Intrinsic non-commutativity of closed string theory

DOE PAGES

Freidel, Laurent; Leigh, Robert G.; Minic, Djordje

2017-09-14

We show that the proper interpretation of the cocycle operators appearing in the physical vertex operators of compactified strings is that the closed string target is noncommutative. We track down the appearance of this non-commutativity to the Polyakov action of the at closed string in the presence of translational monodromies (i.e., windings). Here, in view of the unexpected nature of this result, we present detailed calculations from a variety of points of view, including a careful understanding of the consequences of mutual locality in the vertex operator algebra, as well as a detailed analysis of the symplectic structure of themore » Polyakov string. Finally, we also underscore why this non-commutativity was not emphasized previously in the existing literature. This non-commutativity can be thought of as a central extension of the zero-mode operator algebra, an effect set by the string length scale $-$ it is present even in trivial backgrounds. Clearly, this result indicates that the α'→0 limit is more subtle than usually assumed.« less

Intrinsic non-commutativity of closed string theory

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

Freidel, Laurent; Leigh, Robert G.; Minic, Djordje

We show that the proper interpretation of the cocycle operators appearing in the physical vertex operators of compactified strings is that the closed string target is noncommutative. We track down the appearance of this non-commutativity to the Polyakov action of the at closed string in the presence of translational monodromies (i.e., windings). Here, in view of the unexpected nature of this result, we present detailed calculations from a variety of points of view, including a careful understanding of the consequences of mutual locality in the vertex operator algebra, as well as a detailed analysis of the symplectic structure of themore » Polyakov string. Finally, we also underscore why this non-commutativity was not emphasized previously in the existing literature. This non-commutativity can be thought of as a central extension of the zero-mode operator algebra, an effect set by the string length scale $-$ it is present even in trivial backgrounds. Clearly, this result indicates that the α'→0 limit is more subtle than usually assumed.« less

The standard model on non-commutative space-time

NASA Astrophysics Data System (ADS)

Calmet, X.; Jurčo, B.; Schupp, P.; Wess, J.; Wohlgenannt, M.

2002-03-01

We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter θ^{μ ν}. No new particles are introduced; the structure group is SU(3)× SU(2)× U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in θ^{μν} we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered.

Quantum mechanical systems interacting with different polarizations of gravitational waves in noncommutative phase space

NASA Astrophysics Data System (ADS)

Saha, Anirban; Gangopadhyay, Sunandan; Saha, Swarup

2018-02-01

Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase space, a credible possibility of their detection lies in the gravitational wave (GW) detection scenario, where one effectively probes the relative length-scale variations ˜O [10-20-10-23] . With this motivation, we have theoretically constructed how a free particle and a harmonic oscillator will respond to linearly and circularly polarized gravitational waves if their quantum mechanical phase space has a noncommutative structure. We critically analyze the formal solutions which show resonance behavior in the responses of both free particle and HO systems to GW with both kind of polarizations. We discuss the possible implications of these solutions in detecting noncommutativity in a GW detection experiment. We use the currently available upper-bound estimates on various noncommutative parameters to anticipate the relative importance of various terms in the solutions. We also argue how the quantum harmonic oscillator system we considered here can be very relevant in the context of the resonant bar detectors of GW which are already operational.

Fractional conductivity in 2D and 3D crystals

NASA Astrophysics Data System (ADS)

Sidharth, B. G.; Das, Abhishek; Valluri, S. R.

2018-04-01

In this work, we show that the phenomenon of fractional quantum Hall effect can be obtained for 2D and 3D crystal structures, using the noncommutative nature of spacetime and the Lambert W function. This fractional conductivity has been shown to be a consequence of the noncommutative geometry underlying the structure of graphene. Also, it has been shown, for graphene, that in the 3D case the conductivity is extremely small and depends on the self-energy that arises due to random fluctuations or zitterbewegung.

Noncommutative Translations and *-PRODUCT Formalism

NASA Astrophysics Data System (ADS)

Daszkiewicz, Marcin; Lukierski, Jerzy; Woronowicz, Mariusz

2008-09-01

We consider the noncommutative space-times with Lie-algebraic noncommutativity (e.g. κ-deformed Minkowski space). In the framework with classical fields we extend the *-product in order to represent the noncommutative translations in terms of commutative ones. We show the translational invariance of noncommutative bilinear action with local product of noncommutative fields. The quadratic noncommutativity is also briefly discussed.

Probing noncommutative theories with quantum optical experiments

NASA Astrophysics Data System (ADS)

Dey, Sanjib; Bhat, Anha; Momeni, Davood; Faizal, Mir; Ali, Ahmed Farag; Dey, Tarun Kumar; Rehman, Atikur

2017-11-01

One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment.

Dissipative Quantum Mechanics and Kondo-Like Impurities on Noncommutative Two-Tori

NASA Astrophysics Data System (ADS)

Iacomino, Patrizia; Marotta, Vincenzo; Naddeo, Adele

In a recent paper, by exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter θ (in appropriate units), a general one-to-one correspondence between the m-reduced conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings1,2 ν = (m)/(pm+2) and an Abelian noncommutative field theory (NCFT) has been established.3 That allowed us to add new evidence to the relationship between noncommutativity and quantum Hall fluids.4 On the other hand, the m-reduced CFT is equivalent to a system of two massless scalar bosons with a magnetic boundary interaction as introduced in Ref. 5, at the so-called "magic" points. We are then able to describe, within such a framework, the dissipative quantum mechanics of a particle confined to a plane and subject to an external magnetic field normal to it. Here we develop such a point of view by focusing on the case m=2 which corresponds to a quantum Hall bilayer. The key role of a localized impurity which couples the two layers is emphasized and the effect of noncommutativity in terms of generalized magnetic translations (GMT) is fully exploited. As a result, general GMT operators are introduced, in the form of a tensor product, which act on the QHF and defect space respectively, and a comprehensive study of their rich structure is performed.

Nambu sigma model and effective membrane actions

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter

2012-07-01

We propose an effective action for a p‧-brane with open p-branes ending on it. The action has dual descriptions similar to the commutative and non-commutative ones of the DBI action for D-branes and open strings. The Poisson structure governing the non-commutativity of the D-brane is replaced by a Nambu structure and the open-closed string relations are generalized to the case of p-branes utilizing a novel Nambu sigma model description of p-branes. In the case of an M5-brane our action interpolates between M5-actions already proposed in the literature and matrix-model like actions involving Nambu structures.

Composite system in rotationally invariant noncommutative phase space

NASA Astrophysics Data System (ADS)

Gnatenko, Kh. P.; Tkachuk, V. M.

2018-03-01

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on these conditions, the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

Dolan Grady relations and noncommutative quasi-exactly solvable systems

NASA Astrophysics Data System (ADS)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

Phase transition and entropy inequality of noncommutative black holes in a new extended phase space

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

Miao, Yan-Gang; Xu, Zhen-Ming, E-mail: miaoyg@nankai.edu.cn, E-mail: xuzhenm@mail.nankai.edu.cn

We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as the noncommutative pressure . In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former dominates the UV regime while the latter does the IR regime, respectively. In addition, by means of themore » reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.« less

Black hole remnants in Hayward solutions and noncommutative effects

NASA Astrophysics Data System (ADS)

Mehdipour, S. Hamid; Ahmadi, M. H.

2018-01-01

In this paper, we explore the final stages of the black hole evaporation for Hayward solutions. Our results show that the behavior of Hawking's radiation changes considerably at the small radii regime such that the black hole does not evaporate completely and a stable remnant is left. We show that stability conditions hold for the Hayward solutions found in the Einstein gravity coupled with nonlinear electrodynamics. We analyze the effect that an inspired model of the noncommutativity of spacetime can have on the thermodynamics of Hayward spacetimes. This has been done by applying the noncommutative effects to the non-rotating and rotating Hayward black holes. In this setup, all point structures get replaced by smeared distributions owing to this inspired approach. The noncommutative effects result in a colder black hole in the small radii regime as Hayward's free parameter g increases. As well as the effects of noncommutativity and the rotation factor, the configuration of the remnant can be substantially affected by the parameter g. However, in the rotating solution it is not so sensitive to g with respect to the non-rotating case. As a consequence, Hayward's parameter, the noncommutativity and the rotation may raise the minimum value of energy for the possible formation of black holes in TeV-scale collisions. This observation can be used as a potential explanation for the absence of black holes in the current energy scales produced at particle colliders. However, it is also found that if extra dimensions do exist, then the possibility of the black hole production at energy scales accessible at the LHC for large numbers of extra dimensions will be larger.

A Dream of Yukawa — Non-Local Fields out of Non-Commutative Spacetime —

NASA Astrophysics Data System (ADS)

Naka, Shigefumi; Toyoda, Haruki; Takanashi, Takahiro; Umezawa, Eizo

The coordinates of κ-Minkowski spacetime form Lie algebraic elements, in which time and space coordinates do not commute in spite of that space coordinates commute each other. The non-commutativity is realized by a Planck-length-scale constant κ - 1( ne 0), which is a universal constant other than the light velocity under the κ-Poincare transformation. Such a non-commutative structure can be realized by SO(1,4) generators in dS4 spacetime. In this work, we try to construct a κ-Minkowski like spacetime with commutative 4-dimensional spacetime based on Adsn+1 spacetime. Another aim of this work is to study invariant wave equations in this spacetime from the viewpoint of non-local field theory by H. Yukawa, who expected to realize elementary particle theories without divergence according to this viewpoint.

Continual Lie algebras and noncommutative counterparts of exactly solvable models

NASA Astrophysics Data System (ADS)

Zuevsky, A.

2004-01-01

Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.

Calculating the jet quenching parameter in the plasma of noncommutative Yang-Mills theory from gauge/gravity duality

NASA Astrophysics Data System (ADS)

Chakraborty, Somdeb; Roy, Shibaji

2012-02-01

A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in (3+1) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as T7 for fixed noncommutativity and fixed ’t Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.

Non-Commutative Rational Yang-Baxter Maps

NASA Astrophysics Data System (ADS)

Doliwa, Adam

2014-03-01

Starting from multidimensional consistency of non-commutative lattice-modified Gel'fand-Dikii systems, we present the corresponding solutions of the functional (set-theoretic) Yang-Baxter equation, which are non-commutative versions of the maps arising from geometric crystals. Our approach works under additional condition of centrality of certain products of non-commuting variables. Then we apply such a restriction on the level of the Gel'fand-Dikii systems what allows to obtain non-autonomous (but with central non-autonomous factors) versions of the equations. In particular, we recover known non-commutative version of Hirota's lattice sine-Gordon equation, and we present an integrable non-commutative and non-autonomous lattice modified Boussinesq equation.

Mirror symmetry in emergent gravity

NASA Astrophysics Data System (ADS)

Yang, Hyun Seok

2017-09-01

Given a six-dimensional symplectic manifold (M , B), a nondegenerate, co-closed four-form C introduces a dual symplectic structure B ˜ = * C independent of B via the Hodge duality *. We show that the doubling of symplectic structures due to the Hodge duality results in two independent classes of noncommutative U (1) gauge fields by considering the Seiberg-Witten map for each symplectic structure. As a result, emergent gravity suggests a beautiful picture that the variety of six-dimensional manifolds emergent from noncommutative U (1) gauge fields is doubled. In particular, the doubling for the variety of emergent Calabi-Yau manifolds allows us to arrange a pair of Calabi-Yau manifolds such that they are mirror to each other. Therefore, we argue that the mirror symmetry of Calabi-Yau manifolds is the Hodge theory for the deformation of symplectic and dual symplectic structures.

Noncommutativity and Humanity — Julius Wess and his Legacy

NASA Astrophysics Data System (ADS)

Djordjevic, Goran S.

2012-03-01

A personal view on Julius Wess's human and scientific legacy in Serbia and the Balkan region is given. Motivation for using noncommutative and nonarchimedean geometry on very short distances is presented. In addition to some mathematical preliminaries, we present a short introduction in adelic quantum mechanics in a way suitable for its noncommutative generalization. We also review the basic ideas and tools embedded in q-deformed and noncommutative quantum mechanics. A rather fundamental approach, called deformation quantization, is noted. A few relations between noncommutativity and nonarchimedean spaces, as well as similarities between corresponding quantum theories, in particular, quantum cosmology are pointed out. An extended Moyal product in a frame of an adelic noncommutative quantum mechanics is also considered.

Laplace-Runge-Lenz vector in quantum mechanics in noncommutative space

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

Gáliková, Veronika; Kováčik, Samuel; Prešnajder, Peter

2013-12-15

The main point of this paper is to examine a “hidden” dynamical symmetry connected with the conservation of Laplace-Runge-Lenz vector (LRL) in the hydrogen atom problem solved by means of non-commutative quantum mechanics (NCQM). The basic features of NCQM will be introduced to the reader, the key one being the fact that the notion of a point, or a zero distance in the considered configuration space, is abandoned and replaced with a “fuzzy” structure in such a way that the rotational invariance is preserved. The main facts about the conservation of LRL vector in both classical and quantum theory willmore » be reviewed. Finally, we will search for an analogy in the NCQM, provide our results and their comparison with the QM predictions. The key notions we are going to deal with are non-commutative space, Coulomb-Kepler problem, and symmetry.« less

Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type

NASA Astrophysics Data System (ADS)

Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah

2015-11-01

We propose a noncommutative version of the Euclidean Lie algebra E 2. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra.

Realization of Cohen-Glashow very special relativity on noncommutative space-time.

PubMed

Sheikh-Jabbari, M M; Tureanu, A

2008-12-31

We show that the Cohen-Glashow very special relativity (VSR) theory [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] can be realized as the part of the Poincaré symmetry preserved on a noncommutative Moyal plane with lightlike noncommutativity. Moreover, we show that the three subgroups relevant to VSR can also be realized in the noncommutative space-time setting. For all of these three cases, the noncommutativity parameter theta(mu upsilon) should be lightlike (theta(mu upsilon) theta mu upsilon = 0). We discuss some physical implications of this realization of the Cohen-Glashow VSR.

Construction of non-Abelian gauge theories on noncommutative spaces

NASA Astrophysics Data System (ADS)

Jurčo, B.; Möller, L.; Schraml, S.; Schupp, P.; Wess, J.

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.

Global exponential stability of octonion-valued neural networks with leakage delay and mixed delays.

PubMed

Popa, Călin-Adrian

2018-06-08

This paper discusses octonion-valued neural networks (OVNNs) with leakage delay, time-varying delays, and distributed delays, for which the states, weights, and activation functions belong to the normed division algebra of octonions. The octonion algebra is a nonassociative and noncommutative generalization of the complex and quaternion algebras, but does not belong to the category of Clifford algebras, which are associative. In order to avoid the nonassociativity of the octonion algebra and also the noncommutativity of the quaternion algebra, the Cayley-Dickson construction is used to decompose the OVNNs into 4 complex-valued systems. By using appropriate Lyapunov-Krasovskii functionals, with double and triple integral terms, the free weighting matrix method, and simple and double integral Jensen inequalities, delay-dependent criteria are established for the exponential stability of the considered OVNNs. The criteria are given in terms of complex-valued linear matrix inequalities, for two types of Lipschitz conditions which are assumed to be satisfied by the octonion-valued activation functions. Finally, two numerical examples illustrate the feasibility, effectiveness, and correctness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Black holes thermodynamics in a new kind of noncommutative geometry

NASA Astrophysics Data System (ADS)

Faizal, Mir; Amorim, R. G. G.; Ulhoa, S. C.

Motivated by the energy-dependent metric in gravity’s rainbow, we will propose a new kind of energy-dependent noncommutative geometry. It will be demonstrated that like gravity’s rainbow, this new noncommutative geometry is described by an energy-dependent metric. We will analyze the effect of this noncommutative deformation on the Schwarzschild black holes and Kerr black holes. We will perform our analysis by relating the commutative and this new energy-dependent noncommutative metrics using an energy-dependent Moyal star product. We will also analyze the thermodynamics of these new noncommutative black hole solutions. We will explicitly derive expression for the corrected entropy and temperature for these black hole solutions. It will be demonstrated that, for these deformed solutions, black remnants cannot form. This is because these corrections increase rather than reduce the temperature of the black holes.

Vacuum energy from noncommutative models

NASA Astrophysics Data System (ADS)

Mignemi, S.; Samsarov, A.

2018-04-01

The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory. Our calculations show however that this depends on the particular model considered: in some cases the divergences are suppressed and the vacuum energy is only logarithmically divergent, in other cases they are stronger than in the commutative theory.

Quantum Information as a Non-Kolmogorovian Generalization of Shannon's Theory

NASA Astrophysics Data System (ADS)

Holik, Federico; Bosyk, Gustavo; Bellomo, Guido

2015-10-01

In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a new family of generalized entropic measures.

Realization of Cohen-Glashow Very Special Relativity on Noncommutative Space-Time

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

Sheikh-Jabbari, M. M.; Tureanu, A.

2008-12-31

We show that the Cohen-Glashow very special relativity (VSR) theory [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] can be realized as the part of the Poincare symmetry preserved on a noncommutative Moyal plane with lightlike noncommutativity. Moreover, we show that the three subgroups relevant to VSR can also be realized in the noncommutative space-time setting. For all of these three cases, the noncommutativity parameter {theta}{sup {mu}}{sup {nu}} should be lightlike ({theta}{sup {mu}}{sup {nu}}{theta}{sub {mu}}{sub {nu}}=0). We discuss some physical implications of this realization of the Cohen-Glashow VSR.

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

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

Gamel, Omar E.; Fleming, Graham R.

Noncommuting observables cannot be simultaneously measured; however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fréchet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits.more » These inequalities place limits on the local hidden variable models that define joint probabilities for noncommuting observables. We also found that the Quasi-Bell inequalities have a quantum to classical violation as high as 3/2 on two qubit, higher than conventional Bell inequalities. Our result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics and provides an insightful generalization of Bell inequalities.« less

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

DOE PAGES

Gamel, Omar E.; Fleming, Graham R.

2017-05-01

Noncommuting observables cannot be simultaneously measured; however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fréchet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits.more » These inequalities place limits on the local hidden variable models that define joint probabilities for noncommuting observables. We also found that the Quasi-Bell inequalities have a quantum to classical violation as high as 3/2 on two qubit, higher than conventional Bell inequalities. Our result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics and provides an insightful generalization of Bell inequalities.« less

Abelian Toda field theories on the noncommutative plane

NASA Astrophysics Data System (ADS)

Cabrera-Carnero, Iraida

2005-10-01

Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.

On the generalized geometry origin of noncommutative gauge theory

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2013-07-01

We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.

Noncommutative Valuation of Options

NASA Astrophysics Data System (ADS)

Herscovich, Estanislao

2016-12-01

The aim of this note is to show that the classical results in finance theory for pricing of derivatives, given by making use of the replication principle, can be extended to the noncommutative world. We believe that this could be of interest in quantum probability. The main result called the First fundamental theorem of asset pricing, states that a noncommutative stock market admits no-arbitrage if and only if it admits a noncommutative equivalent martingale probability.

On noncommutative Levi-Civita connections

NASA Astrophysics Data System (ADS)

Peterka, Mira A.; Sheu, Albert Jeu-Liang

We make some observations about Rosenberg’s Levi-Civita connections on noncommutative tori, noting the non-uniqueness of general torsion-free metric-compatible connections without prescribed connection operator for the inner *-derivations, the nontrivial curvature form of the inner *-derivations, and the validity of the Gauss-Bonnet theorem for two classes of nonconformal deformations of the flat metric on the noncommutative two-tori, including the case of noncommuting scalings along the principal directions of a two-torus.

Accretion onto a noncommutative-inspired Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Gangopadhyay, Sunandan; Paik, Biplab; Mandal, Rituparna

2018-05-01

In this paper, we investigate the problem of ordinary baryonic matter accretion onto the noncommutative (NC) geometry-inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the NC parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. The profile of the thermal environment is finally investigated below the sonic radius and at the event horizon and is found to be affected by noncommutativity.

Galilean symmetry in a noncommutative gravitational quantum well

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

Saha, Anirban

2010-06-15

A thorough analysis of Galilean symmetries for the gravitational well problem on a noncommutative plane is presented. A complete closure of the one-parameter centrally extended Galilean algebra is realized for the model. This implies that the field theoretic model constructed to describe noncommutative gravitational quantum well in [A. Saha, Eur. Phys. J. C 51, 199 (2007).] is indeed independent of the coordinate choice. Hence the energy spectrum predicted by the model can be associated with the experimental results to establish the upper bound on a time-space noncommutative parameter. Interestingly, noncommutativity is shown to increase the gravitational pull on the neutronmore » trapped in the gravitational well.« less

Abel's theorem in the noncommutative case

NASA Astrophysics Data System (ADS)

Leitenberger, Frank

2004-03-01

We define noncommutative binary forms. Using the typical representation of Hermite we prove the fundamental theorem of algebra and we derive a noncommutative Cardano formula for cubic forms. We define quantized elliptic and hyperelliptic differentials of the first kind. Following Abel we prove Abel's theorem.

Noncommutative Quantum Mechanics based on Representations of Exotic Galilei Group

NASA Astrophysics Data System (ADS)

Amorim, R. G. G.; Ulhoa, S. C.

2018-02-01

Using elements of symmetry, we constructed the Noncommutative Schrödinger Equation from a representation of Exotic Galilei Group. As a consequence, we derive the Ehrenfest theorem using noncommutative coordinates. We also have showed others features of quantum mechanics in such a manifold. As an important result, we find out that a linear potential in the noncommutative Schrödinger equation is completely analogous to the ordinary case. We also worked with harmonic and anharmonic oscillators, giving corrections in the energy for each one.

Influences of the coordinate dependent noncommutative space on charged and spin currents

NASA Astrophysics Data System (ADS)

Ren, Ya-Jie; Ma, Kai

2018-06-01

We study the charged and spin currents on a coordinate dependent noncommutative space. Starting from the noncommutative extended relativistic equation of motion, the nonrelativistic approximation is obtained by using the Foldy-Wouthuysen transformation, and then the charged and spin currents are derived by using the extended Drude model. We find that the charged current is twisted by modifying the off-diagonal elements of the Hall conductivity, however, the spin current is not affected up to leading order of the noncommutative parameter.

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

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

Laangvik, Miklos; Salminen, Tapio; Tureanu, Anca

2011-04-15

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

Instantons, quivers and noncommutative Donaldson-Thomas theory

NASA Astrophysics Data System (ADS)

Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

2011-12-01

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

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.

Noncommutative gauge theories and Kontsevich's formality theorem

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schupp, P.; Wess, J.

2001-09-01

The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a "Mini Seiberg-Witten map" that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor.

Quantum information aspects of noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro

2018-01-01

Some fundamental aspects related with the construction of Robertson-Schrödinger-like uncertainty-principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum systems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.

Paired quantum Hall states on noncommutative two-tori

NASA Astrophysics Data System (ADS)

Marotta, Vincenzo; Naddeo, Adele

2010-08-01

By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter θ (in appropriate units), a one-to-one correspondence between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings ν=mp/m+2 Cristofano et al. (2000) [1], recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in Marotta and Naddeo (2008) [2] for the Jain series ν=>m2p/m+1. The case m=2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids.

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

Bootstrapping non-commutative gauge theories from L∞ algebras

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter

2018-05-01

Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.

Noncommutative GUTs, Standard Model and C, P, T

NASA Astrophysics Data System (ADS)

Aschieri, P.; Jurčo, B.; Schupp, P.; Wess, J.

2003-02-01

Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter θ, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in θ. We study in detail the reality, Hermiticity and C, P, T properties of the Seiberg-Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg-Witten map.

Quantum phase transitions in the noncommutative Dirac oscillator

NASA Astrophysics Data System (ADS)

Panella, O.; Roy, P.

2014-10-01

We study the (2 + 1)-dimensional Dirac oscillator in a homogeneous magnetic field in the noncommutative plane. It is shown that the effect of noncommutativity is twofold: (i) momentum noncommuting coordinates simply shift the critical value (Bcr) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); (ii) noncommutativity in the space coordinates induces a new critical value of the magnetic field, Bcr*, where there is a second quantum phase transition (right-left): this critical point disappears in the commutative limit. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetization of the system. Possible applications to the physics of silicene and graphene are briefly discussed.

Deformation of the quintom cosmological model and its consequences

NASA Astrophysics Data System (ADS)

Sadeghi, J.; Pourhassan, B.; Nekouee, Z.; Shokri, M.

In this paper, we investigate the effects of noncommutative phase-space on the quintom cosmological model. In that case, we discuss about some cosmological parameters and show that they depend on the deformation parameters. We find that the noncommutative parameter plays important role which helps to re-arrange the divergency of cosmological constant. We draw time-dependent scale factor and investigate the effect of noncommutative parameters. Finally, we take advantage from noncommutative phase-space and obtain the deformed Lagrangian for the quintom model. In order to discuss some cosmological phenomena as dark energy and inflation, we employ Noether symmetry.

