bahramy, M. S.; Kozuka, Y.; Maryenko, D.; Falson, J.; Tsukazaki, A.; Tokura, Y.; Kawasaki, M.

2016-01-01

The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems. PMID:27228903

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

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.

Quantization and fractional quantization of currents in periodically driven stochastic systems. I. Average currents

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Klein, John R.; Sinitsyn, Nikolai A.

2012-04-01

This article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically time-dependent transition rates that satisfy the detailed balance condition at any time. We show that under general conditions, the currents in the system on average become quantized or fractionally quantized for adiabatic driving at sufficiently low temperature. We develop the quantitative theory of this quantization and interpret it in terms of topological invariants. By implementing the celebrated Kirchhoff theorem we derive a general and explicit formula for the average generated current that plays a role of an efficient tool for treating the current quantization effects.

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.

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.

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.

An alternative expression to the Sackur-Tetrode entropy formula for an ideal gas

NASA Astrophysics Data System (ADS)

Nagata, Shoichi

2018-03-01

An expression for the entropy of a monoatomic classical ideal gas is known as the Sackur-Tetrode equation. This pioneering investigation about 100 years ago incorporates quantum considerations. The purpose of this paper is to provide an alternative expression for the entropy in terms of the Heisenberg uncertainty relation. The analysis is made on the basis of fluctuation theory, for a canonical system in thermal equilibrium at temperature T. This new formula indicates manifestly that the entropy of macroscopic world is recognized as a measure of uncertainty in microscopic quantum world. The entropy in the Sackur-Tetrode equation can be re-interpreted from a different perspective viewpoint. The emphasis is on the connection between the entropy and the uncertainty relation in quantum consideration.

Electroencephalographic field influence on calcium momentum waves.

PubMed

Ingber, Lester; Pappalepore, Marco; Stesiak, Ronald R

2014-02-21

Macroscopic electroencephalographic (EEG) fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered is macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential A. The bottom-up process considered is Ca(2+) waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of A on Ca(2+) momentum, p. The canonical momentum of a charged particle in an electromagnetic field, Π=p+qA (SI units), is calculated, where the charge of Ca(2+) is q=-2e, e is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG A can be quite influential on the momentum p of Ca(2+) ions, in both classical and quantum mechanics. Molecular scales of Ca(2+) wave dynamics are coupled with A fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting A models to EEG data as reported here, building tripartite models to develop A models, and studying long coherence times of Ca(2+) waves in the presence of A due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the p+qA interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention. © 2013 Published by Elsevier Ltd. All rights reserved.

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.

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.

Topological quantization in units of the fine structure constant.

PubMed

Maciejko, Joseph; Qi, Xiao-Liang; Drew, H Dennis; Zhang, Shou-Cheng

2010-10-15

Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine structure constant α=e²/ℏc. In this Letter, we propose an optical experiment to directly measure this topological quantization phenomenon, independent of material details. Our proposal also provides a way to measure the half-quantized Hall conductances on the two surfaces of the topological insulator independently of each other.

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.

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.

Observables and density matrices embedded in dual Hilbert spaces

NASA Astrophysics Data System (ADS)

Prosen, T.; Martignon, L.; Seligman, T. H.

2015-06-01

The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured that we deal with Hilbert spaces although the mathematical background was not entirely clear, particularly, when dealing with bosonic operators. This in turn caused some doubts about the correct way to combine bosonic and fermionic operators or, in other words, regular and Grassmann variables. In this paper we present a formal answer to the problems on a simple and very general basis. We illustrate the resulting construction by revisiting the Bargmann transform and finding the known connection between {{L}}2({{R}}) and the Bargmann-Hilbert space. We pursue this line of thinking one step further and discuss the representations of complex extensions of linear canonical transformations as isometries between dual Hilbert spaces. We then use the formalism to give an explicit formulation for Fock spaces involving both fermions and bosons thus solving the problem at the origin of our considerations.

Casimir forces on a bi-anisotropic absorbing magneto-dielectric slab between two parallel conducting plates

NASA Astrophysics Data System (ADS)

Amooshahi, Majid; Shoughi, Ali

2018-05-01

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers-Kronig relations. The Maxwell’s equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab.

Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

NASA Astrophysics Data System (ADS)

Triantafyllopoulos, A.; Stavrinos, P. C.

2018-04-01

We study field equations for a weak anisotropic model on the tangent Lorentz bundle TM of a spacetime manifold. A geometrical extension of general relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer 4‑velocity. In this approach, we consider a metric on TM as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein–Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework.

Entanglement Criteria of Two Two-Level Atoms Interacting with Two Coupled Modes

NASA Astrophysics Data System (ADS)

Baghshahi, Hamid Reza; Tavassoly, Mohammad Kazem; Faghihi, Mohammad Javad

2015-08-01

In this paper, we study the interaction between two two-level atoms and two coupled modes of a quantized radiation field in the form of parametric frequency converter injecting within an optical cavity enclosed by a medium with Kerr nonlinearity. It is demonstrated that, by applying the Bogoliubov-Valatin canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Then, under particular initial conditions for the atoms (in a coherent superposition of its ground and upper states) and the fields (in a standard coherent state) which may be prepared, the time evolution of state vector of the entire system is analytically evaluated. In order to understand the degree of entanglement between subsystems (atom-field and atom-atom), the dynamics of entanglement through different measures, namely, von Neumann reduced entropy, concurrence and negativity is evaluated. In each case, the effects of Kerr nonlinearity and detuning parameter on the above measures are numerically analyzed, in detail. It is illustrated that the amount of entanglement can be tuned by choosing the evolved parameters, appropriately.

Statistical Mechanics of Coherent Ising Machine — The Case of Ferromagnetic and Finite-Loading Hopfield Models —

NASA Astrophysics Data System (ADS)

Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa

2017-10-01

The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.

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.

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.

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.

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.

Quantization of geometric phase with integer and fractional topological characterization in a quantum Ising chain with long-range interaction.

PubMed

Sarkar, Sujit

2018-04-12

An attempt is made to study and understand the behavior of quantization of geometric phase of a quantum Ising chain with long range interaction. We show the existence of integer and fractional topological characterization for this model Hamiltonian with different quantization condition and also the different quantized value of geometric phase. The quantum critical lines behave differently from the perspective of topological characterization. The results of duality and its relation to the topological quantization is presented here. The symmetry study for this model Hamiltonian is also presented. Our results indicate that the Zak phase is not the proper physical parameter to describe the topological characterization of system with long range interaction. We also present quite a few exact solutions with physical explanation. Finally we present the relation between duality, symmetry and topological characterization. Our work provides a new perspective on topological quantization.

Anomalous atomic displacement parameters and local dynamics in the Curie range of a Pb-free relaxor ferroelectric system (Bi1-xBax)(Fe1-xTix)O3(0.36 ≤ x ≤ 0.50)

NASA Astrophysics Data System (ADS)

Singh, Anar; Moriyoshi, Chikako; Kuroiwa, Yoshihiro; Pandey, Dhananjai

2018-04-01

We report here the relaxor ferroelectric (RFE) behaviour in a multiferroic solid solution system, (Bi1-xBax)(Fe1-xTix)O3, at a critical disorder level of xC ˜ 0.35 in BiFeO3 and 0.65 (i.e., 1-xC = 0.35) in BaTiO3 similar to the 1:2 ratio of Mg2+ and Nb5+ in the canonical RFE Pb(Mg1/3Nb2/3)O3. This Pb-free system, like canonical Pb-based RFEs, does not exhibit macroscopic symmetry breaking and shows only the signatures of ergodicity breaking at Vogel-Fulcher freezing temperature (TVF). The atomic displacement parameters (ADPs) of Fe3+/Ti4+ and O2-, obtained using high wave vector (Q) and high-resolution synchrotron x-ray diffraction data as a function of temperature, show anomalous diffuse peaks in the Curie range. It is shown that the diffuse peak in ADPs is due to softening of the vibrational frequencies of the B-O chain (B = Fe3+/Ti4+ and O = O2-) below the Burns temperature (TB) followed by hardening below the characteristic temperature (T'm), which corresponds to a peak in the dielectric permittivity (ɛ').

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.

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.

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.

Buckling shells are also swimmers

NASA Astrophysics Data System (ADS)

Quilliet, Catherine; Dyfcom Bubbleboost Team

We present an experimental and numerical study on the displacement of shells undergoing deformations in a fluid. When submitted to cycles of pressure difference between outside and inside, a shell buckles and debuckles, showing a succession of shapes and a dynamics that are different during the two phases. Hence such objects are likely to swim, including at low Reynolds (microscopic scale). We studied the swimming of buckling/debuckling shells at macroscopic scale using different approaches (force quantization, shape recording, displacement along a frictionless rail, study of external flow using PIV), and showed that inertia plays a role in propulsion, even in situations where dimensionless numbers correspond also to microswimmers in water. Different fluid viscosities were explored, showing an optimum for the displacement. Interestingly, the most favorable cases lead to displacements in the same direction and sense during both motor stroke (buckling phase) and recovery stroke (de-buckling phase). This work opens the route for the synthesis with high throughput of abusively simple synthetic swimmers, possibly gathered into nanorobots, actuated by a scalar field such as the pressure in echographic devices. Universite Grenoble Alpes, CNRS, European Research Council.

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.

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.

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.

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.

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

Quantized Rabi oscillations and circular dichroism in quantum Hall systems

NASA Astrophysics Data System (ADS)

Tran, D. T.; Cooper, N. R.; Goldman, N.

2018-06-01

The dissipative response of a quantum system upon periodic driving can be exploited as a probe of its topological properties. Here we explore the implications of such phenomena in two-dimensional gases subjected to a uniform magnetic field. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying nontrivial topology. Based on selection rules, we find that this quantized effect can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantization laws. We discuss how quantized dissipative responses can be probed locally, both in the bulk and at the boundaries of the system. This work suggests alternative forms of topological probes based on circular dichroism.

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.

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.

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.

Strong field QED in lepton colliders and electron/laser interactions

NASA Astrophysics Data System (ADS)

Hartin, Anthony

2018-05-01

The studies of strong field particle physics processes in electron/laser interactions and lepton collider interaction points (IPs) are reviewed. These processes are defined by the high intensity of the electromagnetic fields involved and the need to take them into account as fully as possible. Thus, the main theoretical framework considered is the Furry interaction picture within intense field quantum field theory. In this framework, the influence of a background electromagnetic field in the Lagrangian is calculated nonperturbatively, involving exact solutions for quantized charged particles in the background field. These “dressed” particles go on to interact perturbatively with other particles, enabling the background field to play both macroscopic and microscopic roles. Macroscopically, the background field starts to polarize the vacuum, in effect rendering it a dispersive medium. Particles encountering this dispersive vacuum obtain a lifetime, either radiating or decaying into pair particles at a rate dependent on the intensity of the background field. In fact, the intensity of the background field enters into the coupling constant of the strong field quantum electrodynamic Lagrangian, influencing all particle processes. A number of new phenomena occur. Particles gain an intensity-dependent rest mass shift that accounts for their presence in the dispersive vacuum. Multi-photon events involving more than one external field photon occur at each vertex. Higher order processes which exchange a virtual strong field particle resonate via the lifetimes of the unstable strong field states. Two main arenas of strong field physics are reviewed; those occurring in relativistic electron interactions with intense laser beams, and those occurring in the beam-beam physics at the interaction point of colliders. This review outlines the theory, describes its significant novel phenomenology and details the experimental schema required to detect strong field effects and the simulation programs required to model them.

Quantum Dynamics of a d-wave Josephson Junction

NASA Astrophysics Data System (ADS)

Bauch, Thilo

2007-03-01

Thilo Bauch ^1, Floriana Lombardi ^1, Tobias Lindstr"om ^2, Francesco Tafuri ^3, Giacomo Rotoli ^4, Per Delsing ^1, Tord Claeson ^1 1 Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, S-412 96 G"oteborg, Sweden. 2 National Physical Laboratory, Queens Road, Teddington, Middlesex TW11 0LW, UK. 3 Istituto Nazionale per la Fisica della Materia-Dipartimento Ingegneria dell'Informazione, Seconda Universita di Napoli, Aversa (CE), Italy. 4 Dipartimento di Ingegneria Meccanica, Energetica e Gestionale, Universita of L'Aquila, Localita Monteluco, L'Aquila, Italy. We present direct observation of macroscopic quantum properties in an all high critical temperature superconductor d-wave Josephson junction. Although dissipation caused by low energy excitations is expected to strongly suppress quantum effects we demonstrate macroscopic quantum tunneling [1] and energy level quantization [2] in our d-wave Josephson junction. The results clearly indicate that the role of dissipation mechanisms in high temperature superconductors has to be revised, and may also have consequences for a new class of solid state ``quiet'' quantum bit with superior coherence time. We show that the dynamics of the YBCO grain boundary Josephson junctions fabricated on a STO substrate are strongly affected by their environment. As a first approximation we model the environment by the stray capacitance and stray inductance of the junction electrodes. The total system consisting of the junction and stray elements has two degrees of freedom resulting in two characteristic resonance frequencies. Both frequencies have to be considered to describe the quantum mechanical behavior of the Josephson circuit. [1] T. Bauch et al, Phys. Rev. Lett. 94, 087003 (2005). [2] T. Bauch et al, Science 311, 57 (2006).

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.

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

Livine, Etera R.

We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient C{sup 2N}//SU(2). A framed polyhedron is then parametrized by N spinors living in C{sup 2} satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N−2)).more » We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in a similar fashion trading the unitary group for the orthogonal group. We conclude with a discussion of the possible (deformation) dynamics that one can define on the space of polygons or polyhedra. This work is a priori useful in the context of discrete geometry but it should hopefully also be relevant to (loop) quantum gravity in 2+1 and 3+1 dimensions when the quantum geometry is defined in terms of gluing of (quantized) polygons and polyhedra.« less

Computational study of ibuprofen removal from water by adsorption in realistic activated carbons.

PubMed

Bahamon, Daniel; Carro, Leticia; Guri, Sonia; Vega, Lourdes F

2017-07-15

Molecular simulations using the Grand Canonical Monte Carlo (GCMC) method have been performed in order to obtain physical insights on how the interaction between ibuprofen (IBP) and activated carbons (ACs) in aqueous mixtures affects IBP removal from water by ACs. A nanoporous carbon model based on units of polyaromatic molecules with different number of rings, defects and polar-oxygenated sites is described. Individual effects of factors such as porous features and chemical heterogeneities in the adsorbents are investigated and quantified. Results are in good agreement with experimental adsorption data, highlightening the ability of GCMC simulation to describe the macroscopic adsorption performance in drug removal applications, while also providing additional insights into the IBP/water adsorption mechanism. The simulation results allow finding the optimal type of activated carbon material for separating this pollutant in water treatment. Copyright © 2017 Elsevier Inc. All rights reserved.

Quantum phases for point-like charged particles and for electrically neutral dipoles in an electromagnetic field

NASA Astrophysics Data System (ADS)

Kholmetskii, A. L.; Missevitch, O. V.; Yarman, T.

2018-05-01

We point out that the known quantum phases for an electric/magnetic dipole moving in an electromagnetic (EM) field must be presented as the superposition of more fundamental quantum phases emerging for elementary charges. Using this idea, we find two new fundamental quantum phases for point-like charges, next to the known electric and magnetic Aharonov-Bohm (A-B) phases, named by us as the complementary electric and magnetic phases, correspondingly. We further demonstrate that these new phases can indeed be derived via the Schrödinger equation for a particle in an EM field, where however the operator of momentum is re-defined via the replacement of the canonical momentum of particle by the sum of its mechanical momentum and interactional field momentum for a system "charged particle and a macroscopic source of EM field". The implications of the obtained results are discussed.

Bidimensional nano-optomechanics and topological backaction in a non-conservative radiation force field.

PubMed

Gloppe, A; Verlot, P; Dupont-Ferrier, E; Siria, A; Poncharal, P; Bachelier, G; Vincent, P; Arcizet, O

2014-11-01

Optomechanics, which explores the fundamental coupling between light and mechanical motion, has made important advances in manipulating macroscopic mechanical oscillators down to the quantum level. However, dynamical effects related to the vectorial nature of the optomechanical interaction remain to be investigated. Here we study a nanowire with subwavelength dimensions coupled strongly to a tightly focused beam of light, enabling an ultrasensitive readout of the nanoresonator dynamics. We determine experimentally the vectorial structure of the optomechanical interaction and demonstrate that a bidimensional dynamical backaction governs the nanowire dynamics. Moreover, the spatial topology of the optomechanical interaction is responsible for novel canonical signatures of strong coupling between mechanical modes, which leads to a topological instability that underlies the non-conservative nature of the optomechanical interaction. These results have a universal character and illustrate the increased sensitivity of nanomechanical devices towards spatially varying interactions, opening fundamental perspectives in nanomechanics, optomechanics, ultrasensitive scanning force microscopy and nano-optics.

Fast adaptive flat-histogram ensemble to enhance the sampling in large systems

NASA Astrophysics Data System (ADS)

Xu, Shun; Zhou, Xin; Jiang, Yi; Wang, YanTing

2015-09-01

An efficient novel algorithm was developed to estimate the Density of States (DOS) for large systems by calculating the ensemble means of an extensive physical variable, such as the potential energy, U, in generalized canonical ensembles to interpolate the interior reverse temperature curve , where S( U) is the logarithm of the DOS. This curve is computed with different accuracies in different energy regions to capture the dependence of the reverse temperature on U without setting prior grid in the U space. By combining with a U-compression transformation, we decrease the computational complexity from O( N 3/2) in the normal Wang Landau type method to O( N 1/2) in the current algorithm, as the degrees of freedom of system N. The efficiency of the algorithm is demonstrated by applying to Lennard Jones fluids with various N, along with its ability to find different macroscopic states, including metastable states.

Hydration Phase Diagram of Clay Particles from Molecular Simulations.

PubMed

Honorio, Tulio; Brochard, Laurent; Vandamme, Matthieu

2017-11-07

Adsorption plays a fundamental role in the behavior of clays. Because of the confinement between solid clay layers on the nanoscale, adsorbed water is structured in layers, which can occupy a specific volume. The transition between these states is intimately related to key features of clay thermo-hydro-mechanical behavior. In this article, we consider the hydration states of clays as phases and the transition between these states as phase changes. The thermodynamic formulation supporting this idea is presented. Then, the results from grand canonical Monte Carlo simulations of sodium montmorillonite are used to derive hydration phase diagrams. The stability analysis presented here explains the coexistence of different hydration states at clay particle scale and improves our understanding of the irreversibilities of clay thermo-hydro-mechanical behavior. Our results provide insights into the mechanics of the elementary constituents of clays, which is crucial for a better understanding of the macroscopic behavior of clay-rich rocks and soils.

Quantum Structure of Space and Time

NASA Astrophysics Data System (ADS)

Duff, M. J.; Isham, C. J.

2012-07-01

Foreword Abdus Salam; Preface; List of participants; Part I. Quantum Gravity, Fields and Topology: 1. Some remarks on gravity and quantum mechanics Roger Penrose; 2. An experimental test of quantum gravity Don N. Page and C. D. Geilker; 3. Quantum mechanical origin of the sandwich theorem in classical gravitation theory Claudio Teitelboim; 4. θ-States induced by the diffeomorphism group in canonically quantized gravity C. J. Isham; 5. Strong coupling quantum gravity: an introduction Martin Pilati; 6. Quantizing fourth order gravity theories S. M. Christensen; 7. Green's functions, states and renormalisation M. R. Brown and A. C. Ottewill; 8. Introduction to quantum regge calculus Martin Roček and Ruth Williams; 9. Spontaneous symmetry breaking in curved space-time D. J. Toms; 10. Spontaneous symmetry breaking near a black hole M. S. Fawcett and B. F. Whiting; 11. Yang-Mills vacua in a general three-space G. Kunstatter; 12. Fermion fractionization in physics R. Jackiw; Part II. Supergravity: 13. The new minimal formulation of N=1 supergravity and its tensor calculus M. F. Sohnius and P. C. West; 14. A new deteriorated energy-momentum tensor M. J. Duff and P. K. Townsend; 15. Off-shell N=2 and N=4 supergravity in five dimensions P. Howe; 16. Supergravity in high dimensions P. van Niewenhuizen; 17. Building linearised extended supergravities J. G. Taylor; 18. (Super)gravity in the complex angular momentum plane M. T. Grisaru; 19. The multiplet structure of solitons in the O(2) supergravity theory G. W. Gibbons; 20. Ultra-violet properties of supersymmetric gauge theory S. Ferrara; 21. Extended supercurrents and the ultra-violet finiteness of N=4 supersymmetric Yang-Mills theories K. S. Stelle; 22. Duality rotations B. Zumino; Part III. Cosmology and the Early Universe: 23. Energy, stability and cosmological constant S. Deser; 24. Phase transitions in the early universe T. W. B. Kibble; 25. Complete cosmological theories L. P. Grishchuk and Ya. B. Zeldovich; 26. The cosmological constant and the weak anthropic principle S. W. Hawking.

Current algebras, measures quasi-invariant under diffeomorphism groups, and infinite quantum systems with accumulation points

NASA Astrophysics Data System (ADS)

Sakuraba, Takao

The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A rigorous construction of measures quasi-invariant under the group of diffeomorphisms of d-dimensional space stabilizing a point is given.

Quantized vortices in arbitrary dimensions and the normal-to-superfluid phase transition

NASA Astrophysics Data System (ADS)

Bora, Florin

The structure and energetics of superflow around quantized vortices, and the motion inherited by these vortices from this superflow, are explored in the general setting of a superfluid in arbitrary dimensions. The vortices may be idealized as objects of co-dimension two, such as one-dimensional loops and two-dimensional closed surfaces, respectively, in the cases of three- and four-dimensional superfluidity. By using the analogy between vortical superflow and Ampere-Maxwell magnetostatics, the equilibrium superflow containing any specified collection of vortices is constructed. The energy of the superflow is found to take on a simple form for vortices that are smooth and asymptotically large, compared with the vortex core size. The motion of vortices is analyzed in general, as well as for the special cases of hyper-spherical and weakly distorted hyper-planar vortices. In all dimensions, vortex motion reflects vortex geometry. In dimension four and higher, this includes not only extrinsic but also intrinsic aspects of the vortex shape, which enter via the first and second fundamental forms of classical geometry. For hyper-spherical vortices, which generalize the vortex rings of three dimensional superfluidity, the energy-momentum relation is determined. Simple scaling arguments recover the essential features of these results, up to numerical and logarithmic factors. Extending these results to systems containing multiple vortices is elementary due to the linearity of the theory. The energy for multiple vortices is thus a sum of self-energies and power-law interaction terms. The statistical mechanics of a system containing vortices is addressed via the grand canonical partition function. A renormalization-group analysis in which the low energy excitations are integrated approximately, is used to compute certain critical coefficients. The exponents obtained via this approximate procedure are compared with values obtained previously by other means. For dimensions higher than three the superfluid density is found to vanish as the critical temperature is approached from below.

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.

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.

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.

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.

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.

Response of two-band systems to a single-mode quantized field

NASA Astrophysics Data System (ADS)

Shi, Z. C.; Shen, H. Z.; Wang, W.; Yi, X. X.

2016-03-01

The response of topological insulators (TIs) to an external weakly classical field can be expressed in terms of Kubo formula, which predicts quantized Hall conductivity of the quantum Hall family. The response of TIs to a single-mode quantized field, however, remains unexplored. In this work, we take the quantum nature of the external field into account and define a Hall conductance to characterize the linear response of a two-band system to the quantized field. The theory is then applied to topological insulators. Comparisons with the traditional Hall conductance are presented and discussed.

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.

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.

Synthetic resistivity calculations for the canonical depth-to-bedrock problem: A critical examination of the thin interbed problem and electrical equivalence theories

NASA Astrophysics Data System (ADS)

Weiss, C. J.; Knight, R.

2009-05-01

One of the key factors in the sensible inference of subsurface geologic properties from both field and laboratory experiments is the ability to quantify the linkages between the inherently fine-scale structures, such as bedding planes and fracture sets, and their macroscopic expression through geophysical interrogation. Central to this idea is the concept of a "minimal sampling volume" over which a given geophysical method responds to an effective medium property whose value is dictated by the geometry and distribution of sub- volume heterogeneities as well as the experiment design. In this contribution we explore the concept of effective resistivity volumes for the canonical depth-to-bedrock problem subject to industry-standard DC resistivity survey designs. Four models representing a sedimentary overburden and flat bedrock interface were analyzed through numerical experiments of six different resistivity arrays. In each of the four models, the sedimentary overburden consists of a thinly interbedded resistive and conductive laminations, with equivalent volume-averaged resistivity but differing lamination thickness, geometry, and layering sequence. The numerical experiments show striking differences in the apparent resistivity pseudo-sections which belie the volume-averaged equivalence of the models. These models constitute the synthetic data set offered for inversion in this Back to Basics Resistivity Modeling session and offer the promise to further our understanding of how the sampling volume, as affected by survey design, can be constrained by joint-array inversion of resistivity data.

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.

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.

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.

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.

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.

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.

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.

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.

Can noncommutative effects account for the present speed up of the cosmic expansion?