Quantum gravity from noncommutative spacetime

NASA Astrophysics Data System (ADS)

Lee, Jungjai; Yang, Hyun Seok

2014-12-01

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

Solitons on Noncommutative Torus as Elliptic Calogero-Gaudin Models, Branes and Laughlin Wave Functions

NASA Astrophysics Data System (ADS)

Hou, Bo-Yu; Peng, Dan-Tao; Shi, Kang-Jie; Yue, Rui-Hong

For the noncommutative torus T, in the case of the noncommutative parameter θ = (Z)/(n), we construct the basis of Hilbert space Hn in terms of θ functions of the positions zi of n solitons. The wrapping around the torus generates the algebra An, which is the Zn × Zn Heisenberg group on θ functions. We find the generators g of a local elliptic su(n), which transform covariantly by the global gauge transformation of An. By acting on Hn we establish the isomorphism of An and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero-Moser models to give the dynamics. The moment map of this twisted cotangent sunT) bundle is matched to the D-equation with the Fayet-Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k, u) of the spectral curve det|L(u) - k| = 0 describes the brane configuration, with the dynamical variables zi of the noncommutative solitons as the moduli T⊗ n/Sn. Furthermore, in the noncommutative Chern-Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative sunT cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.

Aspects of noncommutative (1+1)-dimensional black holes

NASA Astrophysics Data System (ADS)

Mureika, Jonas R.; Nicolini, Piero

2011-08-01

We present a comprehensive analysis of the spacetime structure and thermodynamics of (1+1)-dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length θ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass M, cosmological constant Λ, etc.), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.

Minimal measures for Euler-Lagrange flows on finite covering spaces

NASA Astrophysics Data System (ADS)

Wang, Fang; Xia, Zhihong

2016-12-01

In this paper we study the minimal measures for positive definite Lagrangian systems on compact manifolds. We are particularly interested in manifolds with more complicated fundamental groups. Mather’s theory classifies the minimal or action-minimizing measures according to the first (co-)homology group of a given manifold. We extend Mather’s notion of minimal measures to a larger class for compact manifolds with non-commutative fundamental groups, and use finite coverings to study the structure of these extended minimal measures. We also define action-minimizers and minimal measures in the homotopical sense. Our program is to study the structure of homotopical minimal measures by considering Mather’s minimal measures on finite covering spaces. Our goal is to show that, in general, manifolds with a non-commutative fundamental group have a richer set of minimal measures, hence a richer dynamical structure. As an example, we study the geodesic flow on surfaces of higher genus. Indeed, by going to the finite covering spaces, the set of minimal measures is much larger and more interesting.

Cosmological perturbations and noncommutative tachyon inflation

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

Liu Daojun; Li Xinzhou

2004-12-15

The motivation for studying the rolling tachyon and noncommutative inflation comes from string theory. In the tachyon inflation scenario, metric perturbations are created by tachyon field fluctuations during inflation. We drive the exact mode equation for scalar perturbations of the metric and investigate the cosmological perturbations in the commutative and noncommutative inflationary spacetime driven by the tachyon field which have a Born-Infeld Lagrangian. Although at lowest order the predictions of tachyon inflation are no different than those from standard slow-roll inflation, due to the modified inflationary dynamics there exists modifications to the power spectra of fluctuations generated during inflation. Inmore » the noncommutative tachyon inflation scenario, the stringy noncommutativity of spacetime results in corrections to the primordial power spectrum that lead to a spectral index that is greater than 1 on large scales and less than 1 on small scales as the first-year results of the Wilkinson Microwave Anisotropy Probe indicate.« less

On the plethora of representations arising in noncommutative quantum mechanics and an explicit construction of noncommutative 4-tori

NASA Astrophysics Data System (ADS)

Chowdhury, S. Hasibul Hassan

2017-06-01

We construct a 2-parameter family of unitarily equivalent irreducible representations of the triply extended group GNC of translations of R4 associated with a family of its 4-dimensional coadjoint orbits and show how a continuous 2-parameter family of gauge potentials emerges from these unitarily equivalent representations. We show that the Landau and the symmetric gauges of noncommutative quantum mechanics, widely used in the literature, in fact, belong to this 2-parameter family of gauges. We also provide an explicit construction of noncommutative 4-tori and compute the associated star products using the unitary dual of the group GNC that was studied at length in an earlier paper [S. H. H. Chowdhury and S. T. Ali, J. Phys. A: Math. Theor. 47, 085301 (2014)]. Finally, we construct projective modules over such noncommutative 4-tori and compute constant curvature connections on them using Rieffel's method.

On the index of noncommutative elliptic operators over C*-algebras

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

Savin, Anton Yu; Sternin, Boris Yu

2010-05-11

We consider noncommutative elliptic operators over C*-algebras, associated with a discrete group of isometries of a manifold. The main result of the paper is a formula expressing the Chern characters of the index (Connes invariants) in topological terms. As a corollary to this formula a simple proof of higher index formulae for noncommutative elliptic operators is obtained. Bibliography: 36 titles.

Dirac equation in noncommutative space for hydrogen atom

NASA Astrophysics Data System (ADS)

Adorno, T. C.; Baldiotti, M. C.; Chaichian, M.; Gitman, D. M.; Tureanu, A.

2009-11-01

We consider the energy levels of a hydrogen-like atom in the framework of θ-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S1 / 2, 2P1 / 2 and 2P3 / 2 is lifted completely, such that new transition channels are allowed.

Noncommutative gauge theory for Poisson manifolds

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Wess, Julius

2000-09-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

Dominance and noncommutativity effects in concept conjunctions: extensional or intensional basis?

PubMed

Storms, G; de Boeck, P; Van Mechelen, I; Geeraerts, D

1993-11-01

Dominance and noncommutativity effects are investigated in relative clause descriptions of five conjunctive concepts (birds and pets, sports and games, vehicles and machines, office equipment and writing implements, and shoes and sports equipment). Both asymmetry phenomena are studied at the extensional level (using membership ratings) and at the intensional level (using feature-importance ratings). A clear dominance effect was found for both the membership ratings and the feature-importance ratings, whereas the noncommutativity effect emerged only occasionally in the membership ratings and almost never in the feature-importance ratings. The data suggested that the dominance effect and the much weaker noncommutativity effect have an extensional basis.

Statistical mechanics of free particles on space with Lie-type noncommutativity

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Khorrami, Mohammad; Fatollahi, Amir H.

2010-07-01

Effects of Lie-type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the thermodynamic limit is calculated. Two possible definitions for the pressure are discussed, which are equivalent when the noncommutativity vanishes. The thermodynamic observables are extracted from the partition function. Different limits are discussed where either the noncommutativity or the quantum effects are important. Finally, specific cases are discussed where the group is SU(2) or SO(3), and the partition function of a nondegenerate gas is calculated.

The Hamiltonian structure of the (2+1)-dimensional Ablowitz--Kaup--Newell--Segur hierarchy

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

Athorne, C.; Dorfman, I.Y.

1993-08-01

By considering Hamiltonian theory over a suitable (noncommutative) ring the nonlinear evolution equations of the Ablowitz--Kaup--Newell--Segur (2+1) hierarchy are incorporated into a Hamiltonian framework and a modified Lenard scheme.

Editors' preface for the topical issue on Seven papers on Noncommutative Geometry and Operator Algebras

NASA Astrophysics Data System (ADS)

Guido, Daniele; Landi, Giovanni; Vassout, Stéphane

2016-07-01

This topical issue grew out of the International Conference ;Noncommutative Geometry and Applications; held 16-21 June 2014 at Villa Mondragone, Frascati (Roma). The main purpose of the conference was to have a unified view of different incarnations of noncommutative geometry and its applications. The seven papers collected in the present topical issue represent a good sample of the topics covered at the workshop. The conference itself was one of the climaxes of the Franco-Italian project GREFI-GENCO, which was initiated in 2007 by CNRS and INDAM to promote and enhance collaboration and exchanges between French and Italian researchers in the area of noncommutative geometry.

Extended generalized geometry and a DBI-type effective action for branes ending on branes

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-08-01

Starting from the Nambu-Goto bosonic membrane action, we develop a geometric description suitable for p-brane backgrounds. With tools of generalized geometry we derive the pertinent generalization of the string open-closed relations to the p-brane case. Nambu-Poisson structures are used in this context to generalize the concept of semi-classical noncommutativity of D-branes governed by a Poisson tensor. We find a natural description of the correspondence of recently proposed commutative and noncommutative versions of an effective action for p-branes ending on a p '-brane. We calculate the power series expansion of the action in background independent gauge. Leading terms in the double scaling limit are given by a generalization of a (semi-classical) matrix model.

Quantum Bianchi identities via DG categories

NASA Astrophysics Data System (ADS)

Beggs, Edwin J.; Majid, Shahn

2018-01-01

We use DG categories to derive analogues of the Bianchi identities for the curvature of a connection in noncommutative differential geometry. We also revisit the Chern-Connes pairing but following the line of Chern's original derivation. We show that a related DG category of extendable bimodule connections is a monoidal tensor category and in the metric compatible case obtain an analogue of a classical antisymmetry of the Riemann tensor. The monoidal structure implies the existence of a cup product on noncommutative sheaf cohomology. Another application shows that the curvature of a line module reduces to a 2-form on the base algebra. We illustrate the theory on the q-sphere, the permutation group S3 and the bicrossproduct quantum spacetime [ r , t ] = λr.

Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory

NASA Astrophysics Data System (ADS)

Chen, Guang-Hong; Wu, Yong-Shi

2002-02-01

A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents νm and βk, whose values are determined to be 1/4 and 1/2, respectively, at mean-field level.

Instantons on a non-commutative T4 from twisted (2,0) and little string theories

NASA Astrophysics Data System (ADS)

Cheung, Yeuk-Kwan E.; Ganor, Ori J.; Krogh, Morten; Mikhailov, Andrei Yu.

We show that the moduli space of the (2,0) and little-string theories compactified on T3 with R-symmetry twists is equal to the moduli space of U(1) instantons on a non-commutative T4. The moduli space of U( q) instantons on a non-commutative T4 is obtained from little-string theories of NS5-branes at Aq-1 singularities with twists. A large class of gauge theories with N=4 SUSY in 2+1D and N=2 SUSY in 3+1D are limiting cases of these theories. Hence, the moduli spaces of these gauge theories can be read off from the moduli spaces of instantons on non-commutative tori. We study the phase transitions in these theories and the action of T-duality. On the purely mathematical side, we give a prediction for the moduli space of two U(1) instantons on a non-commutative T4.

Noncommutative geometry and arithmetics

NASA Astrophysics Data System (ADS)

Almeida, P.

2009-09-01

We intend to illustrate how the methods of noncommutative geometry are currently used to tackle problems in class field theory. Noncommutative geometry enables one to think geometrically in situations in which the classical notion of space formed of points is no longer adequate, and thus a “noncommutative space” is needed; a full account of this approach is given in [3] by its main contributor, Alain Connes. The class field theory, i.e., number theory within the realm of Galois theory, is undoubtedly one of the main achievements in arithmetics, leading to an important algebraic machinery; for a modern overview, see [23]. The relationship between noncommutative geometry and number theory is one of the many themes treated in [22, 7-9, 11], a small part of which we will try to put in a more down-to-earth perspective, illustrating through an example what should be called an “application of physics to mathematics,” and our only purpose is to introduce nonspecialists to this beautiful area.

New Phenomena in NC Field Theory and Emergent Spacetime Geometry

NASA Astrophysics Data System (ADS)

Ydri, Badis

2010-10-01

We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar φ4 field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at θ = 0 there must exist a novel fixed point at θ = ∞ corresponding to the quartic hermitian matrix model.

Open string with a background B field as the first order mechanics, noncommutativity, and soldering formalism

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

Deriglazov, A. A.; Neves, C.; Oliveira, W.

2007-09-15

To study noncommutativity properties of the open string with constant B field, we construct a mechanical action that reproduces classical dynamics of the string sector under consideration. It allows one to apply the Dirac quantization procedure for constrained systems in a direct and unambiguous way. The mechanical action turns out to be the first order system without taking the strong field limit B{yields}{infinity}. In particular, it is true for the zero mode of the string coordinate, which means that the noncommutativity is an intrinsic property of this mechanical system. We describe the arbitrariness in the relation existing between the mechanicalmore » and the string variables and show that noncommutativity of the string variables on the boundary can be removed. This is in correspondence with the result of Seiberg and Witten on the relation among noncommutative and ordinary Yang-Mills theories. The recently developed soldering formalism helps us to establish a connection between the original open string action and the Polyakov action.« less

Observation of non-classical correlations in sequential measurements of photon polarization

NASA Astrophysics Data System (ADS)

Suzuki, Yutaro; Iinuma, Masataka; Hofmann, Holger F.

2016-10-01

A sequential measurement of two non-commuting quantum observables results in a joint probability distribution for all output combinations that can be explained in terms of an initial joint quasi-probability of the non-commuting observables, modified by the resolution errors and back-action of the initial measurement. Here, we show that the error statistics of a sequential measurement of photon polarization performed at different measurement strengths can be described consistently by an imaginary correlation between the statistics of resolution and back-action. The experimental setup was designed to realize variable strength measurements with well-controlled imaginary correlation between the statistical errors caused by the initial measurement of diagonal polarizations, followed by a precise measurement of the horizontal/vertical polarization. We perform the experimental characterization of an elliptically polarized input state and show that the same complex joint probability distribution is obtained at any measurement strength.

Thermodynamics of a Higher Dimensional Noncommutative Inspired Anti-de Sitter-Einstein-Born-Infeld Black Hole

NASA Astrophysics Data System (ADS)

González, Angélica; Linares, Román; Maceda, Marco; Sánchez-Santos, Oscar

2018-04-01

We analyze noncommutative deformations of a higher dimensional anti-de Sitter-Einstein-Born-Infeld black hole. Two models based on noncommutative inspired distributions of mass and charge are discussed and their thermodynamical properties such as the equation of state are explicitly calculated. In the (3 + 1)-dimensional case the Gibbs energy function of each model is used to discuss the presence of phase transitions.

The theory of pseudo-differential operators on the noncommutative n-torus

NASA Astrophysics Data System (ADS)

Tao, J.

2018-02-01

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.

Virtual quantum subsystems.

PubMed

Zanardi, P

2001-08-13

The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set A of operationally relevant observables. The algebraic structure of A selects a preferred tensor product structure, i.e., a partition into subsystems. The notion of compoundness for quantum systems is accordingly relativized. Universal control over virtual subsystems can be achieved by using quantum noncommutative holonomies

The Standard Model in noncommutative geometry: fundamental fermions as internal forms

NASA Astrophysics Data System (ADS)

Dąbrowski, Ludwik; D'Andrea, Francesco; Sitarz, Andrzej

2018-05-01

Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-Morita equivalence bimodule for the associated Clifford algebra.

Spacetime Non-Commutativity Corrections to the Cardy-Verlinde Formula of Achúcarro-Ortiz Black Hole

NASA Astrophysics Data System (ADS)

Setare, M. R.

2007-02-01

In this letter we compute the corrections to the Cardy-Verlinde formula of Achúcarro-Ortiz black hole, which is the most general two-dimensional black hole derived from the three-dimensional rotating Banados-Teitelboim-Zanelli black hole. These corrections stem from the space non-commutativity. We show that in non-commutative case, non-rotating Achúcarro-Ortiz black hole in contrast with commutative case has two horizons.

Non-Commutative Martingale Inequalities

NASA Astrophysics Data System (ADS)

Pisier, Gilles; Xu, Quanhua

We prove the analogue of the classical Burkholder-Gundy inequalites for non-commutative martingales. As applications we give a characterization for an Ito-Clifford integral to be an Lp-martingale via its integrand, and then extend the Ito-Clifford integral theory in L2, developed by Barnett, Streater and Wilde, to Lp for all 1

Holography and noncommutative yang-mills theory

PubMed

Li; Wu

2000-03-06

In this Letter a recently proposed gravity dual of noncommutative Yang-Mills theory is derived from the relations between closed string moduli and open string moduli recently suggested by Seiberg and Witten. The only new input one needs is a simple form of the running string tension as a function of energy. This derivation provides convincing evidence that string theory integrates with the holographical principle and demonstrates a direct link between noncommutative Yang-Mills theory and holography.

An arena for model building in the Cohen-Glashow very special relativity

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

Sheikh-Jabbari, M. M., E-mail: jabbari@theory.ipm.ac.i; Tureanu, A., E-mail: anca.tureanu@helsinki.f

2010-02-15

The Cohen-Glashow Very Special Relativity (VSR) algebra is defined as the part of the Lorentz algebra which upon addition of CP or T invariance enhances to the full Lorentz group, plus the space-time translations. We show that noncommutative space-time, in particular noncommutative Moyal plane, with light- like noncommutativity provides a robust mathematical setting for quantum field theories which are VSR invariant and hence set the stage for building VSR invariant particle physics models. In our setting the VSR invariant theories are specified with a single deformation parameter, the noncommutativity scale {Lambda}{sub NC}. Preliminary analysis with the available data leads tomore » {Lambda}{sub NC} {>=} 1-10 TeV.« less

Quantization of noncompact coverings and its physical applications

NASA Astrophysics Data System (ADS)

Ivankov, Petr

2018-02-01

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

On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

NASA Astrophysics Data System (ADS)

Arnlind, Joakim; Wilson, Mitsuru

2017-01-01

We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.

Drell-Yan process as an avenue to test a noncommutative standard model at the Large Hadron Collider

NASA Astrophysics Data System (ADS)

J, Selvaganapathy; Das, Prasanta Kumar; Konar, Partha

2016-06-01

We study the Drell-Yan process at the Large Hadron Collider in the presence of the noncommutative extension of the standard model. Using the Seiberg-Witten map, we calculate the production cross section to first order in the noncommutative parameter Θμ ν . Although this idea has been evolving for a long time, only a limited amount of phenomenological analysis has been completed, and this was mostly in the context of the linear collider. An outstanding feature from this nonminimal noncommutative standard model not only modifies the couplings over the SM production channel but also allows additional nonstandard vertices which can play a significant role. Hence, in the Drell-Yan process, as studied in the present analysis, one also needs to account for the gluon fusion process at the tree level. Some of the characteristic signatures, such as oscillatory azimuthal distributions, are an outcome of the momentum-dependent effective couplings. We explore the noncommutative scale ΛNC≥0.4 TeV , considering different machine energy ranging from 7 to 13 TeV.

Noncommutative coherent states and related aspects of Berezin-Toeplitz quantization

NASA Astrophysics Data System (ADS)

Hasibul Hassan Chowdhury, S.; Twareque Ali, S.; Engliš, Miroslav

2017-05-01

In this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of Gnc , a connected, simply connected nilpotent Lie group, which was identified as the kinematical symmetry group of noncommutative quantum mechanics for a system of two degrees of freedom in an earlier paper. Similarly described are the degenerate noncommutative coherent states arising from the degenerate UIRs of Gnc . We then compute the reproducing kernels associated with both these families of coherent states and study the Berezin-Toeplitz quantization of the observables on the underlying 4-dimensional phase space, analyzing in particular the semi-classical asymptotics for both these cases. Dedicated by the first and the third authors to the memory of the second author, with gratitude for his friendship and for all they learnt from him.

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

Rodriguez R., Miguel E.

2018-01-01

Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-Bohm effect which involves a coherent superposition of particles with opposite charges moving along a single open interferometric path. By means of the experimental considerations a limit √{θ }≃(0.13TeV)-1 is achieved, improving by 10 orders of magnitude the results derived by Chaichian et al. [Phys. Lett. B 527, 149 (2002), 10.1016/S0370-2693(02)01176-0] for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.

Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative black hole space-time

NASA Astrophysics Data System (ADS)

Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.

2018-06-01

We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

Noncommutative FRW Apparent Horizon and Hawking Radiation

NASA Astrophysics Data System (ADS)

Bouhallouf, H.; Mebarki, N.; Aissaoui, H.

2017-11-01

In the context of noncommutative (NCG) gauge gravity, and using a cosmic time power law formula for the scale factor, a Friedman-Robertson-Walker (FRW) like metric is obtained. Within the fermions tunneling effect approach and depending on the various intervals of the power parameter, expressions of the apparent horizon are also derived. It is shown that in some regions of the parameter space, a pure NCG trapped horizon does exist leading to new interpretation of the role played by the noncommutativity of the space-time.

On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for C*-Dynamical Systems

NASA Astrophysics Data System (ADS)

Fathizadeh, Farzad; Gabriel, Olivier

2016-02-01

The analog of the Chern-Gauss-Bonnet theorem is studied for a C^*-dynamical system consisting of a C^*-algebra A equipped with an ergodic action of a compact Lie group G. The structure of the Lie algebra g of G is used to interpret the Chevalley-Eilenberg complex with coefficients in the smooth subalgebra A subset A as noncommutative differential forms on the dynamical system. We conformally perturb the standard metric, which is associated with the unique G-invariant state on A, by means of a Weyl conformal factor given by a positive invertible element of the algebra, and consider the Hermitian structure that it induces on the complex. A Hodge decomposition theorem is proved, which allows us to relate the Euler characteristic of the complex to the index properties of a Hodge-de Rham operator for the perturbed metric. This operator, which is shown to be selfadjoint, is a key ingredient in our construction of a spectral triple on A and a twisted spectral triple on its opposite algebra. The conformal invariance of the Euler characteristic is interpreted as an indication of the Chern-Gauss-Bonnet theorem in this setting. The spectral triples encoding the conformally perturbed metrics are shown to enjoy the same spectral summability properties as the unperturbed case.

PREFACE: Conceptual and Technical Challenges for Quantum Gravity 2014 - Parallel session: Noncommutative Geometry and Quantum Gravity

NASA Astrophysics Data System (ADS)

Martinetti, P.; Wallet, J.-C.; Amelino-Camelia, G.

2015-08-01

The conference Conceptual and Technical Challenges for Quantum Gravity at Sapienza University of Rome, from 8 to 12 September 2014, has provided a beautiful opportunity for an encounter between different approaches and different perspectives on the quantum-gravity problem. It contributed to a higher level of shared knowledge among the quantum-gravity communities pursuing each specific research program. There were plenary talks on many different approaches, including in particular string theory, loop quantum gravity, spacetime noncommutativity, causal dynamical triangulations, asymptotic safety and causal sets. Contributions from the perspective of philosophy of science were also welcomed. In addition several parallel sessions were organized. The present volume collects contributions from the Noncommutative Geometry and Quantum Gravity parallel session4, with additional invited contributions from specialists in the field. Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: • from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, • from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, • from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. This volume provides an overview of these various topics, interesting for the specialist as well as accessible to the newcomer. 4partially funded by CNRS PEPS /PTI ''Metric aspect of noncommutative geometry: from Monge to Higgs''

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.

Noncommutative Yang-Mills from equivalence of star products

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schupp, P.

2000-05-01

It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume.

The E(2) particle

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

Ghosh, Subir; Pal, Probir; Physics Department, Uluberia College, Uluberia, Howrah 711315

2009-12-15

Recently it has been advocated [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] that for describing nature within the minimal symmetry requirement, certain subgroups of the Lorentz group may play a fundamental role. One such group is E(2) which induces a Lie algebraic noncommutative spacetime [M. M. Sheikh-Jabbari and A. Tureanu, Phys. Rev. Lett. 101, 261601 (2008); arXiv:0811.3670] where translation invariance is not fully maintained. We have constructed a consistent structure of noncommutative phase space for this system, and furthermore we have studied an appropriate point particle action on it. Interestingly, the Einstein dispersion relationmore » p{sup 2}=m{sup 2} remains intact. The model is constructed by exploiting a dual canonical phase space following the scheme developed by us earlier [S. Ghosh and P. Pal, Phys. Rev. D 75, 105021 (2007)].« less

A novel noncommutative KdV-type equation, its recursion operator, and solitons

NASA Astrophysics Data System (ADS)

Carillo, Sandra; Lo Schiavo, Mauro; Porten, Egmont; Schiebold, Cornelia

2018-04-01

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.

Noncommutative massive unquenched ABJM

NASA Astrophysics Data System (ADS)

Bea, Yago; Jokela, Niko; Pönni, Arttu; Ramallo, Alfonso V.

2018-05-01

In this paper, we study noncommutative massive unquenched Chern-Simons matter theory using its gravity dual. We construct this novel background by applying a TsT-transformation on the known parent commutative solution. We discuss several aspects of this solution to the Type IIA supergravity equations of motion and, amongst others, check that it preserves 𝒩 = 1 supersymmetry. We then turn our attention to applications and investigate how dynamical flavor degrees of freedom affect numerous observables of interest. Our framework can be regarded as a key step toward the construction of holographic quantum Hall states on a noncommutative plane.

Noncommutative Field Theories and (super)string Field Theories

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Belov, D. M.; Giryavets, A. A.; Koshelev, A. S.; Medvedev, P. B.

2002-11-01

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, "comma" and matrix representations of vertices.

Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces

NASA Astrophysics Data System (ADS)

Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea

2017-07-01

This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.

Wigner Functions for the Bateman System on Noncommutative Phase Space

NASA Astrophysics Data System (ADS)

Heng, Tai-Hua; Lin, Bing-Sheng; Jing, Si-Cong

2010-09-01

We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra.

A Ring Construction Using Finite Directed Graphs

ERIC Educational Resources Information Center

Bardzell, Michael

2012-01-01

In this paper we discuss an interesting class of noncommutative rings which can be constructed using finite directed graphs. This construction also creates a vector space. These structures provide undergraduate students connections between ring theory and graph theory and, among other things, allow them to see a ring unity element that looks quite…

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.

Differential calculus and gauge transformations on a deformed space

NASA Astrophysics Data System (ADS)

Wess, Julius

2007-08-01

We consider a formalism by which gauge theories can be constructed on noncommutative space time structures. The coordinates are supposed to form an algebra, restricted by certain requirements that allow us to realise the algebra in terms of star products. In this formulation it is useful to define derivatives and to extend the algebra of coordinates by these derivatives. The elements of this extended algebra are deformed differential operators. We then show that there is a morphism between these deformed differential operators and the usual higher order differential operators acting on functions of commuting coordinates. In this way we obtain deformed gauge transformations and a deformed version of the algebra of diffeomorphisms. The deformation of these algebras can be clearly seen in the category of Hopf algebras. The comultiplication will be twisted. These twisted algebras can be realised on noncommutative spaces and allow the construction of deformed gauge theories and deformed gravity theory.

3D quantum gravity and effective noncommutative quantum field theory.

PubMed

Freidel, Laurent; Livine, Etera R

2006-06-09

We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.

The noncommutative Poisson bracket and the deformation of the family algebras

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

Wei, Zhaoting, E-mail: zhaotwei@indiana.edu

The family algebras are introduced by Kirillov in 2000. In this paper, we study the noncommutative Poisson bracket P on the classical family algebra C{sub τ}(g). We show that P controls the first-order 1-parameter formal deformation from C{sub τ}(g) to Q{sub τ}(g) where the latter is the quantum family algebra. Moreover, we will prove that the noncommutative Poisson bracket is in fact a Hochschild 2-coboundary, and therefore, the deformation is infinitesimally trivial. In the last part of this paper, we discuss the relation between Mackey’s analogue and the quantization problem of the family algebras.

q-deformed superstatistics of the Schrödinger equation in commutative and noncommutative spaces with magnetic field

NASA Astrophysics Data System (ADS)

Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

2018-01-01

We discuss the q-deformed algebra and study the Schrödinger equation in commutative and noncommutative spaces, under an external magnetic field. In this work, we obtain the energy spectrum by an analytical method and the thermodynamic properties of the system by using the q-deformed superstatistics are calculated. Actually, we derive a generalized version of the ordinary superstatistic for the non-equilibrium systems. Also, different effective Boltzmann factor descriptions are derived. In addition, we discuss about the results for various values of θ in commutative and noncommutative spaces and, to illustrate the results, some figures are plotted.

On supermatrix models, Poisson geometry, and noncommutative supersymmetric gauge theories

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

Klimčík, Ctirad

2015-12-15

We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the UOSp(2|1) supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already existing in the literature and it was found by using Poisson geometry in a substantial way.

Quantum κ-deformed differential geometry and field theory

NASA Astrophysics Data System (ADS)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Yang-Baxter σ -models, conformal twists, and noncommutative Yang-Mills theory

NASA Astrophysics Data System (ADS)

Araujo, T.; Bakhmatov, I.; Colgáin, E. Ó.; Sakamoto, J.; Sheikh-Jabbari, M. M.; Yoshida, K.

2017-05-01

The Yang-Baxter σ -model is a systematic way to generate integrable deformations of AdS5×S5 . We recast the deformations as seen by open strings, where the metric is undeformed AdS5×S5 with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter Θ . We identify the deformations of AdS5 as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity condition on r -matrices for supergravity solutions translates into Θ being divergence-free. Integrability of the σ -model for unimodular r -matrices implies the existence and planar integrability of the dual NC gauge theory.

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

Comment on 'Noncommutative gauge theories and Lorentz symmetry'

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

Iorio, Alfredo

2008-02-15

We show that Lorentz symmetry is generally absent for noncommutative (Abelian) gauge theories and obtain a compact formula for the divergence of the Noether currents that allows a thorough study of this instance of symmetry violation. We use that formula to explain why the results of ''Noncommutative gauge theories and Lorentz symmetry'', Phys. Rev. D 70, 125004 (2004) by R. Banerjee, B. Chakraborty, and K. Kumar, interpreted there as new criteria for Lorentz invariance, are in fact just a particular case of the general expression for Lorentz violation obtained here. Finally, it is suggested that the divergence formula should holdmore » in a vast class of cases, such as, for instance, the standard model extension.« less

Unitary easy quantum groups: Geometric aspects

NASA Astrophysics Data System (ADS)

Banica, Teodor

2018-03-01

We discuss the classification problem for the unitary easy quantum groups, under strong axioms, of noncommutative geometric nature. Our main results concern the intermediate easy quantum groups ON ⊂ G ⊂ UN+ . To any such quantum group we associate its Schur-Weyl twist G ¯ , two noncommutative spheres S , S ¯ , a noncommutative torus T, and a quantum reflection group K. Studying (S , S ¯ , T , K , G , G ¯) leads then to some natural axioms, which can be used in order to investigate G itself. We prove that the main examples are covered by our formalism, and we conjecture that in what concerns the case UN ⊂ G ⊂ UN+ , our axioms should restrict the list of known examples.

Transmogrifying fuzzy vortices

NASA Astrophysics Data System (ADS)

Murugan, Jeff; Millner, Antony

2004-04-01

We show that the construction of vortex solitons of the noncommutative abelian-Higgs model can be extended to a critically coupled gauged linear sigma model with Fayet-Illiopolous D-terms. Like its commutative counterpart, this fuzzy linear sigma model has a rich spectrum of BPS solutions. We offer an explicit construction of the degree-k static semilocal vortex and study in some detail the infinite coupling limit in which it descends to a degree-k Bbb CBbb PkN instanton. This relation between the fuzzy vortex and noncommutative lump is used to suggest an interpretation of the noncommutative sigma model soliton as tilted D-strings stretched between an NS5-brane and a stack of D3-branes in type-IIB superstring theory.

Galilei group with multiple central extension, vorticity, and entropy generation: Exotic fluid in 3 +1 dimensions

NASA Astrophysics Data System (ADS)

Das, Praloy; Ghosh, Subir

2017-12-01

A noncommutative extension of an ideal (Hamiltonian) fluid model in 3 +1 dimensions is proposed. The model enjoys several interesting features: it allows a multiparameter central extension in Galilean boost algebra (which is significant being contrary to the existing belief that a similar feature can appear only in 2 +1 -dimensions); noncommutativity generates vorticity in a canonically irrotational fluid; it induces a nonbarotropic pressure leading to a nonisentropic system. (Barotropic fluids are entropy preserving as the pressure depends only on the matter density.) Our fluid model is termed "exotic" since it has a close resemblance with the extensively studied planar (2 +1 dimensions) exotic models and exotic (noncommutative) field theories.

Non-commutative geometry of the h-deformed quantum plane

NASA Astrophysics Data System (ADS)

Cho, S.; Madore, J.; Park, K. S.

1998-03-01

The h-deformed quantum plane is a counterpart of the q-deformed one in the set of quantum planes which are covariant under those quantum deformations of GL(2) which admit a central determinant. We have investigated the non-commutative geometry of the h-deformed quantum plane. There is a two-parameter family of torsion-free linear connections, a one-parameter sub-family of which are compatible with a skew-symmetric non-degenerate bilinear map. The skew-symmetric map resembles a symplectic 2-form and induces a metric. It is also shown that the extended h-deformed quantum plane is a non-commutative version of the Poincaré half-plane, a surface of constant negative Gaussian

A symmetry breaking mechanism by parity assignment in the noncommutative Higgs model

NASA Astrophysics Data System (ADS)

Yang, Masaki J. S.

2017-12-01

We apply the orbifold grand unified theory (GUT) mechanism to the noncommutative Higgs model. An assignment of Z2 parity to the “constituent fields” induces parity assignments of both the gauge and Higgs bosons, because these bosons are treated as some kind of composite fields in this formalism.

Extremal noncommutative black holes as dark matter furnaces

NASA Astrophysics Data System (ADS)

Kawamoto, Shoichi; Wei, Chun-Yu; Wen, Wen-Yu

2017-09-01

In this paper, we consider dark matter annihilation in the gravitational field of noncommutative black holes. Instead of a violent fate predicted in the usual Hawking radiation, we propose a thermal equilibrium state where a mildly burning black hole relic is fueled by dark matter accretion at the final stage of evaporation.

Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

NASA Astrophysics Data System (ADS)

Jurco, B.; Schraml, S.; Schupp, P.; Wess, J.

2000-11-01

An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.

Spacetime deformation effect on the early universe and the PTOLEMY experiment

NASA Astrophysics Data System (ADS)

Horvat, Raul; Trampetic, Josip; You, Jiangyang

2017-09-01

Using a fully-fledged formulation of gauge field theory deformed by the spacetime noncommutativity, we study its impact on relic neutrino direct detection, as proposed recently by the PTOLEMY experiment. The noncommutative background tends to influence the propagating neutrinos by providing them with a tree-level vector-like coupling to photons, enabling thus otherwise sterile right-handed (RH) neutrinos to be thermally produced in the early universe. Such a new component in the universe's background radiation has been switched today to the almost fully active sea of non-relativistic neutrinos, exerting consequently some impact on the capture on tritium at PTOLEMY. The peculiarities of our nonperturbative approach tend to reflect in the cosmology as well, upon the appearances of the coupling temperature, above which RH neutrinos stay permanently decoupled from thermal environment. This entails the maximal scale of noncommutativity as well, being of order of 10-4MPl, above which there is no impact whatsoever on the capture rates at PTOLEMY. The latter represents an exceptional upper bound on the scale of noncommutativity coming from phenomenology.

Nambu-Poisson gauge theory

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2014-06-01

We generalize noncommutative gauge theory using Nambu-Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg-Witten map. We construct a covariant Nambu-Poisson gauge theory action, give its first order expansion in the Nambu-Poisson tensor and relate it to a Nambu-Poisson matrix model.

Classification of digital affine noncommutative geometries

NASA Astrophysics Data System (ADS)

Majid, Shahn; Pachoł, Anna

2018-03-01

It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."

Commuting behaviors and exposure to air pollution in Montreal, Canada.

PubMed

Miao, Qun; Bouchard, Michèle; Chen, Dongmei; Rosenberg, Mark W; Aronson, Kristan J

2015-03-01

Vehicular traffic is a major source of outdoor air pollution in urban areas, and studies have shown that air pollution is worse during hours of commuting to and from work and school. However, it is unclear to what extent different commuting behaviors are a source of air pollution compared to non-commuters, and if air pollution exposure actually differs by the mode of commuting. This study aimed to examine the relationships between commuting behaviors and air pollution exposure levels measured by urinary 1-OHP (1-hydroxypyrene), a biomarker of exposure to polycyclic aromatic hydrocarbons (PAHs). A cross-sectional study of 174 volunteers living in Montreal, 92 females and 82 males, aged 20 to 53 years was conducted in 2011. Each participant completed a questionnaire regarding demographic factors, commuting behaviors, home and workplace addresses, and potential sources of PAH exposure, and provided a complete first morning void urine sample for 1-OHP analysis. Multivariable general linear regression models were used to examine the relationships between different types of commuting and urinary 1-OHP levels. Compared to non-commuters, commuters traveling by foot or bicycle and by car or truck had a significantly higher urinary 1-OHP concentration in urine (p=0.01 for foot or bicycle vs. non-commuters; p=0.02 for car or truck vs. non-commuters); those traveling with public transportation and combinations of two or more types of modes tended to have an increased 1-OHP level in urine (p=0.06 for public transportation vs. non-commuters; p=0.05 for commuters with combinations of two or more types of modes vs. non-commuters). No significant difference in urinary 1-OHP variation was found by mode of commuting. This preliminary study suggests that despite the mode of commuting, all types of commuting during rush hours increase exposure to air pollution as measured by a sensitive PAH metabolite biomarker, and mode of commuting did not explain exposure variation. Copyright © 2014 Elsevier B.V. All rights reserved.

Utilizing Crowdsourced Data for Studies of Cycling and Air Pollution Exposure: A Case Study Using Strava Data.

PubMed

Sun, Yeran; Mobasheri, Amin

2017-03-08

With the development of information and communications technology, user-generated content and crowdsourced data are playing a large role in studies of transport and public health. Recently, Strava, a popular website and mobile app dedicated to tracking athletic activity (cycling and running), began offering a data service called Strava Metro, designed to help transportation researchers and urban planners to improve infrastructure for cyclists and pedestrians. Strava Metro data has the potential to promote studies of cycling and health by indicating where commuting and non-commuting cycling activities are at a large spatial scale (street level and intersection level). The assessment of spatially varying effects of air pollution during active travel (cycling or walking) might benefit from Strava Metro data, as a variation in air pollution levels within a city would be expected. In this paper, to explore the potential of Strava Metro data in research of active travel and health, we investigate spatial patterns of non-commuting cycling activities and associations between cycling purpose (commuting and non-commuting) and air pollution exposure at a large scale. Additionally, we attempt to estimate the number of non-commuting cycling trips according to environmental characteristics that may help identify cycling behavior. Researchers who are undertaking studies relating to cycling purpose could benefit from this approach in their use of cycling trip data sets that lack trip purpose. We use the Strava Metro Nodes data from Glasgow, United Kingdom in an empirical study. Empirical results reveal some findings that (1) when compared with commuting cycling activities, non-commuting cycling activities are more likely to be located in outskirts of the city; (2) spatially speaking, cyclists riding for recreation and other purposes are more likely to be exposed to relatively low levels of air pollution than cyclists riding for commuting; and (3) the method for estimating of the number of non-commuting cycling activities works well in this study. The results highlight: (1) a need for policymakers to consider how to improve cycling infrastructure and road safety in outskirts of cities; and (2) a possible way of estimating the number of non-commuting cycling activities when the trip purpose of cycling data is unknown.

Utilizing Crowdsourced Data for Studies of Cycling and Air Pollution Exposure: A Case Study Using Strava Data

PubMed Central

Sun, Yeran; Mobasheri, Amin

2017-01-01

With the development of information and communications technology, user-generated content and crowdsourced data are playing a large role in studies of transport and public health. Recently, Strava, a popular website and mobile app dedicated to tracking athletic activity (cycling and running), began offering a data service called Strava Metro, designed to help transportation researchers and urban planners to improve infrastructure for cyclists and pedestrians. Strava Metro data has the potential to promote studies of cycling and health by indicating where commuting and non-commuting cycling activities are at a large spatial scale (street level and intersection level). The assessment of spatially varying effects of air pollution during active travel (cycling or walking) might benefit from Strava Metro data, as a variation in air pollution levels within a city would be expected. In this paper, to explore the potential of Strava Metro data in research of active travel and health, we investigate spatial patterns of non-commuting cycling activities and associations between cycling purpose (commuting and non-commuting) and air pollution exposure at a large scale. Additionally, we attempt to estimate the number of non-commuting cycling trips according to environmental characteristics that may help identify cycling behavior. Researchers who are undertaking studies relating to cycling purpose could benefit from this approach in their use of cycling trip data sets that lack trip purpose. We use the Strava Metro Nodes data from Glasgow, United Kingdom in an empirical study. Empirical results reveal some findings that (1) when compared with commuting cycling activities, non-commuting cycling activities are more likely to be located in outskirts of the city; (2) spatially speaking, cyclists riding for recreation and other purposes are more likely to be exposed to relatively low levels of air pollution than cyclists riding for commuting; and (3) the method for estimating of the number of non-commuting cycling activities works well in this study. The results highlight: (1) a need for policymakers to consider how to improve cycling infrastructure and road safety in outskirts of cities; and (2) a possible way of estimating the number of non-commuting cycling activities when the trip purpose of cycling data is unknown. PMID:28282865

On total noncommutativity in quantum mechanics

NASA Astrophysics Data System (ADS)

Lahti, Pekka J.; Ylinen, Kari

1987-11-01

It is shown within the Hilbert space formulation of quantum mechanics that the total noncommutativity of any two physical quantities is necessary for their satisfying the uncertainty relation or for their being complementary. The importance of these results is illustrated with the canonically conjugate position and momentum of a free particle and of a particle closed in a box.

Curved noncommutative tori as Leibniz quantum compact metric spaces

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

Latrémolière, Frédéric, E-mail: frederic@math.du.edu

We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.

A group filter algorithm for sea mine detection

NASA Astrophysics Data System (ADS)

Cobb, J. Tory; An, Myoung; Tolimieri, Richard

2005-06-01

Automatic detection of sea mines in coastal regions is a difficult task due to the highly variable sea bottom conditions present in the underwater environment. Detection systems must be able to discriminate objects which vary in size, shape, and orientation from naturally occurring and man-made clutter. Additionally, these automated systems must be computationally efficient to be incorporated into unmanned underwater vehicle (UUV) sensor systems characterized by high sensor data rates and limited processing abilities. Using noncommutative group harmonic analysis, a fast, robust sea mine detection system is created. A family of unitary image transforms associated to noncommutative groups is generated and applied to side scan sonar image files supplied by Naval Surface Warfare Center Panama City (NSWC PC). These transforms project key image features, geometrically defined structures with orientations, and localized spectral information into distinct orthogonal components or feature subspaces of the image. The performance of the detection system is compared against the performance of an independent detection system in terms of probability of detection (Pd) and probability of false alarm (Pfa).

Notes on "Quantum Gravity" and Noncommutative Geometry

NASA Astrophysics Data System (ADS)

Gracia-Bondía, J. M.

I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide against just selling my mathematical wares, and for a survey, necessarily very selective, but taking a global phenomenological approach to its subject matter. After all, noncommutative geometry does not purport yet to solve the riddle of quantum gravity; it is more of an insurance policy against the probable failure of the other approaches. The plan is as follows: the introduction invites students to the fruitful doubts and conundrums besetting the application of even classical gravity. Next, the first experiments detecting quantum gravitational states inoculate us a healthy dose of scepticism on some of the current ideologies. In Sect. 1.3 we look at the action for general relativity as a consequence of gauge theory for quantum tensor fields. Section 1.4 briefly deals with the unimodular variants. Section 1.5 arrives at noncommutative geometry. I am convinced that, if this is to play a role in quantum gravity, commutative and noncommutative manifolds must be treated on the same footing, which justifies the place granted to the reconstruction theorem. Together with Sect. 1.3, this part constitutes the main body of the notes. Only very summarily at the end of this section do we point to some approaches to gravity within the noncommutative realm. The last section delivers a last dose of scepticism. My efforts will have been rewarded if someone from the young generation learns to mistrust current mindsets.

Quasideterminant solutions of the extended noncommutative Kadomtsev-Petviashvili hierarchy

NASA Astrophysics Data System (ADS)

Wu, Hongxia; Liu, Jingxin; Li, Chunxia

2017-07-01

We construct a nonauto Darboux transformation for the extended noncommutative Kadomtsev-Petviashvili (ncKP) hierarchy and consequently derive its quasi-Wronskian solution. We also obtain the quasi-Wronskian solution of the ncKP equation with self-consistent sources (ncKPESCS) as a by-product. Finally, we use the direct verification method to prove the quasi-Wronskian solution of the ncKPESCS.

Group field theory with noncommutative metric variables.

PubMed

Baratin, Aristide; Oriti, Daniele

2010-11-26

We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.

Noncommuting Momenta of Topological Solitons

NASA Astrophysics Data System (ADS)

Watanabe, Haruki; Murayama, Hitoshi

2014-05-01

We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes

NASA Astrophysics Data System (ADS)

Ghosh, Sushant G.

2018-04-01

Low energy limits of a string theory suggests that the gravity action should include quadratic and higher-order curvature terms, in the form of dimensionally continued Gauss–Bonnet densities. Einstein–Gauss–Bonnet is a natural extension of the general relativity to higher dimensions in which the first and second-order terms correspond, respectively, to general relativity and Einstein–Gauss–Bonnet gravity. We obtain five-dimensional (5D) black hole solutions, inspired by a noncommutative geometry, with a static spherically symmetric, Gaussian mass distribution as a source both in the general relativity and Einstein–Gauss–Bonnet gravity cases, and we also analyzes their thermodynamical properties. Owing the noncommutative corrected black hole, the thermodynamic quantities have also been modified, and phase transition is shown to be achievable. The phase transitions for the thermodynamic stability, in both the theories, are characterized by a discontinuity in the specific heat at r_+=rC , with the stable (unstable) branch for r < (>) rC . The metric of the noncommutative inspired black holes smoothly goes over to the Boulware–Deser solution at large distance. The paper has been appended with a calculation of black hole mass using holographic renormalization.

Komar energy and Smarr formula for noncommutative inspired Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Banerjee, Rabin; Gangopadhyay, Sunandan

2011-11-01

We calculate the Komar energy E for a noncommutative inspired Schwarzschild black hole. A deformation from the conventional identity E = 2 ST H is found in the next to leading order computation in the noncommutative parameter θ (i.e. {{O}(sqrt{θ}e^{-M^2/θ})}) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point T H = 0 of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result M = 2 ST H , where the mass ( M) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter-Schwarzschild geometry.

Shadow of noncommutative geometry inspired black hole

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

Wei, Shao-Wen; Cheng, Peng; Zhong, Yi

2015-08-01

In this paper, the shadow casted by the rotating black hole inspired by noncommutative geometry is investigated. In addition to the dimensionless spin parameter a/M{sub 0} with M{sub 0} black hole mass and inclination angle i, the dimensionless noncommutative parameter √θ/M{sub 0} is also found to affect the shape of the black hole shadow. The result shows that the size of the shadow slightly decreases with the parameter √θ/M{sub 0}, while the distortion increases with it. Compared to the Kerr black hole, the parameter √θ/M{sub 0} increases the deformation of the shadow. This may offer a way to distinguish noncommutativemore » geometry inspired black hole from Kerr one via astronomical instruments in the near future.« less

Noncommutative QED+QCD and the {beta} function for QED

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

Ettefaghi, M. M.; Haghighat, M.; Mohammadi, R.

2010-11-15

QED based on {theta}-unexpanded noncomutative space-time in contrast with the noncommutative QED based on {theta}-expanded U(1) gauge theory via the Seiberg-Witten map is one-loop renormalizable. Meanwhile it suffers from asymptotic freedom that is not in agreement with the experiment. We show that the QED part of the U{sub *}(3)xU{sub *}(1) gauge group as an appropriate gauge group for the noncommutative QED+QCD is not only one-loop renormalizable but also has a {beta} function that can be positive, negative and even zero. In fact the {beta} function depends on the mixing parameter {delta}{sub 13} as a free parameter and it will bemore » equal to its counterpart in the ordinary QED for {delta}{sub 13}=0.367{pi}.« less

Enabling quaternion derivatives: the generalized HR calculus

PubMed Central

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.

2015-01-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555

Enabling quaternion derivatives: the generalized HR calculus.

PubMed

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C; Mandic, Danilo P

2015-08-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis.

Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing

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

Martins, R. A.

The recent extension of the standard model to include massive neutrinos in the framework of noncommutative geometry and the spectral action principle involves new scalar fields and their interactions with the usual complex scalar doublet. After ensuring that they bring no unphysical consequences, we address the question of how these fields affect the physics predicted in the Weinberg-Salam theory, particularly in the context of the electroweak phase transition. Applying the Dolan-Jackiw procedure, we calculate the finite temperature corrections, and find that the phase transition is first order. The new scalar interactions significantly improve the stability of the electroweak Z string,more » through the 'bag' phenomenon described by Vachaspati and Watkins ['Bound states can stabilize electroweak strings', Phys. Lett. B 318, 163-168 (1993)]. (Recently, cosmic strings have climbed back into interest due to a new evidence.) Sourced by static embedded strings, an internal space analogy of Cartan's torsion is drawn, and a possible Higgs-force-like 'gravitational' effect of this nonpropagating torsion on the fermion masses is described. We also check that the field generating the Majorana mass for the {nu}{sub R} is nonzero in the physical vacuum.« less

Explicit construction of BRST charge of noncommutative D-brane system

NASA Astrophysics Data System (ADS)

Hong, Soon-Tae

2006-01-01

In the BRST BFV scheme for noncommutative D-branes with constant NS B-field, introducing ghost degrees of freedom we construct the gauge-fixed Hamiltonian and corresponding effective Lagrangian invariant under nilpotent BRST charge. It is also shown that the presence of auxiliary variables introduced via the improved Dirac formalism plays a crucial role in the construction of the BRST invariant Lagrangian.

Single-photon test of hyper-complex quantum theories using a metamaterial.

PubMed

Procopio, Lorenzo M; Rozema, Lee A; Wong, Zi Jing; Hamel, Deny R; O'Brien, Kevin; Zhang, Xiang; Dakić, Borivoje; Walther, Philip

2017-04-21

In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial with a negative refractive index, and a positive phase shifter. To accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. We show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories.

Single-photon test of hyper-complex quantum theories using a metamaterial

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

Procopio, Lorenzo M.; Rozema, Lee A.; Wong, Zi Jing

In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial withmore » a negative refractive index, and a positive phase shifter. In order to accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. Here, we show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories.« less

Single-photon test of hyper-complex quantum theories using a metamaterial

DOE PAGES

Procopio, Lorenzo M.; Rozema, Lee A.; Wong, Zi Jing; ...

2017-04-21

In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial withmore » a negative refractive index, and a positive phase shifter. In order to accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. Here, we show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories.« less

Single-photon test of hyper-complex quantum theories using a metamaterial

PubMed Central

Procopio, Lorenzo M.; Rozema, Lee A.; Wong, Zi Jing; Hamel, Deny R.; O'Brien, Kevin; Zhang, Xiang; Dakić, Borivoje; Walther, Philip

2017-01-01

In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial with a negative refractive index, and a positive phase shifter. To accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. We show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories. PMID:28429711

Geometry, topology, and string theory

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

Varadarajan, Uday

A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

Two interacting Hofstadter butterflies

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

Barelli, A.; Bellissard, J.; Jacquod, P.