NASA Astrophysics Data System (ADS)

Obregon, Octavio; Quiros, Israel

2011-08-01

In this paper we investigate to which extent noncommutativity, an intrinsically quantum property, may influence the Friedmann-Robertson-Walker cosmological dynamics at late times/large scales. To our purpose it will be enough to explore the asymptotic properties of the cosmological model in the phase space. Our recipe to build noncommutativity into our model is based in the approach of Ref. and can be summarized in the following steps: i) the Hamiltonian is derived from the Einstein-Hilbert action (plus a self-interacting scalar field action) for a Friedmann-Robertson-Walker space-time with flat spatial sections, ii) canonical quantization recipe is applied, i.e., the mini-superspace variables are promoted to operators, and the WDW equation is written in terms of these variables, iii) noncommutativity in the mini-superspace is achieved through the replacement of the standard product of functions by the Moyal star product in the WDW equation, and, finally, iv) semiclassical cosmological equations are obtained by means of the WKB approximation applied to the (equivalent) modified Hamilton-Jacobi equation. We demonstrate, indeed, that noncommutative effects of the kind considered here can be those responsible for the present speed up of the cosmic expansion.

Lorentz covariance of loop quantum gravity

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

Rovelli, Carlo; Speziale, Simone

2011-05-15

The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the projected spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleulermore » formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are precisely in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.« less

Simplicity constraints: A 3D toy model for loop quantum gravity

NASA Astrophysics Data System (ADS)

Charles, Christoph

2018-05-01

In loop quantum gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity constraints. Their geometrical interpretation is however unsatisfactory as they do not constitute a space-time connection. It would be possible to resolve this point by using a full Lorentz connection or, equivalently, by using the self-dual Ashtekar variables. This leads however to simplicity constraints or reality conditions which are notoriously difficult to implement in the quantum theory. We explore in this paper the possibility of using completely degenerate actions to impose such constraints at the quantum level in the context of canonical quantization. To do so, we define a simpler model, in 3D, with similar constraints by extending the phase space to include an independent vielbein. We define the classical model and show that a precise quantum theory by gauge unfixing can be defined out of it, completely equivalent to the standard 3D Euclidean quantum gravity. We discuss possible future explorations around this model as it could help as a stepping stone to define full-fledged covariant loop quantum gravity.

Change of Electroweak Nuclear Reaction Rates by CP- and Isospin Symmetry Breaking - A Model Calculation

NASA Astrophysics Data System (ADS)

Stumpf, Harald

2006-09-01

Based on the assumption that electroweak bosons, leptons and quarks possess a substructure of elementary fermionic constituents, in previous papers the effect of CP-symmetry breaking on the effective dynamics of these particles was calculated. Motivated by the phenomenological procedure in this paper, isospin symmetry breaking will be added and the physical consequences of these calculations will be discussed. The dynamical law of the fermionic constituents is given by a relativistically invariant nonlinear spinor field equation with local interaction, canonical quantization, selfregularization and probability interpretation. The corresponding effective dynamics is derived by algebraic weak mapping theorems. In contrast to the commonly applied modifications of the quark mass matrices, CP-symmetry breaking is introduced into this algebraic formalism by an inequivalent vacuum with respect to the CP-invariant case, represented by a modified spinor field propagator. This leads to an extension of the standard model as effective theory which contains besides the "electric" electroweak bosons additional "magnetic" electroweak bosons and corresponding interactions. If furthermore the isospin invariance of the propagator is broken too, it will be demonstrated in detail that in combination with CP-symmetry breaking this induces a considerable modification of electroweak nuclear reaction rates.

Effect of Vacuum Properties on Electroweak Processes - A Theoretical Interpretation of Experiments

NASA Astrophysics Data System (ADS)

Stumpf, Harald

2008-06-01

Recently for discharges in fluids induced nuclear transmutations have been observed. It is our hypothesis that these reactions are due to a symmetry breaking of the electroweak vacuum by the experimental arrangement. The treatment of this hypothesis is based on the assumption that electroweak bosons, leptons and quarks possess a substructure of elementary fermionic constituents. The dynamical law of these fermionic constituents is given by a relativistically invariant nonlinear spinor field equation with local interaction, canonical quantization, selfregularization and probability interpretation. Phenomenological quantities of electroweak processes follow from the derivation of corresponding effective theories obtained by algebraic weak mapping theorems where the latter theories depend on the spinor field propagator, i. e. a vacuum expectation value. This propagator and its equation are studied for conserved and for broken discrete symmetries. For combined CP- and isospin symmetry breaking it is shown that the propagator corresponds to the experimental arrangements under consideration. The modifications of the effective electroweak theory due to this modified propagator are discussed. Based on these results a mechanism is sketched which offers a qualitative interpretation of the appearance of induced nuclear transmutations. A numerical estimate of electron capture is given.

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.

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.

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.

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.

BOOK REVIEW: Modern Canonical Quantum General Relativity

NASA Astrophysics Data System (ADS)

Kiefer, Claus

2008-06-01

The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly divided into two classes: either one seeks a unified quantum framework of all interactions or one starts with a direct quantization of general relativity. In the first class, string theory (M-theory) is the only known example. In the second class, one can make an additional methodological distinction: while covariant approaches such as path-integral quantization use the four-dimensional metric as an essential ingredient of their formalism, canonical approaches start with a foliation of spacetime into spacelike hypersurfaces in order to arrive at a Hamiltonian formulation. The present book is devoted to one of the canonical approaches—loop quantum gravity. It is named modern canonical quantum general relativity by the author because it uses connections and holonomies as central variables, which are analogous to the variables used in Yang Mills theories. In fact, the canonically conjugate variables are a holonomy of a connection and the flux of a non-Abelian electric field. This has to be contrasted with the older geometrodynamical approach in which the metric of three-dimensional space and the second fundamental form are the fundamental entities, an approach which is still actively being pursued. It is the author's ambition to present loop quantum gravity in a way in which every step is formulated in a mathematically rigorous form. In his own words: 'loop quantum gravity is an attempt to construct a mathematically rigorous, background-independent, non-perturbative quantum field theory of Lorentzian general relativity and all known matter in four spacetime dimensions, not more and not less'. The formal Leitmotiv of loop quantum gravity is background independence. Non-gravitational theories are usually quantized on a given non-dynamical background. In contrast, due to the geometrical nature of gravity, no such background exists in quantum gravity. Instead, the notion of a background is supposed to emerge a posteriori as an approximate notion from quantum states of geometry. As a consequence, the standard ultraviolet divergences of quantum field theory do not show up because there is no limit of Δx → 0 to be taken in a given spacetime. On the other hand, it is open whether the theory is free of any type of divergences and anomalies. A central feature of any canonical approach, independent of the choice of variables, is the existence of constraints. In geometrodynamics, these are the Hamiltonian and diffeomorphism constraints. They also hold in loop quantum gravity, but are supplemented there by the Gauss constraint, which emerges due to the use of triads in the formalism. These constraints capture all the physics of the quantum theory because no spacetime is present anymore (analogous to the absence of trajectories in quantum mechanics), so no additional equations of motion are needed. This book presents a careful and comprehensive discussion of these constraints. In particular, the constraint algebra is calculated in a transparent and explicit way. The author makes the important assumption that a Hilbert-space structure is still needed on the fundamental level of quantum gravity. In ordinary quantum theory, such a structure is needed for the probability interpretation, in particular for the conservation of probability with respect to external time. It is thus interesting to see how far this concept can be extrapolated into the timeless realm of quantum gravity. On the kinematical level, that is, before the constraints are imposed, an essentially unique Hilbert space can be constructed in terms of spin-network states. Potentially problematic features are the implementation of the diffeomorphism and Hamiltonian constraints. The Hilbert space Hdiff defined on the diffeomorphism subspace can throw states out of the kinematical Hilbert space and is thus not contained in it. Moreover, the Hamiltonian constraint does not seem to preserve Hdiff, so its implementation remains open. To avoid some of these problems, the author proposes his 'master constraint programme' in which the infinitely many local Hamiltonian constraints are combined into one master constraint. This is a subject of his current research. With regard to this situation, it is not surprising that the main results in loop quantum gravity are found on the kinematical level. An especially important feature are the discrete spectra of geometric operators such as the area operator. This quantifies the earlier heuristic ideas about a discreteness at the Planck scale. The hope is that these results survive the consistent implementation of all constraints. The status of loop quantum gravity is concisely and competently summarized in this volume, whose author is himself one of the pioneers of this approach. What is the relation of this book to the other monograph on loop quantum gravity, written by Carlo Rovelli and published in 2004 under the title Quantum Gravity with the same company? In the words of the present author: 'the two books are complementary in the sense that they can be regarded almost as volume I ('introduction and conceptual framework') and volume II ('mathematical framework and applications') of a general presentation of quantum general relativity in general and loop quantum gravity in particular'. In fact, the present volume gives a complete and self-contained presentation of the required mathematics, especially on the approximately 200 pages of chapters 18 33. As for the physical applications, the main topic is the microscopic derivation of the black-hole entropy. This is presented in a clear and detailed form. Employing the concept of an isolated horizon (a local generalization of an event horizon), the counting of surface states gives an entropy proportional to the horizon area. It also contains the Barbero Immirzi parameter β, which is a free parameter of the theory. Demanding, on the other hand, that the entropy be equal to the Bekenstein Hawking entropy would fix this parameter. Other applications such as loop quantum cosmology are only briefly touched upon. Since loop quantum gravity is a very active field of research, the author warns that the present book can at best be seen as a snapshot. Part of the overall picture may thus in the future be subject to modifications. For example, recent work by the author using a concept of dust time is not yet covered here. Nevertheless, I expect that this volume will continue to serve as a valuable introduction and reference book. It is essential reading for everyone working on loop quantum gravity.

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.

Bulk-edge correspondence in topological transport and pumping

NASA Astrophysics Data System (ADS)

Imura, Ken-Ichiro; Yoshimura, Yukinori; Fukui, Takahiro; Hatsugai, Yasuhiro

2018-03-01

The bulk-edge correspondence (BEC) refers to a one-to-one relation between the bulk and edge properties ubiquitous in topologically nontrivial systems. Depending on the setup, BEC manifests in different forms and govern the spectral and transport properties of topological insulators and semimetals. Although the topological pump is theoretically old, BEC in the pump has been established just recently [1] motivated by the state-of-the-art experiments using cold atoms [2, 3]. The center of mass (CM) of a system with boundaries shows a sequence of quantized jumps in the adiabatic limit associated with the edge states. Despite that the bulk is adiabatic, the edge is inevitably non-adiabatic in the experimental setup or in any numerical simulations. Still the pumped charge is quantized and carried by the bulk. Its quantization is guaranteed by a compensation between the bulk and edges. We show that in the presence of disorder the pumped charge continues to be quantized despite the appearance of non-quantized jumps.

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.

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.

How quantum entanglement in DNA synchronizes double-strand breakage by type II restriction endonucleases.

PubMed

Kurian, P; Dunston, G; Lindesay, J

2016-02-21

Macroscopic quantum effects in living systems have been studied widely in pursuit of fundamental explanations for biological energy transport and sensing. While it is known that type II endonucleases, the largest class of restriction enzymes, induce DNA double-strand breaks by attacking phosphodiester bonds, the mechanism by which simultaneous cutting is coordinated between the catalytic centers remains unclear. We propose a quantum mechanical model for collective electronic behavior in the DNA helix, where dipole-dipole oscillations are quantized through boundary conditions imposed by the enzyme. Zero-point modes of coherent oscillations would provide the energy required for double-strand breakage. Such quanta may be preserved in the presence of thermal noise by the enzyme's displacement of water surrounding the DNA recognition sequence. The enzyme thus serves as a decoherence shield. Palindromic mirror symmetry of the enzyme-DNA complex should conserve parity, because symmetric bond-breaking ceases when the symmetry of the complex is violated or when physiological parameters are perturbed from optima. Persistent correlations in DNA across longer spatial separations-a possible signature of quantum entanglement-may be explained by such a mechanism. Copyright © 2015 Elsevier Ltd. All rights reserved.

Controlling Photons, Qubits and their Interactions in Superconducting Electronic Circuits

NASA Astrophysics Data System (ADS)

Wallraff, Andreas

2009-03-01

A combination of ideas from atomic physics, quantum optics and solid state physics allows us to investigate the fundamental interaction of matter and light on the level of single quanta in electronic circuits. In an approach known as circuit quantum electrodynamics, we coherently couple individual photons stored in a high quality microwave frequency resonator to a fully controllable superconducting two-level system (qubit) realized in a macroscopic electronic circuit [1]. In particular, we have recently observed the simultaneous interaction of one, two and three photons with a single qubit. In these experiments, we have probed the quantum nonlinearity of the qubit/light interaction governed by the Jaynes-Cummings hamiltonian, clearly demonstrating the quantization of the radiation field in the on-chip cavity. We have also performed quantum optics experiments with no photons at all. In this situation, i.e. in pure vacuum, we have resolved the renormalization of the qubit transition frequency - known as the Lamb shift - due to its non-resonant interaction with the cavity vacuum fluctuations [3].[4pt] [1] A. Wallraff et al., Nature (London) 431, 162 (2004)[0pt] [2] J. Fink et al., Nature (London) 454, 315 (2008)[0pt] [3] A. Fragner et al., Science 322, 1357 (2008)

How quantum entanglement in DNA synchronizes double-strand breakage by type II restriction endonucleases

PubMed Central

Kurian, P.; Dunston, G.; Lindesay, J.

2015-01-01

Macroscopic quantum effects in living systems have been studied widely in pursuit of fundamental explanations for biological energy transport and sensing. While it is known that type II endonucleases, the largest class of restriction enzymes, induce DNA double-strand breaks by attacking phosphodiester bonds, the mechanism by which simultaneous cutting is coordinated between the catalytic centers remains unclear. We propose a quantum mechanical model for collective electronic behavior in the DNA helix, where dipole-dipole oscillations are quantized through boundary conditions imposed by the enzyme. Zero-point modes of coherent oscillations would provide the energy required for double-strand breakage. Such quanta may be preserved in the presence of thermal noise by the enzyme’s displacement of water surrounding the DNA recognition sequence. The enzyme thus serves as a decoherence shield. Palindromic mirror symmetry of the enzyme-DNA complex should conserve parity, because symmetric bond-breaking ceases when the symmetry of the complex is violated or when physiological parameters are perturbed from optima. Persistent correlations in DNA across longer spatial separations—a possible signature of quantum entanglement—may be explained by such a mechanism. PMID:26682627

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.

From Weyl to Born-Jordan quantization: The Schrödinger representation revisited

NASA Astrophysics Data System (ADS)

de Gosson, Maurice A.

2016-03-01

The ordering problem has been one of the long standing and much discussed questions in quantum mechanics from its very beginning. Nowadays, there is more or less a consensus among physicists that the right prescription is Weyl's rule, which is closely related to the Moyal-Wigner phase space formalism. We propose in this report an alternative approach by replacing Weyl quantization with the less well-known Born-Jordan quantization. This choice is actually natural if we want the Heisenberg and Schrödinger pictures of quantum mechanics to be mathematically equivalent. It turns out that, in addition, Born-Jordan quantization can be recovered from Feynman's path integral approach provided that one used short-time propagators arising from correct formulas for the short-time action, as observed by Makri and Miller. These observations lead to a slightly different quantum mechanics, exhibiting some unexpected features, and this without affecting the main existing theory; for instance quantizations of physical Hamiltonian functions are the same as in the Weyl correspondence. The differences are in fact of a more subtle nature; for instance, the quantum observables will not correspond in a one-to-one fashion to classical ones, and the dequantization of a Born-Jordan quantum operator is less straightforward than that of the corresponding Weyl operator. The use of Born-Jordan quantization moreover solves the "angular momentum dilemma", which already puzzled L. Pauling. Born-Jordan quantization has been known for some time (but not fully exploited) by mathematicians working in time-frequency analysis and signal analysis, but ignored by physicists. One of the aims of this report is to collect and synthesize these sporadic discussions, while analyzing the conceptual differences with Weyl quantization, which is also reviewed in detail. Another striking feature is that the Born-Jordan formalism leads to a redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution reducing interference effects.

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.

Quantization error of CCD cameras and their influence on phase calculation in fringe pattern analysis.

PubMed

Skydan, Oleksandr A; Lilley, Francis; Lalor, Michael J; Burton, David R

2003-09-10

We present an investigation into the phase errors that occur in fringe pattern analysis that are caused by quantization effects. When acquisition devices with a limited value of camera bit depth are used, there are a limited number of quantization levels available to record the signal. This may adversely affect the recorded signal and adds a potential source of instrumental error to the measurement system. Quantization effects also determine the accuracy that may be achieved by acquisition devices in a measurement system. We used the Fourier fringe analysis measurement technique. However, the principles can be applied equally well for other phase measuring techniques to yield a phase error distribution that is caused by the camera bit depth.

Performance of customized DCT quantization tables on scientific data

NASA Technical Reports Server (NTRS)

Ratnakar, Viresh; Livny, Miron

1994-01-01

We show that it is desirable to use data-specific or customized quantization tables for scaling the spatial frequency coefficients obtained using the Discrete Cosine Transform (DCT). DCT is widely used for image and video compression (MP89, PM93) but applications typically use default quantization matrices. Using actual scientific data gathered from divers sources such as spacecrafts and electron-microscopes, we show that the default compression/quality tradeoffs can be significantly improved upon by using customized tables. We also show that significant improvements are possible for the standard test images Lena and Baboon. This work is part of an effort to develop a practical scheme for optimizing quantization matrices for any given image or video stream, under any given quality or compression constraints.

Gravitational surface Hamiltonian and entropy quantization

NASA Astrophysics Data System (ADS)

Bakshi, Ashish; Majhi, Bibhas Ranjan; Samanta, Saurav

2017-02-01

The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos-Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.

Algebra of constraints for a string in curved background

NASA Astrophysics Data System (ADS)

Wess, Julius

1990-06-01

A string field theory with curved background develops anomalies and Schwinger terms in the conformal algebra. It is generally believed that these Schwinger terms and anomalies are expressible in terms of the curvature tensor of the background metric 1 and that, therefore, they are covariant under a change of coordinates in the target space. As far as I know, all the relevant computations have been done in special gauges, i.e. in Riemann normal coordinates. The question remains whether this is true in any gauge. We have tried to investigate this problem in a Hamiltonian formulation of the model. A classical Lagrangian serves to define the canonical variables and the classical constraints. They are expressed in terms of the canonical variables and, classically, they are first class. When quantized, an ordering prescription has to be imposed which leads to anomalies and Schwinger terms. We then try to redefine the constraints in such a way that the Schwinger terms depend on the curvature tensor only. The redefinition of the constraints is limited by the requirement that it should be local and that the energy momentum tensor should be conserved. In our approach, it is natural that the constraints are improved, order by order, in the number of derivatives: we find that, up to third order in the derivatives, Schwinger terms and anomalies are expressible in terms of the curvature tensor. In the fourth order of the derivaties however, we find a contribution to the Schwinger terms that cannot be removed by a redefinition and that cannot be cast in a covariant form. The anomaly on the other hand is fully expressible in terms of the curvature scalar. The energy momentum tensor ceases to be symmetric which indicates a Lorentz anomaly as well. The question remains if the Schwinger terms take a covariant form if we allow Einstein anomalies as well 2.

Image Coding Based on Address Vector Quantization.

NASA Astrophysics Data System (ADS)

Feng, Yushu

Image coding is finding increased application in teleconferencing, archiving, and remote sensing. This thesis investigates the potential of Vector Quantization (VQ), a relatively new source coding technique, for compression of monochromatic and color images. Extensions of the Vector Quantization technique to the Address Vector Quantization method have been investigated. In Vector Quantization, the image data to be encoded are first processed to yield a set of vectors. A codeword from the codebook which best matches the input image vector is then selected. Compression is achieved by replacing the image vector with the index of the code-word which produced the best match, the index is sent to the channel. Reconstruction of the image is done by using a table lookup technique, where the label is simply used as an address for a table containing the representative vectors. A code-book of representative vectors (codewords) is generated using an iterative clustering algorithm such as K-means, or the generalized Lloyd algorithm. A review of different Vector Quantization techniques are given in chapter 1. Chapter 2 gives an overview of codebook design methods including the Kohonen neural network to design codebook. During the encoding process, the correlation of the address is considered and Address Vector Quantization is developed for color image and monochrome image coding. Address VQ which includes static and dynamic processes is introduced in chapter 3. In order to overcome the problems in Hierarchical VQ, Multi-layer Address Vector Quantization is proposed in chapter 4. This approach gives the same performance as that of the normal VQ scheme but the bit rate is about 1/2 to 1/3 as that of the normal VQ method. In chapter 5, a Dynamic Finite State VQ based on a probability transition matrix to select the best subcodebook to encode the image is developed. In chapter 6, a new adaptive vector quantization scheme, suitable for color video coding, called "A Self -Organizing Adaptive VQ Technique" is presented. In addition to chapters 2 through 6 which report on new work, this dissertation includes one chapter (chapter 1) and part of chapter 2 which review previous work on VQ and image coding, respectively. Finally, a short discussion of directions for further research is presented in conclusion.

Quantization of Gaussian samples at very low SNR regime in continuous variable QKD applications

NASA Astrophysics Data System (ADS)

Daneshgaran, Fred; Mondin, Marina

2016-09-01

The main problem for information reconciliation in continuous variable Quantum Key Distribution (QKD) at low Signal to Noise Ratio (SNR) is quantization and assignment of labels to the samples of the Gaussian Random Variables (RVs) observed at Alice and Bob. Trouble is that most of the samples, assuming that the Gaussian variable is zero mean which is de-facto the case, tend to have small magnitudes and are easily disturbed by noise. Transmission over longer and longer distances increases the losses corresponding to a lower effective SNR exasperating the problem. This paper looks at the quantization problem of the Gaussian samples at very low SNR regime from an information theoretic point of view. We look at the problem of two bit per sample quantization of the Gaussian RVs at Alice and Bob and derive expressions for the mutual information between the bit strings as a result of this quantization. The quantization threshold for the Most Significant Bit (MSB) should be chosen based on the maximization of the mutual information between the quantized bit strings. Furthermore, while the LSB string at Alice and Bob are balanced in a sense that their entropy is close to maximum, this is not the case for the second most significant bit even under optimal threshold. We show that with two bit quantization at SNR of -3 dB we achieve 75.8% of maximal achievable mutual information between Alice and Bob, hence, as the number of quantization bits increases beyond 2-bits, the number of additional useful bits that can be extracted for secret key generation decreases rapidly. Furthermore, the error rates between the bit strings at Alice and Bob at the same significant bit level are rather high demanding very powerful error correcting codes. While our calculations and simulation shows that the mutual information between the LSB at Alice and Bob is 0.1044 bits, that at the MSB level is only 0.035 bits. Hence, it is only by looking at the bits jointly that we are able to achieve a mutual information of 0.2217 bits which is 75.8% of maximum achievable. The implication is that only by coding both MSB and LSB jointly can we hope to get close to this 75.8% limit. Hence, non-binary codes are essential to achieve acceptable performance.

Bidirectional global spontaneous network activity precedes the canonical unidirectional circuit organization in the developing hippocampus.

PubMed

Shi, Yulin; Ikrar, Taruna; Olivas, Nicholas D; Xu, Xiangmin

2014-06-15

Spontaneous network activity is believed to sculpt developing neural circuits. Spontaneous giant depolarizing potentials (GDPs) were first identified with single-cell recordings from rat CA3 pyramidal neurons, but here we identify and characterize a large-scale spontaneous network activity we term global network activation (GNA) in the developing mouse hippocampal slices, which is measured macroscopically by fast voltage-sensitive dye imaging. The initiation and propagation of GNA in the mouse is largely GABA-independent and dominated by glutamatergic transmission via AMPA receptors. Despite the fact that signal propagation in the adult hippocampus is strongly unidirectional through the canonical trisynaptic circuit (dentate gyrus [DG] to CA3 to CA1), spontaneous GNA in the developing hippocampus originates in distal CA3 and propagates both forward to CA1 and backward to DG. Photostimulation-evoked GNA also shows prominent backward propagation in the developing hippocampus from CA3 to DG. Mouse GNA is strongly correlated to electrophysiological recordings of highly localized single-cell and local field potential events. Photostimulation mapping of neural circuitry demonstrates that the enhancement of local circuit connections to excitatory pyramidal neurons occurs over the same time course as GNA and reveals the underlying pathways accounting for GNA backward propagation from CA3 to DG. The disappearance of GNA coincides with a transition to the adult-like unidirectional circuit organization at about 2 weeks of age. Taken together, our findings strongly suggest a critical link between GNA activity and maturation of functional circuit connections in the developing hippocampus. Copyright © 2013 Wiley Periodicals, Inc.

Green-Kubo relations for the viscosity of biaxial nematic liquid crystals

NASA Astrophysics Data System (ADS)

Sarman, Sten

1996-09-01

We derive Green-Kubo relations for the viscosities of a biaxial nematic liquid crystal. In this system there are seven shear viscosities, three twist viscosities, and three cross coupling coefficients between the antisymmetric strain rate and the symmetric traceless pressure tensor. According to the Onsager reciprocity relations these couplings are equal to the cross couplings between the symmetric traceless strain rate and the antisymmetric pressure. Our method is based on a comparison of the microscopic linear response generated by the SLLOD equations of motion for planar Couette flow (so named because of their close connection to the Doll's tensor Hamiltonian) and the macroscopic linear phenomenological relations between the pressure tensor and the strain rate. In order to obtain simple Green-Kubo relations we employ an equilibrium ensemble where the angular velocities of the directors are identically zero. This is achieved by adding constraint torques to the equations for the molecular angular accelerations. One finds that all the viscosity coefficients can be expressed as linear combinations of time correlation function integrals (TCFIs). This is much simpler compared to the expressions in the conventional canonical ensemble, where the viscosities are complicated rational functions of the TCFIs. The reason for this is, that in the constrained angular velocity ensemble, the thermodynamic forces are given external parameters whereas the thermodynamic fluxes are ensemble averages of phase functions. This is not the case in the canonical ensemble. The simplest way of obtaining numerical estimates of viscosity coefficients of a particular molecular model system is to evaluate these fluctuation relations by equilibrium molecular dynamics simulations.