1997-04-01

The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More precisely, a semiclassical approach based on noncommutative geometry techniques is used to understand the intricate structure of such a spectrum. An interaction induced localization effect is furthermore emphasized. We discuss the application of our results on a two-dimensional model of two particles in a uniform magnetic field with on-site interaction. {copyright} {ital 1997} {ital The American Physical Society}

Observables and dispersion relations in κ-Minkowski spacetime

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Borowiec, Andrzej; Pachoł, Anna

2017-10-01

We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.

Joint measurement of multiple noncommuting parameters

NASA Astrophysics Data System (ADS)

Li, Jiamin; Liu, Yuhong; Cui, Liang; Huo, Nan; Assad, Syed M.; Li, Xiaoying; Ou, Z. Y.

2018-05-01

Although quantum metrology allows us to make precision measurements beyond the standard quantum limit, it mostly works on the measurement of only one observable due to the Heisenberg uncertainty relation on the measurement precision of noncommuting observables for one system. In this paper, we study the schemes of joint measurement of multiple observables which do not commute with each other using the quantum entanglement between two systems. We focus on analyzing the performance of a SU(1,1) nonlinear interferometer on fulfilling the task of joint measurement. The results show that the information encoded in multiple noncommuting observables on an optical field can be simultaneously measured with a signal-to-noise ratio higher than the standard quantum limit, and the ultimate limit of each observable is still the Heisenberg limit. Moreover, we find a resource conservation rule for the joint measurement.

Wigner functions for noncommutative quantum mechanics: A group representation based construction

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

Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com; Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8; Ali, S. Twareque, E-mail: twareque.ali@concordia.ca

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and thosemore » of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.« less

The Lorentzian distance formula in noncommutative geometry

NASA Astrophysics Data System (ADS)

Franco, Nicolas

2018-02-01

For almost twenty years, a search for a Lorentzian version of the well-known Connes’ distance formula has been undertaken. Several authors have contributed to this search, providing important milestones, and the time has now come to put those elements together in order to get a valid and functional formula. This paper presents a historical review of the construction and the proof of a Lorentzian distance formula suitable for noncommutative geometry.

An anthology of non-local QFT and QFT on non-commutative spacetime

NASA Astrophysics Data System (ADS)

Schroer, Bert

2005-09-01

Ever since the appearance of renormalization theory, there have been several differently motivated attempts at non-localized (in the sense of not generated by pointlike fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review in the light of previous results on this subject.

Thermodynamic resource theories, non-commutativity and maximum entropy principles

NASA Astrophysics Data System (ADS)

Lostaglio, Matteo; Jennings, David; Rudolph, Terry

2017-04-01

We discuss some features of thermodynamics in the presence of multiple conserved quantities. We prove a generalisation of Landauer principle illustrating tradeoffs between the erasure costs paid in different ‘currencies’. We then show how the maximum entropy and complete passivity approaches give different answers in the presence of multiple observables. We discuss how this seems to prevent current resource theories from fully capturing thermodynamic aspects of non-commutativity.

Noncommutative Jackiw-Pi model: One-loop renormalization

NASA Astrophysics Data System (ADS)

Bufalo, R.; Ghasemkhani, M.; Alipour, M.

2018-06-01

In this paper, we study the quantum behavior of the noncommutative Jackiw-Pi model. After establishing the Becchi-Rouet-Store-Tyutin (BRST) invariant action, the perturbative renormalizability is discussed, allowing us to introduce the renormalized mass and gauge coupling. We then proceed to compute the one-loop correction to the basic 1PI functions, necessary to determine the renormalized parameters (mass and charge), next we discuss the physical behavior of these parameters.

Noncommutative Differential Geometry of Generalized Weyl Algebras

NASA Astrophysics Data System (ADS)

Brzeziński, Tomasz

2016-06-01

Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p;q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p;q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p;q) are constructed, and three-dimensional first-order differential calculi induced by these derivations are described. The associated integrals are computed and it is shown that the dimension of the integral space coincides with the order of the defining polynomial p(z). It is proven that the restriction of these first-order differential calculi to the calculi on B(p;q) is isomorphic to the direct sum of degree 2 and degree -2 components of A(p;q). A Dirac operator for B(p;q) is constructed from a (strong) connection with respect to this differential calculus on the (free) spinor bimodule defined as the direct sum of degree 1 and degree -1 components of A(p;q). The real structure of KO-dimension two for this Dirac operator is also described.

Neurons the decision makers, Part I: The firing function of a single neuron.

PubMed

Saaty, Thomas

2017-02-01

This paper is concerned with understanding synthesis of electric signals in the neural system based on making pairwise comparisons. Fundamentally, every person and every animal are born with the talent to compare stimuli from things that share properties in space or over time. Comparisons always need experience to distinguish among things. Pairwise comparisons are numerically reciprocal. If a value is assigned to the larger of two elements that have a given property when compared with the smaller one, then the smaller has the reciprocal of that value when compared with the larger. Because making comparisons requires the reciprocal property, we need mathematics that can cope with division. There are four division algebras that would allow us to use our reciprocals arising from comparisons: The real numbers, the complex numbers, the non-commutative quaternions and the non-associative octonions. Rather than inferring function as from electric flow in a network, in this paper we infer the flow from function. Neurons fire in response to stimuli and their firings vary relative to the intensities of the stimuli. We believe neurons use some kind of pairwise comparison mechanism to determine when to fire based on the stimuli they receive. The ideas we develop here about flows are used to deduce how a system based on this kind of firing determination works and can be described. Furthermore the firing of neurons requires continuous comparisons. To develop a formula describing the output of these pairwise comparisons requires solving Fredholm's equation of the second kind which is satisfied if and only if a simple functional equation has solutions. The Fourier transform of the real solution of this equation leads to inverse square laws like those that are common in physics. The Fourier transform applied to a complex valued solution leads to Dirac type of firings. Such firings are dense in the very general fields of functions known as Sobolev spaces and thus can be used to represent the very diverse phenomena in and around us. The non-commutative solution in quaternions can be interpreted as rotations in space. The also non-commutative and non-associative solution in octonions has yet to be adequately interpreted outside physics. Copyright © 2016 Elsevier Ltd. All rights reserved.

Joint Services Electronics Program.

DTIC Science & Technology

1981-09-30

devices and a structure in which an interrupted superconduc- tive film strip lies on a highly doped silicon surface. We have also developed a strong...Slusher, and H. Sturge, reported at 2nd Int’l Conf. on Submillimeter Waves and Their Applications, San Juan , P.R., December 1967. (12) T. DeGraauw, H... lies in the noncommutative property of matrix multiplication. However, we believe that techniques can be developed to deal with special classes of non

Quantum field theory in generalised Snyder spaces

NASA Astrophysics Data System (ADS)

Meljanac, S.; Meljanac, D.; Mignemi, S.; Štrajn, R.

2017-05-01

We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.

Using an intense laser beam in interaction with muon/electron beam to probe the noncommutative QED

NASA Astrophysics Data System (ADS)

Tizchang, S.; Batebi, S.; Haghighat, M.; Mohammadi, R.

2017-02-01

It is known that the linearly polarized photons can partly transform to circularly polarized ones via forward Compton scattering in a background such as the external magnetic field or noncommutative space time. Based on this fact we explore the effects of the NC-background on the scattering of a linearly polarized laser beam from an intense beam of charged leptons. We show that for a muon/electron beam flux {overline{ɛ}}_{μ, e}˜ 1{0}^{12}/{10}^{10} TeV cm-2 sec-1 and a linearly polarized laser beam with energy k 0 ˜1 eV and average power {overline{P}}_{laser}˜eq 1{0}^3 KW, the generation rate of circularly polarized photons is about R V ˜ 104 /sec for noncommutative energy scale ΛNC ˜ 10 TeV. This is fairly large and can grow for more intense beams in near future.

Excluding joint probabilities from quantum theory

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Danageozian, Arshag

2018-03-01

Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.

Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures

NASA Astrophysics Data System (ADS)

Miyadera, Takayuki; Imai, Hideki

2008-11-01

A limitation on simultaneous measurement of two arbitrary positive-operator-valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner’s formulation, we introduce a distance between observables to quantify an accuracy of measurement. We derive an inequality that relates the achievable accuracy with noncommutativity between two observables. As a byproduct a necessary condition for two positive-operator-valued measures to be simultaneously measurable is obtained.

Quantum gravity boundary terms from the spectral action of noncommutative space.

PubMed

Chamseddine, Ali H; Connes, Alain

2007-08-17

We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that the spectral action predicts uniquely the gravitational boundary term required for consistency of quantum gravity with the correct sign and coefficient. This is a remarkable result given the lack of freedom in the spectral action to tune this term.

Topics in string theory

NASA Astrophysics Data System (ADS)

Jejjala, Vishnumohan

2002-01-01

This Thesis explores aspects of superstring theory on orbifold spaces and applies some of the intuition gleaned from the study of the non-commutative geometry of space-time to understanding the fractional quantum Hall effect. The moduli space of vacua of marginal and relevant deformations of N = 4 super-Yang-Mills gauge theory in four dimensions is interpreted in terms of non-commutative geometry. A formalism for thinking about the algebraic geometry of the moduli space is developed. Within this framework, the representation theory of the algebras studied provides a natural exposition of D-brane fractionation. The non-commutative moduli space of deformations preserving N = 1 supersymmetry is examined in detail through various examples. In string theory, by the AdS/CFT correspondence, deformations of the N = 4 field theory are dual to the near-horizon geometries of D-branes on orbifolds of AdS5 x S 5. The physics of D-branes on the dual AdS backgrounds is explored. Quivers encapsulate the matter content of supersymmetric field theories on the worldvolumes of D-branes at orbifold singularities. New techniques for constructing quivers are presented here. When N is a normal subgroup of a finite group G, the quiver corresponding to fixed points of the orbifold M/G is computed from a G/N action on the quiver corresponding to M/G . These techniques prove useful for constructing non-Abelian quivers and for examining discrete torsion orbifolds. Quivers obtained through our constructions contain interesting low-energy phenomenology. The matter content on a brane at an isolated singularity of the Delta27 orbifold embeds the Standard Model. The symmetries of the quiver require exactly three generations of fields in the particle spectrum. Lepton masses are suppressed relative to quark masses because lepton Yukawa couplings do not appear in the superpotential. Lepton masses are generated through the Kahler potential and are related to the supersymmetry breaking scale. The model makes falsifiable predictions about TeV scale physics. Susskind has proposed that the fractional quantum Hall system can be realized through an Abelian Chern-Simons theory with a Moyal product. Susskind's Chern-Simons field is a hydrodynamical quantity. Lopez and Fradkin have an alternate Chern-Simons description couched in terms of a statistical gauge field. We show that this statistical Chern-Simons theory also possesses a non-commutative structure and develop the dictionary between the two Chern-Simons pictures.

Conformal twists, Yang–Baxter σ-models & holographic noncommutativity

NASA Astrophysics Data System (ADS)

Araujo, Thiago; Bakhmatov, Ilya; Colgáin, Eoin Ó.; Sakamoto, Jun-ichi; Sheikh-Jabbari, Mohammad M.; Yoshida, Kentaroh

2018-06-01

Expanding upon earlier results (Araujo et al 2017 Phys. Rev. D 95 105006), we present a compendium of σ-models associated with integrable deformations of AdS5 generated by solutions to homogenous classical Yang–Baxter equation. Each example we study from four viewpoints: conformal (Drinfeld) twists, closed string gravity backgrounds, open string parameters and proposed dual noncommutative (NC) gauge theory. Irrespective of whether the deformed background is a solution to supergravity or generalized supergravity, we show that the open string metric associated with each gravity background is undeformed AdS5 with constant open string coupling and the NC structure Θ is directly related to the conformal twist. One novel feature is that Θ exhibits ‘holographic noncommutativity’: while it may exhibit non-trivial dependence on the holographic direction, its value everywhere in the bulk is uniquely determined by its value at the boundary, thus facilitating introduction of a dual NC gauge theory. We show that the divergence of the NC structure Θ is directly related to the unimodularity of the twist. We discuss the implementation of an outer automorphism of the conformal algebra as a coordinate transformation in the AdS bulk and discuss its implications for Yang–Baxter σ-models and self-T-duality based on fermionic T-duality. Finally, we comment on implications of our results for the integrability of associated open strings and planar integrability of dual NC gauge theories.

The non-commutative topology of two-dimensional dirty superconductors

NASA Astrophysics Data System (ADS)

De Nittis, Giuseppe; Schulz-Baldes, Hermann

2018-01-01

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

Quantum morphogenesis: A variation on Thom's catastrophe theory

NASA Astrophysics Data System (ADS)

Aerts, Dirk; Czachor, Marek; Gabora, Liane; Kuna, Maciej; Posiewnik, Andrzej; Pykacz, Jarosław; Syty, Monika

2003-05-01

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including “birth and death of an organism” and “development of complementary properties.”

Time-ordering dependence of measurements in teleportation

NASA Astrophysics Data System (ADS)

Bertlmann, Reinhold A.; Narnhofer, Heide; Thirring, Walter

2013-03-01

We trace back the phenomenon of "delayed-choice entanglement swapping" as it was realized in a recent experiment to the commutativity of the projection operators that are involved in the corresponding measurement process. We also propose an experimental set-up which depends on the order of successive measurements corresponding to noncommutative projection operators. In this case entanglement swapping is used to teleport a quantum state from Alice to Bob, where Bob has now the possibility to examine the noncommutativity within the quantum history.

Noncommuting local common causes for correlations violating the Clauser-Horne inequality

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

Hofer-Szabo, Gabor; Vecsernyes, Peter

2012-12-15

In the paper, the EPR-Bohm scenario will be reproduced in an algebraic quantum field theoretical setting with locally finite degrees of freedom. It will be shown that for a set of spatially separated correlating events (projections) maximally violating the Clauser-Horne inequality there can be given a common causal explanation if commutativity is abandoned between the common cause and the correlating events. Moreover, the noncommuting common cause will be local and supported in the common past of the correlating events.

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.

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

NASA Astrophysics Data System (ADS)

Katsura, Hosho; Koma, Tohru

2018-03-01

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

Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges

PubMed Central

Yunger Halpern, Nicole; Faist, Philippe; Oppenheim, Jonathan; Winter, Andreas

2016-01-01

The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented by operators that fail to commute. Whether such a system thermalizes and what form the thermal state has are questions about truly quantum thermodynamics. Here we investigate this thermal state from three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system-and-bath composite, tracing out the bath yields the system's thermal state. This state is expected to be the equilibrium point, we argue, of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity—the inability to extract work from equilibrium states—implies the thermal state's form, too. Our work opens new avenues into equilibrium in the presence of quantum noncommutation. PMID:27384494

Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

NASA Astrophysics Data System (ADS)

Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

2017-11-01

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

Noncommutative wormhole solutions in F(T, T𝒢) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Nazir, Kanwal

2017-04-01

This paper is devoted to the study of static spherically symmetric wormhole solutions along with noncommutative geometry in the background of F(T, T𝒢) gravity. We assume a nonzero redshift function as well as two well-known models of this gravity and discuss the behavior of null/weak energy conditions graphically. We conclude that there does not exist any physically acceptable wormhole solution for the first model, but there is a chance to develop physically acceptable wormhole solution in a particular region for the second model.

Quantum Koszul formula on quantum spacetime

NASA Astrophysics Data System (ADS)

Majid, Shahn; Williams, Liam

2018-07-01

Noncommutative or quantum Riemannian geometry has been proposed as an effective theory for aspects of quantum gravity. Here the metric is an invertible bimodule map Ω1⊗AΩ1 → A where A is a possibly noncommutative or 'quantum' spacetime coordinate algebra and (Ω1 , d) is a specified bimodule of 1-forms or 'differential calculus' over it. In this paper we explore the proposal of a 'quantum Koszul formula' in Majid [12] with initial data a degree - 2 bilinear map ⊥ on the full exterior algebra Ω obeying the 4-term relations

Comparing exact energy solutions of quartic eigenvalue polynomials in commutative, non-commutative and non-commutative phase frameworks for boson π‑

NASA Astrophysics Data System (ADS)

Derakhshani, Z.; Ghominejad, M.

2018-04-01

In this paper, the behavior of a Duffin-Kemmer-Petiau (DKP) boson particle in the presence of a harmonic energy-dependent interaction, under the influence of an external magnetic field is precisely studied. In order to exactly solve all equations in commutative (C), non-commutative (NC) and non-commutative phase (NCP) frameworks, the Nikiforov-Uvarov (NU) powerful exact approach is employed. All these attempts end up with solving their quartic equations, trying to find and discuss on their discriminant function Δ, in a unique way which has never been discussed for any boson in any other research, especially for the boson π‑ on which, we have been exclusively concerned. We finally succeeded to obtain the exact energy spectrums and wave functions under the effects of NC and NCP parameters and energy-dependent interaction on energy eigenvalues. In this step, we analyze the behaviors of their quartic energy eigenvalue polynomials in three sections and accurately compare all achieved physical-admissible roots one by one. This comparison surprisingly shows that the NC and NCP effects on the other hand, and the assumed harmonic energy-dependent interaction on the other hand, have almost the same order of perturbation effects for limited amounts of the magnetic field in a system of DKP bosons. Furthermore, through some calculations within this paper, we came up with a very crucial point about the NU method which was mistakenly being used in many papers by several researchers and improved it to be used safely.

Issues on 3D noncommutative electromagnetic duality

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

Rodrigues, Davi C.; Wotzasek, Clovis

We extend the ordinary 3D electromagnetic duality to the noncommutative (NC) space-time through a Seiberg-Witten map to second order in the noncommutativity parameter {theta}, defining a new scalar field model. There are similarities with the 4D NC duality; these are exploited to clarify properties of both cases. Up to second order in {theta}, we find that duality interchanges the 2-form {theta} with its 1-form Hodge dual *{theta} times the gauge coupling constant, i.e., {theta}{yields}*{theta}g{sup 2} (similar to the 4D NC electromagnetic duality). We directly prove that this property is false in the third order expansion in both 3D and 4Dmore » space-times, unless the slowly varying fields limit is imposed. Outside this limit, starting from the third order expansion, {theta} cannot be rescaled to attain an S-duality. In addition to possible applications on effective models, the 3D space-time is useful for studying general properties of NC theories. In particular, in this dimension, we deduce an expression that significantly simplifies the Seiberg-Witten mapped Lagrangian to all orders in {theta}.« less

Spectral geometry of {kappa}-Minkowski space

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

D'Andrea, Francesco

After recalling Snyder's idea [Phys. Rev. 71, 38 (1947)] of using vector fields over a smooth manifold as 'coordinates on a noncommutative space', we discuss a two-dimensional toy-model whose 'dual' noncommutative coordinates form a Lie algebra: this is the well-known {kappa}-Minkowski space [Phys. Lett. B 334, 348 (1994)]. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of {kappa}-Minkowski as linear operators on an Hilbert space (a major problem in the construction of a physical theory), study its 'spectral properties', and discuss how tomore » obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of Dimitrijevic et al. [Eur. Phys. J. C 31, 129 (2003)] can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.« less

Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds

NASA Astrophysics Data System (ADS)

Liu, Yang

2017-11-01

We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the j-function (which defines the A ˆ -class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.

Dark solitons, D-branes and noncommutative tachyon field theory

NASA Astrophysics Data System (ADS)

Giaccari, Stefano; Nian, Jun

2017-11-01

In this paper we discuss the boson/vortex duality by mapping the (3+1)D Gross-Pitaevskii theory into an effective string theory in the presence of boundaries. Via the effective string theory, we find the Seiberg-Witten map between the commutative and the noncommutative tachyon field theories, and consequently identify their soliton solutions with D-branes in the effective string theory. We perform various checks of the duality map and the identification of soliton solutions. This new insight between the Gross-Pitaevskii theory and the effective string theory explains the similarity of these two systems at quantitative level.

Singlet particles as cold dark matter in a noncommutative space-time

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

Ettefaghi, M. M.

2009-03-15

We extend the noncommutative (NC) standard model to incorporate singlet particles as cold dark matter. In the NC space-time, the singlet particles can be coupled to the U(1) gauge field in the adjoint representation. We study the relic density of the singlet particles due to the NC induced interaction. Demanding either the singlet fermion or the singlet scalar to serve as cold dark matter and the NC induced interactions to be relevant to the dark matter production, we obtain the corresponding relations between the NC scale and the dark matter masses, which are consistent with some existing bounds.

Noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

Gamboa, J.; Loewe, M.; Rojas, J. C.

2001-09-01

A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.

Poisson structure on a space with linear SU(2) fuzziness

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Fatollahi, Amir H.; Shariati, Ahmad

2009-07-01

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which the counterpart of the angular momentum as well as the Euler parametrization of the phase space are introduced. SU(2)-invariant classical systems are discussed, and it is observed that the path of particle can be obtained by the solution of a first-order equation, as the case with such models on commutative spaces. The examples of free particle, rotationally invariant potentials, and specially the isotropic harmonic oscillator are investigated in more detail.

Meixner Class of Non-commutative Generalized Stochastic Processes with Freely Independent Values II. The Generating Function

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Lytvynov, Eugene

2011-03-01

Let T be an underlying space with a non-atomic measure σ on it. In [ Comm. Math. Phys. 292, 99-129 (2009)] the Meixner class of non-commutative generalized stochastic processes with freely independent values, {ω=(ω(t))_{tin T}} , was characterized through the continuity of the corresponding orthogonal polynomials. In this paper, we derive a generating function for these orthogonal polynomials. The first question we have to answer is: What should serve as a generating function for a system of polynomials of infinitely many non-commuting variables? We construct a class of operator-valued functions {Z=(Z(t))_{tin T}} such that Z( t) commutes with ω( s) for any {s,tin T}. Then a generating function can be understood as {G(Z,ω)=sum_{n=0}^infty int_{T^n}P^{(n)}(ω(t_1),dots,ω(t_n))Z(t_1)dots Z(t_n)} {σ(dt_1) dots σ(dt_n)} , where {P^{(n)}(ω(t_1),dots,ω(t_n))} is (the kernel of the) n th orthogonal polynomial. We derive an explicit form of G( Z, ω), which has a resolvent form and resembles the generating function in the classical case, albeit it involves integrals of non-commuting operators. We finally discuss a related problem of the action of the annihilation operators {partial_t,t in T} . In contrast to the classical case, we prove that the operators ∂ t related to the free Gaussian and Poisson processes have a property of globality. This result is genuinely infinite-dimensional, since in one dimension one loses the notion of globality.

The coordinate coherent states approach revisited

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

Miao, Yan-Gang, E-mail: miaoyg@nankai.edu.cn; Zhang, Shao-Jun, E-mail: sjzhang@mail.nankai.edu.cn

2013-02-15

We revisit the coordinate coherent states approach through two different quantization procedures in the quantum field theory on the noncommutative Minkowski plane. The first procedure, which is based on the normal commutation relation between an annihilation and creation operators, deduces that a point mass can be described by a Gaussian function instead of the usual Dirac delta function. However, we argue this specific quantization by adopting the canonical one (based on the canonical commutation relation between a field and its conjugate momentum) and show that a point mass should still be described by the Dirac delta function, which implies thatmore » the concept of point particles is still valid when we deal with the noncommutativity by following the coordinate coherent states approach. In order to investigate the dependence on quantization procedures, we apply the two quantization procedures to the Unruh effect and Hawking radiation and find that they give rise to significantly different results. Under the first quantization procedure, the Unruh temperature and Unruh spectrum are not deformed by noncommutativity, but the Hawking temperature is deformed by noncommutativity while the radiation specturm is untack. However, under the second quantization procedure, the Unruh temperature and Hawking temperature are untack but the both spectra are modified by an effective greybody (deformed) factor. - Highlights: Black-Right-Pointing-Pointer Suggest a canonical quantization in the coordinate coherent states approach. Black-Right-Pointing-Pointer Prove the validity of the concept of point particles. Black-Right-Pointing-Pointer Apply the canonical quantization to the Unruh effect and Hawking radiation. Black-Right-Pointing-Pointer Find no deformations in the Unruh temperature and Hawking temperature. Black-Right-Pointing-Pointer Provide the modified spectra of the Unruh effect and Hawking radiation.« less

Twisted sigma-model solitons on the quantum projective line

NASA Astrophysics Data System (ADS)

Landi, Giovanni

2018-04-01

On the configuration space of projections in a noncommutative algebra, and for an automorphism of the algebra, we use a twisted Hochschild cocycle for an action functional and a twisted cyclic cocycle for a topological term. The latter is Hochschild-cohomologous to the former and positivity in twisted Hochschild cohomology results into a lower bound for the action functional. While the equations for the critical points are rather involved, the use of the positivity and the bound by the topological term lead to self-duality equations (thus yielding twisted noncommutative sigma-model solitons, or instantons). We present explicit nontrivial solutions on the quantum projective line.

Minimal scales from an extended Hilbert space

NASA Astrophysics Data System (ADS)

Kober, Martin; Nicolini, Piero

2010-12-01

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to noncommutative geometry. We explore, as a toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.