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.

Development of Advanced Technologies for Complete Genomic and Proteomic Characterization of Quantized Human Tumor Cells

DTIC Science & Technology

2014-07-01

establishment of Glioblastoma ( GBM ) cell lines from GBM patient’s tumor samples and quantized cell populations of each of the parental GBM cell lines, we... GBM patients are now well established and from the basis of the molecular characterization of the tumor development and signatures presented by these...analysis of these quantized cell sub populations and have begun to assemble the protein signatures of GBM tumors underpinned by the comprehensive

Differential calculus on quantized simple lie groups

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1991-07-01

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q ∈ ℝ are also discussed.

Light-hole quantization in the optical response of ultra-wide GaAs/Al(x)Ga(1-x)As quantum wells.

PubMed

Solovyev, V V; Bunakov, V A; Schmult, S; Kukushkin, I V

2013-01-16

Temperature-dependent reflectivity and photoluminescence spectra are studied for undoped ultra-wide 150 and 250 nm GaAs quantum wells. It is shown that spectral features previously attributed to a size quantization of the exciton motion in the z-direction coincide well with energies of quantized levels for light holes. Furthermore, optical spectra reveal very similar properties at temperatures above the exciton dissociation point.

Deformation quantizations with separation of variables on a Kähler manifold

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

1996-10-01

We give a simple geometric description of all formal differentiable deformation quantizations on a Kähler manifold M such that for each open subset U⊂ M ⋆-multiplication from the left by a holomorphic function and from the right by an antiholomorphic function on U coincides with the pointwise multiplication by these functions. We show that these quantizations are in 1-1 correspondence with the formal deformations of the original Kähler metrics on M.

Extension of loop quantum gravity to f(R) theories.

PubMed

Zhang, Xiangdong; Ma, Yongge

2011-04-29

The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.

Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles

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

Gonçalves, L.A.; Olavo, L.S.F., E-mail: olavolsf@gmail.com

Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension ofmore » a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). - Highlights: • A Quantization process independent of the Hamiltonian formulation of quantum Mechanics is proposed. • This quantization method is applied to dissipative or absorptive systems. • A Dissipative Schrödinger equation is derived from first principles.« less

Can one ADM quantize relativistic bosonicstrings and membranes?

NASA Astrophysics Data System (ADS)

Moncrief, Vincent

2006-04-01

The standard methods for quantizing relativistic strings diverge significantly from the Dirac-Wheeler-DeWitt program for quantization of generally covariant systems and one wonders whether the latter could be successfully implemented as an alternative to the former. As a first step in this direction, we consider the possibility of quantizing strings (and also relativistic membranes) via a partially gauge-fixed ADM (Arnowitt, Deser and Misner) formulation of the reduced field equations for these systems. By exploiting some (Euclidean signature) Hamilton-Jacobi techniques that Mike Ryan and I had developed previously for the quantization of Bianchi IX cosmological models, I show how to construct Diff( S 1)-invariant (or Diff(Σ)-invariant in the case of membranes) ground state wave functionals for the cases of co-dimension one strings and membranes embedded in Minkowski spacetime. I also show that the reduced Hamiltonian density operators for these systems weakly commute when applied to physical (i.e. Diff( S 1) or Diff(Σ)-invariant) states. While many open questions remain, these preliminary results seem to encourage further research along the same lines.

Application of heterogeneous pulse coupled neural network in image quantization

NASA Astrophysics Data System (ADS)

Huang, Yi; Ma, Yide; Li, Shouliang; Zhan, Kun

2016-11-01

On the basis of the different strengths of synaptic connections between actual neurons, this paper proposes a heterogeneous pulse coupled neural network (HPCNN) algorithm to perform quantization on images. HPCNNs are developed from traditional pulse coupled neural network (PCNN) models, which have different parameters corresponding to different image regions. This allows pixels of different gray levels to be classified broadly into two categories: background regional and object regional. Moreover, an HPCNN also satisfies human visual characteristics. The parameters of the HPCNN model are calculated automatically according to these categories, and quantized results will be optimal and more suitable for humans to observe. At the same time, the experimental results of natural images from the standard image library show the validity and efficiency of our proposed quantization method.

Tampered Region Localization of Digital Color Images Based on JPEG Compression Noise

NASA Astrophysics Data System (ADS)

Wang, Wei; Dong, Jing; Tan, Tieniu

With the availability of various digital image edit tools, seeing is no longer believing. In this paper, we focus on tampered region localization for image forensics. We propose an algorithm which can locate tampered region(s) in a lossless compressed tampered image when its unchanged region is output of JPEG decompressor. We find the tampered region and the unchanged region have different responses for JPEG compression. The tampered region has stronger high frequency quantization noise than the unchanged region. We employ PCA to separate different spatial frequencies quantization noises, i.e. low, medium and high frequency quantization noise, and extract high frequency quantization noise for tampered region localization. Post-processing is involved to get final localization result. The experimental results prove the effectiveness of our proposed method.

Vector quantizer designs for joint compression and terrain categorization of multispectral imagery

NASA Technical Reports Server (NTRS)

Gorman, John D.; Lyons, Daniel F.

1994-01-01

Two vector quantizer designs for compression of multispectral imagery and their impact on terrain categorization performance are evaluated. The mean-squared error (MSE) and classification performance of the two quantizers are compared, and it is shown that a simple two-stage design minimizing MSE subject to a constraint on classification performance has a significantly better classification performance than a standard MSE-based tree-structured vector quantizer followed by maximum likelihood classification. This improvement in classification performance is obtained with minimal loss in MSE performance. The results show that it is advantageous to tailor compression algorithm designs to the required data exploitation tasks. Applications of joint compression/classification include compression for the archival or transmission of Landsat imagery that is later used for land utility surveys and/or radiometric analysis.

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.

Asymptotic Equivalence of Probability Measures and Stochastic Processes

NASA Astrophysics Data System (ADS)

Touchette, Hugo

2018-03-01

Let P_n and Q_n be two probability measures representing two different probabilistic models of some system (e.g., an n-particle equilibrium system, a set of random graphs with n vertices, or a stochastic process evolving over a time n) and let M_n be a random variable representing a "macrostate" or "global observable" of that system. We provide sufficient conditions, based on the Radon-Nikodym derivative of P_n and Q_n, for the set of typical values of M_n obtained relative to P_n to be the same as the set of typical values obtained relative to Q_n in the limit n→ ∞. This extends to general probability measures and stochastic processes the well-known thermodynamic-limit equivalence of the microcanonical and canonical ensembles, related mathematically to the asymptotic equivalence of conditional and exponentially-tilted measures. In this more general sense, two probability measures that are asymptotically equivalent predict the same typical or macroscopic properties of the system they are meant to model.

Isolation and molecular characterization of Toxoplasma gondii in a colony of captive black-capped squirrel monkeys (Saimiri boliviensis).

PubMed

Pardini, L; Dellarupe, A; Bacigalupe, D; Quiroga, M A; Moré, G; Rambeaud, M; Basso, W; Unzaga, J M; Schares, G; Venturini, M C

2015-12-01

Toxoplasmosis is commonly asymptomatic; however, it can be a fatal multisystemic disease in some animal species, such as New World monkeys. An outbreak of acute fatal toxoplasmosis was reported in a colony of black-capped squirrel monkeys (Saimiri boliviensis) from the zoo of La Plata, Argentina. Post-mortem examination of two monkeys revealed macroscopical and microscopical lesions compatible with acute toxoplasmosis. The presence of Toxoplasma gondii was confirmed by immunohistochemistry on monkey tissues, bioassay in mice and PCR using the specific primers B22-B23. By PCR-RFLP analysis, T. gondii isolated in mice, deriving from both monkeys, showed the same restriction pattern, with most markers showing a type III restriction pattern, except for C22-8 (type II) and C29-2 (type I). To our knowledge this is the first report of fatal toxoplasmosis in S. boliviensis caused by a non-canonical or atypical genotype of T. gondii. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Symmetry Guide to Ferroaxial Transitions

NASA Astrophysics Data System (ADS)

Hlinka, J.; Privratska, J.; Ondrejkovic, P.; Janovec, V.

2016-04-01

The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .

Quantized phase coding and connected region labeling for absolute phase retrieval.

PubMed

Chen, Xiangcheng; Wang, Yuwei; Wang, Yajun; Ma, Mengchao; Zeng, Chunnian

2016-12-12

This paper proposes an absolute phase retrieval method for complex object measurement based on quantized phase-coding and connected region labeling. A specific code sequence is embedded into quantized phase of three coded fringes. Connected regions of different codes are labeled and assigned with 3-digit-codes combining the current period and its neighbors. Wrapped phase, more than 36 periods, can be restored with reference to the code sequence. Experimental results verify the capability of the proposed method to measure multiple isolated objects.

The wavelet/scalar quantization compression standard for digital fingerprint images

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

Bradley, J.N.; Brislawn, C.M.

1994-04-01

A new digital image compression standard has been adopted by the US Federal Bureau of Investigation for use on digitized gray-scale fingerprint images. The algorithm is based on adaptive uniform scalar quantization of a discrete wavelet transform image decomposition and is referred to as the wavelet/scalar quantization standard. The standard produces archival quality images at compression ratios of around 20:1 and will allow the FBI to replace their current database of paper fingerprint cards with digital imagery.

Table look-up estimation of signal and noise parameters from quantized observables

NASA Technical Reports Server (NTRS)

Vilnrotter, V. A.; Rodemich, E. R.

1986-01-01

A table look-up algorithm for estimating underlying signal and noise parameters from quantized observables is examined. A general mathematical model is developed, and a look-up table designed specifically for estimating parameters from four-bit quantized data is described. Estimator performance is evaluated both analytically and by means of numerical simulation, and an example is provided to illustrate the use of the look-up table for estimating signal-to-noise ratios commonly encountered in Voyager-type data.

Digital television system design study

NASA Technical Reports Server (NTRS)

Huth, G. K.

1976-01-01

The use of digital techniques for transmission of pictorial data is discussed for multi-frame images (television). Video signals are processed in a manner which includes quantization and coding such that they are separable from the noise introduced into the channel. The performance of digital television systems is determined by the nature of the processing techniques (i.e., whether the video signal itself or, instead, something related to the video signal is quantized and coded) and to the quantization and coding schemes employed.

Rotating effects on the Landau quantization for an atom with a magnetic quadrupole moment

NASA Astrophysics Data System (ADS)

Fonseca, I. C.; Bakke, K.

2016-01-01

Based on the single particle approximation [Dmitriev et al., Phys. Rev. C 50, 2358 (1994) and C.-C. Chen, Phys. Rev. A 51, 2611 (1995)], the Landau quantization associated with an atom with a magnetic quadrupole moment is introduced, and then, rotating effects on this analogue of the Landau quantization is investigated. It is shown that rotating effects can modify the cyclotron frequency and breaks the degeneracy of the analogue of the Landau levels.

Investigation of Coding Techniques for Memory and Delay Efficient Interleaving in Slow Rayleigh Fading

DTIC Science & Technology

1991-11-01

2 mega joule/m 2 (MJ/m 2 ) curie 3.700000 x E +1 *giga becquerel (GBq) degree (angle) 1.745329 x E -2 radian (rad) degree Farenheit tK = (tp...quantization assigned two quantization values. One value was assigned for demodulation values that was larger than zero and another quantization value to...demodulation values that were smaller than zero (for maximum-likelihood decisions). Logic 0 was assigned for a positive demodulation value and a logic 1 was

Rotating effects on the Landau quantization for an atom with a magnetic quadrupole moment

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

Fonseca, I. C.; Bakke, K., E-mail: kbakke@fisica.ufpb.br

2016-01-07

Based on the single particle approximation [Dmitriev et al., Phys. Rev. C 50, 2358 (1994) and C.-C. Chen, Phys. Rev. A 51, 2611 (1995)], the Landau quantization associated with an atom with a magnetic quadrupole moment is introduced, and then, rotating effects on this analogue of the Landau quantization is investigated. It is shown that rotating effects can modify the cyclotron frequency and breaks the degeneracy of the analogue of the Landau levels.

Gold nanoparticles produced in situ mediate bioelectricity and hydrogen production in a microbial fuel cell by quantized capacitance charging.

PubMed

Kalathil, Shafeer; Lee, Jintae; Cho, Moo Hwan

2013-02-01

Oppan quantized style: By adding a gold precursor at its cathode, a microbial fuel cell (MFC) is demonstrated to form gold nanoparticles that can be used to simultaneously produce bioelectricity and hydrogen. By exploiting the quantized capacitance charging effect, the gold nanoparticles mediate the production of hydrogen without requiring an external power supply, while the MFC produces a stable power density. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Reformulation of the covering and quantizer problems as ground states of interacting particles.

PubMed

Torquato, S

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d-dimensional Euclidean space R(d) interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in R(d) that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the "void" nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their "dual" solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

Reformulation of the covering and quantizer problems as ground states of interacting particles

NASA Astrophysics Data System (ADS)

Torquato, S.

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d -dimensional Euclidean space Rd interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in Rd that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the “void” nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their “dual” solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

Error diffusion concept for multi-level quantization

NASA Astrophysics Data System (ADS)

Broja, Manfred; Michalowski, Kristina; Bryngdahl, Olof

1990-11-01

The error diffusion binarization procedure is adapted to multi-level quantization. The threshold parameters then available have a noticeable influence on the process. Characteristic features of the technique are shown together with experimental results.

Natural inflation from polymer quantization

NASA Astrophysics Data System (ADS)

Ali, Masooma; Seahra, Sanjeev S.

2017-11-01

We study the polymer quantization of a homogeneous massive scalar field in the early Universe using a prescription inequivalent to those previously appearing in the literature. Specifically, we assume a Hilbert space for which the scalar field momentum is well defined but its amplitude is not. This is closer in spirit to the quantization scheme of loop quantum gravity, in which no unique configuration operator exists. We show that in the semiclassical approximation, the main effect of this polymer quantization scheme is to compactify the phase space of chaotic inflation in the field amplitude direction. This gives rise to an effective scalar potential closely resembling that of hybrid natural inflation. Unlike polymer schemes in which the scalar field amplitude is well defined, the semiclassical dynamics involves a past cosmological singularity; i.e., this approach does not mitigate the big bang.

Optimal sampling and quantization of synthetic aperture radar signals

NASA Technical Reports Server (NTRS)

Wu, C.

1978-01-01

Some theoretical and experimental results on optimal sampling and quantization of synthetic aperture radar (SAR) signals are presented. It includes a description of a derived theoretical relationship between the pixel signal to noise ratio of processed SAR images and the number of quantization bits per sampled signal, assuming homogeneous extended targets. With this relationship known, a solution may be realized for the problem of optimal allocation of a fixed data bit-volume (for specified surface area and resolution criterion) between the number of samples and the number of bits per sample. The results indicate that to achieve the best possible image quality for a fixed bit rate and a given resolution criterion, one should quantize individual samples coarsely and thereby maximize the number of multiple looks. The theoretical results are then compared with simulation results obtained by processing aircraft SAR data.

Effect of temperature degeneracy and Landau quantization on drift solitary waves and double layers

NASA Astrophysics Data System (ADS)

Shan, Shaukat Ali; Haque, Q.

2018-01-01

The linear and nonlinear drift ion acoustic waves have been investigated in an inhomogeneous, magnetized, dense degenerate, and quantized magnetic field plasma. The linear drift ion acoustic wave propagation along with the nonlinear structures like double layers and solitary waves has been found to be strongly dependent on the drift speed, magnetic field quantization parameter β, and the temperature degeneracy. The graphical illustrations show that the frequency of linear waves and the amplitude of the solitary waves increase with the increase in temperature degeneracy and Landau quantization effect, while the amplitude of the double layers decreases with the increase in η and T. The relevance of the present study is pointed out in the plasma environment of fast ignition inertial confinement fusion, the white dwarf stars, and short pulsed petawatt laser technology.

Time-Symmetric Quantization in Spacetimes with Event Horizons

NASA Astrophysics Data System (ADS)

Kobakhidze, Archil; Rodd, Nicholas

2013-08-01

The standard quantization formalism in spacetimes with event horizons implies a non-unitary evolution of quantum states, as initial pure states may evolve into thermal states. This phenomenon is behind the famous black hole information loss paradox which provoked long-standing debates on the compatibility of quantum mechanics and gravity. In this paper we demonstrate that within an alternative time-symmetric quantization formalism thermal radiation is absent and states evolve unitarily in spacetimes with event horizons. We also discuss the theoretical consistency of the proposed formalism. We explicitly demonstrate that the theory preserves the microcausality condition and suggest a "reinterpretation postulate" to resolve other apparent pathologies associated with negative energy states. Accordingly as there is a consistent alternative, we argue that choosing to use time-asymmetric quantization is a necessary condition for the black hole information loss paradox.

Adaptive robust fault tolerant control design for a class of nonlinear uncertain MIMO systems with quantization.

PubMed

Ao, Wei; Song, Yongdong; Wen, Changyun

2017-05-01

In this paper, we investigate the adaptive control problem for a class of nonlinear uncertain MIMO systems with actuator faults and quantization effects. Under some mild conditions, an adaptive robust fault-tolerant control is developed to compensate the affects of uncertainties, actuator failures and errors caused by quantization, and a range of the parameters for these quantizers is established. Furthermore, a Lyapunov-like approach is adopted to demonstrate that the ultimately uniformly bounded output tracking error is guaranteed by the controller, and the signals of the closed-loop system are ensured to be bounded, even in the presence of at most m-q actuators stuck or outage. Finally, numerical simulations are provided to verify and illustrate the effectiveness of the proposed adaptive schemes. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Quantization of charged fields in the presence of critical potential steps

NASA Astrophysics Data System (ADS)

Gavrilov, S. P.; Gitman, D. M.

2016-02-01

QED with strong external backgrounds that can create particles from the vacuum is well developed for the so-called t -electric potential steps, which are time-dependent external electric fields that are switched on and off at some time instants. However, there exist many physically interesting situations where external backgrounds do not switch off at the time infinity. E.g., these are time-independent nonuniform electric fields that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x -electric potential steps for charged particles. They can also create particles from the vacuum, the Klein paradox being closely related to this process. Approaches elaborated for treating quantum effects in the t -electric potential steps are not directly applicable to the x -electric potential steps and their generalization for x -electric potential steps was not sufficiently developed. We believe that the present work represents a consistent solution of the latter problem. We have considered a canonical quantization of the Dirac and scalar fields with x -electric potential step and have found in- and out-creation and annihilation operators that allow one to have particle interpretation of the physical system under consideration. To identify in- and out-operators we have performed a detailed mathematical and physical analysis of solutions of the relativistic wave equations with an x -electric potential step with subsequent QFT analysis of correctness of such an identification. We elaborated a nonperturbative (in the external field) technique that allows one to calculate all characteristics of zero-order processes, such, for example, scattering, reflection, and electron-positron pair creation, without radiation corrections, and also to calculate Feynman diagrams that describe all characteristics of processes with interaction between the in-, out-particles and photons. These diagrams have formally the usual form, but contain special propagators. Expressions for these propagators in terms of in- and out-solutions are presented. We apply the elaborated approach to two popular exactly solvable cases of x -electric potential steps, namely, to the Sauter potential and to the Klein step.

Explorations in fuzzy physics and non-commutative geometry

NASA Astrophysics Data System (ADS)

Kurkcuoglu, Seckin

Fuzzy spaces arise as discrete approximations to continuum manifolds. They are usually obtained through quantizing coadjoint orbits of compact Lie groups and they can be described in terms of finite-dimensional matrix algebras, which for large matrix sizes approximate the algebra of functions of the limiting continuum manifold. Their ability to exactly preserve the symmetries of their parent manifolds is especially appealing for physical applications. Quantum Field Theories are built over them as finite-dimensional matrix models preserving almost all the symmetries of their respective continuum models. In this dissertation, we first focus our attention to the study of fuzzy supersymmetric spaces. In this regard, we obtain the fuzzy supersphere S2,2F through quantizing the supersphere, and demonstrate that it has exact supersymmetry. We derive a finite series formula for the *-product of functions over S2,2F and analyze the differential geometric information encoded in this formula. Subsequently, we show that quantum field theories on S2,2F are realized as finite-dimensional supermatrix models, and in particular we obtain the non-linear sigma model over the fuzzy supersphere by constructing the fuzzy supersymmetric extensions of a certain class of projectors. We show that this model too, is realized as a finite-dimensional supermatrix model with exact supersymmetry. Next, we show that fuzzy spaces have a generalized Hopf algebra structure. By focusing on the fuzzy sphere, we establish that there is a *-homomorphism from the group algebra SU(2)* of SU(2) to the fuzzy sphere. Using this and the canonical Hopf algebra structure of SU(2)* we show that both the fuzzy sphere and their direct sum are Hopf algebras. Using these results, we discuss processes in which a fuzzy sphere with angular momenta J splits into fuzzy spheres with angular momenta K and L. Finally, we study the formulation of Chern-Simons (CS) theory on an infinite strip of the non-commutative plane. We develop a finite-dimensional matrix model, whose large size limit approximates the CS theory on the infinite strip, and show that there are edge observables in this model obeying a finite-dimensional Lie algebra, that resembles the Kac-Moody algebra.

The Holographic Electron Density Theorem, de-quantization, re-quantization, and nuclear charge space extrapolations of the Universal Molecule Model

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2017-11-01

Two strongly related theorems on non-degenerate ground state electron densities serve as the basis of "Molecular Informatics". The Hohenberg-Kohn theorem is a statement on global molecular information, ensuring that the complete electron density contains the complete molecular information. However, the Holographic Electron Density Theorem states more: the local information present in each and every positive volume density fragment is already complete: the information in the fragment is equivalent to the complete molecular information. In other words, the complete molecular information provided by the Hohenberg-Kohn Theorem is already provided, in full, by any positive volume, otherwise arbitrarily small electron density fragment. In this contribution some of the consequences of the Holographic Electron Density Theorem are discussed within the framework of the "Nuclear Charge Space" and the Universal Molecule Model. In the Nuclear Charge Space" the nuclear charges are regarded as continuous variables, and in the more general Universal Molecule Model some other quantized parameteres are also allowed to become "de-quantized and then re-quantized, leading to interrelations among real molecules through abstract molecules. Here the specific role of the Holographic Electron Density Theorem is discussed within the above context.

Medical Image Compression Based on Vector Quantization with Variable Block Sizes in Wavelet Domain

PubMed Central

Jiang, Huiyan; Ma, Zhiyuan; Hu, Yang; Yang, Benqiang; Zhang, Libo

2012-01-01

An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality. PMID:23049544

Medical image compression based on vector quantization with variable block sizes in wavelet domain.

PubMed

Jiang, Huiyan; Ma, Zhiyuan; Hu, Yang; Yang, Benqiang; Zhang, Libo

2012-01-01

An optimized medical image compression algorithm based on wavelet transform and improved vector quantization is introduced. The goal of the proposed method is to maintain the diagnostic-related information of the medical image at a high compression ratio. Wavelet transformation was first applied to the image. For the lowest-frequency subband of wavelet coefficients, a lossless compression method was exploited; for each of the high-frequency subbands, an optimized vector quantization with variable block size was implemented. In the novel vector quantization method, local fractal dimension (LFD) was used to analyze the local complexity of each wavelet coefficients, subband. Then an optimal quadtree method was employed to partition each wavelet coefficients, subband into several sizes of subblocks. After that, a modified K-means approach which is based on energy function was used in the codebook training phase. At last, vector quantization coding was implemented in different types of sub-blocks. In order to verify the effectiveness of the proposed algorithm, JPEG, JPEG2000, and fractal coding approach were chosen as contrast algorithms. Experimental results show that the proposed method can improve the compression performance and can achieve a balance between the compression ratio and the image visual quality.

Spectrally efficient digitized radio-over-fiber system with k-means clustering-based multidimensional quantization.

PubMed

Zhang, Lu; Pang, Xiaodan; Ozolins, Oskars; Udalcovs, Aleksejs; Popov, Sergei; Xiao, Shilin; Hu, Weisheng; Chen, Jiajia

2018-04-01

We propose a spectrally efficient digitized radio-over-fiber (D-RoF) system by grouping highly correlated neighboring samples of the analog signals into multidimensional vectors, where the k-means clustering algorithm is adopted for adaptive quantization. A 30  Gbit/s D-RoF system is experimentally demonstrated to validate the proposed scheme, reporting a carrier aggregation of up to 40 100 MHz orthogonal frequency division multiplexing (OFDM) channels with quadrate amplitude modulation (QAM) order of 4 and an aggregation of 10 100 MHz OFDM channels with a QAM order of 16384. The equivalent common public radio interface rates from 37 to 150  Gbit/s are supported. Besides, the error vector magnitude (EVM) of 8% is achieved with the number of quantization bits of 4, and the EVM can be further reduced to 1% by increasing the number of quantization bits to 7. Compared with conventional pulse coding modulation-based D-RoF systems, the proposed D-RoF system improves the signal-to-noise-ratio up to ∼9  dB and greatly reduces the EVM, given the same number of quantization bits.

Prediction-guided quantization for video tone mapping

NASA Astrophysics Data System (ADS)

Le Dauphin, Agnès.; Boitard, Ronan; Thoreau, Dominique; Olivier, Yannick; Francois, Edouard; LeLéannec, Fabrice

2014-09-01

Tone Mapping Operators (TMOs) compress High Dynamic Range (HDR) content to address Low Dynamic Range (LDR) displays. However, before reaching the end-user, this tone mapped content is usually compressed for broadcasting or storage purposes. Any TMO includes a quantization step to convert floating point values to integer ones. In this work, we propose to adapt this quantization, in the loop of an encoder, to reduce the entropy of the tone mapped video content. Our technique provides an appropriate quantization for each mode of both the Intra and Inter-prediction that is performed in the loop of a block-based encoder. The mode that minimizes a rate-distortion criterion uses its associated quantization to provide integer values for the rest of the encoding process. The method has been implemented in HEVC and was tested over two different scenarios: the compression of tone mapped LDR video content (using the HM10.0) and the compression of perceptually encoded HDR content (HM14.0). Results show an average bit-rate reduction under the same PSNR for all the sequences and TMO considered of 20.3% and 27.3% for tone mapped content and 2.4% and 2.7% for HDR content.

Improved image decompression for reduced transform coding artifacts

NASA Technical Reports Server (NTRS)

Orourke, Thomas P.; Stevenson, Robert L.

1994-01-01

The perceived quality of images reconstructed from low bit rate compression is severely degraded by the appearance of transform coding artifacts. This paper proposes a method for producing higher quality reconstructed images based on a stochastic model for the image data. Quantization (scalar or vector) partitions the transform coefficient space and maps all points in a partition cell to a representative reconstruction point, usually taken as the centroid of the cell. The proposed image estimation technique selects the reconstruction point within the quantization partition cell which results in a reconstructed image which best fits a non-Gaussian Markov random field (MRF) image model. This approach results in a convex constrained optimization problem which can be solved iteratively. At each iteration, the gradient projection method is used to update the estimate based on the image model. In the transform domain, the resulting coefficient reconstruction points are projected to the particular quantization partition cells defined by the compressed image. Experimental results will be shown for images compressed using scalar quantization of block DCT and using vector quantization of subband wavelet transform. The proposed image decompression provides a reconstructed image with reduced visibility of transform coding artifacts and superior perceived quality.

Landau quantization effects on hole-acoustic instability in semiconductor plasmas

NASA Astrophysics Data System (ADS)

Sumera, P.; Rasheed, A.; Jamil, M.; Siddique, M.; Areeb, F.

2017-12-01

The growth rate of the hole acoustic waves (HAWs) exciting in magnetized semiconductor quantum plasma pumped by the electron beam has been investigated. The instability of the waves contains quantum effects including the exchange and correlation potential, Bohm potential, Fermi-degenerate pressure, and the magnetic quantization of semiconductor plasma species. The effects of various plasma parameters, which include relative concentration of plasma particles, beam electron temperature, beam speed, plasma temperature (temperature of electrons/holes), and Landau electron orbital magnetic quantization parameter η, on the growth rate of HAWs, have been discussed. The numerical study of our model of acoustic waves has been applied, as an example, to the GaAs semiconductor exposed to electron beam in the magnetic field environment. An increment in either the concentration of the semiconductor electrons or the speed of beam electrons, in the presence of magnetic quantization of fermion orbital motion, enhances remarkably the growth rate of the HAWs. Although the growth rate of the waves reduces with a rise in the thermal temperature of plasma species, at a particular temperature, we receive a higher instability due to the contribution of magnetic quantization of fermions to it.

Exact renormalization group in Batalin-Vilkovisky theory

NASA Astrophysics Data System (ADS)

Zucchini, Roberto

2018-03-01

In this paper, inspired by the Costello's seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and Laplacian structure as well as the BV effective action (EA) depend on an effective energy scale. The BV EA at a certain scale satisfies the BV quantum master equation at that scale. The RG flow of the EA is implemented by BV canonical maps intertwining the BV structures at different scales. Infinitesimally, this generates the BV exact renormalization group equation (RGE). We show that BV RG theory can be extended by augmenting the scale parameter space R to its shifted tangent bundle T [1]ℝ. The extra odd direction in scale space allows for a BV RG supersymmetry that constrains the structure of the BV RGE bringing it to Polchinski's form [6]. We investigate the implications of BV RG supersymmetry in perturbation theory. Finally, we illustrate our findings by constructing free models of BV RG flow and EA exhibiting RG supersymmetry in the degree -1 symplectic framework and studying the perturbation theory thereof. We find in particular that the odd partner of effective action describes perturbatively the deviation of the interacting RG flow from its free counterpart.

Tripartite entanglement dynamics and entropic squeezing of a three-level atom interacting with a bimodal cavity field

NASA Astrophysics Data System (ADS)

Faghihi, M. J.; Tavassoly, M. K.; Bagheri Harouni, M.

2014-04-01

In this paper, we study the interaction between a Λ-type three-level atom and two quantized electromagnetic fields which are simultaneously injected in a bichromatic cavity surrounded by a Kerr medium in the presence of field-field interaction (parametric down conversion) and detuning parameters. By applying a canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Under particular initial conditions which may be prepared for the atom and the field, the time evolution of the state vector of the entire system is analytically evaluated. Then, the dynamics of the atom is studied through the evolution of the atomic population inversion. In addition, two different measures of entanglement between the tripartite system (three entities make the system: two field modes and one atom), i.e., von Neumann and linear entropy are investigated. Also, two kinds of entropic uncertainty relations, from which entropy squeezing can be obtained, are discussed. In each case, the influences of the detuning parameters and Kerr medium on the above nonclassicality features are analyzed in detail via numerical results. It is illustrated that the amount of the above-mentioned physical phenomena can be tuned by choosing the evolved parameters, appropriately.

Asymptotic states and the definition of the S-matrix in quantum gravity

NASA Astrophysics Data System (ADS)

Wiesendanger, C.

2013-04-01

Viewing gravitational energy-momentum p_G^\\mu as equal by observation, but different in essence from inertial energy-momentum p_I^\\mu naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space M4. The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit—mapping the gravitational energy-momentum onto the inertial energy-momentum to account for their observed equality—is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic in- to out-states in the gauge theory of volume-preserving diffeomorphisms. The so-defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy-momentum. Finally, generalized Lehmann-Symanzik-Zimmermann reduction formulae for scalar, Dirac and gauge fields are established which allow us to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in Wiesendanger (2011 arXiv:1103.1012) any transition amplitude can in principle be computed consistently to any order in perturbative quantum gravity.

Quantization of Space-like States in Lorentz-Violating Theories

NASA Astrophysics Data System (ADS)

Colladay, Don

2018-01-01

Lorentz violation frequently induces modified dispersion relations that can yield space-like states that impede the standard quantization procedures. In certain cases, an extended Hamiltonian formalism can be used to define observer-covariant normalization factors for field expansions and phase space integrals. These factors extend the theory to include non-concordant frames in which there are negative-energy states. This formalism provides a rigorous way to quantize certain theories containing space-like states and allows for the consistent computation of Cherenkov radiation rates in arbitrary frames and avoids singular expressions.

Correspondence between quantization schemes for two-player nonzero-sum games and CNOT complexity

NASA Astrophysics Data System (ADS)

Vijayakrishnan, V.; Balakrishnan, S.

2018-05-01

The well-known quantization schemes for two-player nonzero-sum games are Eisert-Wilkens-Lewenstein scheme and Marinatto-Weber scheme. In this work, we establish the connection between the two schemes from the perspective of quantum circuits. Further, we provide the correspondence between any game quantization schemes and the CNOT complexity, where CNOT complexity is up to the local unitary operations. While CNOT complexity is known to be useful in the analysis of universal quantum circuit, in this work, we find its applicability in quantum game theory.

Luminance-model-based DCT quantization for color image compression

NASA Technical Reports Server (NTRS)

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

1992-01-01

A model is developed to approximate visibility thresholds for discrete cosine transform (DCT) coefficient quantization error based on the peak-to-peak luminance of the error image. Experimentally measured visibility thresholds for R, G, and B DCT basis functions can be predicted by a simple luminance-based detection model. This model allows DCT coefficient quantization matrices to be designed for display conditions other than those of the experimental measurements: other display luminances, other veiling luminances, and other spatial frequencies (different pixel spacings, viewing distances, and aspect ratios).

Image Data Compression Having Minimum Perceptual Error

NASA Technical Reports Server (NTRS)

Watson, Andrew B. (Inventor)

1997-01-01

A method is presented for performing color or grayscale image compression that eliminates redundant and invisible image components. 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 quantization matrix comprises visual masking by luminance and contrast technique all resulting in a minimum perceptual error for any given bit rate, or minimum bit rate for a given perceptual error.

JND measurements of the speech formants parameters and its implication in the LPC pole quantization

NASA Astrophysics Data System (ADS)

Orgad, Yaakov

1988-08-01

The inherent sensitivity of auditory perception is explicitly used with the objective of designing an efficient speech encoder. Speech can be modelled by a filter representing the vocal tract shape that is driven by an excitation signal representing glottal air flow. This work concentrates on the filter encoding problem, assuming that excitation signal encoding is optimal. Linear predictive coding (LPC) techniques were used to model a short speech segment by an all-pole filter; each pole was directly related to the speech formants. Measurements were made of the auditory just noticeable difference (JND) corresponding to the natural speech formants, with the LPC filter poles as the best candidates to represent the speech spectral envelope. The JND is the maximum precision required in speech quantization; it was defined on the basis of the shift of one pole parameter of a single frame of a speech segment, necessary to induce subjective perception of the distortion, with .75 probability. The average JND in LPC filter poles in natural speech was found to increase with increasing pole bandwidth and, to a lesser extent, frequency. The JND measurements showed a large spread of the residuals around the average values, indicating that inter-formant coupling and, perhaps, other, not yet fully understood, factors were not taken into account at this stage of the research. A future treatment should consider these factors. The average JNDs obtained in this work were used to design pole quantization tables for speech coding and provided a better bit-rate than the standard quantizer of reflection coefficient; a 30-bits-per-frame pole quantizer yielded a speech quality similar to that obtained with a standard 41-bits-per-frame reflection coefficient quantizer. Owing to the complexity of the numerical root extraction system, the practical implementation of the pole quantization approach remains to be proved.

Electron transport through magnetic quantum point contacts

NASA Astrophysics Data System (ADS)

Day, Timothy Ellis

Spin-based electronics, or spintronics, has generated a great deal of interest as a possible next-generation integrated circuit technology. Recent experimental and theoretical work has shown that these devices could exhibit increased processing speed, decreased power consumption, and increased integration densities as compared with conventional semiconductor devices. The spintronic device that was designed, fabricated, and tested throughout the course of this work aimed to study the generation of spin-polarized currents in semiconductors using magnetic fringe fields. The device scheme relied on the Zeeman effect in combination with a quantum mechanical barrier to generate spin-polarized currents. The Zeeman effect was used to break the degeneracy of spin-up and spin-down electrons and the quantum mechanical potential to transmit one while rejecting the other. The design was dictated by the drive to maximize the strength of the magnetic fringe field and in turn maximize the energy separation of the two spin species. The device was fabricated using advanced techniques in semiconductor processing including electron beam lithography and DC magnetron sputtering. Measurements were performed in a 3He cryostat equipped with a superconducting magnet at temperatures below 300 mK. Preliminary characterization of the device revealed magnetoconductance oscillations produced by the effect of the transverse confining potential on the density of states and the mobility. Evidence of the effect of the magnetic fringe fields on the transport properties of electrons in the device were observed in multiple device measurements. An abrupt washout of the quantized conductance steps was observed over a minute range of the applied magnetic field. The washout was again observed as electrons were shifted closer to the magnetic gates. In addition, bias spectroscopy demonstrated that the washout occurred despite stronger electron confinement, as compared to a non-magnetic split-gate. Thus, the measurements indicated that conductance quantization breaks down in a non-uniform magnetic field, possibly due to changes to the stationary Landau states. It was also demonstrated that non-integer conductance plateaus at high source-drain bias are not caused by a macroscopic asymmetry in the potential drop.

Scale relativity and hierarchical structuring of planetary systems

NASA Astrophysics Data System (ADS)

Galopeau, P. H. M.; Nottale, L.; da Rocha, D.; Tran Minh, N.

2003-04-01

The theory of scale relativity, applied to macroscopic gravitational systems like planetary systems, allows one to predict quantization laws of several key parameters characterizing those systems (distance between planets and central star, obliquity, eccentricity...) which are organized in a hierarchical way. In the framework of the scale relativity approach, one demonstrates that the motion (at relatively large time-scales) of the bodies in planetary systems, described in terms of fractal geodesic trajectories, is governed by a Schrödinger-like equation. Preferential orbits are predicted in terms of probability density peaks with semi-major axis given by: a_n = GMn^2/w^2 (M is the mass of the central star and w is a velocity close to 144 km s-1 in the case of our inner solar system and of the presently observed exoplanets). The velocity of the planet orbiting at this distance satisfies the relation v_n = w/n. Moreover, the mass distribution of the planets in our solar system can be accounted for in this model. These predictions are in good agreement with the observed values of the actual orbital parameters. Furthermore, the exoplanets which have been recently discovered around nearby stars also follow the same law in terms of the same constant in a highly significant statistical way. The theory of scale relativity also predicts structures for the obliquities and inclinations of the planets and satellites: the probability density of their distribution between 0 and pi are expected to display peaks at particular angles θ_k = kpi/n. A statistical agreement is obtained for our solar system with n=7. Another prediction concerns the distribution of the planets eccentricities e. The theory foresees a quantization law e = k/n where k is an integer and n is the quantum number that characterizes semi-major axes. The presently known exoplanet eccentricities are compatible with this theoretical prediction. Finally, although all these planetary systems may look very different from our solar system, they actually present universal structures comparable to ours, so that a high probability to discover exoplanets having orbital characteristics very similar to the Earth's ones can be expected.

On the Perturbative Equivalence Between the Hamiltonian and Lagrangian Quantizations

NASA Astrophysics Data System (ADS)

Batalin, I. A.; Tyutin, I. V.

The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be perturbatively equivalent to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.

Fill-in binary loop pulse-torque quantizer

NASA Technical Reports Server (NTRS)

Lory, C. B.

1975-01-01

Fill-in binary (FIB) loop provides constant heating of torque generator, an advantage of binary current switching. At the same time, it avoids mode-related dead zone and data delay of binary, an advantage of ternary quantization.

Theory of quantized systems: formal basis for DEVS/HLA distributed simulation environment

NASA Astrophysics Data System (ADS)

Zeigler, Bernard P.; Lee, J. S.

1998-08-01

In the context of a DARPA ASTT project, we are developing an HLA-compliant distributed simulation environment based on the DEVS formalism. This environment will provide a user- friendly, high-level tool-set for developing interoperable discrete and continuous simulation models. One application is the study of contract-based predictive filtering. This paper presents a new approach to predictive filtering based on a process called 'quantization' to reduce state update transmission. Quantization, which generates state updates only at quantum level crossings, abstracts a sender model into a DEVS representation. This affords an alternative, efficient approach to embedding continuous models within distributed discrete event simulations. Applications of quantization to message traffic reduction are discussed. The theory has been validated by DEVSJAVA simulations of test cases. It will be subject to further test in actual distributed simulations using the DEVS/HLA modeling and simulation environment.

Locally adaptive vector quantization: Data compression with feature preservation

NASA Technical Reports Server (NTRS)

Cheung, K. M.; Sayano, M.

1992-01-01

A study of a locally adaptive vector quantization (LAVQ) algorithm for data compression is presented. This algorithm provides high-speed one-pass compression and is fully adaptable to any data source and does not require a priori knowledge of the source statistics. Therefore, LAVQ is a universal data compression algorithm. The basic algorithm and several modifications to improve performance are discussed. These modifications are nonlinear quantization, coarse quantization of the codebook, and lossless compression of the output. Performance of LAVQ on various images using irreversible (lossy) coding is comparable to that of the Linde-Buzo-Gray algorithm, but LAVQ has a much higher speed; thus this algorithm has potential for real-time video compression. Unlike most other image compression algorithms, LAVQ preserves fine detail in images. LAVQ's performance as a lossless data compression algorithm is comparable to that of Lempel-Ziv-based algorithms, but LAVQ uses far less memory during the coding process.

Landau quantization of Dirac fermions in graphene and its multilayers

NASA Astrophysics Data System (ADS)

Yin, Long-Jing; Bai, Ke-Ke; Wang, Wen-Xiao; Li, Si-Yu; Zhang, Yu; He, Lin

2017-08-01

When electrons are confined in a two-dimensional (2D) system, typical quantum-mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum-mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behaviors of Dirac fermions in monolayer and multilayer graphene by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Through STS measurement of the strong magnetic fields, distinct Landau-level spectra and rich level-splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fundamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties.

Necessary conditions for the optimality of variable rate residual vector quantizers

NASA Technical Reports Server (NTRS)

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

1993-01-01

Residual vector quantization (RVQ), or multistage VQ, as it is also called, has recently been shown to be a competitive technique for data compression. The competitive performance of RVQ reported in results from the joint optimization of variable rate encoding and RVQ direct-sum code books. In this paper, necessary conditions for the optimality of variable rate RVQ's are derived, and an iterative descent algorithm based on a Lagrangian formulation is introduced for designing RVQ's having minimum average distortion subject to an entropy constraint. Simulation results for these entropy-constrained RVQ's (EC-RVQ's) are presented for memory less Gaussian, Laplacian, and uniform sources. A Gauss-Markov source is also considered. The performance is superior to that of entropy-constrained scalar quantizers (EC-SQ's) and practical entropy-constrained vector quantizers (EC-VQ's), and is competitive with that of some of the best source coding techniques that have appeared in the literature.

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.

Quantization of gauge fields, graph polynomials and graph homology

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

Kreimer, Dirk, E-mail: kreimer@physik.hu-berlin.de; Sars, Matthias; Suijlekom, Walter D. van

2013-09-15

We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology.more » -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.« less

Augmenting Phase Space Quantization to Introduce Additional Physical Effects

NASA Astrophysics Data System (ADS)

Robbins, Matthew P. G.

Quantum mechanics can be done using classical phase space functions and a star product. The state of the system is described by a quasi-probability distribution. A classical system can be quantized in phase space in different ways with different quasi-probability distributions and star products. A transition differential operator relates different phase space quantizations. The objective of this thesis is to introduce additional physical effects into the process of quantization by using the transition operator. As prototypical examples, we first look at the coarse-graining of the Wigner function and the damped simple harmonic oscillator. By generalizing the transition operator and star product to also be functions of the position and momentum, we show that additional physical features beyond damping and coarse-graining can be introduced into a quantum system, including the generalized uncertainty principle of quantum gravity phenomenology, driving forces, and decoherence.

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.

Distributed Adaptive Containment Control for a Class of Nonlinear Multiagent Systems With Input Quantization.

PubMed

Wang, Chenliang; Wen, Changyun; Hu, Qinglei; Wang, Wei; Zhang, Xiuyu

2018-06-01

This paper is devoted to distributed adaptive containment control for a class of nonlinear multiagent systems with input quantization. By employing a matrix factorization and a novel matrix normalization technique, some assumptions involving control gain matrices in existing results are relaxed. By fusing the techniques of sliding mode control and backstepping control, a two-step design method is proposed to construct controllers and, with the aid of neural networks, all system nonlinearities are allowed to be unknown. Moreover, a linear time-varying model and a similarity transformation are introduced to circumvent the obstacle brought by quantization, and the controllers need no information about the quantizer parameters. The proposed scheme is able to ensure the boundedness of all closed-loop signals and steer the containment errors into an arbitrarily small residual set. The simulation results illustrate the effectiveness of the scheme.

Model predictive control of non-linear systems over networks with data quantization and packet loss.

PubMed

Yu, Jimin; Nan, Liangsheng; Tang, Xiaoming; Wang, Ping

2015-11-01

This paper studies the approach of model predictive control (MPC) for the non-linear systems under networked environment where both data quantization and packet loss may occur. The non-linear controlled plant in the networked control system (NCS) is represented by a Tagaki-Sugeno (T-S) model. The sensed data and control signal are quantized in both links and described as sector bound uncertainties by applying sector bound approach. Then, the quantized data are transmitted in the communication networks and may suffer from the effect of packet losses, which are modeled as Bernoulli process. A fuzzy predictive controller which guarantees the stability of the closed-loop system is obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Fine structure constant and quantized optical transparency of plasmonic nanoarrays.

PubMed

Kravets, V G; Schedin, F; Grigorenko, A N

2012-01-24

Optics is renowned for displaying quantum phenomena. Indeed, studies of emission and absorption lines, the photoelectric effect and blackbody radiation helped to build the foundations of quantum mechanics. Nevertheless, it came as a surprise that the visible transparency of suspended graphene is determined solely by the fine structure constant, as this kind of universality had been previously reserved only for quantized resistance and flux quanta in superconductors. Here we describe a plasmonic system in which relative optical transparency is determined solely by the fine structure constant. The system consists of a regular array of gold nanoparticles fabricated on a thin metallic sublayer. We show that its relative transparency can be quantized in the near-infrared, which we attribute to the quantized contact resistance between the nanoparticles and the metallic sublayer. Our results open new possibilities in the exploration of universal dynamic conductance in plasmonic nanooptics.

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.

Mixed Linear/Square-Root Encoded Single-Slope Ramp Provides Low-Noise ADC with High Linearity for Focal Plane Arrays

NASA Technical Reports Server (NTRS)

Wrigley, Chris J.; Hancock, Bruce R.; Newton, Kenneth W.; Cunningham, Thomas J.

2013-01-01

Single-slope analog-to-digital converters (ADCs) are particularly useful for onchip digitization in focal plane arrays (FPAs) because of their inherent monotonicity, relative simplicity, and efficiency for column-parallel applications, but they are comparatively slow. Squareroot encoding can allow the number of code values to be reduced without loss of signal-to-noise ratio (SNR) by keeping the quantization noise just below the signal shot noise. This encoding can be implemented directly by using a quadratic ramp. The reduction in the number of code values can substantially increase the quantization speed. However, in an FPA, the fixed pattern noise (FPN) limits the use of small quantization steps at low signal levels. If the zero-point is adjusted so that the lowest column is onscale, the other columns, including those at the center of the distribution, will be pushed up the ramp where the quantization noise is higher. Additionally, the finite frequency response of the ramp buffer amplifier and the comparator distort the shape of the ramp, so that the effective ramp value at the time the comparator trips differs from the intended value, resulting in errors. Allowing increased settling time decreases the quantization speed, while increasing the bandwidth increases the noise. The FPN problem is solved by breaking the ramp into two portions, with some fraction of the available code values allocated to a linear ramp and the remainder to a quadratic ramp. To avoid large transients, both the value and the slope of the linear and quadratic portions should be equal where they join. The span of the linear portion must cover the minimum offset, but not necessarily the maximum, since the fraction of the pixels above the upper limit will still be correctly quantized, albeit with increased quantization noise. The required linear span, maximum signal and ratio of quantization noise to shot noise at high signal, along with the continuity requirement, determines the number of code values that must be allocated to each portion. The distortion problem is solved by using a lookup table to convert captured code values back to signal levels. The values in this table will be similar to the intended ramp value, but with a correction for the finite bandwidth effects. Continuous-time comparators are used, and their bandwidth is set below the step rate, which smoothes the ramp and reduces the noise. No settling time is needed, as would be the case for clocked comparators, but the low bandwidth enhances the distortion of the non-linear portion. This is corrected by use of a return lookup table, which differs from the one used to generate the ramp. The return lookup table is obtained by calibrating against a stepped precision DC reference. This results in a residual non-linearity well below the quantization noise. This method can also compensate for differential non-linearity (DNL) in the DAC used to generate the ramp. The use of a ramp with a combination of linear and quadratic portions for a single-slope ADC is novel. The number of steps is minimized by keeping the step size just below the photon shot noise. This in turn maximizes the speed of the conversion. High resolution is maintained by keeping small quantization steps at low signals, and noise is minimized by allowing the lowest analog bandwidth, all without increasing the quantization noise. A calibrated return lookup table allows the system to maintain excellent linearity.

Perspectives of Light-Front Quantized Field Theory: Some New Results

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

Srivastava, Prem P.

1999-08-13

A review of some basic topics in the light-front (LF) quantization of relativistic field theory is made. It is argued that the LF quantization is equally appropriate as the conventional one and that they lead, assuming the microcausality principle, to the same physical content. This is confirmed in the studies on the LF of the spontaneous symmetry breaking (SSB), of the degenerate vacua in Schwinger model (SM) and Chiral SM (CSM), of the chiral boson theory, and of the QCD in covariant gauges among others. The discussion on the LF is more economical and more transparent than that found inmore » the conventional equal-time quantized theory. The removal of the constraints on the LF phase space by following the Dirac method, in fact, results in a substantially reduced number of independent dynamical variables. Consequently, the descriptions of the physical Hilbert space and the vacuum structure, for example, become more tractable. In the context of the Dyson-Wick perturbation theory the relevant propagators in the front form theory are causal. The Wick rotation can then be performed to employ the Euclidean space integrals in momentum space. The lack of manifest covariance becomes tractable, and still more so if we employ, as discussed in the text, the Fourier transform of the fermionic field based on a special construction of the LF spinor. The fact that the hyperplanes x{sup {+-}} = 0 constitute characteristic surfaces of the hyperbolic partial differential equation is found irrelevant in the quantized theory; it seems sufficient to quantize the theory on one of the characteristic hyperplanes.« less

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.