Noncommuting observables in quantum detection and estimation theory

NASA Technical Reports Server (NTRS)

Helstrom, C. W.

1972-01-01

Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.

Survey on nonlocal games and operator space theory

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

Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es; Vidick, Thomas, E-mail: vidick@cms.caltech.edu

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify themore » nonlocality of different classes of entangled states.« less

T-duality simplifies bulk-boundary correspondence: the noncommutative case

NASA Astrophysics Data System (ADS)

Hannabuss, Keith C.; Mathai, Varghese; Thiang, Guo Chuan

2018-05-01

We state and prove a general result establishing that T-duality, or the Connes-Thom isomorphism, simplifies the bulk-boundary correspondence, given by a boundary map in K-theory, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to string theory and to the study of the quantum Hall effect and topological insulators with defects in condensed matter physics.

Moduli of quantum Riemannian geometries on <=4 points

NASA Astrophysics Data System (ADS)

Majid, S.; Raineri, E.

2004-12-01

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously [S. Majid, Commun. Math. Phys. 225, 131 (2002)]. The full moduli space is found for ⩽3 points, and a restricted moduli space for 4 points. Generalized Levi-Cività connections and their curvatures are found for a variety of models including models of a discrete torus. The topological part of the moduli space is found for ⩽9 points based on the known atlas of regular graphs. We also remark on aspects of quantum gravity in this approach.

Quantum group structure and local fields in the algebraic approach to 2D gravity

NASA Astrophysics Data System (ADS)

Schnittger, J.

1995-07-01

This review contains a summary of the work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables — the Liouville exponentials and the Liouville field itself — and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.

Constraining the noncommutative spectral action via astrophysical observations.

PubMed

Nelson, William; Ochoa, Joseph; Sakellariadou, Mairi

2010-09-03

The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of particle physics in this setting, in addition to a modified version of Einstein-Hilbert gravity. In this Letter we use observations of pulsar timings, assuming that no deviation from general relativity has been observed, to constrain the gravitational sector of this theory. While the bounds on the coupling constants remain rather weak, they are comparable to existing bounds on deviations from general relativity in other settings and are likely to be further constrained by future observations.

Noncommutative-geometry model for closed bosonic strings

NASA Technical Reports Server (NTRS)

Sen, Siddhartha; Holman, R.

1987-01-01

It is shown how Witten's (1986) noncommutative geometry may be extended to describe the closed bosonic string. For closed strings, an explicit representation is provided of the integral operator needed to construct an action and of an associative product on string fields. The proper choice of the action of the integral operator and the associative product in order to give rise to a reasonable theory is explained, and the consequences of such a choice are discussed. It is shown that the ghost numbers of the operator and associative product can be chosen arbitrarily for both open and closed strings, and that this construct can be used as an action for interacting closed bosonic strings.

Cosmological perturbations of a perfect fluid and noncommutative variables

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

De Felice, Antonio; Gerard, Jean-Marc; Suyama, Teruaki

2010-03-15

We describe the linear cosmological perturbations of a perfect fluid at the level of an action, providing thus an alternative to the standard approach based only on the equations of motion. This action is suited not only to perfect fluids with a barotropic equation of state, but also to those for which the pressure depends on two thermodynamical variables. By quantizing the system we find that (1) some perturbation fields exhibit a noncommutativity quite analogous to the one observed for a charged particle moving in a strong magnetic field, (2) local curvature and pressure perturbations cannot be measured simultaneously, (3)more » ghosts appear if the null energy condition is violated.« less

Gauge Theory on a Space with Linear Lie Type Fuzziness

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Fatollahi, Amir H.; Shariati, Ahmad

2013-03-01

The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translations in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory, the object playing the role of flux of field strength per plaquette, as well as the action, is constructed. It is observed that the theory, in comparison with ordinary U(1) gauge theory, has an extra gauge field component. This phenomena is reminiscent of similar ones in formulation of SU(N) gauge theory in space with canonical noncommutativity, and also appearance of gauge field component in discrete direction of Connes' construction of the Standard Model.

Lagrange multiplier and Wess-Zumino variable as extra dimensions in the torus universe

NASA Astrophysics Data System (ADS)

Nejad, Salman Abarghouei; Dehghani, Mehdi; Monemzadeh, Majid

2018-01-01

We study the effect of the simplest geometry which is imposed via the topology of the universe by gauging non-relativistic particle model on torus and 3-torus with the help of symplectic formalism of constrained systems. Also, we obtain generators of gauge transformations for gauged models. Extracting corresponding Poisson structure of existed constraints, we show the effect of the shape of the universe on canonical structure of phase-spaces of models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of extra dimensions in the phase-spaces of gauged embedded models are exactly two. Moreover, in classical form, we talk over modification of Newton's second law in order to study the origin of the terms appeared in the gauged theory.

Transverse Laplacians for Substitution Tilings

NASA Astrophysics Data System (ADS)

Julien, Antoine; Savinien, Jean

2011-01-01

Pearson and Bellissard recently built a spectral triple - the data of Riemannian noncommutative geometry - for ultrametric Cantor sets. They derived a family of Laplace-Beltrami like operators on those sets. Motivated by the applications to specific examples, we revisit their work for the transversals of tiling spaces, which are particular self-similar Cantor sets. We use Bratteli diagrams to encode the self-similarity, and Cuntz-Krieger algebras to implement it. We show that the abscissa of convergence of the ζ-function of the spectral triple gives indications on the exponent of complexity of the tiling. We determine completely the spectrum of the Laplace-Beltrami operators, give an explicit method of calculation for their eigenvalues, compute their Weyl asymptotics, and a Seeley equivalent for their heat kernels.

Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes

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

Houshmand, Monireh; Hosseini-Khayat, Saied

2011-02-15

Quantum convolutional codes, like their classical counterparts, promise to offer higher error correction performance than block codes of equivalent encoding complexity, and are expected to find important applications in reliable quantum communication where a continuous stream of qubits is transmitted. Grassl and Roetteler devised an algorithm to encode a quantum convolutional code with a ''pearl-necklace'' encoder. Despite their algorithm's theoretical significance as a neat way of representing quantum convolutional codes, it is not well suited to practical realization. In fact, there is no straightforward way to implement any given pearl-necklace structure. This paper closes the gap between theoretical representation andmore » practical implementation. In our previous work, we presented an efficient algorithm to find a minimal-memory realization of a pearl-necklace encoder for Calderbank-Shor-Steane (CSS) convolutional codes. This work is an extension of our previous work and presents an algorithm for turning a pearl-necklace encoder for a general (non-CSS) quantum convolutional code into a realizable quantum convolutional encoder. We show that a minimal-memory realization depends on the commutativity relations between the gate strings in the pearl-necklace encoder. We find a realization by means of a weighted graph which details the noncommutative paths through the pearl necklace. The weight of the longest path in this graph is equal to the minimal amount of memory needed to implement the encoder. The algorithm has a polynomial-time complexity in the number of gate strings in the pearl-necklace encoder.« less

Gauge Theories on Noncommutative Spacetime Treated by the Seiberg-Witten Method*

NASA Astrophysics Data System (ADS)

Wess, J.

The idea of noncommutative coordinates (NCC) is almost as old as quantum field theory (QFT) itself. It was W.Heisenberg who proposed NCC in 1930 in a letter to Peierls [1]. He expressed the hope that uncertainty relations of the coordinates, derived from NCC, might provide a natural cut-off for divergent integrals in QFT. This idea propagated via W.Pauli, R.Oppenheimer and Oppenheimer's student H.S.Snyder [2]. He then published the first analysis of a quantum thoery on NCC. Paul [3] called this work mathematically ingenious but rejected it for reasons of physics, arguing that an effective cut-off would act like a universal length and thus lead to strange consequences for large momenta of order h/l0.

Labeled trees and the efficient computation of derivations

NASA Technical Reports Server (NTRS)

Grossman, Robert; Larson, Richard G.

1989-01-01

The effective parallel symbolic computation of operators under composition is discussed. Examples include differential operators under composition and vector fields under the Lie bracket. Data structures consisting of formal linear combinations of rooted labeled trees are discussed. A multiplication on rooted labeled trees is defined, thereby making the set of these data structures into an associative algebra. An algebra homomorphism is defined from the original algebra of operators into this algebra of trees. An algebra homomorphism from the algebra of trees into the algebra of differential operators is then described. The cancellation which occurs when noncommuting operators are expressed in terms of commuting ones occurs naturally when the operators are represented using this data structure. This leads to an algorithm which, for operators which are derivations, speeds up the computation exponentially in the degree of the operator. It is shown that the algebra of trees leads naturally to a parallel version of the algorithm.

Non-singular Brans-Dicke collapse in deformed phase space

NASA Astrophysics Data System (ADS)

Rasouli, S. M. M.; Ziaie, A. H.; Jalalzadeh, S.; Moniz, P. V.

2016-12-01

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans-Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.

Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states

NASA Astrophysics Data System (ADS)

Lapa, Matthew F.; Hughes, Taylor L.

2018-05-01

We study geometric aspects of the Laughlin fractional quantum Hall (FQH) states using a description of these states in terms of a matrix quantum mechanics model known as the Chern-Simons matrix model (CSMM). This model was proposed by Polychronakos as a regularization of the noncommutative Chern-Simons theory description of the Laughlin states proposed earlier by Susskind. Both models can be understood as describing the electrons in a FQH state as forming a noncommutative fluid, i.e., a fluid occupying a noncommutative space. Here, we revisit the CSMM in light of recent work on geometric response in the FQH effect, with the goal of determining whether the CSMM captures this aspect of the physics of the Laughlin states. For this model, we compute the Hall viscosity, Hall conductance in a nonuniform electric field, and the Hall viscosity in the presence of anisotropy (or intrinsic geometry). Our calculations show that the CSMM captures the guiding center contribution to the known values of these quantities in the Laughlin states, but lacks the Landau orbit contribution. The interesting correlations in a Laughlin state are contained entirely in the guiding center part of the state/wave function, and so we conclude that the CSMM accurately describes the most important aspects of the physics of the Laughlin FQH states, including the Hall viscosity and other geometric properties of these states, which are of current interest.

Noncommutative de Rham Cohomology of Finite Groups

NASA Astrophysics Data System (ADS)

Castellani, L.; Catenacci, R.; Debernardi, M.; Pagani, C.

We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S3, the dihedral group D4 and the quaternion group Q. Poincaré duality holds in every case, and under some assumptions (essentially the existence of a top form) we find that it must hold in general. A short review of the bicovariant (noncommutative) differential calculus on finite G is given for selfconsistency. Exterior derivative, exterior product, metric, Hodge dual, connections, torsion, curvature, and biinvariant integration can be defined algebraically. A projector decomposition of the braiding operator is found, and used in constructing the projector on the space of two-forms. By means of the braiding operator and the metric a knot invariant is defined for any finite group.

Correlators in simultaneous measurement of non-commuting qubit observables

NASA Astrophysics Data System (ADS)

Atalaya, Juan; Hacohen-Gourgy, Shay; Martin, Leigh S.; Siddiqi, Irfan; Korotkov, Alexander N.

We consider simultaneous continuous measurement of non-commuting qubit observables and analyze multi-time correlators 〈i κ1 (t1) ^i κN (tN) 〉 for output signals i κ (t) from the detectors. Both informational (''spooky'') and phase backactions from cQED-type measurements with phase-sensitive amplifiers are taken into account. We find an excellent agreement between analytical results and experimental data for two-time correlators of the output signals from simultaneous measurement of qubit observables σx and σφ =σx cosφ +σy sinφ . The correlators can be used to extract small deviations of experimental parameters, e.g., phase backaction and residual Rabi frequency. The multi-time correlators are important in analysis of Bacon-Shor error correction/detection codes, operated with continuous measurements.

Euler polynomials and identities for non-commutative operators

NASA Astrophysics Data System (ADS)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

The noncommutative family Atiyah-Patodi-Singer index theorem

NASA Astrophysics Data System (ADS)

Wang, Yong

2016-12-01

In this paper, we define the eta cochain form and prove its regularity when the kernel of a family of Dirac operators is a vector bundle. We decompose the eta form as a pairing of the eta cochain form with the Chern character of an idempotent matrix and we also decompose the Chern character of the index bundle for a fibration with boundary as a pairing of the family Chern-Connes character for a manifold with boundary with the Chern character of an idempotent matrix. We define the family b-Chern-Connes character and then we prove that it is entire and give its variation formula. By this variation formula, we prove another noncommutative family Atiyah-Patodi-Singer index theorem. Thus, we extend the results of Getzler and Wu to the family case.

Simultaneous continuous measurement of non-commuting observables and correlation in qubit trajectories

NASA Astrophysics Data System (ADS)

Chantasri, Areeya; Jordan, Andrew

We consider the continuous quantum measurement of two or more non-commuting observables of a single qubit. Examples are presented for the measurement of two observables which can be mapped to two measurement axes on the Bloch sphere; a special case being the measurement along the X and Z bases. The qubit dynamics is described by the stochastic master equations which include the effect of decoherence and measurement inefficiencies. We investigate the qubit trajectories, their most likely paths, and their correlation functions using the stochastic path integral formalism. The correlation functions in qubit trajectories can be derived exactly for a special case and perturbatively for general cases. The theoretical predictions are compared with numerical simulations, as well as with trajectory data from the transmon superconducting qubit experiments.

Heat asymptotics for nonminimal Laplace type operators and application to noncommutative tori

NASA Astrophysics Data System (ADS)

Iochum, B.; Masson, T.

2018-07-01

Let P be a Laplace type operator acting on a smooth hermitean vector bundle V of fiber CN over a compact Riemannian manifold given locally by P = - [gμν u(x) ∂μ∂ν +vν(x) ∂ν + w(x) ] where u ,vν , w are MN(C) -valued functions with u(x) positive and invertible. For any a ∈ Γ(End(V)) , we consider the asymptotics Tr(ae-tP) ∼ t↓0+ ∑r=0∞ ar(a , P) t (r - d) / 2 where the coefficients ar(a , P) can be written as an integral of the functions ar(a , P) (x) = tr [ a(x) Rr(x) ] . The computation of R2 is performed opening the opportunity to calculate the modular scalar curvature for noncommutative tori.

Accretion onto a noncommutative geometry inspired black hole

NASA Astrophysics Data System (ADS)

Kumar, Rahul; Ghosh, Sushant G.

2017-09-01

The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rate \\dot{M}, sonic speed a_s and other flow parameters are generalized for the NC inspired static black hole and compared with the results obtained for the standard Schwarzschild black holes. Also explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon are derived. This analysis is a generalization of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters also have been modified. It turns out that \\dot{M} ≈ {M^2} is still achievable but r_s seems to be substantially decreased due to the NC effects. They in turn do affect the accretion process.

Relativistic differential-difference momentum operators and noncommutative differential calculus

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

Mir-Kasimov, R. M., E-mail: mirkr@theor.jinr.ru

2013-09-15

The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irrepsmore » of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.« less

Non-commuting two-local Hamiltonians for quantum error suppression

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Rieffel, Eleanor G.

2017-04-01

Physical constraints make it challenging to implement and control many-body interactions. For this reason, designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. Enabling error suppression with two-local Hamiltonians is particularly challenging. A no-go theorem of Marvian and Lidar (Phys Rev Lett 113(26):260504, 2014) demonstrates that, even allowing particles with high Hilbert space dimension, it is impossible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms. Here, we get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes (Bacon in Phys Rev A 73(1):012340, 2006) and generalized-Bacon-Shor code (Bravyi in Phys Rev A 83(1):012320, 2011). Our results imply that non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. While far from providing full fault tolerance, this approach improves the robustness achievable in near-term implementable quantum storage and adiabatic quantum computations, reducing the number of higher-order terms required to encode commonly used adiabatic Hamiltonians such as the Ising Hamiltonians common in adiabatic quantum optimization and quantum annealing.

Size and shape of Brain may be such as to take advantage of two Dimensions of Time

NASA Astrophysics Data System (ADS)

Kriske, Richard

2014-03-01

This author had previously Theorized that there are two non-commuting Dimensions of time. One is Clock Time and the other is Information Time (which we generally refer to as Information, like Spin Up or Spin Down). When time does not commute with another Dimension of Time, one takes the Clock Time at one point in space and the Information time is not known; that is different than if one takes the Information time at that point and the Clock time is not known--This is not explicitly about time but rather space. An example of this non-commutation is that if one knows the Spin at one point and the Time at one point of space then simultaneosly, one knows the Spin at another point of Space and the Time there (It is the same time), it is a restatement of the EPR paradox. As a matter of fact two Dimensions of Time would prove the EPR paradox. It is obvious from that argument that if one needed to take advantage of Information, then a fairly large space needs to be used, a large amount of Energy needs to be Generated and a symmetry needs to be established in Space-like the lobes of a Brain in order to detect the fact that the Tclock and Tinfo are not Commuting. This Non-Commuting deposits a large amount of Information simultaneously in that space, and synchronizes the time there.

Non-singular Brans–Dicke collapse in deformed phase space

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

Rasouli, S.M.M., E-mail: mrasouli@ubi.pt; Centro de Matemática e Aplicações; Physics Group, Qazvin Branch, Islamic Azad University, Qazvin

2016-12-15

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theorymore » is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.« less

Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields

NASA Astrophysics Data System (ADS)

Bonezzi, Roberto; Boulanger, Nicolas; De Filippi, David; Sundell, Per

2017-11-01

We first prove that, in Vasiliev’s theory, the zero-form charges studied in Sezgin E and Sundell P 2011 (arXiv:1103.2360 [hep-th]) and Colombo N and Sundell P 20 (arXiv:1208.3880 [hep-th]) are twisted open Wilson lines in the noncommutative Z space. This is shown by mapping Vasiliev’s higher-spin model on noncommutative Yang-Mills theory. We then prove that, prior to Bose-symmetrising, the cyclically-symmetric higher-spin invariants given by the leading order of these n-point zero-form charges are equal to corresponding cyclically-invariant building blocks of n-point correlation functions of bilinear operators in free conformal field theories (CFT) in three dimensions. On the higher spin gravity side, our computation reproduces the results of Didenko V and Skvortsov E 2013 J. High Energy Phys. JHEP04(2013)158 using an alternative method amenable to the computation of subleading corrections obtained by perturbation theory in normal order. On the free CFT side, our proof involves the explicit computation of the separate cyclic building blocks of the correlation functions of n conserved currents in arbitrary dimension d>2 using polarization vectors, which is an original result. It is shown to agree, for d=3 , with the results obtained in Gelfond O A and Vasiliev M A 2013 Nucl. Phys. B 876 871-917 in various dimensions and where polarization spinors were used.

Representation of the contextual statistical model by hyperbolic amplitudes

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

Khrennikov, Andrei

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. Wemore » also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy.« less

Representation of the contextual statistical model by hyperbolic amplitudes

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2005-06-01

We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy.

How weak values emerge in joint measurements on cloned quantum systems.

PubMed

Hofmann, Holger F

2012-07-13

A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but nonpositive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems, resulting in perfect correlations for all observables. The joint probabilities for noncommuting measurements on separate clones then correspond to the real parts of the complex joint probabilities observed in weak measurements on a single system, where the measurements on the two clones replace the corresponding sequence of weak measurement and postselection. The imaginary parts of weak measurement statics can be obtained by replacing the cloning process with a partial swap operation. A controlled-swap operation combines both processes, making the complete weak measurement statistics accessible as a well-defined contribution to the joint probabilities of fully resolved projective measurements on the two output systems.

Core structure and dynamics of non-Abelian vortices in a biaxial nematic spinor Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Borgh, Magnus O.; Ruostekoski, Janne

2016-05-01

We demonstrate that multiple interaction-dependent defect core structures as well as dynamics of non-Abelian vortices can be realized in the biaxial nematic (BN) phase of a spin-2 atomic Bose-Einstein condensate (BEC). An experimentally simple protocol may be used to break degeneracy with the uniaxial nematic phase. We show that a discrete spin-space symmetry in the core may be reflected in a breaking of its spatial symmetry. The discrete symmetry of the BN order parameter leads to non-commuting vortex charges. We numerically simulate reconnection of non-Abelian vortices, demonstrating formation of the obligatory rung vortex. In addition to atomic BECs, non-Abelian vortices are theorized in, e.g., liquid crystals and cosmic strings. Our results suggest the BN spin-2 BEC as a prime candidate for their realization. We acknowledge financial support from the EPSRC.

Anticommutative extension of the Adler map

NASA Astrophysics Data System (ADS)

Konstantinou-Rizos, S.; Mikhailov, A. V.

2016-07-01

We construct a noncommutative (Grassmann) extension of the well-known Adler Yang-Baxter map. It satisfies the Yang-Baxter equation, it is reversible and birational. Our extension preserves all the properties of the original map except the involutivity.

One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative p^{-2} U(1) Gauge Model

NASA Astrophysics Data System (ADS)

Blaschke, Daniel N.; Rofner, Arnold; Sedmik, René I. P.

2010-05-01

This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θ-deformed non-commutative p-2 model originally introduced by Gurau et al. [Comm. Math. Phys. 287 (2009), 275-290]. It is shown that breaking terms of the form used by Vilar et al. [J. Phys. A: Math. Theor. 43 (2010), 135401, 13 pages] and ourselves [Eur. Phys. J. C: Part. Fields 62 (2009), 433-443] to localize the BRST covariant operator (D2θ2D2)-1 lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.

Quantum spaces, central extensions of Lie groups and related quantum field theories

NASA Astrophysics Data System (ADS)

Poulain, Timothé; Wallet, Jean-Christophe

2018-02-01

Quantum spaces with su(2) noncommutativity can be modelled by using a family of SO(3)-equivariant differential *-representations. The quantization maps are determined from the combination of the Wigner theorem for SU(2) with the polar decomposition of the quantized plane waves. A tracial star-product, equivalent to the Kontsevich product for the Poisson manifold dual to su(2) is obtained from a subfamily of differential *-representations. Noncommutative (scalar) field theories free from UV/IR mixing and whose commutative limit coincides with the usual ϕ 4 theory on ℛ3 are presented. A generalization of the construction to semi-simple possibly non simply connected Lie groups based on their central extensions by suitable abelian Lie groups is discussed. Based on a talk presented by Poulain T at the XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25), Prague, June 6-10 2017.

Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives

NASA Astrophysics Data System (ADS)

Bernardara, M.; Tabuada, G.

2016-06-01

Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when \\dim (S)≤ 1), Grothendieck's standard conjecture of Lefschetz type (when \\dim (S)≤ 2), and Hodge's conjecture (when \\dim(S)≤ 3).

Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study

NASA Astrophysics Data System (ADS)

Amelino-Camelia, Giovanni; Astuti, Valerio

2015-06-01

Alternative approaches to the study of the quantum gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages the introduction of particles and fields, while other approaches assume that spacetime should only be an emergent entity. We here argue that recent progress in the covariant formulation of quantum mechanics, suggests that empty spacetime is not physically meaningful. We illustrate our general thesis in the specific context of the noncommutative Snyder spacetime, which is also of some intrinsic interest, since hundreds of studies were devoted to its analysis. We show that empty Snyder spacetime, described in terms of a suitable kinematical Hilbert space, is discrete, but this is only a formal artifact: the discreteness leaves no trace on the observable properties of particles on the physical Hilbert space.

Noncommutative mapping from the symplectic formalism

NASA Astrophysics Data System (ADS)

De Andrade, M. A.; Neves, C.

2018-01-01

Bopp's shifts will be generalized through a symplectic formalism. A special procedure, like "diagonalization," which drives the completely deformed symplectic matrix to the standard symplectic form was found as suggested by Faddeev-Jackiw. Consequently, the correspondent transformation matrix guides the mapping from commutative to noncommutative (NC) phase-space coordinates. Bopp's shifts may be directly generalized from this mapping. In this context, all the NC and scale parameters, introduced into the brackets, will be lifted to the Hamiltonian. Well-known results, obtained using ⋆-product, will be reproduced without considering that the NC parameters are small (≪1). Besides, it will be shown that different choices for NC algebra among the symplectic variables generate distinct dynamical systems, in which they may not even connect with each other, and that some of them can preserve, break, or restore the symmetry of the system. Further, we will also discuss the charge and mass rescaling in a simple model.

Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

NASA Astrophysics Data System (ADS)

Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel

2017-12-01

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

Pareto-front shape in multiobservable quantum control

NASA Astrophysics Data System (ADS)

Sun, Qiuyang; Wu, Re-Bing; Rabitz, Herschel

2017-03-01

Many scenarios in the sciences and engineering require simultaneous optimization of multiple objective functions, which are usually conflicting or competing. In such problems the Pareto front, where none of the individual objectives can be further improved without degrading some others, shows the tradeoff relations between the competing objectives. This paper analyzes the Pareto-front shape for the problem of quantum multiobservable control, i.e., optimizing the expectation values of multiple observables in the same quantum system. Analytic and numerical results demonstrate that with two commuting observables the Pareto front is a convex polygon consisting of flat segments only, while with noncommuting observables the Pareto front includes convexly curved segments. We also assess the capability of a weighted-sum method to continuously capture the points along the Pareto front. Illustrative examples with realistic physical conditions are presented, including NMR control experiments on a 1H-13C two-spin system with two commuting or noncommuting observables.