Bfv Quantization of Relativistic Spinning Particles with a Single Bosonic Constraint

NASA Astrophysics Data System (ADS)

Rabello, Silvio J.; Vaidya, Arvind N.

Using the BFV approach we quantize a pseudoclassical model of the spin-1/2 relativistic particle that contains a single bosonic constraint, contrary to the usual locally supersymmetric models that display first and second class constraints.

Quantized Step-up Model for Evaluation of Internship in Teaching of Prospective Science Teachers.

ERIC Educational Resources Information Center

Sindhu, R. S.

2002-01-01

Describes the quantized step-up model developed for the evaluation purposes of internship in teaching which is an analogous model of the atomic structure. Assesses prospective teachers' abilities in lesson delivery. (YDS)

Minimum uncertainty and squeezing in diffusion processes and stochastic quantization

NASA Technical Reports Server (NTRS)

Demartino, S.; Desiena, S.; Illuminati, Fabrizo; Vitiello, Giuseppe

1994-01-01

We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.

A consistent covariant quantization of the Brink-Schwarz superparticle

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

We perform the covariant quantization of the ten-dimensional Brink-Schwarz superparticle by reducing it to a system whose constraints are all first class, covariant and have only two levels of reducibility. Research supported by the Rothschild Fellowship.

A statistical analysis of the dependency of closure assumptions in cumulus parameterization on the horizontal resolution

NASA Technical Reports Server (NTRS)

Xu, Kuan-Man

1994-01-01

Simulated data from the UCLA cumulus ensemble model are used to investigate the quasi-universal validity of closure assumptions used in existing cumulus parameterizations. A closure assumption is quasi-universally valid if it is sensitive neither to convective cloud regimes nor to horizontal resolutions of large-scale/mesoscale models. The dependency of three types of closure assumptions, as classified by Arakawa and Chen, on the horizontal resolution is addressed in this study. Type I is the constraint on the coupling of the time tendencies of large-scale temperature and water vapor mixing ratio. Type II is the constraint on the coupling of cumulus heating and cumulus drying. Type III is a direct constraint on the intensity of a cumulus ensemble. The macroscopic behavior of simulated cumulus convection is first compared with the observed behavior in view of Type I and Type II closure assumptions using 'quick-look' and canonical correlation analyses. It is found that they are statistically similar to each other. The three types of closure assumptions are further examined with simulated data averaged over selected subdomain sizes ranging from 64 to 512 km. It is found that the dependency of Type I and Type II closure assumptions on the horizontal resolution is very weak and that Type III closure assumption is somewhat dependent upon the horizontal resolution. The influences of convective and mesoscale processes on the closure assumptions are also addressed by comparing the structures of canonical components with the corresponding vertical profiles in the convective and stratiform regions of cumulus ensembles analyzed directly from simulated data. The implication of these results for cumulus parameterization is discussed.

Transforming growth factor-beta1 promotes articular cartilage repair through canonical Smad and Hippo pathways in bone mesenchymal stem cells.

PubMed

Ying, Jun; Wang, Pinger; Zhang, Shanxing; Xu, Taotao; Zhang, Lei; Dong, Rui; Xu, Shibing; Tong, Peijian; Wu, Chengliang; Jin, Hongting

2018-01-01

Transforming growth factor-β1 (TGF-β1) is a chondrogenic factor and has been reported to be able to enhance chondrocyte differentiation from bone marrow mesenchymal stem cells (BMSCs). Here we investigate the molecular mechanism through which TGF-β1 chronically promotes the repair of cartilage defect and inhibit chondrocyte hypertrophy. Animal models of full thickness cartilage defects were divided into three groups: model group, BMSCs group (treated with BMSCs/calcium alginate gel) and BMSCs+TGF-β1 group (treated with Lentivirus-TGF-β1-EGFP transduced BMSCs/calcium alginate gel). 4 and 8weeks after treatment, macroscopic observation, histopathological study and quantitative reverse transcription-polymerase chain reaction (qRT-PCR) were done to analyze phenotypes of the animals. BMSCs were transduced with Lentivirus-TGF-β1-EGFP in vitro and Western blot analysis was performed. We found that TGF-β1-expressiing BMSCs improved the repair of the cartilage defect. The impaired cartilage contained higher amount of GAG and type II collagen and was integrated to the surrounding normal cartilage and higher content of GAG and type II collagen. The major events include increased expression of type II collagen following Smad2/3 phosphorylation, and inhibition of cartilage hypertrophy by increasing Yes-associated protein-1 (YAP-1) and inhibiting Runx2 and Col10 after the completion of chondrogenic differentiation. We conclude that TGF-β1 is beneficial to chondrogenic differentiation of BMSCs via canonical Smad pathway to promote early-repairing of cartilage defect. Furthermore, TGF-β1 inhibits chondrocyte hypertrophy by decreasing hypertrophy marker gene expression via Hippo signaling. Long-term rational use of TGF-β1 may be an alternative approach in clinic for cartilage repair and regeneration. Copyright © 2017. Published by Elsevier Inc.

Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

NASA Astrophysics Data System (ADS)

Song, Haiyu; Yu, Li; Zhang, Dan; Zhang, Wen-An

2012-12-01

This paper is concerned with the finite-time quantized H∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.

High Order Entropy-Constrained Residual VQ for Lossless Compression of Images

NASA Technical Reports Server (NTRS)

Kossentini, Faouzi; Smith, Mark J. T.; Scales, Allen

1995-01-01

High order entropy coding is a powerful technique for exploiting high order statistical dependencies. However, the exponentially high complexity associated with such a method often discourages its use. In this paper, an entropy-constrained residual vector quantization method is proposed for lossless compression of images. The method consists of first quantizing the input image using a high order entropy-constrained residual vector quantizer and then coding the residual image using a first order entropy coder. The distortion measure used in the entropy-constrained optimization is essentially the first order entropy of the residual image. Experimental results show very competitive performance.

Toward a perceptual image quality assessment of color quantized images

NASA Astrophysics Data System (ADS)

Frackiewicz, Mariusz; Palus, Henryk

2018-04-01

Color image quantization is an important operation in the field of color image processing. In this paper, we consider new perceptual image quality metrics for assessment of quantized images. These types of metrics, e.g. DSCSI, MDSIs, MDSIm and HPSI achieve the highest correlation coefficients with MOS during tests on the six publicly available image databases. Research was limited to images distorted by two types of compression: JPG and JPG2K. Statistical analysis of correlation coefficients based on the Friedman test and post-hoc procedures showed that the differences between the four new perceptual metrics are not statistically significant.

Constraints on operator ordering from third quantization

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

Ohkuwa, Yoshiaki; Faizal, Mir, E-mail: f2mir@uwaterloo.ca; Ezawa, Yasuo

2016-02-15

In this paper, we analyse the Wheeler–DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models.

Information efficiency in visual communication

NASA Astrophysics Data System (ADS)

Alter-Gartenberg, Rachel; Rahman, Zia-ur

1993-08-01

This paper evaluates the quantization process in the context of the end-to-end performance of the visual-communication channel. Results show that the trade-off between data transmission and visual quality revolves around the information in the acquired signal, not around its energy. Improved information efficiency is gained by frequency dependent quantization that maintains the information capacity of the channel and reduces the entropy of the encoded signal. Restorations with energy bit-allocation lose both in sharpness and clarity relative to restorations with information bit-allocation. Thus, quantization with information bit-allocation is preferred for high information efficiency and visual quality in optimized visual communication.

Method for calculating the duration of vacuum drying of a metal-concrete container for spent nuclear fuel

NASA Astrophysics Data System (ADS)

Karyakin, Yu. E.; Nekhozhin, M. A.; Pletnev, A. A.

2013-07-01

A method for calculating the quantity of moisture in a metal-concrete container in the process of its charging with spent nuclear fuel is proposed. A computing method and results obtained by it for conservative estimation of the time of vacuum drying of a container charged with spent nuclear fuel by technologies with quantization and without quantization of the lower fuel element cluster are presented. It has been shown that the absence of quantization in loading spent fuel increases several times the time of vacuum drying of the metal-concrete container.

Information efficiency in visual communication

NASA Technical Reports Server (NTRS)

Alter-Gartenberg, Rachel; Rahman, Zia-Ur

1993-01-01

This paper evaluates the quantization process in the context of the end-to-end performance of the visual-communication channel. Results show that the trade-off between data transmission and visual quality revolves around the information in the acquired signal, not around its energy. Improved information efficiency is gained by frequency dependent quantization that maintains the information capacity of the channel and reduces the entropy of the encoded signal. Restorations with energy bit-allocation lose both in sharpness and clarity relative to restorations with information bit-allocation. Thus, quantization with information bit-allocation is preferred for high information efficiency and visual quality in optimized visual communication.

Cascade Error Projection with Low Bit Weight Quantization for High Order Correlation Data

NASA Technical Reports Server (NTRS)

Duong, Tuan A.; Daud, Taher

1998-01-01

In this paper, we reinvestigate the solution for chaotic time series prediction problem using neural network approach. The nature of this problem is such that the data sequences are never repeated, but they are rather in chaotic region. However, these data sequences are correlated between past, present, and future data in high order. We use Cascade Error Projection (CEP) learning algorithm to capture the high order correlation between past and present data to predict a future data using limited weight quantization constraints. This will help to predict a future information that will provide us better estimation in time for intelligent control system. In our earlier work, it has been shown that CEP can sufficiently learn 5-8 bit parity problem with 4- or more bits, and color segmentation problem with 7- or more bits of weight quantization. In this paper, we demonstrate that chaotic time series can be learned and generalized well with as low as 4-bit weight quantization using round-off and truncation techniques. The results show that generalization feature will suffer less as more bit weight quantization is available and error surfaces with the round-off technique are more symmetric around zero than error surfaces with the truncation technique. This study suggests that CEP is an implementable learning technique for hardware consideration.

Group theoretical quantization of isotropic loop cosmology

NASA Astrophysics Data System (ADS)

Livine, Etera R.; Martín-Benito, Mercedes

2012-06-01

We achieve a group theoretical quantization of the flat Friedmann-Robertson-Walker model coupled to a massless scalar field adopting the improved dynamics of loop quantum cosmology. Deparemetrizing the system using the scalar field as internal time, we first identify a complete set of phase space observables whose Poisson algebra is isomorphic to the su(1,1) Lie algebra. It is generated by the volume observable and the Hamiltonian. These observables describe faithfully the regularized phase space underlying the loop quantization: they account for the polymerization of the variable conjugate to the volume and for the existence of a kinematical nonvanishing minimum volume. Since the Hamiltonian is an element in the su(1,1) Lie algebra, the dynamics is now implemented as SU(1, 1) transformations. At the quantum level, the system is quantized as a timelike irreducible representation of the group SU(1, 1). These representations are labeled by a half-integer spin, which gives the minimal volume. They provide superselection sectors without quantization anomalies and no factor ordering ambiguity arises when representing the Hamiltonian. We then explicitly construct SU(1, 1) coherent states to study the quantum evolution. They not only provide semiclassical states but truly dynamical coherent states. Their use further clarifies the nature of the bounce that resolves the big bang singularity.

On-chip integratable all-optical quantizer using strong cross-phase modulation in a silicon-organic hybrid slot waveguide

PubMed Central

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Sang, Xinzhu; Wang, Kuiru; Wu, Qiang; Yan, Binbin; Li, Feng; Zhou, Xian; Zhong, Kangping; Zhou, Guiyao; Yu, Chongxiu; Farrell, Gerald; Lu, Chao; Yaw Tam, Hwa; Wai, P. K. A.

2016-01-01

High performance all-optical quantizer based on silicon waveguide is believed to have significant applications in photonic integratable optical communication links, optical interconnection networks, and real-time signal processing systems. In this paper, we propose an integratable all-optical quantizer for on-chip and low power consumption all-optical analog-to-digital converters. The quantization is realized by the strong cross-phase modulation and interference in a silicon-organic hybrid (SOH) slot waveguide based Mach-Zehnder interferometer. By carefully designing the dimension of the SOH waveguide, large nonlinear coefficients up to 16,000 and 18,069 W−1/m for the pump and probe signals can be obtained respectively, along with a low pulse walk-off parameter of 66.7 fs/mm, and all-normal dispersion in the wavelength regime considered. Simulation results show that the phase shift of the probe signal can reach 8π at a low pump pulse peak power of 206 mW and propagation length of 5 mm such that a 4-bit all-optical quantizer can be realized. The corresponding signal-to-noise ratio is 23.42 dB and effective number of bit is 3.89-bit. PMID:26777054

Noncommutative Line Bundles and Gerbes

NASA Astrophysics Data System (ADS)

Jurčo, B.

We introduce noncommutative line bundles and gerbes within the framework of deformation quantization. The Seiberg-Witten map is used to construct the corresponding noncommutative Čech cocycles. Morita equivalence of star products and quantization of twisted Poisson structures are discussed from this point of view.

Compression of digital images over local area networks. Appendix 1: Item 3. M.S. Thesis

NASA Technical Reports Server (NTRS)

Gorjala, Bhargavi

1991-01-01

Differential Pulse Code Modulation (DPCM) has been used with speech for many years. It has not been as successful for images because of poor edge performance. The only corruption in DPC is quantizer error but this corruption becomes quite large in the region of an edge because of the abrupt changes in the statistics of the signal. We introduce two improved DPCM schemes; Edge correcting DPCM and Edge Preservation Differential Coding. These two coding schemes will detect the edges and take action to correct them. In an Edge Correcting scheme, the quantizer error for an edge is encoded using a recursive quantizer with entropy coding and sent to the receiver as side information. In an Edge Preserving scheme, when the quantizer input falls in the overload region, the quantizer error is encoded and sent to the receiver repeatedly until the quantizer input falls in the inner levels. Therefore these coding schemes increase the bit rate in the region of an edge and require variable rate channels. We implement these two variable rate coding schemes on a token wing network. Timed token protocol supports two classes of messages; asynchronous and synchronous. The synchronous class provides a pre-allocated bandwidth and guaranteed response time. The remaining bandwidth is dynamically allocated to the asynchronous class. The Edge Correcting DPCM is simulated by considering the edge information under the asynchronous class. For the simulation of the Edge Preserving scheme, the amount of information sent each time is fixed, but the length of the packet or the bit rate for that packet is chosen depending on the availability capacity. The performance of the network, and the performance of the image coding algorithms, is studied.

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

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

Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de; Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de; Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru

2016-02-15

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure ofmore » quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.« less

Combining Vector Quantization and Histogram Equalization.

ERIC Educational Resources Information Center

Cosman, Pamela C.; And Others

1992-01-01

Discussion of contrast enhancement techniques focuses on the use of histogram equalization with a data compression technique, i.e., tree-structured vector quantization. The enhancement technique of intensity windowing is described, and the use of enhancement techniques for medical images is explained, including adaptive histogram equalization.…

Introduction to quantized LIE groups and algebras

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

Tjin, T.

1992-10-10

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl[sub 2] is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxtermore » equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl[sub 2] algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.« less

Method and system employing finite state machine modeling to identify one of a plurality of different electric load types

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

Du, Liang; Yang, Yi; Harley, Ronald Gordon

A system is for a plurality of different electric load types. The system includes a plurality of sensors structured to sense a voltage signal and a current signal for each of the different electric loads; and a processor. The processor acquires a voltage and current waveform from the sensors for a corresponding one of the different electric load types; calculates a power or current RMS profile of the waveform; quantizes the power or current RMS profile into a set of quantized state-values; evaluates a state-duration for each of the quantized state-values; evaluates a plurality of state-types based on the powermore » or current RMS profile and the quantized state-values; generates a state-sequence that describes a corresponding finite state machine model of a generalized load start-up or transient profile for the corresponding electric load type; and identifies the corresponding electric load type.« less

Image compression system and method having optimized quantization tables

NASA Technical Reports Server (NTRS)

Ratnakar, Viresh (Inventor); Livny, Miron (Inventor)

1998-01-01

A digital image compression preprocessor for use in a discrete cosine transform-based digital image compression device is provided. The preprocessor includes a gathering mechanism for determining discrete cosine transform statistics from input digital image data. A computing mechanism is operatively coupled to the gathering mechanism to calculate a image distortion array and a rate of image compression array based upon the discrete cosine transform statistics for each possible quantization value. A dynamic programming mechanism is operatively coupled to the computing mechanism to optimize the rate of image compression array against the image distortion array such that a rate-distortion-optimal quantization table is derived. In addition, a discrete cosine transform-based digital image compression device and a discrete cosine transform-based digital image compression and decompression system are provided. Also, a method for generating a rate-distortion-optimal quantization table, using discrete cosine transform-based digital image compression, and operating a discrete cosine transform-based digital image compression and decompression system are provided.

Quantization of Poisson Manifolds from the Integrability of the Modular Function

NASA Astrophysics Data System (ADS)

Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.

2014-10-01

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.

High-resolution quantization based on soliton self-frequency shift and spectral compression in a bi-directional comb-fiber architecture

NASA Astrophysics Data System (ADS)

Zhang, Xuyan; Zhang, Zhiyao; Wang, Shubing; Liang, Dong; Li, Heping; Liu, Yong

2018-03-01

We propose and demonstrate an approach that can achieve high-resolution quantization by employing soliton self-frequency shift and spectral compression. Our approach is based on a bi-directional comb-fiber architecture which is composed of a Sagnac-loop-based mirror and a comb-like combination of N sections of interleaved single-mode fibers and high nonlinear fibers. The Sagnac-loop-based mirror placed at the terminal of a bus line reflects the optical pulses back to the bus line to achieve additional N-stage spectral compression, thus single-stage soliton self-frequency shift (SSFS) and (2 N - 1)-stage spectral compression are realized in the bi-directional scheme. The fiber length in the architecture is numerically optimized, and the proposed quantization scheme is evaluated by both simulation and experiment in the case of N = 2. In the experiment, a quantization resolution of 6.2 bits is obtained, which is 1.2-bit higher than that of its uni-directional counterpart.

Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology

NASA Astrophysics Data System (ADS)

Singh, Parampreet; Wilson-Ewing, Edward

2014-02-01

We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaître-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaître-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.

The electronic structure of Au25 clusters: between discrete and continuous

NASA Astrophysics Data System (ADS)

Katsiev, Khabiboulakh; Lozova, Nataliya; Wang, Lu; Sai Krishna, Katla; Li, Ruipeng; Mei, Wai-Ning; Skrabalak, Sara E.; Kumar, Challa S. S. R.; Losovyj, Yaroslav

2016-08-01

Here, an approach based on synchrotron resonant photoemission is employed to explore the transition between quantization and hybridization of the electronic structure in atomically precise ligand-stabilized nanoparticles. While the presence of ligands maintains quantization in Au25 clusters, their removal renders increased hybridization of the electronic states in the vicinity of the Fermi level. These observations are supported by DFT studies.Here, an approach based on synchrotron resonant photoemission is employed to explore the transition between quantization and hybridization of the electronic structure in atomically precise ligand-stabilized nanoparticles. While the presence of ligands maintains quantization in Au25 clusters, their removal renders increased hybridization of the electronic states in the vicinity of the Fermi level. These observations are supported by DFT studies. Electronic supplementary information (ESI) available: Experimental details including chemicals, sample preparation, and characterization methods. Computation techniques, SV-AUC, GIWAXS, XPS, UPS, MALDI-TOF, ESI data of Au25 clusters. See DOI: 10.1039/c6nr02374f

Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism ( S-quantization)

NASA Astrophysics Data System (ADS)

Ivanov, K. A.; Nikolaev, V. V.; Gubaydullin, A. R.; Kaliteevski, M. A.

2017-10-01

Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures ( S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate difficulties that arise in the analysis of the Purcell effect because of the divergence of the integral describing the effective volume of the mode in open systems.

Exact quantization of Einstein-Rosen waves coupled to massless scalar matter.

PubMed

Barbero G, J Fernando; Garay, Iñaki; Villaseñor, Eduardo J S

2005-07-29

We show in this Letter that gravity coupled to a massless scalar field with full cylindrical symmetry can be exactly quantized by an extension of the techniques used in the quantization of Einstein-Rosen waves. This system provides a useful test bed to discuss a number of issues in quantum general relativity, such as the emergence of the classical metric, microcausality, and large quantum gravity effects. It may also provide an appropriate framework to study gravitational critical phenomena from a quantum point of view, issues related to black hole evaporation, and the consistent definition of test fields and particles in quantum gravity.

Efficient storage and management of radiographic images using a novel wavelet-based multiscale vector quantizer

NASA Astrophysics Data System (ADS)

Yang, Shuyu; Mitra, Sunanda

2002-05-01

Due to the huge volumes of radiographic images to be managed in hospitals, efficient compression techniques yielding no perceptual loss in the reconstructed images are becoming a requirement in the storage and management of such datasets. A wavelet-based multi-scale vector quantization scheme that generates a global codebook for efficient storage and transmission of medical images is presented in this paper. The results obtained show that even at low bit rates one is able to obtain reconstructed images with perceptual quality higher than that of the state-of-the-art scalar quantization method, the set partitioning in hierarchical trees.

Subband Image Coding with Jointly Optimized Quantizers

NASA Technical Reports Server (NTRS)

Kossentini, Faouzi; Chung, Wilson C.; Smith Mark J. T.

1995-01-01

An iterative design algorithm for the joint design of complexity- and entropy-constrained subband quantizers and associated entropy coders is proposed. Unlike conventional subband design algorithms, the proposed algorithm does not require the use of various bit allocation algorithms. Multistage residual quantizers are employed here because they provide greater control of the complexity-performance tradeoffs, and also because they allow efficient and effective high-order statistical modeling. The resulting subband coder exploits statistical dependencies within subbands, across subbands, and across stages, mainly through complexity-constrained high-order entropy coding. Experimental results demonstrate that the complexity-rate-distortion performance of the new subband coder is exceptional.

Second quantization techniques in the scattering of nonidentical composite bodies

NASA Technical Reports Server (NTRS)

Norbury, J. W.; Townsend, L. W.; Deutchman, P. A.

1986-01-01

Second quantization techniques for describing elastic and inelastic interactions between nonidentical composite bodies are presented and are applied to nucleus-nucleus collisions involving ground-state and one-particle-one-hole excitations. Evaluations of the resultant collision matrix elements are made through use of Wick's theorem.

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

Prior-Based Quantization Bin Matching for Cloud Storage of JPEG Images.

PubMed

Liu, Xianming; Cheung, Gene; Lin, Chia-Wen; Zhao, Debin; Gao, Wen

2018-07-01

Millions of user-generated images are uploaded to social media sites like Facebook daily, which translate to a large storage cost. However, there exists an asymmetry in upload and download data: only a fraction of the uploaded images are subsequently retrieved for viewing. In this paper, we propose a cloud storage system that reduces the storage cost of all uploaded JPEG photos, at the expense of a controlled increase in computation mainly during download of requested image subset. Specifically, the system first selectively re-encodes code blocks of uploaded JPEG images using coarser quantization parameters for smaller storage sizes. Then during download, the system exploits known signal priors-sparsity prior and graph-signal smoothness prior-for reverse mapping to recover original fine quantization bin indices, with either deterministic guarantee (lossless mode) or statistical guarantee (near-lossless mode). For fast reverse mapping, we use small dictionaries and sparse graphs that are tailored for specific clusters of similar blocks, which are classified via tree-structured vector quantizer. During image upload, cluster indices identifying the appropriate dictionaries and graphs for the re-quantized blocks are encoded as side information using a differential distributed source coding scheme to facilitate reverse mapping during image download. Experimental results show that our system can reap significant storage savings (up to 12.05%) at roughly the same image PSNR (within 0.18 dB).

A constrained joint source/channel coder design and vector quantization of nonstationary sources

NASA Technical Reports Server (NTRS)

Sayood, Khalid; Chen, Y. C.; Nori, S.; Araj, A.

1993-01-01

The emergence of broadband ISDN as the network for the future brings with it the promise of integration of all proposed services in a flexible environment. In order to achieve this flexibility, asynchronous transfer mode (ATM) has been proposed as the transfer technique. During this period a study was conducted on the bridging of network transmission performance and video coding. The successful transmission of variable bit rate video over ATM networks relies on the interaction between the video coding algorithm and the ATM networks. Two aspects of networks that determine the efficiency of video transmission are the resource allocation algorithm and the congestion control algorithm. These are explained in this report. Vector quantization (VQ) is one of the more popular compression techniques to appear in the last twenty years. Numerous compression techniques, which incorporate VQ, have been proposed. While the LBG VQ provides excellent compression, there are also several drawbacks to the use of the LBG quantizers including search complexity and memory requirements, and a mismatch between the codebook and the inputs. The latter mainly stems from the fact that the VQ is generally designed for a specific rate and a specific class of inputs. In this work, an adaptive technique is proposed for vector quantization of images and video sequences. This technique is an extension of the recursively indexed scalar quantization (RISQ) algorithm.

Metabolite Profiling and Classification of DNA-Authenticated Licorice Botanicals

PubMed Central

Simmler, Charlotte; Anderson, Jeffrey R.; Gauthier, Laura; Lankin, David C.; McAlpine, James B.; Chen, Shao-Nong; Pauli, Guido F.

2015-01-01

Raw licorice roots represent heterogeneous materials obtained from mainly three Glycyrrhiza species. G. glabra, G. uralensis, and G. inflata exhibit marked metabolite differences in terms of flavanones (Fs), chalcones (Cs), and other phenolic constituents. The principal objective of this work was to develop complementary chemometric models for the metabolite profiling, classification, and quality control of authenticated licorice. A total of 51 commercial and macroscopically verified samples were DNA authenticated. Principal component analysis and canonical discriminant analysis were performed on 1H NMR spectra and area under the curve values obtained from UHPLC-UV chromatograms, respectively. The developed chemometric models enable the identification and classification of Glycyrrhiza species according to their composition in major Fs, Cs, and species specific phenolic compounds. Further key outcomes demonstrated that DNA authentication combined with chemometric analyses enabled the characterization of mixtures, hybrids, and species outliers. This study provides a new foundation for the botanical and chemical authentication, classification, and metabolomic characterization of crude licorice botanicals and derived materials. Collectively, the proposed methods offer a comprehensive approach for the quality control of licorice as one of the most widely used botanical dietary supplements. PMID:26244884

A four-field model for collisionless reconnection: Hamiltonian structure and numerical simulations

NASA Astrophysics Data System (ADS)

Tassi, Emanuele; Grasso, Daniela; Pegoraro, Francesco

2008-11-01

A 4-field model for magnetic reconnection in collisionless plasmas is investigated both analytically and numerically. The model equations are shown to admit a non-canonical Hamiltonian formulation with four infinite families of Casimir invariants [1]. Numerical simulations show that, consistently with previously investigated models [2,3], in the absence of significant fluctuations along the toroidal direction, reconnection can lead to a macroscopic saturated state exhibiting filamentation on microsocopic scales, or to a secondary Kelvin-Helmholtz-like instability, depending on the value of a parameter measuring the compressibility of the electron fluid. The novel feature exhibited by the four-field model is the coexistence of significant filamentation with a secondary instability when magnetic and velocity perturbations along the toroidal direction are no longer negligible. An interpretation of this phenomenon in terms of Casimir invariants is given.[0pt] [1] E. Tassi et al., Plasma Phys. Contr. Fus., 50, 085014 (2008)[0pt] [2] D. Grasso et al., Phys. Rev. Lett. 86, 5051 (2001)[0pt] [3] D. Del Sarto, F. Califano and F. Pegoraro, Phys. Plasmas 12, 012317 (2005)

Crystal Structure of Bicc1 SAM Polymer and Mapping of Interactions between the Ciliopathy-Associated Proteins Bicc1, ANKS3, and ANKS6.

PubMed

Rothé, Benjamin; Leettola, Catherine N; Leal-Esteban, Lucia; Cascio, Duilio; Fortier, Simon; Isenschmid, Manuela; Bowie, James U; Constam, Daniel B

2018-02-06

Head-to-tail polymers of sterile alpha motifs (SAM) can scaffold large macromolecular complexes. Several SAM-domain proteins that bind each other are mutated in patients with cystic kidneys or laterality defects, including the Ankyrin (ANK) and SAM domain-containing proteins ANKS6 and ANKS3, and the RNA-binding protein Bicc1. To address how their interactions are regulated, we first determined a high-resolution crystal structure of a Bicc1-SAM polymer, revealing a canonical SAM polymer with a high degree of flexibility in the subunit interface orientations. We further mapped interactions between full-length and distinct domains of Bicc1, ANKS3, and ANKS6. Neither ANKS3 nor ANKS6 alone formed macroscopic homopolymers in vivo. However, ANKS3 recruited ANKS6 to Bicc1, and the three proteins together cooperatively generated giant macromolecular complexes. Thus, the giant assemblies are shaped by SAM domains, their flanking sequences, and SAM-independent protein-protein and protein-mRNA interactions. Copyright © 2017 Elsevier Ltd. All rights reserved.

Visual data mining for quantized spatial data

NASA Technical Reports Server (NTRS)

Braverman, Amy; Kahn, Brian

2004-01-01

In previous papers we've shown how a well known data compression algorithm called Entropy-constrained Vector Quantization ( can be modified to reduce the size and complexity of very large, satellite data sets. In this paper, we descuss how to visualize and understand the content of such reduced data sets.

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.

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.

Quantized Algebra I Texts

ERIC Educational Resources Information Center

DeBuvitz, William

2014-01-01

I am a volunteer reader at the Princeton unit of "Learning Ally" (formerly "Recording for the Blind & Dyslexic") and I recently discovered that high school students are introduced to the concept of quantization well before they take chemistry and physics. For the past few months I have been reading onto computer files a…

Techniques for decoding speech phonemes and sounds: A concept

NASA Technical Reports Server (NTRS)

Lokerson, D. C.; Holby, H. G.

1975-01-01

Techniques studied involve conversion of speech sounds into machine-compatible pulse trains. (1) Voltage-level quantizer produces number of output pulses proportional to amplitude characteristics of vowel-type phoneme waveforms. (2) Pulses produced by quantizer of first speech formants are compared with pulses produced by second formants.

Quantum Model of a Charged Black Hole

NASA Astrophysics Data System (ADS)

Gladush, V. D.

A canonical approach for constructing of the classical and quantum description spherically-symmetric con guration gravitational and electromagnetic elds is considered. According to the sign of the square of the Kodama vector, space-time is divided into R-and T-regions. By virtue of the generalized Birkho theorem, one can choose coordinate systems such that the desired metric functions in the T-region depend on the time, and in the R-domain on the space coordinate. Then, the initial action for the con guration breaks up into terms describing the elds in the T- and R-regions with the time and space evolutionary variable, respectively. For these regions, Lagrangians of the con guration are constructed, which contain dynamic and non-dynamic degrees of freedom, leading to constrains. We concentrate our attention on dynamic T-regions. There are two additional conserved physical quantities: the charge and the total mass of the system. The Poisson bracket of the total mass with the Hamiltonian function vanishes in the weak sense. A classical solution of the eld equations in the con guration space (minisuperspace) is constructed without xing non-dynamic variable. In the framework of the canonical approach to the quantum mechanics of the system under consideration, physical states are found by solving the Hamiltonian constraint in the operator form (the DeWitt equation) for the system wave function Ψ. It also requires that Ψ is an eigenfunction of the operators of charge and total mass. For the symmetric of the mass operator the corresponding ordering of operators is carried out. Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions must be constructed in conjunction with the solution of the DeWitt equation. The consistency condition leads to the ansatz, with the help of which the solution of the DeWitt equation for the state Ψem with a defined total mass and charge is constructed, taking into account the regularity condition on the horizon. The mass and charge spectra of the con guration in this approach turn out to be continuous. It is interesting that formal quantization in the R-region with a space evolutionary coordinate leads to a similar result.

Quantization with maximally degenerate Poisson brackets: the harmonic oscillator!

NASA Astrophysics Data System (ADS)

Nutku, Yavuz

2003-07-01

Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these degenerate Poisson brackets are brought to the form of Heisenberg's equations. We propose a definition for constructing quantum operators for classical functions, which enables us to turn the maximally degenerate Poisson brackets into operators. They pose a set of eigenvalue problems for a new state vector. The requirement of the single-valuedness of this eigenfunction leads to quantization. The example of the harmonic oscillator is used to illustrate this general procedure for quantizing a class of maximally super-integrable systems.

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

Kovchavtsev, A. P., E-mail: kap@isp.nsc.ru; Tsarenko, A. V.; Guzev, A. A.

The influence of electron energy quantization in a space-charge region on the accumulation capacitance of the InAs-based metal-oxide-semiconductor capacitors (MOSCAPs) has been investigated by modeling and comparison with the experimental data from Au/anodic layer(4-20 nm)/n-InAs(111)A MOSCAPs. The accumulation capacitance for MOSCAPs has been calculated by the solution of Poisson equation with different assumptions and the self-consistent solution of Schrödinger and Poisson equations with quantization taken into account. It was shown that the quantization during the MOSCAPs accumulation capacitance calculations should be taken into consideration for the correct interface states density determination by Terman method and the evaluation of gate dielectric thicknessmore » from capacitance-voltage measurements.« less

Accelerating Families of Fuzzy K-Means Algorithms for Vector Quantization Codebook Design

PubMed Central

Mata, Edson; Bandeira, Silvio; de Mattos Neto, Paulo; Lopes, Waslon; Madeiro, Francisco

2016-01-01

The performance of signal processing systems based on vector quantization depends on codebook design. In the image compression scenario, the quality of the reconstructed images depends on the codebooks used. In this paper, alternatives are proposed for accelerating families of fuzzy K-means algorithms for codebook design. The acceleration is obtained by reducing the number of iterations of the algorithms and applying efficient nearest neighbor search techniques. Simulation results concerning image vector quantization have shown that the acceleration obtained so far does not decrease the quality of the reconstructed images. Codebook design time savings up to about 40% are obtained by the accelerated versions with respect to the original versions of the algorithms. PMID:27886061

Accelerating Families of Fuzzy K-Means Algorithms for Vector Quantization Codebook Design.

PubMed

Mata, Edson; Bandeira, Silvio; de Mattos Neto, Paulo; Lopes, Waslon; Madeiro, Francisco

2016-11-23

The performance of signal processing systems based on vector quantization depends on codebook design. In the image compression scenario, the quality of the reconstructed images depends on the codebooks used. In this paper, alternatives are proposed for accelerating families of fuzzy K-means algorithms for codebook design. The acceleration is obtained by reducing the number of iterations of the algorithms and applying efficient nearest neighbor search techniques. Simulation results concerning image vector quantization have shown that the acceleration obtained so far does not decrease the quality of the reconstructed images. Codebook design time savings up to about 40% are obtained by the accelerated versions with respect to the original versions of the algorithms.

Fractional quantization of the magnetic flux in cylindrical unconventional superconductors.

PubMed

Loder, F; Kampf, A P; Kopp, T

2013-07-26

The magnetic flux threading a conventional superconducting ring is typically quantized in units of Φ0=hc/2e. The factor of 2 in the denominator of Φ0 originates from the existence of two different types of pairing states with minima of the free energy at even and odd multiples of Φ0. Here we show that spatially modulated pairing states exist with energy minima at fractional flux values, in particular, at multiples of Φ0/2. In such states, condensates with different center-of-mass momenta of the Cooper pairs coexist. The proposed mechanism for fractional flux quantization is discussed in the context of cuprate superconductors, where hc/4e flux periodicities were observed.

Floating-point system quantization errors in digital control systems

NASA Technical Reports Server (NTRS)

Phillips, C. L.

1973-01-01

The results are reported of research into the effects on system operation of signal quantization in a digital control system. The investigation considered digital controllers (filters) operating in floating-point arithmetic in either open-loop or closed-loop systems. An error analysis technique is developed, and is implemented by a digital computer program that is based on a digital simulation of the system. As an output the program gives the programing form required for minimum system quantization errors (either maximum of rms errors), and the maximum and rms errors that appear in the system output for a given bit configuration. The program can be integrated into existing digital simulations of a system.

The uniform quantized electron gas revisited

NASA Astrophysics Data System (ADS)

Lomba, Enrique; Høye, Johan S.

2017-11-01

In this article we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature T=0 . As before, we utilize the methods, properties, and results obtained by means of classical statistical mechanics. These were extended to quantized systems via the Feynman path integral formalism. The latter translates the quantum problem into a classical polymer problem in four dimensions. Again, the well known RPA (random phase approximation) is recovered as a basic result which we then modify and improve upon. Here we analyze the condition of thermodynamic self-consistency. Our numerical calculations exhibit a remarkable agreement with well known results of a standard parameterization of Monte Carlo correlation energies.

Spacetime algebra as a powerful tool for electromagnetism

NASA Astrophysics Data System (ADS)

Dressel, Justin; Bliokh, Konstantin Y.; Nori, Franco

2015-08-01

We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric-magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.

Quantum Sets and Clifford Algebras

NASA Astrophysics Data System (ADS)

Finkelstein, David

1982-06-01

The mathematical language presently used for quantum physics is a high-level language. As a lowest-level or basic language I construct a quantum set theory in three stages: (1) Classical set theory, formulated as a Clifford algebra of “ S numbers” generated by a single monadic operation, “bracing,” Br = {…}. (2) Indefinite set theory, a modification of set theory dealing with the modal logical concept of possibility. (3) Quantum set theory. The quantum set is constructed from the null set by the familiar quantum techniques of tensor product and antisymmetrization. There are both a Clifford and a Grassmann algebra with sets as basis elements. Rank and cardinality operators are analogous to Schroedinger coordinates of the theory, in that they are multiplication or “ Q-type” operators. “ P-type” operators analogous to Schroedinger momenta, in that they transform the Q-type quantities, are bracing (Br), Clifford multiplication by a set X, and the creator of X, represented by Grassmann multiplication c( X) by the set X. Br and its adjoint Br* form a Bose-Einstein canonical pair, and c( X) and its adjoint c( X)* form a Fermi-Dirac or anticanonical pair. Many coefficient number systems can be employed in this quantization. I use the integers for a discrete quantum theory, with the usual complex quantum theory as limit. Quantum set theory may be applied to a quantum time space and a quantum automaton.

Quantization of higher abelian gauge theory in generalized differential cohomology

NASA Astrophysics Data System (ADS)

Szabo, R.

We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.

Radiation dose-rate meter using an energy-sensitive counter

DOEpatents

Kopp, Manfred K.

1988-01-01

A radiation dose-rate meter is provided which uses an energy-sensitive detector and combines charge quantization and pulse-rate measurement to monitor radiation dose rates. The charge from each detected photon is quantized by level-sensitive comparators so that the resulting total output pulse rate is proportional to the dose-rate.

Quantized Chiral Magnetic Current from Reconnections of Magnetic Flux.

PubMed

Hirono, Yuji; Kharzeev, Dmitri E; Yin, Yi

2016-10-21

We introduce a new mechanism for the chiral magnetic effect that does not require an initial chirality imbalance. The chiral magnetic current is generated by reconnections of magnetic flux that change the magnetic helicity of the system. The resulting current is entirely determined by the change of magnetic helicity, and it is quantized.

Quantized Chiral Magnetic Current from Reconnections of Magnetic Flux

DOE PAGES

Hirono, Yuji; Kharzeev, Dmitri E.; Yin, Yi

2016-10-20

We introduce a new mechanism for the chiral magnetic e ect that does not require an initial chirality imbalance. The chiral magnetic current is generated by reconnections of magnetic ux that change the magnetic helicity of the system. The resulting current is entirely determined by the change of magnetic helicity, and it is quantized.

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.

Monopoles for gravitation and for higher spin fields

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

Bunster, Claudio; Portugues, Ruben; Cnockaert, Sandrine

2006-05-15

We consider massless higher spin gauge theories with both electric and magnetic sources, with a special emphasis on the spin two case. We write the equations of motion at the linear level (with conserved external sources) and introduce Dirac strings so as to derive the equations from a variational principle. We then derive a quantization condition that generalizes the familiar Dirac quantization condition, and which involves the conserved charges associated with the asymptotic symmetries for higher spins. Next we discuss briefly how the result extends to the nonlinear theory. This is done in the context of gravitation, where the Taub-NUTmore » solution provides the exact solution of the field equations with both types of sources. We rederive, in analogy with electromagnetism, the quantization condition from the quantization of the angular momentum. We also observe that the Taub-NUT metric is asymptotically flat at spatial infinity in the sense of Regge and Teitelboim (including their parity conditions). It follows, in particular, that one can consistently consider in the variational principle configurations with different electric and magnetic masses.« less

Conductance Quantization in Resistive Random Access Memory

NASA Astrophysics Data System (ADS)

Li, Yang; Long, Shibing; Liu, Yang; Hu, Chen; Teng, Jiao; Liu, Qi; Lv, Hangbing; Suñé, Jordi; Liu, Ming

2015-10-01

The intrinsic scaling-down ability, simple metal-insulator-metal (MIM) sandwich structure, excellent performances, and complementary metal-oxide-semiconductor (CMOS) technology-compatible fabrication processes make resistive random access memory (RRAM) one of the most promising candidates for the next-generation memory. The RRAM device also exhibits rich electrical, thermal, magnetic, and optical effects, in close correlation with the abundant resistive switching (RS) materials, metal-oxide interface, and multiple RS mechanisms including the formation/rupture of nanoscale to atomic-sized conductive filament (CF) incorporated in RS layer. Conductance quantization effect has been observed in the atomic-sized CF in RRAM, which provides a good opportunity to deeply investigate the RS mechanism in mesoscopic dimension. In this review paper, the operating principles of RRAM are introduced first, followed by the summarization of the basic conductance quantization phenomenon in RRAM and the related RS mechanisms, device structures, and material system. Then, we discuss the theory and modeling of quantum transport in RRAM. Finally, we present the opportunities and challenges in quantized RRAM devices and our views on the future prospects.

Combinatorial quantization of the Hamiltonian Chern-Simons theory II

NASA Astrophysics Data System (ADS)

Alekseev, Anton Yu.; Grosse, Harald; Schomerus, Volker

1996-01-01

This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of “functions on the quantum moduli space of flat connections” and comes equipped with a positive functional ω (“integration”). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.

Conductance Quantization in Resistive Random Access Memory.

PubMed

Li, Yang; Long, Shibing; Liu, Yang; Hu, Chen; Teng, Jiao; Liu, Qi; Lv, Hangbing; Suñé, Jordi; Liu, Ming

2015-12-01

The intrinsic scaling-down ability, simple metal-insulator-metal (MIM) sandwich structure, excellent performances, and complementary metal-oxide-semiconductor (CMOS) technology-compatible fabrication processes make resistive random access memory (RRAM) one of the most promising candidates for the next-generation memory. The RRAM device also exhibits rich electrical, thermal, magnetic, and optical effects, in close correlation with the abundant resistive switching (RS) materials, metal-oxide interface, and multiple RS mechanisms including the formation/rupture of nanoscale to atomic-sized conductive filament (CF) incorporated in RS layer. Conductance quantization effect has been observed in the atomic-sized CF in RRAM, which provides a good opportunity to deeply investigate the RS mechanism in mesoscopic dimension. In this review paper, the operating principles of RRAM are introduced first, followed by the summarization of the basic conductance quantization phenomenon in RRAM and the related RS mechanisms, device structures, and material system. Then, we discuss the theory and modeling of quantum transport in RRAM. Finally, we present the opportunities and challenges in quantized RRAM devices and our views on the future prospects.

Thin noble metal films on Si (111) investigated by optical second-harmonic generation and photoemission

NASA Astrophysics Data System (ADS)

Pedersen, K.; Kristensen, T. B.; Pedersen, T. G.; Morgen, P.; Li, Z.; Hoffmann, S. V.

2002-05-01

Thin noble metal films (Ag, Au and Cu) on Si (111) have been investigated by optical second-harmonic generation (SHG) in combination with synchrotron radiation photoemission spectroscopy. The valence band spectra of Ag films show a quantization of the sp-band in the 4-eV energy range from the Fermi level down to the onset of the d-bands. For Cu and Au the corresponding energy range is much narrower and quantization effects are less visible. Quantization effects in SHG are observed as oscillations in the signal as a function of film thickness. The oscillations are strongest for Ag and less pronounced for Cu, in agreement with valence band photoemission spectra. In the case of Au, a reacted layer floating on top of the Au film masks the observation of quantum well levels by photoemission. However, SHG shows a well-developed quantization of levels in the Au film below the reacted layer. For Ag films, the relation between film thickness and photon energy of the SHG resonances indicates different types of resonances, some of which involve both quantum well and substrate states.

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

The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae

NASA Astrophysics Data System (ADS)

Kolli, Avinash; O'Reilly, Edward J.; Scholes, Gregory D.; Olaya-Castro, Alexandra

2012-11-01

The influence of fast vibrations on energy transfer and conversion in natural molecular aggregates is an issue of central interest. This article shows the important role of high-energy quantized vibrations and their non-equilibrium dynamics for energy transfer in photosynthetic systems with highly localized excitonic states. We consider the cryptophyte antennae protein phycoerythrin 545 and show that coupling to quantized vibrations, which are quasi-resonant with excitonic transitions is fundamental for biological function as it generates non-cascaded transport with rapid and wider spatial distribution of excitation energy. Our work also indicates that the non-equilibrium dynamics of such vibrations can manifest itself in ultrafast beating of both excitonic populations and coherences at room temperature, with time scales in agreement with those reported in experiments. Moreover, we show that mechanisms supporting coherent excitonic dynamics assist coupling to selected modes that channel energy to preferential sites in the complex. We therefore argue that, in the presence of strong coupling between electronic excitations and quantized vibrations, a concrete and important advantage of quantum coherent dynamics is precisely to tune resonances that promote fast and effective energy distribution.

Optically-synchronized encoder and multiplexer scheme for interleaved photonics analog-to-digital conversion

NASA Astrophysics Data System (ADS)

Villa, Carlos; Kumavor, Patrick; Donkor, Eric

2008-04-01

Photonics Analog-to-Digital Converters (ADCs) utilize a train of optical pulses to sample an electrical input waveform applied to an electrooptic modulator or a reverse biased photodiode. In the former, the resulting train of amplitude-modulated optical pulses is detected (converter to electrical) and quantized using a conversional electronics ADC- as at present there are no practical, cost-effective optical quantizers available with performance that rival electronic quantizers. In the latter, the electrical samples are directly quantized by the electronics ADC. In both cases however, the sampling rate is limited by the speed with which the electronics ADC can quantize the electrical samples. One way to increase the sampling rate by a factor N is by using the time-interleaved technique which consists of a parallel array of N electrical ADC converters, which have the same sampling rate but different sampling phase. Each operating at a quantization rate of fs/N where fs is the aggregated sampling rate. In a system with no real-time operation, the N channels digital outputs are stored in memory, and then aggregated (multiplexed) to obtain the digital representation of the analog input waveform. Alternatively, for real-time operation systems the reduction of storing time in the multiplexing process is desired to improve the time response of the ADC. The complete elimination of memories come expenses of concurrent timing and synchronization in the aggregation of the digital signal that became critical for a good digital representation of the analog signal waveform. In this paper we propose and demonstrate a novel optically synchronized encoder and multiplexer scheme for interleaved photonics ADCs that utilize the N optical signals used to sample different phases of an analog input signal to synchronize the multiplexing of the resulting N digital output channels in a single digital output port. As a proof of concept, four 320 Megasamples/sec 12-bit of resolution digital signals were multiplexed to form an aggregated 1.28 Gigasamples/sec single digital output signal.

Wavelet subband coding of computer simulation output using the A++ array class library

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

Bradley, J.N.; Brislawn, C.M.; Quinlan, D.J.

1995-07-01

The goal of the project is to produce utility software for off-line compression of existing data and library code that can be called from a simulation program for on-line compression of data dumps as the simulation proceeds. Naturally, we would like the amount of CPU time required by the compression algorithm to be small in comparison to the requirements of typical simulation codes. We also want the algorithm to accomodate a wide variety of smooth, multidimensional data types. For these reasons, the subband vector quantization (VQ) approach employed in has been replaced by a scalar quantization (SQ) strategy using amore » bank of almost-uniform scalar subband quantizers in a scheme similar to that used in the FBI fingerprint image compression standard. This eliminates the considerable computational burdens of training VQ codebooks for each new type of data and performing nearest-vector searches to encode the data. The comparison of subband VQ and SQ algorithms in indicated that, in practice, there is relatively little additional gain from using vector as opposed to scalar quantization on DWT subbands, even when the source imagery is from a very homogeneous population, and our subjective experience with synthetic computer-generated data supports this stance. It appears that a careful study is needed of the tradeoffs involved in selecting scalar vs. vector subband quantization, but such an analysis is beyond the scope of this paper. Our present work is focused on the problem of generating wavelet transform/scalar quantization (WSQ) implementations that can be ported easily between different hardware environments. This is an extremely important consideration given the great profusion of different high-performance computing architectures available, the high cost associated with learning how to map algorithms effectively onto a new architecture, and the rapid rate of evolution in the world of high-performance computing.« less

Parallel Prebiotic Origin of Canonical and Non-Canonical Purine Nucleosides

NASA Astrophysics Data System (ADS)

Becker, S.; Carell, T.

2017-07-01

RNA of all living organisms is highly modified. It is unclear if these non-canonical bases are ancestors of an early Earth or biological inventions. We investigated a prebiotic pathway that leads to canonical and non-canonical purine nucleosides.

Are neoclassical canons valid for southern Chinese faces?

PubMed

Jayaratne, Yasas S N; Deutsch, Curtis K; McGrath, Colman P J; Zwahlen, Roger A

2012-01-01

Proportions derived from neoclassical canons, initially described by Renaissance sculptors and painters, are still being employed as aesthetic guidelines during the clinical assessment of the facial morphology. 1. to determine the applicability of neoclassical canons for Southern Chinese faces and 2. to explore gender differences in relation to the applicability of the neoclassical canons and their variants. 3-D photographs acquired from 103 young adults (51 males and 52 females) without facial dysmorphology were used to test applicability of four neoclassical canons. Standard anthropometric measurements that determine the facial canons were made on these 3-D images. The validity of the canons as well as their different variants were quantified. The neoclassical cannons seldom applied to these individuals, and facial three-section and orbital canons did not apply at all. The orbitonasal canon was most frequently applicable, with a frequency of 19%. Significant sexual dimorphism was found relative to the prevalence of the variants of facial three-section and orbitonasal canons. The neoclassical canons did not appear to apply to our sample when rigorous quantitative measurements were employed. Thus, they should not be used as esthetic goals for craniofacial surgical interventions.