Cosmological power spectrum in a noncommutative spacetime

NASA Astrophysics Data System (ADS)

Kothari, Rahul; Rath, Pranati K.; Jain, Pankaj

2016-09-01

We propose a generalized star product that deviates from the standard one when the fields are considered at different spacetime points by introducing a form factor in the standard star product. We also introduce a recursive definition by which we calculate the explicit form of the generalized star product at any number of spacetime points. We show that our generalized star product is associative and cyclic at linear order. As a special case, we demonstrate that our recursive approach can be used to prove the associativity of standard star products for same or different spacetime points. The introduction of a form factor has no effect on the standard Lagrangian density in a noncommutative spacetime because it reduces to the standard star product when spacetime points become the same. We show that the generalized star product leads to physically consistent results and can fit the observed data on hemispherical anisotropy in the cosmic microwave background radiation.

A reconstruction theorem for Connes-Landi deformations of commutative spectral triples

NASA Astrophysics Data System (ADS)

Ćaćić, Branimir

2015-12-01

We formulate and prove an extension of Connes's reconstruction theorem for commutative spectral triples to so-called Connes-Landi or isospectral deformations of commutative spectral triples along the action of a compact Abelian Lie group G, also known as toric noncommutative manifolds. In particular, we propose an abstract definition for such spectral triples, where noncommutativity is entirely governed by a deformation parameter sitting in the second group cohomology of the Pontryagin dual of G, and then show that such spectral triples are well-behaved under further Connes-Landi deformation, thereby allowing for both quantisation from and dequantisation to G-equivariant abstract commutative spectral triples. We then use a refinement of the Connes-Dubois-Violette splitting homomorphism to conclude that suitable Connes-Landi deformations of commutative spectral triples by a rational deformation parameter are almost-commutative in the general, topologically non-trivial sense.

Quantum space and quantum completeness

NASA Astrophysics Data System (ADS)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Gravitational waves in the spectral action of noncommutative geometry

NASA Astrophysics Data System (ADS)

Nelson, William; Ochoa, Joseph; Sakellariadou, Mairi

2010-10-01

The spectral triple approach to noncommutative geometry allows one to develop the entire standard model (and supersymmetric extensions) of particle physics from a purely geometry standpoint and thus treats both gravity and particle physics on the same footing. The bosonic sector of the theory contains a modification to Einstein-Hilbert gravity, involving a nonconformal coupling of curvature to the Higgs field and conformal Weyl term (in addition to a nondynamical topological term). In this paper we derive the weak-field limit of this gravitational theory and show that the production and dynamics of gravitational waves are significantly altered. In particular, we show that the graviton contains a massive mode that alters the energy lost to gravitational radiation, in systems with evolving quadrupole moment. We explicitly calculate the general solution and apply it to systems with periodically varying quadrupole moments, focusing, in particular, on the well-known energy loss formula for circular binaries.

On the energy-momentum tensor in Moyal space

DOE PAGES

Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; ...

2015-06-26

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another starproduct. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gaugemore » fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.« less

Probing quantumness with joint continuous measurements of non-commuting qubit observables

NASA Astrophysics Data System (ADS)

Garcia-Pintos, Luis Pedro; Dressel, Justin

In this talk we consider continuous weak measurements as a means to probe foundational issues in quantum mechanics. We consider the simultaneous monitoring of two noncommuting observables-as recently implemented by the Siddiqi group at UC Berkeley. Contrary to naive expectation, the output of such experiment can be used to simultaneously track the approximate observable dynamics. Despite this seeming realism, we also show that the readouts violate macrorealistic Leggett-Garg inequalities for arbitrarily short temporal correlations, and that the derived inequalities are manifestly violated even in the absence of Hamiltonian evolution. Such violations should indicate the failure of at least one postulate of macrorealism: either physical quantities do not have well defined values at all times, or the measurement process itself disturbs what is being measured. Despite this macrorealism violation, we construct a realistic, but epistemically restricted, model that perfectly emulates both the qubit evolution and the observed noisy signals, thus also emulating the violations.

Trace theorem for quasi-Fuchsian groups

NASA Astrophysics Data System (ADS)

Connes, A.; Sukochev, F. A.; Zanin, D. V.

2017-10-01

We complete the proof of the Trace Theorem in the quantized calculus for quasi-Fuchsian groups which was stated and sketched, but not fully proved, on pp. 322-325 of the book Noncommutative geometry of the first author. Bibliography: 34 titles.

Quantum formalism for classical statistics

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

Elementary Particle Physics at Syracuse. Final Report

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

Catterall, Simon; Hubisz, Jay; Balachandran, Aiyalam

2013-01-05

This final report describes the activities of the high energy theory group at Syracuse University for the period 1 January 2010 through April 30 2013. The research conducted by the group includes lattice gauge theory, non-commutative geometry, phenomenology and mathematical physics.

Non-adiabatic holonomic quantum computation in linear system-bath coupling

PubMed Central

Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang

2016-01-01

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities. PMID:26846444

Non-adiabatic holonomic quantum computation in linear system-bath coupling.

PubMed

Sun, Chunfang; Wang, Gangcheng; Wu, Chunfeng; Liu, Haodi; Feng, Xun-Li; Chen, Jing-Ling; Xue, Kang

2016-02-05

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.

Expecting the unexpected: Signals for new physics

NASA Astrophysics Data System (ADS)

Conley, John Anthony

In the near future our theories of Beyond the Standard Model physics will be confronted with a wealth of new data. The impending turn-on of the LHC and the continued proliferation of cosmology and dark matter experiments are ushering in a new era for high energy physics. It will be crucial for theorists to be ready to anticipate the full breadth of experimental signatures that new physics could bring. In this thesis, we discuss a diverse set of examples of such signatures. First we examine the effects of the extended gauge sector of the Littlest Higgs model in high energy e+e - collisions. We find that a study of the processes e+e- → f f¯ and e+e - → Zh at s = 500 GeV International Linear Collider can cover essentially the entire parameter region of this model. This allows for confirmation of the structure of the cancellation of the Higgs mass quadratic divergence and would verify the little Higgs mechanism. We then consider the large extra dimensions scenario, examining the production and evolution of microscopic black holes in the early universe. We demonstrate that, unlike in the standard four-dimensional cosmology, in large extra dimensions absorption of matter from the primordial plasma by the black holes is significant and can lead to rapid growth of the black hole mass density. This effect can be used to constrain the conditions present in the very early universe. We demonstrate that this constraint is applicable in regions of parameter space not excluded by existing bounds. The third signature we study is W pair production in the Noncommutative Standard Model constructed with the Seiberg-Witten map. We consider partial wave unitarity in the reactions W+ W- → W+ W- and e+ e- → W+ W-, and show that tree-level unitarity is violated when scattering energies and the noncommutative scale are around a TeV. We find that while WW production at the LHC is not sensitive to scales above the unitarity bounds, noncommutative scales below 300--400 GeV are excluded by LEP-II, and the ILC is sensitive to scales up to 10--20 TeV. In addition, we find that the ability to measure the helicity states of the final state W bosons at the ILC provides a diagnostic tool to determine and disentangle the different possible noncommutative contributions. We then turn our attention to the recently proposed unparticle scenario. We explore how modifications to the unparticle propagator from conformal symmetry breaking and vacuum polarization corrections affect the calculation of the lepton anomalous magnetic moment. Our numerical study shows that allowing various SM fermions to run in the unparticle self-energy loops does not significantly affect the value of g - 2. We also investigate the limits on a characteristic mass scale for the unparticle sector in the case that the conformal symmetry is broken. Finally, we study LHC signatures of the Minimal Supersymmetric Standard Model. We perform a scan of MSSM parameter space, and apply all relevant experimental constraints to obtain a general set of viable MSSM models. We pass our models through a detailed LHC analysis and discover a large number of novel SUSY signatures. By studying these new signatures, we help elucidate the true breadth of the MSSM.

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

Liang, Jun

2018-01-01

Not Available Supported by the Natural Science Foundation of Education Department of Shannxi Province under Grant No 15JK1077, and the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No BJ12-02.

New public key cryptosystem based on quaternions

NASA Astrophysics Data System (ADS)

Durcheva, Mariana; Karailiev, Kristian

2017-12-01

Quaternions are not commonly used in cryptography. Nevertheless, the noncommutativity of their multiplication makes them suitable for cryptographic purposes. In this paper we suggest a Diffie-Hellman like cryptosystem based on the the quaternions. Additionally, a computer realization of the protocol is given.

Marginal deformations of gauge theories and their dual description

NASA Astrophysics Data System (ADS)

Kulaxizi, Manuela

Holography and its realization in string theory as the AdS/CFT correspondence, offers an equivalence between gauge theories and gravity that provides a means to explore the otherwise inaccessible large N and strong coupling region of SU(N) gauge theories. While considerable progress has been made in this area, a concrete method for specifying the gravitational background dual to a given gauge theory is still lacking. This is the question addressed in this thesis in the context of exactly marginal deformations of N = 4 SYM. First, a precise relation between the deformation of the superpotential and transverse space noncommutativity is established. In particular, the appropriate noncommutativity matrix theta is determined, relying solely on data from the gauge theory lagrangian and basic notions of the AdS/CFT correspondence. The set ( G , theta) of open string parameters, with G the metric of the transverse space, is then understood as a way to encode information pertaining to the moduli space of the gauge theory. It seems thus natural to expect that it may be possible to obtain the corresponding gravitational solution by mapping the open string fields ( G , theta) to the closed string ones (g, B). This hints at a purely algebraic method for constructing gravity duals to given conformal gauge theories. The idea is tested within the context of the beta-deformed theory where the dual gravity description is known and then used to construct the background for the rho-deformed theory up to third order in the deformation parameter rho. Discrepancy of the higher order in rho terms in the latter case is traced to the nonassociativity of the noncommutative matrix theta.

Noncommutative Common Cause Principles in algebraic quantum field theory

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

Hofer-Szabo, Gabor; Vecsernyes, Peter

2013-04-15

States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{submore » B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.« less

Non-Abelian strategies in quantum penny flip game

NASA Astrophysics Data System (ADS)

Mishima, Hiroaki

2018-01-01

In this paper, we formulate and analyze generalizations of the quantum penny flip game. In the penny flip game, one coin has two states, heads or tails, and two players apply alternating operations on the coin. In the original Meyer game, the first player is allowed to use quantum (i.e., non-commutative) operations, but the second player is still only allowed to use classical (i.e., commutative) operations. In our generalized games, both players are allowed to use non-commutative operations, with the second player being partially restricted in what operators they use. We show that even if the second player is allowed to use "phase-variable" operations, which are non-Abelian in general, the first player still has winning strategies. Furthermore, we show that even when the second player is allowed to choose one from two or more elements of the group U(2), the second player has winning strategies under certain conditions. These results suggest that there is often a method for restoring the quantum state disturbed by another agent.

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

NASA Astrophysics Data System (ADS)

Song, Juntao; Fine, Carolyn; Prodan, Emil

2014-11-01

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

Cumulants, free cumulants and half-shuffles

PubMed Central

Ebrahimi-Fard, Kurusch; Patras, Frédéric

2015-01-01

Free cumulants were introduced as the proper analogue of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants. Whereas the combinatorics of classical cumulants is well expressed in terms of set partitions, that of free cumulants is described and often introduced in terms of non-crossing set partitions. The formal series approach to classical and free cumulants also largely differs. The purpose of this study is to put forward a different approach to these phenomena. Namely, we show that cumulants, whether classical or free, can be understood in terms of the algebra and combinatorics underlying commutative as well as non-commutative (half-)shuffles and (half-) unshuffles. As a corollary, cumulants and free cumulants can be characterized through linear fixed point equations. We study the exponential solutions of these linear fixed point equations, which display well the commutative, respectively non-commutative, character of classical and free cumulants. PMID:27547078

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

Girelli, Florian; Livine, Etera R.; Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69007 Lyon

Deformed special relativity (DSR) is obtained by imposing a maximal energy to special relativity and deforming the Lorentz symmetry (more exactly, the Poincare symmetry) to accommodate this requirement. One can apply the same procedure in the context of Galilean relativity by imposing a maximal speed (the speed of light). Effectively, one deforms the Galilean group and this leads to a noncommutative space structure, together with the deformations of composition of speed and conservation of energy momentum. In doing so, one runs into most of the ambiguities that one stumbles onto in the DSR context. However, this time, special relativity ismore » there to tell us what is the underlying physics, in such a way we can understand and interpret these ambiguities. We use these insights to comment on the physics of DSR.« less

Multiverse effects on the CMB angular correlation function in the framework of NCG

NASA Astrophysics Data System (ADS)

Arabzadeh, Sahar; Kaviani, Kamran

Following many theories that predict the existence of the multiverse and by conjecture that our space-time may have a generalized geometrical structure at the fundamental level, we are interested in using a non-commutative geometry (NCG) formalism to study a suggested two-layer space that contains our 4-dimensional (4D) universe and a re-derived photon propagator. It can be shown that the photon propagator and a cosmic microwave background (CMB) angular correlation function are comparable, and if there exists such a multiverse system, the distance between the two layers can be estimated to be within the observable universe’s radius. Furthermore, this study revealed that our results are not limited to CMB but can be applied to many other types of radiation, such as X-rays.

Noncommutative differential geometry related to the Young-Baxter equation

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

Gurevich, D.; Radul, A.; Rubtsov, V.

1995-11-10

An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf Z`s considered in which local solutions of the Young-Baxter quantum equation are defined but there is no global section.

A Variant of the Mukai Pairing via Deformation Quantization

NASA Astrophysics Data System (ADS)

Ramadoss, Ajay C.

2012-06-01

Let X be a smooth projective complex variety. The Hochschild homology HH•( X) of X is an important invariant of X, which is isomorphic to the Hodge cohomology of X via the Hochschild-Kostant-Rosenberg isomorphism. On HH•( X), one has the Mukai pairing constructed by Caldararu. An explicit formula for the Mukai pairing at the level of Hodge cohomology was proven by the author in an earlier work (following ideas of Markarian). This formula implies a similar explicit formula for a closely related variant of the Mukai pairing on HH•( X). The latter pairing on HH•( X) is intimately linked to the study of Fourier-Mukai transforms of complex projective varieties. We give a new method to prove a formula computing the aforementioned variant of Caldararu's Mukai pairing. Our method is based on some important results in the area of deformation quantization. In particular, we use part of the work of Kashiwara and Schapira on Deformation Quantization modules together with an algebraic index theorem of Bressler, Nest and Tsygan. Our new method explicitly shows that the "Noncommutative Riemann-Roch" implies the classical Riemann-Roch. Further, it is hoped that our method would be useful for generalization to settings involving certain singular varieties.

Effective Perron-Frobenius eigenvalue for a correlated random map

NASA Astrophysics Data System (ADS)

Pool, Roman R.; Cáceres, Manuel O.

2010-09-01

We investigate the evolution of random positive linear maps with various type of disorder by analytic perturbation and direct simulation. Our theoretical result indicates that the statistics of a random linear map can be successfully described for long time by the mean-value vector state. The growth rate can be characterized by an effective Perron-Frobenius eigenvalue that strongly depends on the type of correlation between the elements of the projection matrix. We apply this approach to an age-structured population dynamics model. We show that the asymptotic mean-value vector state characterizes the population growth rate when the age-structured model has random vital parameters. In this case our approach reveals the nontrivial dependence of the effective growth rate with cross correlations. The problem was reduced to the calculation of the smallest positive root of a secular polynomial, which can be obtained by perturbations in terms of Green’s function diagrammatic technique built with noncommutative cumulants for arbitrary n -point correlations.

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.

Soliton structure versus singularity analysis: Third-order completely intergrable nonlinear differential equations in 1 + 1-dimensions

NASA Astrophysics Data System (ADS)

Fuchssteiner, Benno; Carillo, Sandra

1989-01-01

Bäcklund transformations between all known completely integrable third-order differential equations in (1 + 1)-dimensions are established and the corresponding transformations formulas for their hereditary operators and Hamiltonian formulations are exhibited. Some of these Bäcklund transformations are not injective; therefore additional non-commutative symmetry groups are found for some equations. These non-commutative symmetry groups are classified as having a semisimple part isomorphic to the affine algebra A(1)1. New completely integrable third-order integro-differential equations, some depending explicitly on x, are given. These new equations give rise to nonin equation. Connections between the singularity equations (from the Painlevé analysis) and the nonlinear equations for interacting solitons are established. A common approach to singularity analysis and soliton structure is introduced. The Painlevé analysis is modified in such a sense that it carries over directly and without difficulty to the time evolution of singularity manifolds of equations like the sine-Gordon and nonlinear Schrödinger equation. A method to recover the Painlevé series from its constant level term is exhibit. The soliton-singularity transform is recognized to be connected to the Möbius group. This gives rise to a Darboux-like result for the spectral properties of the recursion operator. These connections are used in order to explain why poles of soliton equations move like trajectories of interacting solitons. Furthermore it is explicitly computed how solitons of singularity equations behave under the effect of this soliton-singularity transform. This then leads to the result that only for scaling degrees α = -1 and α = -2 the usual Painlevé analysis can be carried out. A new invariance principle, connected to kernels of differential operators is discovered. This new invariance, for example, connects the explicit solutions of the Liouville equation with the Miura transform. Simple methods are exhibited which allow to compute out of N-soliton solutions of the KdV (Bargman potentials) explicit solutions of equations like the Harry Dym equation. Certain solutions are plotted.

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole: Gravitational, Electromagnetic and Massless Dirac Perturbations

NASA Astrophysics Data System (ADS)

Liang, >Jun

2018-05-01

Not Available Supported by the Natural Science Foundation of Education Department of Shannxi Province under Grant No 15JK1077, and the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No BJ12-02.

A COMPARISON OF THE COMMUTING AND NON-COMMUTING STUDENT.

ERIC Educational Resources Information Center

DRESSEL, PAUL L.; NISULA, EINAR S.

AN EXPLORATORY SURVEY INVESTIGATED THE COLLEGE EXPERIENCES AMONG COMMUTING STUDENTS, ATTENDING THREE TYPES OF INSTITUTIONS TO COMPARE COLLEGE EXPERIENCES BETWEEN COMMUTING AND RESIDENT STUDENTS. STUDENTS SELECTED FOR STUDY WERE (1) 100 COMMUTERS FROM A LARGE, PRIMARILY RESIDENT UNIVERSITY, (2) 100 COMMUTERS FROM A COMMUNITY COLLEGE WITH NO…

The SU(2) action-angle variables

NASA Technical Reports Server (NTRS)

Ellinas, Demosthenes

1993-01-01

Operator angle-action variables are studied in the frame of the SU(2) algebra, and their eigenstates and coherent states are discussed. The quantum mechanical addition of action-angle variables is shown to lead to a noncommutative Hopf algebra. The group contraction is used to make the connection with the harmonic oscillator.

Beyond the Quantum

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Theo M.; Mehmani, Bahar; Špička, Václav; Aghdami, Maryam J.; Khrennikov, Andrei Yu

2007-09-01

pt. A. Introductions. The mathematical basis for deterministic quantum mechanics / G.'t Hooft. What did we learn from quantum gravity? / A. Ashtekar. Bose-Einstein condensates and EPR quantum non-locality / F. Laloe. The quantum measurement process: lessons from an exactly solvable model / A.E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen -- pt. B. Quantum mechanics and quantum information. POVMs: a small but important step beyond standard quantum mechanics / W. M. de Muynck. State reduction by measurements with a null result / G. Nienhuis. Solving open questions in the Bose-Einstein condensation of an ideal gas via a hybrid mixture of laser and statistical physics / M. Kim, A. Svidzinsky and M.O. Scully. Twin-Photon light scattering and causality / G. Puentes, A. Aiello and J. P. Woerdman. Simultaneous measurement of non-commuting observables / G. Aquino and B. Mehmani. Quantum decoherence and gravitational waves / M.T. Jaekel ... [et al.]. Role of various entropies in the black hole information loss problem / Th. M. Nieuwenhuizen and I.V. Volovich. Quantum and super-quantum correlations / G.S. Jaeger -- pt. C. Long distance correlations and bell inequalities. Understanding long-distance quantum correlations / L. Marchildon. Connection of probability models to EPR experiments: probability spaces and Bell's theorem / K. Hess and W. Philipp. Fair sampling vs no-signalling principle in EPR experiments / G. Adenier and A. Yu. Khrennikov -- pt. D. Mathematical foundations. Where the mathematical structure of quantum mechanics comes from / G.M. D'Ariano. Phase space description of quantum mechanics and non-commutative geometry: Wigner-Moyal and Bohm in a wider context / B.J. Hiley. Quantum mechanics as simple algorithm for approximation of classical integrals / A. Yu. Khrennikov. Noncommutative quantum mechanics viewed from Feynman Formalism / J. Lages ... [et al.]. Beyond the quantum in Snyder space / J.F.S. van Huele and M. K. Transtrum -- pt. E. Stochastic electrodynamics. Some quantum experiments from the point of view of Stochastic electrodynamics / V. Spicka ... [et al.]. On the ergodic behaviour of atomic systems under the action of the zero-point radiation field / L. De La Peña and A. M. Cetto. Inertia and the vacuum-view on the emergence of the inertia reaction force / A. Rueda and H. Sunahata -- pt. F. Models for the electron. Rotating Hopf-Kinks: oscillators in the sense of de Broglie / U. Enz. Kerr-Newman particles: symmetries and other properties / H.I. Arcos and J.G. Pereira. Kerr geometry beyond the quantum theory / Th. M. Nieuwenhuizen -- pt. G. Philosophical considerations. Probability in non-collapse interpretations of a quantum mechanics / D. Dieks. The Schrödinger-Park paradox about the concept of "State" in quantum statistical mechanics and quantum information theory is still open: one more reason to go beyond? / G.P. Beretta. The conjecture that local realism is possible / E. Santos -- pt. H. The round table. Round table discussion / A.M. Cetto ... [et al.].

Algebraic K-theory, K-regularity, and -duality of -stable C ∗-algebras

NASA Astrophysics Data System (ADS)

Mahanta, Snigdhayan

2015-12-01

We develop an algebraic formalism for topological -duality. More precisely, we show that topological -duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known isomorphism between twisted K-theories (up to a shift). In order to establish this result we model topological K-theory by algebraic K-theory. We also construct an E ∞ -operad starting from any strongly self-absorbing C ∗-algebra . Then we show that there is a functorial topological K-theory symmetric spectrum construction on the category of separable C ∗-algebras, such that is an algebra over this operad; moreover, is a module over this algebra. Along the way we obtain a new symmetric spectra valued functorial model for the (connective) topological K-theory of C ∗-algebras. We also show that -stable C ∗-algebras are K-regular providing evidence for a conjecture of Rosenberg. We conclude with an explicit description of the algebraic K-theory of a x+ b-semigroup C ∗-algebras coming from number theory and that of -stabilized noncommutative tori.

Quantization of spacetime based on a spacetime interval operator

NASA Astrophysics Data System (ADS)

Chiang, Hsu-Wen; Hu, Yao-Chieh; Chen, Pisin

2016-04-01

Motivated by both concepts of Adler's recent work on utilizing Clifford algebra as the linear line element d s =⟨γμ⟩ d Xμ and the fermionization of the cylindrical worldsheet Polyakov action, we introduce a new type of spacetime quantization that is fully covariant. The theory is based on the reinterpretation of Adler's linear line element as d s =γμ⟨λ γμ⟩ , where λ is the characteristic length of the theory. We name this new operator the "spacetime interval operator" and argue that it can be regarded as a natural extension to the one-forms in the U (s u (2 )) noncommutative geometry. By treating Fourier momentum as the particle momentum, the generalized uncertainty principle of the U (s u (2 )) noncommutative geometry, as an approximation to the generalized uncertainty principle of our theory, is derived and is shown to have a lowest order correction term of the order p2 similar to that of Snyder's. The holography nature of the theory is demonstrated and the predicted fuzziness of the geodesic is shown to be much smaller than conceivable astrophysical bounds.

Using alternatives to the car and risk of all-cause, cardiovascular and cancer mortality.