Electron-phonon interactions in semiconductor nanostructures

NASA Astrophysics Data System (ADS)

Yu, Segi

In this dissertation, electron-phonon interactions are studied theoretically in semiconductor nanoscale heterostructures. Interactions of electrons with interface optical phonons dominate over other electron-phonon interactions in narrow width heterostructures. Hence, a transfer matrix method is used to establish a formalism for determining the dispersion relations and electrostatic potentials of the interface phonons for multiple-interface heterostructure within the macroscopic dielectric continuum model. This method facilitates systematic calculations for complex structures where the conventional method is difficult to implement. Several specific cases are treated to illustrate advantages of the formalism. Electrophonon resonance (EPR) is studied in cylindrical quantum wires using the confined/interface optical phonons representation and bulk phonon representation. It has been found that interface phonon contribution to EPR is small compared with confined phonon. Different selection rules for bulk phonons and confined phonons result in different EPR behaviors as the radius of cylindrical wire changes. Experiment is suggested to test which phonon representation is appropriate for EPR. The effects of phonon confinement on elect ron-acoustic-phonon scattering is studied in cylindrical and rectangular quantum wires. In the macroscopic elastic continuum model, the confined-phonon dispersion relations are obtained for several crystallographic directions with free-surface and clamped-surface boundary conditions in cylindrical wires. The scattering rates due to the deformation potential are obtained for these confined phonons and are compared with those of bulk-like phonons. The results show that the inclusion of acoustic phonon confinement may be crucial for calculating accurate low-energy electron scattering rates. Furthermore, it has been found that there is a scaling rule governing the directional dependence of the scattering rates. The Hamiltonian describing the deformation-potential of confined acoustic phonons is derived by quantizing the appropriate, experimentally verified approximate compressional acoustic-phonon modes in a free-standing rectangular quantum wire. The scattering rate is obtained for GaAs quantum wires with a range of cross-sectional dimensions. The results demonstrate that a proper treatment of confined acoustic phonons may be essential to correctly model electron scattering rates at low energies in nanoscale structures.

Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle

NASA Astrophysics Data System (ADS)

El, G. A.; Kamchatnov, A. M.; Khodorovskii, V. V.; Annibale, E. S.; Gammal, A.

2009-10-01

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schrödinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear “ship-wave” pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

NanoSQUIDs: Basics & recent advances

NASA Astrophysics Data System (ADS)

José Martínez-Pérez, Maria; Koelle, Dieter

2017-08-01

Superconducting Quantum Interference Devices (SQUIDs) are one of the most popular devices in superconducting electronics. They combine the Josephson effect with the quantization of magnetic flux in superconductors. This gives rise to one of the most beautiful manifestations of macroscopic quantum coherence in the solid state. In addition, SQUIDs are extremely sensitive sensors allowing us to transduce magnetic flux into measurable electric signals. As a consequence, any physical observable that can be converted into magnetic flux, e.g., current, magnetization, magnetic field or position, becomes easily accessible to SQUID sensors. In the late 1980s it became clear that downsizing the dimensions of SQUIDs to the nanometric scale would encompass an enormous increase of their sensitivity to localized tiny magnetic signals. Indeed, nanoSQUIDs opened the way to the investigation of, e.g., individual magnetic nanoparticles or surface magnetic states with unprecedented sensitivities. The purpose of this chapter is to present a detailed survey of microscopic and nanoscopic SQUID sensors. We will start by discussing the principle of operation of SQUIDs, placing the emphasis on their application as ultrasensitive detectors for small localized magnetic signals. We will continue by reviewing a number of existing devices based on different kinds of Josephson junctions and materials, focusing on their advantages and drawbacks. The last sections are left for applications of nanoSQUIDs in the fields of scanning SQUID microscopy and magnetic particle characterization, placing special stress on the investigation of individual magnetic nanoparticles.

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

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.

Quantized Vector Potential and the Photon Wave-function

NASA Astrophysics Data System (ADS)

Meis, C.; Dahoo, P. R.

2017-12-01

The vector potential function {\\overrightarrow{α }}kλ (\\overrightarrow{r},t) for a k-mode and λ-polarization photon, with the quantized amplitude α 0k (ω k ) = ξω k , satisfies the classical wave propagation equation as well as the Schrodinger’s equation with the relativistic massless Hamiltonian \\mathop{H}\\limits∼ =-i\\hslash c\\overrightarrow{\

Floating-point system quantization errors in digital control systems

NASA Technical Reports Server (NTRS)

Phillips, C. L.; Vallely, D. P.

1978-01-01

This paper considers digital controllers (filters) operating in floating-point arithmetic in either open-loop or closed-loop systems. A quantization error analysis technique is developed, and is implemented by a digital computer program that is based on a digital simulation of the system. The program can be integrated into existing digital simulations of a system.

Investigating Students' Mental Models about the Quantization of Light, Energy, and Angular Momentum

ERIC Educational Resources Information Center

Didis, Nilüfer; Eryilmaz, Ali; Erkoç, Sakir

2014-01-01

This paper is the first part of a multiphase study examining students' mental models about the quantization of physical observables--light, energy, and angular momentum. Thirty-one second-year physics and physics education college students who were taking a modern physics course participated in the study. The qualitative analysis of data revealed…

Phase-Quantized Block Noncoherent Communication

DTIC Science & Technology

2013-07-01

2828 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 61, NO. 7, JULY 2013 Phase-Quantized Block Noncoherent Communication Jaspreet Singh and Upamanyu...in a carrier asynchronous system. Specifically, we consider transmission over the block noncoherent additive white Gaussian noise channel, and...block noncoherent channel. Several results, based on the symmetry inherent in the channel model, are provided to characterize this transition density

Tachyon field in loop quantum cosmology: An example of traversable singularity

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

Li Lifang; Zhu Jianyang

2009-06-15

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. But LQC has an ambiguity about the quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)] proposed a new quantization scheme. Similar to others, this new quantization scheme also replaces the big bang singularity with the quantum bounce. More interestingly, it introduces a quantum singularity, which is traversable. We investigate this novel dynamics quantitatively with a tachyon scalar field, which gives us a concrete example. Our result shows that our universe can evolve through the quantum singularity regularly,more » which is different from the classical big bang singularity. So this singularity is only a weak singularity.« less

Quantized magnetoresistance in atomic-size contacts.

PubMed

Sokolov, Andrei; Zhang, Chunjuan; Tsymbal, Evgeny Y; Redepenning, Jody; Doudin, Bernard

2007-03-01

When the dimensions of a metallic conductor are reduced so that they become comparable to the de Broglie wavelengths of the conduction electrons, the absence of scattering results in ballistic electron transport and the conductance becomes quantized. In ferromagnetic metals, the spin angular momentum of the electrons results in spin-dependent conductance quantization and various unusual magnetoresistive phenomena. Theorists have predicted a related phenomenon known as ballistic anisotropic magnetoresistance (BAMR). Here we report the first experimental evidence for BAMR by observing a stepwise variation in the ballistic conductance of cobalt nanocontacts as the direction of an applied magnetic field is varied. Our results show that BAMR can be positive and negative, and exhibits symmetric and asymmetric angular dependences, consistent with theoretical predictions.

Obliquely propagating ion acoustic solitary structures in the presence of quantized magnetic field

NASA Astrophysics Data System (ADS)

Iqbal Shaukat, Muzzamal

2017-10-01

The effect of linear and nonlinear propagation of electrostatic waves have been studied in degenerate magnetoplasma taking into account the effect of electron trapping and finite temperature with quantizing magnetic field. The formation of solitary structures has been investigated by employing the small amplitude approximation both for fully and partially degenerate quantum plasma. It is observed that the inclusion of quantizing magnetic field significantly affects the propagation characteristics of the solitary wave. Importantly, the Zakharov-Kuznetsov equation under consideration has been found to allow the formation of compressive solitary structures only. The present investigation may be beneficial to understand the propagation of nonlinear electrostatic structures in dense astrophysical environments such as those found in white dwarfs.

There are many ways to spin a photon: Half-quantization of a total optical angular momentum

PubMed Central

Ballantine, Kyle E.; Donegan, John F.; Eastham, Paul R.

2016-01-01

The angular momentum of light plays an important role in many areas, from optical trapping to quantum information. In the usual three-dimensional setting, the angular momentum quantum numbers of the photon are integers, in units of the Planck constant ħ. We show that, in reduced dimensions, photons can have a half-integer total angular momentum. We identify a new form of total angular momentum, carried by beams of light, comprising an unequal mixture of spin and orbital contributions. We demonstrate the half-integer quantization of this total angular momentum using noise measurements. We conclude that for light, as is known for electrons, reduced dimensionality allows new forms of quantization. PMID:28861467

Third Quantization and Quantum Universes

NASA Astrophysics Data System (ADS)

Kim, Sang Pyo

2014-01-01

We study the third quantization of the Friedmann-Robertson-Walker cosmology with N-minimal massless fields. The third quantized Hamiltonian for the Wheeler-DeWitt equation in the minisuperspace consists of infinite number of intrinsic time-dependent, decoupled oscillators. The Hamiltonian has a pair of invariant operators for each universe with conserved momenta of the fields that play a role of the annihilation and the creation operators and that construct various quantum states for the universe. The closed universe exhibits an interesting feature of transitions from stable states to tachyonic states depending on the conserved momenta of the fields. In the classical forbidden unstable regime, the quantum states have googolplex growing position and conjugate momentum dispersions, which defy any measurements of the position of the universe.

Validation of a quantized-current source with 0.2 ppm uncertainty

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

Stein, Friederike; Fricke, Lukas, E-mail: lukas.fricke@ptb.de; Scherer, Hansjörg

2015-09-07

We report on high-accuracy measurements of quantized current, sourced by a tunable-barrier single-electron pump at frequencies f up to 1 GHz. The measurements were performed with an ultrastable picoammeter instrument, traceable to the Josephson and quantum Hall effects. Current quantization according to I = ef with e being the elementary charge was confirmed at f = 545 MHz with a total relative uncertainty of 0.2 ppm, improving the state of the art by about a factor of 5. The accuracy of a possible future quantum current standard based on single-electron transport was experimentally validated to be better than the best (indirect) realization of the ampere within themore » present SI.« less

Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state

DOE PAGES

Wang, Jing; Lian, Biao; Qi, Xiao-Liang; ...

2015-08-10

The topological magnetoelectric effect in a three-dimensional topological insulator is a novel phenomenon, where an electric field induces a magnetic field in the same direction, with a universal coefficient of proportionality quantized in units of $e²/2h$. Here in this paper, we propose that the topological magnetoelectric effect can be realized in the zero-plateau quantum anomalous Hall state of magnetic topological insulators or a ferromagnet-topological insulator heterostructure. The finite-size effect is also studied numerically, where the magnetoelectric coefficient is shown to converge to a quantized value when the thickness of the topological insulator film increases. We further propose a device setupmore » to eliminate nontopological contributions from the side surface.« less

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Revisiting Interpretation of Canonical Correlation Analysis: A Tutorial and Demonstration of Canonical Commonality Analysis

ERIC Educational Resources Information Center

Nimon, Kim; Henson, Robin K.; Gates, Michael S.

2010-01-01

In the face of multicollinearity, researchers face challenges interpreting canonical correlation analysis (CCA) results. Although standardized function and structure coefficients provide insight into the canonical variates produced, they fall short when researchers want to fully report canonical effects. This article revisits the interpretation of…

Are Neoclassical Canons Valid for Southern Chinese Faces?

PubMed Central

Jayaratne, Yasas S. N.; Deutsch, Curtis K.; McGrath, Colman P. J.; Zwahlen, Roger A.

2012-01-01

Background Proportions derived from neoclassical canons, initially described by Renaissance sculptors and painters, are still being employed as aesthetic guidelines during the clinical assessment of the facial morphology. Objective 1. to determine the applicability of neoclassical canons for Southern Chinese faces and 2. to explore gender differences in relation to the applicability of the neoclassical canons and their variants. Methodology 3-D photographs acquired from 103 young adults (51 males and 52 females) without facial dysmorphology were used to test applicability of four neoclassical canons. Standard anthropometric measurements that determine the facial canons were made on these 3-D images. The validity of the canons as well as their different variants were quantified. Principal Findings The neoclassical cannons seldom applied to these individuals, and facial three-section and orbital canons did not apply at all. The orbitonasal canon was most frequently applicable, with a frequency of 19%. Significant sexual dimorphism was found relative to the prevalence of the variants of facial three-section and orbitonasal canons. Conclusion The neoclassical canons did not appear to apply to our sample when rigorous quantitative measurements were employed. Thus, they should not be used as esthetic goals for craniofacial surgical interventions. PMID:23285105

Generalized Ehrenfest Relations, Deformation Quantization, and the Geometry of Inter-model Reduction

NASA Astrophysics Data System (ADS)

Rosaler, Joshua

2018-03-01

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum-classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit \\hbar → 0, and, on the other, a certain generalization of Ehrenfest's Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models.

Quantum state of the multiverse

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

Robles-Perez, Salvador; Gonzalez-Diaz, Pedro F.

2010-04-15

A third quantization formalism is applied to a simplified multiverse scenario. A well-defined quantum state of the multiverse is obtained which agrees with standard boundary condition proposals. These states are found to be squeezed, and related to accelerating universes: they share similar properties to those obtained previously by Grishchuk and Siderov. We also comment on related works that have criticized the third quantization approach.

Hadron Spectra, Decays and Scattering Properties Within Basis Light Front Quantization

NASA Astrophysics Data System (ADS)

Vary, James P.; Adhikari, Lekha; Chen, Guangyao; Jia, Shaoyang; Li, Meijian; Li, Yang; Maris, Pieter; Qian, Wenyang; Spence, John R.; Tang, Shuo; Tuchin, Kirill; Yu, Anji; Zhao, Xingbo

2018-07-01

We survey recent progress in calculating properties of the electron and hadrons within the basis light front quantization (BLFQ) approach. We include applications to electromagnetic and strong scattering processes in relativistic heavy ion collisions. We present an initial investigation into the glueball states by applying BLFQ with multigluon sectors, introducing future research possibilities on multi-quark and multi-gluon systems.

Multispectral data compression through transform coding and block quantization

NASA Technical Reports Server (NTRS)

Ready, P. J.; Wintz, P. A.

1972-01-01

Transform coding and block quantization techniques are applied to multispectral aircraft scanner data, and digitized satellite imagery. The multispectral source is defined and an appropriate mathematical model proposed. The Karhunen-Loeve, Fourier, and Hadamard encoders are considered and are compared to the rate distortion function for the equivalent Gaussian source and to the performance of the single sample PCM encoder.

Justification of Fuzzy Declustering Vector Quantization Modeling in Classification of Genotype-Image Phenotypes

NASA Astrophysics Data System (ADS)

Ng, Theam Foo; Pham, Tuan D.; Zhou, Xiaobo

2010-01-01

With the fast development of multi-dimensional data compression and pattern classification techniques, vector quantization (VQ) has become a system that allows large reduction of data storage and computational effort. One of the most recent VQ techniques that handle the poor estimation of vector centroids due to biased data from undersampling is to use fuzzy declustering-based vector quantization (FDVQ) technique. Therefore, in this paper, we are motivated to propose a justification of FDVQ based hidden Markov model (HMM) for investigating its effectiveness and efficiency in classification of genotype-image phenotypes. The performance evaluation and comparison of the recognition accuracy between a proposed FDVQ based HMM (FDVQ-HMM) and a well-known LBG (Linde, Buzo, Gray) vector quantization based HMM (LBG-HMM) will be carried out. The experimental results show that the performances of both FDVQ-HMM and LBG-HMM are almost similar. Finally, we have justified the competitiveness of FDVQ-HMM in classification of cellular phenotype image database by using hypotheses t-test. As a result, we have validated that the FDVQ algorithm is a robust and an efficient classification technique in the application of RNAi genome-wide screening image data.

Quantized Self-Assembly of Discotic Rings in a Liquid Crystal Confined in Nanopores

NASA Astrophysics Data System (ADS)

Sentker, Kathrin; Zantop, Arne W.; Lippmann, Milena; Hofmann, Tommy; Seeck, Oliver H.; Kityk, Andriy V.; Yildirim, Arda; Schönhals, Andreas; Mazza, Marco G.; Huber, Patrick

2018-02-01

Disklike molecules with aromatic cores spontaneously stack up in linear columns with high, one-dimensional charge carrier mobilities along the columnar axes, making them prominent model systems for functional, self-organized matter. We show by high-resolution optical birefringence and synchrotron-based x-ray diffraction that confining a thermotropic discotic liquid crystal in cylindrical nanopores induces a quantized formation of annular layers consisting of concentric circular bent columns, unknown in the bulk state. Starting from the walls this ring self-assembly propagates layer by layer towards the pore center in the supercooled domain of the bulk isotropic-columnar transition and thus allows one to switch on and off reversibly single, nanosized rings through small temperature variations. By establishing a Gibbs free energy phase diagram we trace the phase transition quantization to the discreteness of the layers' excess bend deformation energies in comparison to the thermal energy, even for this near room-temperature system. Monte Carlo simulations yielding spatially resolved nematic order parameters, density maps, and bond-orientational order parameters corroborate the universality and robustness of the confinement-induced columnar ring formation as well as its quantized nature.

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.

Three-dimensional facial analyses of Indian and Malaysian women.

PubMed

Kusugal, Preethi; Ruttonji, Zarir; Gowda, Roopa; Rajpurohit, Ladusingh; Lad, Pritam; Ritu

2015-01-01

Facial measurements serve as a valuable tool in the treatment planning of maxillofacial rehabilitation, orthodontic treatment, and orthognathic surgeries. The esthetic guidelines of face are still based on neoclassical canons, which were used in the ancient art. These canons are considered to be highly subjective, and there is ample evidence in the literature, which raises such questions as whether or not these canons can be applied for the modern population. This study was carried out to analyze the facial features of Indian and Malaysian women by using three-dimensional (3D) scanner and thus determine the prevalence of neoclassical facial esthetic canons in both the groups. The study was carried out on 60 women in the age range of 18-25 years, out of whom 30 were Indian and 30 Malaysian. As many as 16 facial measurements were taken by using a noncontact 3D scanner. Unpaired t-test was used for comparison of facial measurements between Indian and Malaysian females. Two-tailed Fisher exact test was used to determine the prevalence of neoclassical canons. Orbital Canon was prevalent in 80% of Malaysian women; the same was found only in 16% of Indian women (P = 0.00013). About 43% of Malaysian women exhibited orbitonasal canon (P = 0.0470) whereas nasoaural canon was prevalent in 73% of Malaysian and 33% of Indian women (P = 0.0068). Orbital, orbitonasal, and nasoaural canon were more prevalent in Malaysian women. Facial profile canon, nasooral, and nasofacial canons were not seen in either group. Though some canons provide guidelines in esthetic analyses of face, complete reliance on these canons is not justifiable.

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.

Subband directional vector quantization in radiological image compression

NASA Astrophysics Data System (ADS)

Akrout, Nabil M.; Diab, Chaouki; Prost, Remy; Goutte, Robert; Amiel, Michel

1992-05-01

The aim of this paper is to propose a new scheme for image compression. The method is very efficient for images which have directional edges such as the tree-like structure of the coronary vessels in digital angiograms. This method involves two steps. First, the original image is decomposed at different resolution levels using a pyramidal subband decomposition scheme. For decomposition/reconstruction of the image, free of aliasing and boundary errors, we use an ideal band-pass filter bank implemented in the Discrete Cosine Transform domain (DCT). Second, the high-frequency subbands are vector quantized using a multiresolution codebook with vertical and horizontal codewords which take into account the edge orientation of each subband. The proposed method reduces the blocking effect encountered at low bit rates in conventional vector quantization.

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.

The electronic structure of Au25 clusters: between discrete and continuous.

PubMed

Katsiev, Khabiboulakh; Lozova, Nataliya; Wang, Lu; Sai Krishna, Katla; Li, Ruipeng; Mei, Wai-Ning; Skrabalak, Sara E; Kumar, Challa S S R; Losovyj, Yaroslav

2016-08-21

Here, an approach based on synchrotron resonant photoemission is employed to explore the transition between quantization and hybridization of the electronic structure in atomically precise ligand-stabilized nanoparticles. While the presence of ligands maintains quantization in Au25 clusters, their removal renders increased hybridization of the electronic states in the vicinity of the Fermi level. These observations are supported by DFT studies.

The Analysis of Design of Robust Nonlinear Estimators and Robust Signal Coding Schemes.

DTIC Science & Technology

1982-09-16

b - )’/ 12. between uniform and nonuniform quantizers. For the nonuni- Proof: If b - acca then form quantizer we can expect the mean-square error to...in the window greater than or equal to the value at We define f7 ’(s) as the n-times filtered signal p + 1; consequently, point p + 1 is the median and

Index theorem for non-supersymmetric fermions coupled to a non-Abelian string and electric charge quantization

NASA Astrophysics Data System (ADS)

Shifman, M.; Yung, A.

2018-03-01

Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U(N). We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial N dependence.

Course 4: Anyons

NASA Astrophysics Data System (ADS)

Myrheim, J.

Contents 1 Introduction 1.1 The concept of particle statistics 1.2 Statistical mechanics and the many-body problem 1.3 Experimental physics in two dimensions 1.4 The algebraic approach: Heisenberg quantization 1.5 More general quantizations 2 The configuration space 2.1 The Euclidean relative space for two particles 2.2 Dimensions d=1,2,3 2.3 Homotopy 2.4 The braid group 3 Schroedinger quantization in one dimension 4 Heisenberg quantization in one dimension 4.1 The coordinate representation 5 Schroedinger quantization in dimension d ≥ 2 5.1 Scalar wave functions 5.2 Homotopy 5.3 Interchange phases 5.4 The statistics vector potential 5.5 The N-particle case 5.6 Chern-Simons theory 6 The Feynman path integral for anyons 6.1 Eigenstates for position and momentum 6.2 The path integral 6.3 Conjugation classes in SN 6.4 The non-interacting case 6.5 Duality of Feynman and Schroedinger quantization 7 The harmonic oscillator 7.1 The two-dimensional harmonic oscillator 7.2 Two anyons in a harmonic oscillator potential 7.3 More than two anyons 7.4 The three-anyon problem 8 The anyon gas 8.1 The cluster and virial expansions 8.2 First and second order perturbative results 8.3 Regularization by periodic boundary conditions 8.4 Regularization by a harmonic oscillator potential 8.5 Bosons and fermions 8.6 Two anyons 8.7 Three anyons 8.8 The Monte Carlo method 8.9 The path integral representation of the coefficients GP 8.10 Exact and approximate polynomials 8.11 The fourth virial coefficient of anyons 8.12 Two polynomial theorems 9 Charged particles in a constant magnetic field 9.1 One particle in a magnetic field 9.2 Two anyons in a magnetic field 9.3 The anyon gas in a magnetic field 10 Interchange phases and geometric phases 10.1 Introduction to geometric phases 10.2 One particle in a magnetic field 10.3 Two particles in a magnetic field 10.4 Interchange of two anyons in potential wells 10.5 Laughlin's theory of the fractional quantum Hall effect

Can The Periods of Some Extra-Solar Planetary Systems be Quantized?

NASA Astrophysics Data System (ADS)

El Fady Morcos, Abd

A simple formula was derived before by Morcos (2013 ), to relate the quantum numbers of planetary systems and their periods. This formula is applicable perfectly for the solar system planets, and some extra-solar planets , of stars of approximately the same masses like the Sun. This formula has been used to estimate the periods of some extra-solar planet of known quantum numbers. The used quantum numbers were calculated previously by other authors. A comparison between the observed and estimated periods, from the given formula has been done. The differences between the observed and calculated periods for the extra-solar systems have been calculated and tabulated. It is found that there is an error of the range of 10% The same formula has been also used to find the quantum numbers, of some known periods, exo-planet. Keywords: Quantization; Periods; Extra-Planetary; Extra-Solar Planet REFERENCES [1] Agnese, A. G. and Festa, R. “Discretization on the Cosmic Scale Inspirred from the Old Quantum Mechanics,” 1998. http://arxiv.org/abs/astro-ph/9807186 [2] Agnese, A. G. and Festa, R. “Discretizing ups-Andro- medae Planetary System,” 1999. http://arxiv.org/abs/astro-ph/9910534. [3] Barnothy, J. M. “The Stability of the Solar Systemand of Small Stellar Systems,” Proceedings of the IAU Sympo-sium 62, Warsaw, 5-8 September 1973, pp. 23-31. [4] Morcos, A.B. , “Confrontation between Quantized Periods of Some Extra-Solar Planetary Systems and Observations”, International Journal of Astronomy and Astrophysics, 2013, 3, 28-32. [5] Nottale, L. “Fractal Space-Time and Microphysics, To-wards a Theory of Scale Relativity,” World Scientific, London, 1994. [6] Nottale , L., “Scale-Relativity and Quantization of Extra- Solar Planetary Systems,” Astronomy & Astrophysics, Vol. 315, 1996, pp. L9-L12 [7] Nottale, L., Schumacher, G. and Gay, J. “Scale-Relativity and Quantization of the Solar Systems,” Astronomy & Astrophysics letters, Vol. 322, 1997, pp. 1018-10 [8]Nottale, L. “Scale-Relativity and Quantization of Exo- planet Orbital Semi-Major Axes,” Astronomy & Astro- physics, Vol. 361, 2000, pp. 379-387.