PubMed

Panter, Jenna; Mytton, Oliver; Sharp, Stephen; Brage, Søren; Cummins, Steven; Laverty, Anthony A; Wijndaele, Katrien; Ogilvie, David

2018-05-21

To investigate the associations between using alternatives to the car which are more active for commuting and non-commuting purposes, and morbidity and mortality. We conducted a prospective study using data from 3 58 799 participants, aged 37-73 years, from UK Biobank. Commute and non-commute travel were assessed at baseline in 2006-2010. We classified participants according to whether they relied exclusively on the car or used alternative modes of transport that were more active at least some of the time. The main outcome measures were incident cardiovascular disease (CVD) and cancer, and CVD, cancer and all-cause mortality. We excluded events in the first 2 years and conducted analyses separately for those who regularly commuted and those who did not. In maximally adjusted models, regular commuters with more active patterns of travel on the commute had a lower risk of incident (HR 0.89, 95% CI 0.79 to 1.00) and fatal (HR 0.70, 95% CI 0.51 to 0.95) CVD. Those regular commuters who also had more active patterns of non-commute travel had an even lower risk of fatal CVD (HR 0.57, 95% CI 0.39 to 0.85). Among those who were not regular commuters, more active patterns of travel were associated with a lower risk of all-cause mortality (HR 0.92, 95% CI 0.86 to 0.99). More active patterns of travel were associated with a reduced risk of incident and fatal CVD and all-cause mortality in adults. This is an important message for clinicians advising people about how to be physically active and reduce their risk of disease. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

Quasi-probabilities in conditioned quantum measurement and a geometric/statistical interpretation of Aharonov's weak value

NASA Astrophysics Data System (ADS)

Lee, Jaeha; Tsutsui, Izumi

2017-05-01

We show that the joint behavior of an arbitrary pair of (generally noncommuting) quantum observables can be described by quasi-probabilities, which are an extended version of the standard probabilities used for describing the outcome of measurement for a single observable. The physical situations that require these quasi-probabilities arise when one considers quantum measurement of an observable conditioned by some other variable, with the notable example being the weak measurement employed to obtain Aharonov's weak value. Specifically, we present a general prescription for the construction of quasi-joint probability (QJP) distributions associated with a given combination of observables. These QJP distributions are introduced in two complementary approaches: one from a bottom-up, strictly operational construction realized by examining the mathematical framework of the conditioned measurement scheme, and the other from a top-down viewpoint realized by applying the results of the spectral theorem for normal operators and their Fourier transforms. It is then revealed that, for a pair of simultaneously measurable observables, the QJP distribution reduces to the unique standard joint probability distribution of the pair, whereas for a noncommuting pair there exists an inherent indefiniteness in the choice of such QJP distributions, admitting a multitude of candidates that may equally be used for describing the joint behavior of the pair. In the course of our argument, we find that the QJP distributions furnish the space of operators in the underlying Hilbert space with their characteristic geometric structures such that the orthogonal projections and inner products of observables can be given statistical interpretations as, respectively, “conditionings” and “correlations”. The weak value Aw for an observable A is then given a geometric/statistical interpretation as either the orthogonal projection of A onto the subspace generated by another observable B, or equivalently, as the conditioning of A given B with respect to the QJP distribution under consideration.

Statistical model of exotic rotational correlations in emergent space-time

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

Hogan, Craig; Kwon, Ohkyung; Richardson, Jonathan

2017-06-06

A statistical model is formulated to compute exotic rotational correlations that arise as inertial frames and causal structure emerge on large scales from entangled Planck scale quantum systems. Noncommutative quantum dynamics are represented by random transverse displacements that respect causal symmetry. Entanglement is represented by covariance of these displacements in Planck scale intervals defined by future null cones of events on an observer's world line. Light that propagates in a nonradial direction inherits a projected component of the exotic rotational correlation that accumulates as a random walk in phase. A calculation of the projection and accumulation leads to exact predictionsmore » for statistical properties of exotic Planck scale correlations in an interferometer of any configuration. The cross-covariance for two nearly co-located interferometers is shown to depart only slightly from the autocovariance. Specific examples are computed for configurations that approximate realistic experiments, and show that the model can be rigorously tested.« less

Foliated eight-manifolds for M-theory compactification

NASA Astrophysics Data System (ADS)

Babalic, Elena Mirela; Lazaroiu, Calin Iuliu

2015-01-01

We characterize compact eight-manifolds M which arise as internal spaces in flux compactifications of M-theory down to AdS3 using the theory of foliations, for the case when the internal part ξ of the supersymmetry generator is everywhere non-chiral. We prove that specifying such a supersymmetric background is equivalent with giving a codimension one foliation of M which carries a leafwise G 2 structure, such that the O'Neill-Gray tensors, non-adapted part of the normal connection and the torsion classes of the G 2 structure are given in terms of the supergravity four-form field strength by explicit formulas which we derive. We discuss the topology of such foliations, showing that the C * algebra is a noncommutative torus of dimension given by the irrationality rank of a certain cohomology class constructed from G, which must satisfy the Latour obstruction. We also give a criterion in terms of this class for when such foliations are fibrations over the circle. When the criterion is not satisfied, each leaf of is dense in M.

Relation between ``no broadcasting'' for noncommuting states and ``no local broadcasting'' for quantum correlations

NASA Astrophysics Data System (ADS)

Luo, Shunlong; Li, Nan; Cao, Xuelian

2009-05-01

The no-broadcasting theorem, first established by Barnum [Phys. Rev. Lett. 76, 2818 (1996)], states that a set of quantum states can be broadcast if and only if it constitutes a commuting family. Quite recently, Piani [Phys. Rev. Lett. 100, 090502 (2008)] showed, by using an ingenious and sophisticated method, that the correlations in a single bipartite state can be locally broadcast if and only if the state is effectively a classical one (i.e., the correlations therein are classical). In this Brief Report, under the condition of nondegenerate spectrum, we provide an alternative and significantly simpler proof of the latter result based on the original no-broadcasting theorem and the monotonicity of the quantum relative entropy. This derivation motivates us to conjecture the equivalence between these two elegant yet formally different no-broadcasting theorems and indicates a subtle and fundamental issue concerning spectral degeneracy which also lies at the heart of the conflict between the von Neumann projection postulate and the Lüders ansatz for quantum measurements. This relation not only offers operational interpretations for commutativity and classicality but also illustrates the basic significance of noncommutativity in characterizing quantumness from the informational perspective.

Effective action for noncommutative Bianchi I model

NASA Astrophysics Data System (ADS)

Rosenbaum, M.; Vergara, J. D.; Minzoni, A. A.

2013-06-01

Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.

Locality and simultaneous elements of reality

NASA Astrophysics Data System (ADS)

Nisticò, G.; Sestito, A.

2012-12-01

We show that the extension of quantum correlations stemming from a "strict" interpretation of the criterion of reality raises the failure of Hardy's non-locality theorem. Then, by suggesting an ideal experiment, we prove that such an extension, though strictly smaller than the one derived by Einstein, Podolsky and Rosen and usually adopted, allows for the assignment of simultaneous objective values of two non-commuting observables.

The geometric semantics of algebraic quantum mechanics.

PubMed

Cruz Morales, John Alexander; Zilber, Boris

2015-08-06

In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Hardy's argument and successive spin-s measurements

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

Ahanj, Ali

2010-07-15

We consider a hidden-variable theoretic description of successive measurements of noncommuting spin observables on an input spin-s state. In this scenario, the hidden-variable theory leads to a Hardy-type argument that quantum predictions violate it. We show that the maximum probability of success of Hardy's argument in quantum theory is ((1/2)){sup 4s}, which is more than in the spatial case.

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

Agarwala, Susama; Delaney, Colleen

This paper defines a generalization of the Connes-Moscovici Hopf algebra, H(1), that contains the entire Hopf algebra of rooted trees. A relationship between the former, a much studied object in non-commutative geometry, and the latter, a much studied object in perturbative quantum field theory, has been established by Connes and Kreimer. The results of this paper open the door to study the cohomology of the Hopf algebra of rooted trees.

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.

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 application of signal detection theory to optics

NASA Technical Reports Server (NTRS)

Helstrom, C. W.

1972-01-01

The role of measurements of noncommuting quantum observables is considered in the detection of signals and estimation of signal parameters by quantum receivers. The restoration of images focused on a photosensitive surface is discussed for data as numbers of photoelectrons ejected from various parts of the surface. The detection of an image formed on a photosensitive surface in the presence of background illumination for similar data is also considered.

Interferometric constraints on quantum geometrical shear noise correlations

DOE PAGES

Chou, Aaron; Glass, Henry; Richard Gustafson, H.; ...

2017-07-20

Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches formore » faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.« less

From Quantum Fields to Local Von Neumann Algebras

NASA Astrophysics Data System (ADS)

Borchers, H. J.; Yngvason, Jakob

The subject of the paper is an old problem of the general theory of quantized fields: When can the unbounded operators of a Wightman field theory be associated with local algebras of bounded operators in the sense of Haag? The paper reviews and extends previous work on this question, stressing its connections with a noncommutive generalization of the classical Hamburger moment problem. Necessary and sufficient conditions for the existence of a local net of von Neumann algebras corresponding to a given Wightman field are formulated in terms of strengthened versions of the usual positivity property of Wightman functionals. The possibility that the local net has to be defined in an enlarged Hilbert space cannot be ruled out in general. Under additional hypotheses, e.g., if the field operators obey certain energy bounds, such an extension of the Hilbert space is not necessary, however. In these cases a fairly simple condition for the existence of a local net can be given involving the concept of “central positivity” introduced by Powers. The analysis presented here applies to translationally covariant fields with an arbitrary number of components, whereas Lorentz covariance is not needed. The paper contains also a brief discussion of an approach to noncommutative moment problems due to Dubois-Violette, and concludes with some remarks on modular theory for algebras of unbounded operators.

Interferometric constraints on quantum geometrical shear noise correlations

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

Chou, Aaron; Glass, Henry; Richard Gustafson, H.

Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches formore » faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.« less

Problem of quantifying quantum correlations with non-commutative discord

NASA Astrophysics Data System (ADS)

Majtey, A. P.; Bussandri, D. G.; Osán, T. M.; Lamberti, P. W.; Valdés-Hernández, A.

2017-09-01

In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Guo (Sci Rep 6:25241, 2016). By resorting to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt's is used. In order to avoid this basis-dependence feature, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt's. In addition, the resulting measure inherits the main properties of Guo's measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such an optimization. The results show that, in most cases of interest, the use of Guo's measure can result in an overestimation of quantum correlations. However, since Guo's measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.

Geometric low-energy effective action in a doubled spacetime

NASA Astrophysics Data System (ADS)

Ma, Chen-Te; Pezzella, Franco

2018-05-01

The ten-dimensional supergravity theory is a geometric low-energy effective theory and the equations of motion for its fields can be obtained from string theory by computing β functions. With d compact dimensions, an O (d , d ; Z) geometric structure can be added to it giving the supergravity theory with T-duality manifest. In this paper, this is constructed through the use of a suitable star product whose role is the one to implement the weak constraint on the fields and the gauge parameters in order to have a closed gauge symmetry algebra. The consistency of the action here proposed is based on the orthogonality of the momenta associated with fields in their triple star products in the cubic terms defined for d ≥ 1. This orthogonality holds also for an arbitrary number of star products of fields for d = 1. Finally, we extend our analysis to the double sigma model, non-commutative geometry and open string theory.

Beyond heat baths II: framework for generalized thermodynamic resource theories

NASA Astrophysics Data System (ADS)

Yunger Halpern, Nicole

2018-03-01

Thermodynamics, which describes vast systems, has been reconciled with small scales, relevant to single-molecule experiments, in resource theories. Resource theories have been used to model exchanges of energy and information. Recently, particle exchanges were modeled; and an umbrella family of thermodynamic resource theories was proposed to model diverse baths, interactions, and free energies. This paper motivates and details the family’s structure and prospective applications. How to model electrochemical, gravitational, magnetic, and other thermodynamic systems is explained. Szilárd’s engine and Landauer’s Principle are generalized, as resourcefulness is shown to be convertible not only between information and gravitational energy, but also among diverse degrees of freedom. Extensive variables are associated with quantum operators that might fail to commute, introducing extra nonclassicality into thermodynamic resource theories. An early version of this paper partially motivated the later development of noncommutative thermalization. This generalization expands the theories’ potential for modeling realistic systems with which small-scale statistical mechanics might be tested experimentally.

Dark Energy and Dark Matter from Emergent Gravity Picture

NASA Astrophysics Data System (ADS)

Seok Yang, Hyun

2018-01-01

We suggest that dark energy and dark matter may be a cosmic uroboros of quantum gravity due to the coherent vacuum structure of spacetime. We apply the emergent gravity to a large N matrix model by considering the vacuum in the noncommutative (NC) Coulomb branch satisfying the Heisenberg algebra. We observe that UV fluctuations in the NC Coulomb branch are always paired with IR fluctuations and these UV/IR fluctuations can be extended to macroscopic scales. We show that space-like fluctuations give rise to the repulsive gravitational force while time-like fluctuations generate the attractive gravitational force. When considering the fact that the fluctuations are random in nature and we are living in the (3+1)-dimensional spacetime, the ratio of the repulsive and attractive components will end in ¾ : ¼= 75 : 25 and this ratio curiously coincides with the dark composition of our current Universe. If one includes ordinary matters which act as the attractive gravitational force, the emergent gravity may explain the dark sector of our Universe more precisely.

A strong astrophysical constraint on the violation of special relativity by quantum gravity.

PubMed

Jacobson, T; Liberati, S; Mattingly, D

2003-08-28

Special relativity asserts that physical phenomena appear the same to all unaccelerated observers. This is called Lorentz symmetry and relates long wavelengths to short ones: if the symmetry is exact it implies that space-time must look the same at all length scales. Several approaches to quantum gravity, however, suggest that there may be a microscopic structure of space-time that leads to a violation of Lorentz symmetry. This might arise because of the discreteness or non-commutivity of space-time, or through the action of extra dimensions. Here we determine a very strong constraint on a type of Lorentz violation that produces a maximum electron speed less than the speed of light. We use the observation of 100-MeV synchrotron radiation from the Crab nebula to improve the previous limit by a factor of 40 million, ruling out this type of Lorentz violation, and thereby providing an important constraint on theories of quantum gravity.

Communication Policies in Knowledge Networks

NASA Astrophysics Data System (ADS)

Ioannidis, Evangelos; Varsakelis, Nikos; Antoniou, Ioannis

2018-02-01

Faster knowledge attainment within organizations leads to improved innovation, and therefore competitive advantage. Interventions on the organizational network may be risky or costly or time-demanding. We investigate several communication policies in knowledge networks, which reduce the knowledge attainment time without interventions. We examine the resulting knowledge dynamics for real organizational networks, as well as for artificial networks. More specifically, we investigate the dependence of knowledge dynamics on: (1) the Selection Rule of agents for knowledge acquisition, and (2) the Order of implementation of "Selection" and "Filtering". Significant decrease of the knowledge attainment time (up to -74%) can be achieved by: (1) selecting agents of both high knowledge level and high knowledge transfer efficiency, and (2) implementing "Selection" after "Filtering" in contrast to the converse, implicitly assumed, conventional prioritization. The Non-Commutativity of "Selection" and "Filtering", reveals a Non-Boolean Logic of the Network Operations. The results demonstrate that significant improvement of knowledge dynamics can be achieved by implementing "fruitful" communication policies, by raising the awareness of agents, without any intervention on the network structure.

Unambiguous quantum-state filtering

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

Takeoka, Masahiro; Sasaki, Masahide; CREST, Japan Science and Technology Corporation, Tokyo,

2003-07-01

In this paper, we consider a generalized measurement where one particular quantum signal is unambiguously extracted from a set of noncommutative quantum signals and the other signals are filtered out. Simple expressions for the maximum detection probability and its positive operator valued measure are derived. We apply such unambiguous quantum state filtering to evaluation of the sensing of decoherence channels. The bounds of the precision limit for a given quantum state of probes and possible device implementations are discussed.

Quantum 2-Player Gambling and Correlated Pay-Off

NASA Astrophysics Data System (ADS)

Witte, F. M. C.

2005-01-01

In recent years methods have been proposed to extend classical game theory into the quantum domain. In a previous publication the nature of several non-cummutative games was briefly analyzed. Here we give an analysis of the simplest non-commutative quantum game, which is a gambling game much like simple heads or tails. The quantum game displays strategies which, though non direct-product strategies, allow for correlations between the players pay-off.

Matrix Concentration Inequalities via the Method of Exchangeable Pairs

DTIC Science & Technology

2012-01-27

viewed as an exchangeable pairs version of the Burkholder –Davis–Gundy (BDG) inequality from classical martingale theory [Bur73]. Matrix extensions of...non-commutative probability. Math. Ann., 319:1–16, 2001. [Bur73] D. L. Burkholder . Distribution function inequalities for martingales. Ann. Probab., 1...Statist. Assoc., 58(301):13–30, 1963. [JX03] M. Junge and Q. Xu. Noncommutative Burkholder /Rosenthal inequalities. Ann. Probab., 31(2):948–995, 2003

Linear Chord Diagrams with Long Chords

NASA Astrophysics Data System (ADS)

Sullivan, Everett

A linear chord diagram of size n is a partition of the first 2n integers into sets of size two. These diagrams appear in many different contexts in combinatorics and other areas of mathematics, particularly knot theory. We explore various constraints that produce diagrams which have no short chords. A number of patterns appear from the results of these constraints which we can prove using techniques ranging from explicit bijections to non-commutative algebra.

TeV-photon paradox and space with SU(2) fuzziness

NASA Astrophysics Data System (ADS)

Shariati, A.; Khorrami, M.; Fatollahi, A. H.

2008-02-01

The possibility is examined that a model based on space noncommutativity of linear type can explain why photons from distant sources with multi-TeV energies can reach the Earth. In particular within a model in which space coordinates satisfy the algebra of the SU(2) Lie group, it is shown that there is a possibility that the pair production through the reaction of CMB and energetic photons be forbidden kinematically.

The Spectral Shift Function and Spectral Flow

NASA Astrophysics Data System (ADS)

Azamov, N. A.; Carey, A. L.; Sukochev, F. A.

2007-11-01

At the 1974 International Congress, I. M. Singer proposed that eta invariants and hence spectral flow should be thought of as the integral of a one form. In the intervening years this idea has lead to many interesting developments in the study of both eta invariants and spectral flow. Using ideas of [24] Singer’s proposal was brought to an advanced level in [16] where a very general formula for spectral flow as the integral of a one form was produced in the framework of noncommutative geometry. This formula can be used for computing spectral flow in a general semifinite von Neumann algebra as described and reviewed in [5]. In the present paper we take the analytic approach to spectral flow much further by giving a large family of formulae for spectral flow between a pair of unbounded self-adjoint operators D and D + V with D having compact resolvent belonging to a general semifinite von Neumann algebra {mathcal{N}} and the perturbation V in {mathcal{N}} . In noncommutative geometry terms we remove summability hypotheses. This level of generality is made possible by introducing a new idea from [3]. There it was observed that M. G. Krein’s spectral shift function (in certain restricted cases with V trace class) computes spectral flow. The present paper extends Krein’s theory to the setting of semifinite spectral triples where D has compact resolvent belonging to {mathcal{N}} and V is any bounded self-adjoint operator in {mathcal{N}} . We give a definition of the spectral shift function under these hypotheses and show that it computes spectral flow. This is made possible by the understanding discovered in the present paper of the interplay between spectral shift function theory and the analytic theory of spectral flow. It is this interplay that enables us to take Singer’s idea much further to create a large class of one forms whose integrals calculate spectral flow. These advances depend critically on a new approach to the calculus of functions of non-commuting operators discovered in [3] which generalizes the double operator integral formalism of [8-10]. One surprising conclusion that follows from our results is that the Krein spectral shift function is computed, in certain circumstances, by the Atiyah-Patodi-Singer index theorem [2].

Entropic Uncertainty Relation and Information Exclusion Relation for multiple measurements in the presence of quantum memory

NASA Astrophysics Data System (ADS)

Zhang, Jun; Zhang, Yang; Yu, Chang-Shui

2015-06-01

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodecki’s bound entangled state are investigated in details.

Temporal nonlocality in bistable perception

NASA Astrophysics Data System (ADS)

Atmanspacher, Harald; Filk, Thomas

2012-12-01

A novel conceptual framework for theoretical psychology is presented and illustrated for the example of bistable perception. A basic formal feature of this framework is the non-commutativity of operations acting on mental states. A corresponding model for the bistable perception of ambiguous stimuli, the Necker-Zeno model, is sketched and some empirical evidence for it so far is described. It is discussed how a temporal nonlocality of mental states, predicted by the model, can be understood and tested.

UV-IR mixing in nonassociative Snyder ϕ4 theory

NASA Astrophysics Data System (ADS)

Meljanac, Stjepan; Mignemi, Salvatore; Trampetic, Josip; You, Jiangyang

2018-03-01

Using a quantization of the nonassociative and noncommutative Snyder ϕ4 scalar field theory in a Hermitian realization, we present in this article analytical formulas for the momentum-conserving part of the one-loop two-point function of this theory in D -, 4-, and 3-dimensional Euclidean spaces, which are exact with respect to the noncommutative deformation parameter β . We prove that these integrals are regularized by the Snyder deformation. These results indicate that the Snyder deformation does partially regularize the UV divergences of the undeformed theory, as it was proposed decades ago. Furthermore, it is observed that different nonassociative ϕ4 products can generate different momentum-conserving integrals. Finally, most importantly, a logarithmic infrared divergence emerges in one of these interaction terms. We then analyze sample momentum nonconserving integral qualitatively and show that it could exhibit IR divergence too. Therefore, infrared divergences should exist, in general, in the Snyder ϕ4 theory. We consider infrared divergences at the limit p →0 as UV/IR mixings induced by nonassociativity, since they are associated to the matching UV divergence in the zero-momentum limit and appear in specific types of nonassociative ϕ4 products. We also discuss the extrapolation of the Snyder deformation parameter β to negative values as well as certain general properties of one-loop quantum corrections in Snyder ϕ4 theory at the zero-momentum limit.

Two Dimensions of Time could produce a New Supersymmetric Theory

NASA Astrophysics Data System (ADS)

Kriske, Richard

2014-03-01

In the collapse of a system into the eigenstate of an operator,a new type of time, call it ``information time,'' could be inferred. One could look at this time to evolve the quantum state as a type of ``mass.'' This would be a correction to the explaination to the existing Higgs mechanism. Likewise one could see the dual of this in the Dilation in ``clock time'' seen in Special Relativity. In other words we see a time Dilation in ``Information Time'' as being a delay in Acceleration which we call ``mass.'' The two types of Time are Duals to each other and are symmetric. The second dimension of time has been overlooked for this reason. Time Dilation is the dual to persistance of the collapse of a system. This Duality produces some interesting and measurable effects. One conclusion that one can draw from this ``Symmetry'' is that there is a non-commuting set of operators, and a particle that connects the two ``Perpendicular'' time axis. We know from classical Quantum Theory that Momentum and Position do not commute, and this is something like the Noncommuting Time Dimensions, in that Momentum has a time-like construction and Position has a Space like construction, it is something like x, and t, not Commuting. What is the Conserved Quantity between the two types of time, is it Energy?

Dynamical Casimir effect in a Josephson metamaterial

PubMed Central

Lähteenmäki, Pasi; Paraoanu, G. S.; Hassel, Juha; Hakonen, Pertti J.

2013-01-01

The zero-point energy stored in the modes of an electromagnetic cavity has experimentally detectable effects, giving rise to an attractive interaction between the opposite walls, the static Casimir effect. A dynamical version of this effect was predicted to occur when the vacuum energy is changed either by moving the walls of the cavity or by changing the index of refraction, resulting in the conversion of vacuum fluctuations into real photons. Here, we demonstrate the dynamical Casimir effect using a Josephson metamaterial embedded in a microwave cavity at 5.4 GHz. We modulate the effective length of the cavity by flux-biasing the metamaterial based on superconducting quantum interference devices (SQUIDs), which results in variation of a few percentage points in the speed of light. We extract the full 4 × 4 covariance matrix of the emitted microwave radiation, demonstrating that photons at frequencies symmetrical with respect to half of the modulation frequency are generated in pairs. At large detunings of the cavity from half of the modulation frequency, we find power spectra that clearly show the theoretically predicted hallmark of the Casimir effect: a bimodal, “sparrow-tail” structure. The observed substantial photon flux cannot be assigned to parametric amplification of thermal fluctuations; its creation is a direct consequence of the noncommutativity structure of quantum field theory.

Methods of Contemporary Gauge Theory

NASA Astrophysics Data System (ADS)

Makeenko, Yuri

2002-08-01

Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.

Methods of Contemporary Gauge Theory

NASA Astrophysics Data System (ADS)

Makeenko, Yuri

2005-11-01

Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.

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

Osipov, D V

We prove noncommutative reciprocity laws on an algebraic surface defined over a perfect field. These reciprocity laws establish that some central extensions of globally constructed groups split over certain subgroups constructed by points or projective curves on a surface. For a two-dimensional local field with a last finite residue field, the local central extension which is constructed is isomorphic to the central extension which comes from the case of tame ramification of the Abelian two-dimensional local Langlands correspondence suggested by Kapranov. Bibliography: 9 titles.

Noncommutative effects in entropic gravity

NASA Astrophysics Data System (ADS)

Gregory, C. M.; Pinzul, A.

2013-09-01

We analyze the question of possible quantum corrections in the entropic scenario of emergent gravity. Using a fuzzy sphere as a natural quasiclassical approximation for the spherical holographic screen, we analyze whether it is possible to observe such corrections to Newton’s law in principle. The main outcome of our analysis is that without the complete knowledge of the quantum dynamics of the microscopic degrees of freedom, any Plank-scale correction cannot be trusted. Some perturbative corrections might produce reliable predictions well below the Plank scale.

Multitime correlators in continuous measurement of qubit observables

NASA Astrophysics Data System (ADS)

Atalaya, Juan; Hacohen-Gourgy, Shay; Martin, Leigh S.; Siddiqi, Irfan; Korotkov, Alexander N.

2018-02-01

We consider multitime correlators for output signals from linear detectors, continuously measuring several qubit observables at the same time. Using the quantum Bayesian formalism, we show that for unital (symmetric) evolution in the absence of phase backaction, an N -time correlator can be expressed as a product of two-time correlators when N is even. For odd N , there is a similar factorization, which also includes a single-time average. Theoretical predictions agree well with experimental results for two detectors, which simultaneously measure noncommuting qubit observables.