Bit Grooming: statistically accurate precision-preserving quantization with compression, evaluated in the netCDF Operators (NCO, v4.4.8+)

NASA Astrophysics Data System (ADS)

Zender, Charles S.

2016-09-01

Geoscientific models and measurements generate false precision (scientifically meaningless data bits) that wastes storage space. False precision can mislead (by implying noise is signal) and be scientifically pointless, especially for measurements. By contrast, lossy compression can be both economical (save space) and heuristic (clarify data limitations) without compromising the scientific integrity of data. Data quantization can thus be appropriate regardless of whether space limitations are a concern. We introduce, implement, and characterize a new lossy compression scheme suitable for IEEE floating-point data. Our new Bit Grooming algorithm alternately shaves (to zero) and sets (to one) the least significant bits of consecutive values to preserve a desired precision. This is a symmetric, two-sided variant of an algorithm sometimes called Bit Shaving that quantizes values solely by zeroing bits. Our variation eliminates the artificial low bias produced by always zeroing bits, and makes Bit Grooming more suitable for arrays and multi-dimensional fields whose mean statistics are important. Bit Grooming relies on standard lossless compression to achieve the actual reduction in storage space, so we tested Bit Grooming by applying the DEFLATE compression algorithm to bit-groomed and full-precision climate data stored in netCDF3, netCDF4, HDF4, and HDF5 formats. Bit Grooming reduces the storage space required by initially uncompressed and compressed climate data by 25-80 and 5-65 %, respectively, for single-precision values (the most common case for climate data) quantized to retain 1-5 decimal digits of precision. The potential reduction is greater for double-precision datasets. When used aggressively (i.e., preserving only 1-2 digits), Bit Grooming produces storage reductions comparable to other quantization techniques such as Linear Packing. Unlike Linear Packing, whose guaranteed precision rapidly degrades within the relatively narrow dynamic range of values that it can compress, Bit Grooming guarantees the specified precision throughout the full floating-point range. Data quantization by Bit Grooming is irreversible (i.e., lossy) yet transparent, meaning that no extra processing is required by data users/readers. Hence Bit Grooming can easily reduce data storage volume without sacrificing scientific precision or imposing extra burdens on users.

A model of individualized canonical microcircuits supporting cognitive operations

PubMed Central

Peterson, Andre D. H.; Haueisen, Jens; Knösche, Thomas R.

2017-01-01

Major cognitive functions such as language, memory, and decision-making are thought to rely on distributed networks of a large number of basic elements, called canonical microcircuits. In this theoretical study we propose a novel canonical microcircuit model and find that it supports two basic computational operations: a gating mechanism and working memory. By means of bifurcation analysis we systematically investigate the dynamical behavior of the canonical microcircuit with respect to parameters that govern the local network balance, that is, the relationship between excitation and inhibition, and key intrinsic feedback architectures of canonical microcircuits. We relate the local behavior of the canonical microcircuit to cognitive processing and demonstrate how a network of interacting canonical microcircuits enables the establishment of spatiotemporal sequences in the context of syntax parsing during sentence comprehension. This study provides a framework for using individualized canonical microcircuits for the construction of biologically realistic networks supporting cognitive operations. PMID:29200435

Canonical Word Order of Japanese Ditransitive Sentences: A Preliminary Investigation through a Grammaticality Judgment Survey

ERIC Educational Resources Information Center

Shigenaga, Yasumasa

2014-01-01

There have been three competing analyses regarding the canonical word order of Japanese ditransitive sentences: a) "S-'ga' IO-'ni' DO-'o' V" is the canonical word order rather than "S-'ga' DO-'o' IO-'ni' V", b) both word orders are canonical, and c) the canonical word order depends on the type of the verb. The present study…

Non-canonical autophagy: an exception or an underestimated form of autophagy?

PubMed

Scarlatti, Francesca; Maffei, Roberta; Beau, Isabelle; Ghidoni, Riccardo; Codogno, Patrice

2008-11-01

Macroautophagy (hereafter called autophagy) is a dynamic and evolutionarily conserved process used to sequester and degrade cytoplasm and entire organelles in a sequestering vesicle with a double membrane, known as the autophagosome, which ultimately fuses with a lysosome to degrade its autophagic cargo. Recently, we have unraveled two distinct forms of autophagy in cancer cells, which we term canonical and non-canonical autophagy. In contrast to classical or canonical autophagy, non-canonical autophagy is a process that does not require the entire set of autophagy-related (Atg) proteins in particular Beclin 1, to form the autophagosome. Non-canonical autophagy is therefore not blocked by the knockdown of Beclin 1 or of its binding partner hVps34. Moreover overexpression of Bcl-2, which is known to block canonical starvation-induced autophagy by binding to Beclin 1, is unable to reverse the non-canonical autophagy triggered by the polyphenol resveratrol in the breast cancer MCF-7 cell line. In MCF-7 cells, at least, non-canonical autophagy is involved in the caspase-independent cell death induced by resveratrol.

Dynamical Principles of Emotion-Cognition Interaction: Mathematical Images of Mental Disorders

PubMed Central

Rabinovich, Mikhail I.; Muezzinoglu, Mehmet K.; Strigo, Irina; Bystritsky, Alexander

2010-01-01

The key contribution of this work is to introduce a mathematical framework to understand self-organized dynamics in the brain that can explain certain aspects of itinerant behavior. Specifically, we introduce a model based upon the coupling of generalized Lotka-Volterra systems. This coupling is based upon competition for common resources. The system can be regarded as a normal or canonical form for any distributed system that shows self-organized dynamics that entail winnerless competition. Crucially, we will show that some of the fundamental instabilities that arise in these coupled systems are remarkably similar to endogenous activity seen in the brain (using EEG and fMRI). Furthermore, by changing a small subset of the system's parameters we can produce bifurcations and metastable sequential dynamics changing, which bear a remarkable similarity to pathological brain states seen in psychiatry. In what follows, we will consider the coupling of two macroscopic modes of brain activity, which, in a purely descriptive fashion, we will label as cognitive and emotional modes. Our aim is to examine the dynamical structures that emerge when coupling these two modes and relate them tentatively to brain activity in normal and non-normal states. PMID:20877723

Collective behaviour of dislocations in a finite medium

NASA Astrophysics Data System (ADS)

Kooiman, M.; Hütter, M.; Geers, M. G. D.

2014-04-01

We derive the grand-canonical partition function of straight and parallel dislocation lines without making a priori assumptions on the temperature regime. Such a systematic derivation for dislocations has, to the best of our knowledge, not been carried out before, and several conflicting assumptions on the free energy of dislocations have been made in the literature. Dislocations have gained interest as they are the carriers of plastic deformation in crystalline materials and solid polymers, and they constitute a prototype system for two-dimensional Coulomb particles. Our microscopic starting level is the description of dislocations as used in the discrete dislocation dynamics (DDD) framework. The macroscopic level of interest is characterized by the temperature, the boundary deformation and the dislocation density profile. By integrating over state space, we obtain a field theoretic partition function, which is a functional integral of the Boltzmann weight over an auxiliary field. The Hamiltonian consists of a term quadratic in the field and an exponential of this field. The partition function is strongly non-local, and reduces in special cases to the sine-Gordon model. Moreover, we determine implicit expressions for the response functions and the dominant scaling regime for metals, namely the low-temperature regime.

Nanotextured phase coexistence in the correlated insulator V2O3

NASA Astrophysics Data System (ADS)

McLeod, Alexander

The Mott insulator-metal transition remains among the most studied phenomena in correlated electron physics. However, the formation of spontaneous spatial patterns amidst coexisting insulating and metallic phases remains poorly explored on the meso- and nanoscales. Here we present real-space evolution of the insulator-metal transition in a thin film of V2O3, the ``canonical'' Mott insulator, imaged at high spatial resolution by cryogenic near-field infrared microscopy. We resolve spontaneously nanotextured coexistence of metal and correlated Mott insulator phases near the insulator-metal transition (T = 160-180 K) associated with percolation and an underlying structural phase transition. Augmented with macroscopic temperature-resolved X-ray diffraction measurements of the same film, a quantitative analysis of nano-infrared images acquired across the transition suggests decoupling of electronic and structural transformations. Persistent low-temperature metallicity is accompanied by unconventional dimensional scaling among metallic ``puddles,'' implicating relevance of a long-range Coulombic interaction through the film's first-order insulator-metal transition. The speaker and co-authors acknowledge support from DOE-DE-SC0012375, DOE-DE-SC0012592, and AFOSR Grant No. FA9550-12-1-0381. The speaker also acknowledges support from a US Dept. of Energy Office of Science Graduate Fellowship (DOE SCGF).

Dynamical principles of emotion-cognition interaction: mathematical images of mental disorders.

PubMed

Rabinovich, Mikhail I; Muezzinoglu, Mehmet K; Strigo, Irina; Bystritsky, Alexander

2010-09-21

The key contribution of this work is to introduce a mathematical framework to understand self-organized dynamics in the brain that can explain certain aspects of itinerant behavior. Specifically, we introduce a model based upon the coupling of generalized Lotka-Volterra systems. This coupling is based upon competition for common resources. The system can be regarded as a normal or canonical form for any distributed system that shows self-organized dynamics that entail winnerless competition. Crucially, we will show that some of the fundamental instabilities that arise in these coupled systems are remarkably similar to endogenous activity seen in the brain (using EEG and fMRI). Furthermore, by changing a small subset of the system's parameters we can produce bifurcations and metastable sequential dynamics changing, which bear a remarkable similarity to pathological brain states seen in psychiatry. In what follows, we will consider the coupling of two macroscopic modes of brain activity, which, in a purely descriptive fashion, we will label as cognitive and emotional modes. Our aim is to examine the dynamical structures that emerge when coupling these two modes and relate them tentatively to brain activity in normal and non-normal states.

Thermodynamics of single polyethylene and polybutylene glycols with hydrogen-bonding ends: A transition from looped to open conformations

NASA Astrophysics Data System (ADS)

Lee, Eunsang; Paul, Wolfgang

2018-02-01

A variety of linear polymer precursors with hydrogen bonding motifs at both ends enable us to design supramolecular polymer systems with tailored macroscopic properties including self-healing. In this study, we investigate thermodynamic properties of single polyethylene and polybutylene glycols with hydrogen bonding motifs. In this context, we first build a coarse-grained model of building blocks of the supramolecular polymer system based on all-atom molecular structures. The density of states of the single precursor is obtained using the stochastic approximation Monte Carlo method. Constructing canonical partition functions from the density of states, we find the transition from looped to open conformations at transition temperatures which are non-monotonously changing with an increasing degree of polymerization due to the competition between chain stiffness and loop-forming entropy penalty. In the complete range of chain length under investigation, a coexistence of the looped and open morphologies at the transition temperature is shown regardless of whether the transition is first-order-like or continuous. Polyethylene and polybutylene glycols show similar behavior in all the thermodynamic properties but the transition temperature of the more flexible polybutylene glycol is shown to change more gradually.

Second quantization in bit-string physics

NASA Technical Reports Server (NTRS)

Noyes, H. Pierre

1993-01-01

Using a new fundamental theory based on bit-strings, a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/mc along the forward and backward light cones executed at velocity +/- c are derived. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of radiation, these solutions are analogous to a fermion propagator in a second quantized theory. This allows us to interpret the mass parameter in the step length as the physical mass of the free particle. The radiation in interaction with it has the usual harmonic oscillator structure of a second quantized theory. How these free particle masses can be generated gravitationally using the combinatorial hierarchy sequence (3,10,137,2(sup 127) + 136), and some of the predictive consequences are sketched.

Effect of signal intensity and camera quantization on laser speckle contrast analysis

PubMed Central

Song, Lipei; Elson, Daniel S.

2012-01-01

Laser speckle contrast analysis (LASCA) is limited to being a qualitative method for the measurement of blood flow and tissue perfusion as it is sensitive to the measurement configuration. The signal intensity is one of the parameters that can affect the contrast values due to the quantization of the signals by the camera and analog-to-digital converter (ADC). In this paper we deduce the theoretical relationship between signal intensity and contrast values based on the probability density function (PDF) of the speckle pattern and simplify it to a rational function. A simple method to correct this contrast error is suggested. The experimental results demonstrate that this relationship can effectively compensate the bias in contrast values induced by the quantized signal intensity and correct for bias induced by signal intensity variations across the field of view. PMID:23304650

Symmetries and Invariants of Twisted Quantum Algebras and Associated Poisson Algebras

NASA Astrophysics Data System (ADS)

Molev, A. I.; Ragoucy, E.

We construct an action of the braid group BN on the twisted quantized enveloping algebra U q'( {o}N) where the elements of BN act as automorphisms. In the classical limit q → 1, we recover the action of BN on the polynomial functions on the space of upper triangular matrices with ones on the diagonal. The action preserves the Poisson bracket on the space of polynomials which was introduced by Nelson and Regge in their study of quantum gravity and rediscovered in the mathematical literature. Furthermore, we construct a Poisson bracket on the space of polynomials associated with another twisted quantized enveloping algebra U q'( {sp}2n). We use the Casimir elements of both twisted quantized enveloping algebras to reproduce and construct some well-known and new polynomial invariants of the corresponding Poisson algebras.

Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control.

PubMed

Zhang, Wanli; Yang, Shiju; Li, Chuandong; Zhang, Wei; Yang, Xinsong

2018-08-01

This paper focuses on stochastic exponential synchronization of delayed memristive neural networks (MNNs) by the aid of systems with interval parameters which are established by using the concept of Filippov solution. New intermittent controller and adaptive controller with logarithmic quantization are structured to deal with the difficulties induced by time-varying delays, interval parameters as well as stochastic perturbations, simultaneously. Moreover, not only control cost can be reduced but also communication channels and bandwidth are saved by using these controllers. Based on novel Lyapunov functions and new analytical methods, several synchronization criteria are established to realize the exponential synchronization of MNNs with stochastic perturbations via intermittent control and adaptive control with or without logarithmic quantization. Finally, numerical simulations are offered to substantiate our theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Measurement analysis and quantum gravity

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

Albers, Mark; Kiefer, Claus; Reginatto, Marcel

2008-09-15

We consider the question of whether consistency arguments based on measurement theory show that the gravitational field must be quantized. Motivated by the argument of Eppley and Hannah, we apply a DeWitt-type measurement analysis to a coupled system that consists of a gravitational wave interacting with a mass cube. We also review the arguments of Eppley and Hannah and of DeWitt, and investigate a second model in which a gravitational wave interacts with a quantized scalar field. We argue that one cannot conclude from the existing gedanken experiments that gravity has to be quantized. Despite the many physical arguments whichmore » speak in favor of a quantum theory of gravity, it appears that the justification for such a theory must be based on empirical tests and does not follow from logical arguments alone.« less

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

Topological insulators have been proposed to be best characterized as bulk magnetoelectric materials that show response functions quantized in terms of fundamental physical constants. Here, we lower the chemical potential of three-dimensional (3D) Bi2Se3 films to ~30 meV above the Dirac point and probe their low-energy electrodynamic response in the presence of magnetic fields with high-precision time-domain terahertz polarimetry. For fields higher than 5 tesla, we observed quantized Faraday and Kerr rotations, whereas the dc transport is still semiclassical. A nontrivial Berry’s phase offset to these values gives evidence for axion electrodynamics and the topological magnetoelectric effect. The time structure used in these measurements allows a direct measure of the fine-structure constant based on a topological invariant of a solid-state system.

Mass quantization of the Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Vaz, Cenalo; Witten, Louis

1999-07-01

We examine the Wheeler-DeWitt equation for a static, eternal Schwarzschild black hole in Kuchař-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are nonvanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner mass of the black hole according to a relation conjectured long ago by Bekenstein M~nMp. If attention is restricted only to these quantized energy states, a black hole is described not only by its mass but also by its parity. States of indefinite parity do not admit a quantized mass spectrum.

Polymer quantization of the Einstein-Rosen wormhole throat

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

Kunstatter, Gabor; Peltola, Ari; Louko, Jorma

2010-01-15

We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numericalmore » accuracy, the area spectrum obtained from a Schroedinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.« less

Quantized conductance operation near a single-atom point contact in a polymer-based atomic switch

NASA Astrophysics Data System (ADS)

Krishnan, Karthik; Muruganathan, Manoharan; Tsuruoka, Tohru; Mizuta, Hiroshi; Aono, Masakazu

2017-06-01

Highly-controlled conductance quantization is achieved near a single-atom point contact in a redox-based atomic switch device, in which a poly(ethylene oxide) (PEO) film is sandwiched between Ag and Pt electrodes. Current-voltage measurements revealed reproducible quantized conductance of ˜1G 0 for more than 102 continuous voltage sweep cycles under a specific condition, indicating the formation of a well-defined single-atom point contact of Ag in the PEO matrix. The device exhibited a conductance state distribution centered at 1G 0, with distinct half-integer multiples of G 0 and small fractional variations. First-principles density functional theory simulations showed that the experimental observations could be explained by the existence of a tunneling gap and the structural rearrangement of an atomic point contact.

Quantization of the nonlinear sigma model revisited

NASA Astrophysics Data System (ADS)

Nguyen, Timothy

2016-08-01

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the O(N)-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.

Novel properties of the q-analogue quantized radiation field

NASA Technical Reports Server (NTRS)

Nelson, Charles A.

1993-01-01

The 'classical limit' of the q-analog quantized radiation field is studied paralleling conventional quantum optics analyses. The q-generalizations of the phase operator of Susskind and Glogower and that of Pegg and Barnett are constructed. Both generalizations and their associated number-phase uncertainty relations are manifestly q-independent in the n greater than g number basis. However, in the q-coherent state z greater than q basis, the variance of the generic electric field, (delta(E))(sup 2) is found to be increased by a factor lambda(z) where lambda(z) greater than 1 if q not equal to 1. At large amplitudes, the amplitude itself would be quantized if the available resolution of unity for the q-analog coherent states is accepted in the formulation. These consequences are remarkable versus the conventional q = 1 limit.

The graphical brain: Belief propagation and active inference

PubMed Central

Friston, Karl J.; Parr, Thomas; de Vries, Bert

2018-01-01

This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models. Crucially, these models can entertain both discrete and continuous states, leading to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to elucidate the requisite message passing in terms of its form and scheduling. To accommodate mixed generative models (of discrete and continuous states), one also has to consider link nodes or factors that enable discrete and continuous representations to talk to each other. When mapping the implicit computational architecture onto neuronal connectivity, several interesting features emerge. For example, Bayesian model averaging and comparison, which link discrete and continuous states, may be implemented in thalamocortical loops. These and other considerations speak to a computational connectome that is inherently state dependent and self-organizing in ways that yield to a principled (variational) account. We conclude with simulations of reading that illustrate the implicit neuronal message passing, with a special focus on how discrete (semantic) representations inform, and are informed by, continuous (visual) sampling of the sensorium. Author Summary This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models that can entertain both discrete and continuous states. This leads to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to characterize the requisite message passing, and link this formal characterization to canonical microcircuits and extrinsic connectivity in the brain. PMID:29417960

Canonical Correlation: Terms and Descriptions.

ERIC Educational Resources Information Center

Pugh, Richard C.; Hu, Yuehluen

The use of terms to describe and interpret results from canonical correlation analysis has been inconsistent across research studies. This study assembled the terminology related to the use and interpretation of canonical correlation analysis from research articles, textbooks, and computer manuals. Research articles using canonical correlation…

Closed almost-periodic orbits in semiclassical quantization of generic polygons

PubMed

Biswas

2000-05-01

Periodic orbits are the central ingredients of modern semiclassical theories and corrections to these are generally nonclassical in origin. We show here that, for the class of generic polygonal billiards, the corrections are predominantly classical in origin owing to the contributions from closed almost-periodic (CAP) orbit families. Furthermore, CAP orbit families outnumber periodic families but have comparable weights. They are hence indispensable for semiclassical quantization.

Application of Generalized Feynman-Hellmann Theorem in Quantization of LC Circuit in Thermo Bath

NASA Astrophysics Data System (ADS)

Fan, Hong-Yi; Tang, Xu-Bing

For the quantized LC electric circuit, when taking the Joule thermal effect into account, we think that physical observables should be evaluated in the context of ensemble average. We then use the generalized Feynman-Hellmann theorem for ensemble average to calculate them, which seems convenient. Fluctuation of observables in various LC electric circuits in the presence of thermo bath growing with temperature is exhibited.

Symplectic Quantization of a Vector-Tensor Gauge Theory with Topological Coupling

NASA Astrophysics Data System (ADS)

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

We use the symplectic formalism to quantize a gauge theory where vectors and tensors fields are coupled in a topological way. This is an example of reducible theory and a procedure like of ghosts-of-ghosts of the BFV method is applied but in terms of Lagrange multipliers. Our final results are in agreement with the ones found in the literature by using the Dirac method.

Issues in the digital implementation of control compensators. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Moroney, P.

1979-01-01

Techniques developed for the finite-precision implementation of digital filters were used, adapted, and extended for digital feedback compensators, with particular emphasis on steady state, linear-quadratic-Gaussian compensators. Topics covered include: (1) the linear-quadratic-Gaussian problem; (2) compensator structures; (3) architectural issues: serialism, parallelism, and pipelining; (4) finite wordlength effects: quantization noise, quantizing the coefficients, and limit cycles; and (5) the optimization of structures.

Selecting Representative Points in Normal Populations.

DTIC Science & Technology

1983-01-14

where values can be compared. A rather early paper on quantization is by Steinhaus [1956]. In that paper, he demonstrates the two necessary (but not...already noted that Steinhaus lists these two l<i<l conditions. These two necessary conditions for an optimal quantization suggest an iterative...Stanford, California. Steinhaus , H. (1956). Sur la division des corps materiels en parties. Bulletin De L’Academie Polonaise Des Sciences, Cl. III- Vol

Information preserving coding for multispectral data

NASA Technical Reports Server (NTRS)

Duan, J. R.; Wintz, P. A.

1973-01-01

A general formulation of the data compression system is presented. A method of instantaneous expansion of quantization levels by reserving two codewords in the codebook to perform a folding over in quantization is implemented for error free coding of data with incomplete knowledge of the probability density function. Results for simple DPCM with folding and an adaptive transform coding technique followed by a DPCM technique are compared using ERTS-1 data.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

Field quantization and squeezed states generation in resonators with time-dependent parameters

NASA Technical Reports Server (NTRS)

Dodonov, V. V.; Klimov, A. B.; Nikonov, D. E.

1992-01-01

The problem of electromagnetic field quantization is usually considered in textbooks under the assumption that the field occupies some empty box. The case when a nonuniform time-dependent dielectric medium is confined in some space region with time-dependent boundaries is studied. The basis of the subsequent consideration is the system of Maxwell's equations in linear passive time-dependent dielectric and magnetic medium without sources.

Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant

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

Thylwe, Karl-Erik; McCabe, Patrick

2013-05-15

It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov-type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Sommerfeld quantization condition for bound states, and a few particular atomic/ionic and nuclear/hadronic bound-state situations are discussed.

Fedosov Deformation Quantization as a BRST Theory

NASA Astrophysics Data System (ADS)

Grigoriev, M. A.; Lyakhovich, S. L.

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold M is presented as a second class constrained surface in the fibre bundle ?*ρM which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The second class system is converted into the first class one by continuation of the constraints into the extended manifold, being a direct sum of ?*ρM and the tangent bundle TM. This extended manifold is equipped with a nontrivial Poisson bracket which naturally involves two basic ingredients of Fedosov geometry: the symplectic structure and the symplectic connection. The constructed first class constrained theory, being equivalent to the original symplectic manifold, is quantized through the BFV-BRST procedure. The existence theorem is proven for the quantum BRST charge and the quantum BRST invariant observables. The adjoint action of the quantum BRST charge is identified with the Abelian Fedosov connection while any observable, being proven to be a unique BRST invariant continuation for the values defined in the original symplectic manifold, is identified with the Fedosov flat section of the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum BRST invariant observables.

Thermal Counterflow in a Periodic Channel with Solid Boundaries

NASA Astrophysics Data System (ADS)

Baggaley, Andrew W.; Laurie, Jason

2015-01-01

We perform numerical simulations of finite temperature quantum turbulence produced through thermal counterflow in superfluid He, using the vortex filament model. We investigate the effects of solid boundaries along one of the Cartesian directions, assuming a laminar normal fluid with a Poiseuille velocity profile, whilst varying the temperature and the normal fluid velocity. We analyze the distribution of the quantized vortices, reconnection rates, and quantized vorticity production as a function of the wall-normal direction. We find that the quantized vortex lines tend to concentrate close to the solid boundaries with their position depending only on temperature and not on the counterflow velocity. We offer an explanation of this phenomenon by considering the balance of two competing effects, namely the rate of turbulent diffusion of an isotropic tangle near the boundaries and the rate of quantized vorticity production at the center. Moreover, this yields the observed scaling of the position of the peak vortex line density with the mutual friction parameter. Finally, we provide evidence that upon the transition from laminar to turbulent normal fluid flow, there is a dramatic increase in the homogeneity of the tangle, which could be used as an indirect measure of the transition to turbulence in the normal fluid component for experiments.

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.