Fuzzy spaces topology change as a possible solution to the black hole information loss paradox

NASA Astrophysics Data System (ADS)

Silva, C. A. S.

2009-06-01

The black hole information loss paradox is one of the most intricate problems in modern theoretical physics. A proposal to solve this is one related with topology change. However it has found some obstacles related to unitarity and cluster decomposition (locality). In this Letter we argue that modelling the black hole's event horizon as a noncommutative manifold - the fuzzy sphere - we can solve the problems with topology change, getting a possible solution to the black hole information loss paradox.

Synchronized state of coupled dynamics on time-varying networks.

PubMed

Amritkar, R E; Hu, Chin-Kun

2006-03-01

We consider synchronization properties of coupled dynamics on time-varying networks and the corresponding time-average network. We find that if the different Laplacians corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand for noncommuting Laplacians the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.

Entropic Uncertainty Relation and Information Exclusion Relation for multiple measurements in the presence of quantum memory

PubMed Central

Zhang, Jun; Zhang, Yang; Yu, Chang-shui

2015-01-01

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodecki’s bound entangled state are investigated in details. PMID:26118488

Application of ride quality technology to predict ride satisfaction for commuter-type aircraft

NASA Technical Reports Server (NTRS)

Jacobson, I. D.; Kuhlthau, A. R.; Richards, L. G.

1975-01-01

A method was developed to predict passenger satisfaction with the ride environment of a transportation vehicle. This method, a general approach, was applied to a commuter-type aircraft for illustrative purposes. The effect of terrain, altitude and seat location were examined. The method predicts the variation in passengers satisfied for any set of flight conditions. In addition several noncommuter aircraft were analyzed for comparison and other uses of the model described. The method has advantages for design, evaluation, and operating decisions.

Quantum Graphical Models and Belief Propagation

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

Leifer, M.S.; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo Ont., N2L 2Y5; Poulin, D.

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markovmore » Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.« less

Upon Generating (2+1)-dimensional Dynamical Systems

NASA Astrophysics Data System (ADS)

Zhang, Yufeng; Bai, Yang; Wu, Lixin

2016-06-01

Under the framework of the Adler-Gel'fand-Dikii(AGD) scheme, we first propose two Hamiltonian operator pairs over a noncommutative ring so that we construct a new dynamical system in 2+1 dimensions, then we get a generalized special Novikov-Veselov (NV) equation via the Manakov triple. Then with the aid of a special symmetric Lie algebra of a reductive homogeneous group G, we adopt the Tu-Andrushkiw-Huang (TAH) scheme to generate a new integrable (2+1)-dimensional dynamical system and its Hamiltonian structure, which can reduce to the well-known (2+1)-dimensional Davey-Stewartson (DS) hierarchy. Finally, we extend the binormial residue representation (briefly BRR) scheme to the super higher dimensional integrable hierarchies with the help of a super subalgebra of the super Lie algebra sl(2/1), which is also a kind of symmetric Lie algebra of the reductive homogeneous group G. As applications, we obtain a super 2+1 dimensional MKdV hierarchy which can be reduced to a super 2+1 dimensional generalized AKNS equation. Finally, we compare the advantages and the shortcomings for the three schemes to generate integrable dynamical systems.

Drivers` activities and information needs in an automated highway system. Working paper, August 1995-May 1996

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

Levitan, L.; Bloomfield, J.

1996-10-01

In most visions of the AHS--including that of the National Automated Highway System Consortium--it has been assumed that when a vehicle was under automated control, the driver would be allowed to engage in any of a variety of activities not related to driving (e.g, working, reading, sleeping). The objective of the first study reported here--one of the noncommuter studies--was to determine what drivers do when traveling under automated control, and whether the age of and/gender or the driver and/or the intrastring gap have an influence on those activities. One the objectives of the commuter experiment--of relevance for this report--was tomore » determine whether what drivers do when traveling under automated control changes as a function of experience with the AHS (i.e., across trials). As conceptualization of the AHS proceeds, the details of the interface between the driver and the in-vehicle system will become more important. One part of that interface will be information supplied by the AHS to the driver, perhaps about such things as traffic conditions ahead predicted trip time to the driver`s selected exit, and so on. To maximize the utility of that information, it is important to determine what it is that drivers would like to know when traveling under automated control. The objective of the third study reported here--the second of the five noncommuter experiments--was to provide a first investigation of that issue.« less

Noncommutative Geometry of the Moyal Plane: Translation Isometries, Connes' Distance on Coherent States, Pythagoras Equality

NASA Astrophysics Data System (ADS)

Martinetti, Pierre; Tomassini, Luca

2013-10-01

We study the metric aspect of the Moyal plane from Connes' noncommutative geometry point of view. First, we compute Connes' spectral distance associated with the natural isometric action of on the algebra of the Moyal plane . We show that the distance between any state of and any of its translated states is precisely the amplitude of the translation. As a consequence, we obtain the spectral distance between coherent states of the quantum harmonic oscillator as the Euclidean distance on the plane. We investigate the classical limit, showing that the set of coherent states equipped with Connes' spectral distance tends towards the Euclidean plane as the parameter of deformation goes to zero. The extension of these results to the action of the symplectic group is also discussed, with particular emphasis on the orbits of coherent states under rotations. Second, we compute the spectral distance in the double Moyal plane, intended as the product of (the minimal unitization of) by . We show that on the set of states obtained by translation of an arbitrary state of , this distance is given by the Pythagoras theorem. On the way, we prove some Pythagoras inequalities for the product of arbitrary unital and non-degenerate spectral triples. Applied to the Doplicher- Fredenhagen-Roberts model of quantum spacetime [DFR], these two theorems show that Connes' spectral distance and the DFR quantum length coincide on the set of states of optimal localization.

Homogeneous Yang-Baxter deformations as generalized diffeomorphisms

NASA Astrophysics Data System (ADS)

Sakamoto, Jun-ichi; Sakatani, Yuho; Yoshida, Kentaroh

2017-10-01

Yang-Baxter (YB) deformations of string sigma model provide deformed target spaces. We propose that homogeneous YB deformations always lead to a certain class of β-twisted backgrounds and represent the bosonic part of the supergravity fields in terms of the classical r-matrix associated with the YB deformation. We then show that various β-twisted backgrounds can be realized by considering generalized diffeomorphisms in the undeformed background. Our result extends the notable relation between the YB deformations and (non-commuting) TsT transformations. We also discuss more general deformations beyond the YB deformations.

Naked singularities are not singular in distorted gravity

NASA Astrophysics Data System (ADS)

Garattini, Remo; Majumder, Barun

2014-07-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

Quanta of geometry and unification

NASA Astrophysics Data System (ADS)

Chamseddine, Ali H.

2016-11-01

This is a tribute to Abdus Salam’s memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.

On Pythagoras Theorem for Products of Spectral Triples

NASA Astrophysics Data System (ADS)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

A New Scheme of Integrability for (bi)Hamiltonian PDE

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2016-10-01

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

(Super)symmetries of semiclassical models in theoretical and condensed matter physics

NASA Astrophysics Data System (ADS)

Ngome, J.-P.

2011-03-01

Van Holten's covariant algorithm for deriving conserved quantities is presented, with particular attention paid to Runge-Lenz-type vectors. The classical dynamics of isospin-carrying particles is reviewed. Physical applications including non-Abelian monopole-type systems in diatoms, introduced by Moody, Shapere and Wilczek, are considered. Applied to curved space, the formalism of van Holten allows us to describe the dynamical symmetries of generalized Kaluza-Klein monopoles. The framework is extended to supersymmetry and applied to the SUSY of the monopoles. Yet another application concerns the three-dimensional non-commutative oscillator.

Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory

NASA Astrophysics Data System (ADS)

Junge, M.; Palazuelos, C.; Pérez-García, D.; Villanueva, I.; Wolf, M. M.

2010-12-01

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order {Ω left(sqrt{n}/log^2n right)} when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative L p embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.

Comment on 'All quantum observables in a hidden-variable model must commute simultaneously'

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

Nagata, Koji

Malley discussed [Phys. Rev. A 69, 022118 (2004)] that all quantum observables in a hidden-variable model for quantum events must commute simultaneously. In this comment, we discuss that Malley's theorem is indeed valid for the hidden-variable theoretical assumptions, which were introduced by Kochen and Specker. However, we give an example that the local hidden-variable (LHV) model for quantum events preserves noncommutativity of quantum observables. It turns out that Malley's theorem is not related to the LHV model for quantum events, in general.

Quanta of Geometry and Unification

NASA Astrophysics Data System (ADS)

Chamseddine, Ali H.

This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.

High-capacity quantum key distribution via hyperentangled degrees of freedom

NASA Astrophysics Data System (ADS)

Simon, David S.; Sergienko, Alexander V.

2014-06-01

Quantum key distribution (QKD) has long been a promising area for the application of quantum effects in solving real-world problems. However, two major obstacles have stood in the way of its widespread application: low secure key generation rates and short achievable operating distances. In this paper, a new physical mechanism for dealing with the first of these problems is proposed: the interplay between different degrees of freedom in a hyperentangled system (parametric down-conversion) is used to increase the Hilbert space dimension available for key generation while maintaining security. Polarization-based Bell tests provide security checking, while orbital angular momentum (OAM) and total angular momentum (TAM) provide a higher key generation rate. Whether to measure TAM or OAM is decided randomly in each trial. The concurrent noncommutativity of TAM with OAM and polarization provides the physical basis for quantum security. TAM measurements link polarization to OAM, so that if the legitimate participants measure OAM while the eavesdropper measures TAM (or vice-versa), then polarization entanglement is lost, revealing the eavesdropper. In contrast to other OAM-based QKD methods, complex active switching between OAM bases is not required; instead, passive switching by beam splitters combined with much simpler active switching between polarization bases makes implementation at high OAM more practical.

Multicenter Evaluation of a Commercial Cytomegalovirus Quantitative Standard: Effects of Commutability on Interlaboratory Concordance

PubMed Central

Shahbazian, M. D.; Valsamakis, A.; Boonyaratanakornkit, J.; Cook, L.; Pang, X. L.; Preiksaitis, J. K.; Schönbrunner, E. R.; Caliendo, A. M.

2013-01-01

Commutability of quantitative reference materials has proven important for reliable and accurate results in clinical chemistry. As international reference standards and commercially produced calibration material have become available to address the variability of viral load assays, the degree to which such materials are commutable and the effect of commutability on assay concordance have been questioned. To investigate this, 60 archived clinical plasma samples, which previously tested positive for cytomegalovirus (CMV), were retested by five different laboratories, each using a different quantitative CMV PCR assay. Results from each laboratory were calibrated both with lab-specific quantitative CMV standards (“lab standards”) and with common, commercially available standards (“CMV panel”). Pairwise analyses among laboratories were performed using mean results from each clinical sample, calibrated first with lab standards and then with the CMV panel. Commutability of the CMV panel was determined based on difference plots for each laboratory pair showing plotted values of standards that were within the 95% prediction intervals for the clinical specimens. Commutability was demonstrated for 6 of 10 laboratory pairs using the CMV panel. In half of these pairs, use of the CMV panel improved quantitative agreement compared to use of lab standards. Two of four laboratory pairs for which the CMV panel was noncommutable showed reduced quantitative agreement when that panel was used as a common calibrator. Commutability of calibration material varies across different quantitative PCR methods. Use of a common, commutable quantitative standard can improve agreement across different assays; use of a noncommutable calibrator can reduce agreement among laboratories. PMID:24025907

Coulomb Scattering in the Massless Nelson Model III: Ground State Wave Functions and Non-commutative Recurrence Relations

NASA Astrophysics Data System (ADS)

Dybalski, Wojciech; Pizzo, Alessandro

2018-02-01

Let $H_{P,\\sigma}$ be the single-electron fiber Hamiltonians of the massless Nelson model at total momentum $P$ and infrared cut-off $\\sigma>0$. We establish detailed regularity properties of the corresponding $n$-particle ground state wave functions $f^n_{P,\\sigma}$ as functions of $P$ and $\\sigma$. In particular, we show that \\[ |\\partial_{P^j}f^{n}_{P,\\sigma}(k_1,\\ldots, k_n)|, \\ \\ |\\partial_{P^j} \\partial_{P^{j'}} f^{n}_{P,\\sigma}(k_1,\\ldots, k_n)| \\leq \\frac{1}{\\sqrt{n!}} \\frac{(c\\lambda_0)^n}{\\sigma^{\\delta_{\\lambda_0}}} \\prod_{i=1}^n\\frac{ \\chi_{[\\sigma,\\kappa)}(k_i)}{|k_i|^{3/2}}, \\] where $c$ is a numerical constant, $\\lambda_0\\mapsto \\delta_{\\lambda_0}$ is a positive function of the maximal admissible coupling constant which satisfies $\\lim_{\\lambda_0\\to 0}\\delta_{\\lambda_0}=0$ and $\\chi_{[\\sigma,\\kappa)}$ is the (approximate) characteristic function of the energy region between the infrared cut-off $\\sigma$ and the ultraviolet cut-off $\\kappa$. While the analysis of the first derivative is relatively straightforward, the second derivative requires a new strategy. By solving a non-commutative recurrence relation we derive a novel formula for $f^n_{P,\\sigma}$ with improved infrared properties. In this representation $\\partial_{P^{j'}}\\partial_{P^{j}}f^n_{P,\\sigma}$ is amenable to sharp estimates obtained by iterative analytic perturbation theory in part II of this series of papers. The bounds stated above are instrumental for scattering theory of two electrons in the Nelson model, as explained in part I of this series.

Commuting, Life-Satisfaction and Internet Addiction.

PubMed

Lachmann, Bernd; Sariyska, Rayna; Kannen, Christopher; Stavrou, Maria; Montag, Christian

2017-10-05

The focus of the present work was on the association between commuting (business and private), life satisfaction, stress, and (over-) use of the Internet. Considering that digital devices are omnipresent in buses and trains, no study has yet investigated if commuting contributes to the development of Internet addiction. Overall, N = 5039 participants (N = 3477 females, age M = 26.79, SD = 10.68) took part in an online survey providing information regarding their commuting behavior, Internet addiction, personality, life satisfaction, and stress perception. Our findings are as follows: Personality seems to be less suitable to differentiate between commuter and non-commuter groups, which is possibly due to commuters often not having a choice but simply must accept offered job opportunities at distant locations. Second, the highest levels of satisfaction were found with income and lodging in the group commuting for business purposes. This might be related to the fact that commuting results in higher salaries (hence also better and more expensive housing style) due to having a job in another city which might exceed job opportunities at one's own living location. Third, within the business-commuters as well as in the private-commuter groups, females had significantly higher levels of stress than males. This association was not present in the non-commuter group. For females, commuting seems to be a higher burden and more stressful than for males, regardless of whether they commute for business or private reasons. Finally, we observed an association between higher stress perception (more negative attitude towards commuting) and Internet addiction. This finding suggests that some commuters try to compensate their perceived stress with increased Internet use.

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Commuting, Life-Satisfaction and Internet Addiction

PubMed Central

Lachmann, Bernd; Sariyska, Rayna; Kannen, Christopher; Stavrou, Maria

2017-01-01

The focus of the present work was on the association between commuting (business and private), life satisfaction, stress, and (over-) use of the Internet. Considering that digital devices are omnipresent in buses and trains, no study has yet investigated if commuting contributes to the development of Internet addiction. Overall, N = 5039 participants (N = 3477 females, age M = 26.79, SD = 10.68) took part in an online survey providing information regarding their commuting behavior, Internet addiction, personality, life satisfaction, and stress perception. Our findings are as follows: Personality seems to be less suitable to differentiate between commuter and non-commuter groups, which is possibly due to commuters often not having a choice but simply must accept offered job opportunities at distant locations. Second, the highest levels of satisfaction were found with income and lodging in the group commuting for business purposes. This might be related to the fact that commuting results in higher salaries (hence also better and more expensive housing style) due to having a job in another city which might exceed job opportunities at one’s own living location. Third, within the business-commuters as well as in the private-commuter groups, females had significantly higher levels of stress than males. This association was not present in the non-commuter group. For females, commuting seems to be a higher burden and more stressful than for males, regardless of whether they commute for business or private reasons. Finally, we observed an association between higher stress perception (more negative attitude towards commuting) and Internet addiction. This finding suggests that some commuters try to compensate their perceived stress with increased Internet use. PMID:28981452

Built-In Potential in Fe 2 O 3 -Cr 2 O 3 Superlattices for Improved Photoexcited Carrier Separation

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

Kaspar, Tiffany C.; Schreiber, Daniel K.; Spurgeon, Steven R.

2015-12-17

We demonstrate that the different surface terminations exhibited by α-Fe2O3 (hematite) and α-Cr2O3 (eskolaite) in superlattices (SL) of these materials, synthesized with exquisite control by molecular beam epitaxy, determine the heterojunction interface structure and result in controllable, non-commutative band offset values. Precise atomic control of the interface structure allowed us to vary the valence band offset from 0.35 eV to 0.79 eV. This controllable band alignment can be harnessed to generate a built-in potential in Fe2O3-Cr2O3 SLs. For instance, in a 2.5-period SL, a built-in potential of 0.8 eV was realized as measured by x-ray photoelectron spectroscopy of Ti dopantsmore » as probe species. The high quality of the SL structure was confirmed by atom probe tomography and scanning transmission electron microscopy. Enhanced photocurrents were measured for a thick Fe2O3 epitaxial film capped with an (Fe2O3)3-(Cr2O3)3 SL; this enhancement was attributed to efficient electron-hole separation in the SL as a result of the band alignment. The Fe-O-Cr bonds at the SL interfaces also red-shifted the onset of photoconductivity to ~1.6 eV. Exploiting the band alignment and photoabsorption properties of Fe2O3-Cr2O3 SLs has the potential to increase the efficiency of hematite-based photoelectrochemical water splitting.« less

Analysis on singular spaces: Lie manifolds and operator algebras

NASA Astrophysics Data System (ADS)

Nistor, Victor

2016-07-01

We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called ;Lie manifolds; -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.

Transition from AdS universe to DS universe in the BPP model

NASA Astrophysics Data System (ADS)

Kim, Wontae; Yoon, Myungseok

2007-04-01

It can be shown that in the BPP model the smooth phase transition from the asymptotically decelerated AdS universe to the asymptotically accelerated DS universe is possible by solving the modified semiclassical equations of motion. This transition comes from noncommutative Poisson algebra, which gives the constant curvature scalars asymptotically. The decelerated expansion of the early universe is due to the negative energy density with the negative pressure induced by quantum back reaction, and the accelerated late-time universe comes from the positive energy and the negative pressure which behave like dark energy source in recent cosmological models.

Exact solution of matricial Φ23 quantum field theory

NASA Astrophysics Data System (ADS)

Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

2017-12-01

We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

Hybrid normed ideal perturbations of n-tuples of operators I

NASA Astrophysics Data System (ADS)

Voiculescu, Dan-Virgil

2018-06-01

In hybrid normed ideal perturbations of n-tuples of operators, the normed ideal is allowed to vary with the component operators. We begin extending to this setting the machinery we developed for normed ideal perturbations based on the modulus of quasicentral approximation and an adaptation of our non-commutative generalization of the Weyl-von Neumann theorem. For commuting n-tuples of hermitian operators, the modulus of quasicentral approximation remains essentially the same when Cn- is replaced by a hybrid n-tuple Cp1,…- , … , Cpn- , p1-1 + ⋯ + pn-1 = 1. The proof involves singular integrals of mixed homogeneity.

Thermodynamics of BTZ black holes in gravity’s rainbow

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa

2017-05-01

In this paper, we deform the thermodynamics of a BTZ black hole from rainbow functions in gravity’s rainbow. The rainbow functions will be motivated from the results in loop quantum gravity and noncommutative geometry. It will be observed that the thermodynamics gets deformed due to these rainbow functions, indicating the existence of a remnant. However, the Gibbs free energy does not get deformed due to these rainbow functions, and so the critical behavior from Gibbs does not change by this deformation. This is because the deformation in the entropy cancels out the temperature deformation.

Quantum probability and quantum decision-making.

PubMed

Yukalov, V I; Sornette, D

2016-01-13

A rigorous general definition of quantum probability is given, which is valid not only for elementary events but also for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision-making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary. © 2015 The Author(s).

Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula

NASA Astrophysics Data System (ADS)

Dai, Jian; Song, Xing-Chang

2001-07-01

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.

Twisted supersymmetry: Twisted symmetry versus renormalizability

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

Dimitrijevic, Marija; Nikolic, Biljana; Radovanovic, Voja

We discuss a deformation of superspace based on a Hermitian twist. The twist implies a *-product that is noncommutative, Hermitian and finite when expanded in a power series of the deformation parameter. The Leibniz rule for the twisted supersymmetry transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model. We discuss different possibilities to render a renormalizable model.

Comment on ‘Special-case closed form of the Baker-Campbell-Hausdorff formula’

NASA Astrophysics Data System (ADS)

Lo, C. F.

2016-05-01

Recently Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) succeeded in explicitly evaluating the Baker-Campbell-Hausdorff (BCH) expansion series for the noncommuting operators X and Y, provided that the two operators satisfy the commutation relation: [X,Y]={uX}+{vY}+{cI}, and the operator I commutes with both of them. In this comment we show that the closed-form BCH formula of this special case can be straightforwardly derived by the means of the Wei-Norman theorem and no summation of the infinite series is needed.

The application of signal detection theory to optics

NASA Technical Reports Server (NTRS)

Helstrom, C. W.

1971-01-01

The restoration of images focused on a photosensitive surface is treated from the standpoint of maximum likelihood estimation, taking into account the Poisson distributions of the observed data, which are the numbers of photoelectrons from various elements of the surface. A detector of an image focused on such a surface utilizes a certain linear combination of those numbers as the optimum detection statistic. Methods for calculating the false alarm and detection probabilities are proposed. It is shown that measuring noncommuting observables in an ideal quantum receiver cannot yield a lower Bayes cost than that attainable by a system measuring only commuting observables.

Quantum Gravity and Cosmology: an intimate interplay

NASA Astrophysics Data System (ADS)

Sakellariadou, Mairi

2017-08-01

I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological rôle of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.

Transfer Functions Via Laplace- And Fourier-Borel Transforms

NASA Technical Reports Server (NTRS)

Can, Sumer; Unal, Aynur

1991-01-01

Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.

Graph C ∗-algebras and Z2-quotients of quantum spheres

NASA Astrophysics Data System (ADS)

Hajac, Piotr M.; Matthes, Rainer; Szymański, Wojciech

2003-06-01

We consider two Z2-actions on the Podleś generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesmewski q-disc and the quantum real projective space, respectively. The C ∗-algebas of all these quantum spaces are described as graph C ∗-algebras. The K-groups of the thus presented C ∗-algebras are then easily determined from the general theory of graph C ∗-algebas. For the quantum real projective space, we also recall the classification of the classes of irreducible ∗-representations of its algebra and give a linear basis for this algebra.

Experimental realization of non-Abelian non-adiabatic geometric gates.

PubMed

Abdumalikov, A A; Fink, J M; Juliusson, K; Pechal, M; Berger, S; Wallraff, A; Filipp, S

2013-04-25

The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies--the effect of which depends on the order of two consecutive paths--can be obtained. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases or the description of non-Abelian anyon statistics. Moreover, there are proposals to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature. Here we realize non-Abelian non-adiabatic holonomic quantum operations on a single, superconducting, artificial three-level atom by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.

On a boundary-localized Higgs boson in 5D theories.

PubMed

Barceló, Roberto; Mitra, Subhadip; Moreau, Grégory

In the context of a simple five-dimensional (5D) model with bulk matter coupled to a brane-localized Higgs boson, we point out a non-commutativity in the 4D calculation of the mass spectrum for excited fermion towers: the obtained expression depends on the choice in ordering the limits, [Formula: see text] (infinite Kaluza-Klein tower) and [Formula: see text] ([Formula: see text] being the parameter introduced for regularizing the Higgs Dirac peak). This introduces the question of which one is the correct order; we then show that the two possible orders of regularization (called I and II) are experimentally equivalent, as both can typically reproduce the measured observables, but that the one with less degrees of freedom (I) could be uniquely excluded by future experimental constraints. This conclusion is based on the exact matching between the 4D and 5D analytical calculations of the mass spectrum - via regularizations of type I and II. Beyond a deeper insight into the Higgs peak regularizations, this matching brings another confirmation of the validity of the 5D mixed formalism. All the conclusions, deduced from regularizing the Higgs peak through a brane shift or a smoothed square profile, are expected to remain similar in realistic models with a warped extra-dimension. The complementary result of the study is that the non-commutativity disappears, both in the 4D and the 5D calculations, in the presence of higher order derivative operators. For clarity, the 4D and 5D analytical calculations, matching with each other, are presented in the first part of the paper, while the second part is devoted to the interpretation of the results.

Can We Speculate Running Application With Server Power Consumption Trace?

PubMed

Li, Yuanlong; Hu, Han; Wen, Yonggang; Zhang, Jun

2018-05-01

In this paper, we propose to detect the running applications in a server by classifying the observed power consumption series for the purpose of data center energy consumption monitoring and analysis. Time series classification problem has been extensively studied with various distance measurements developed; also recently the deep learning-based sequence models have been proved to be promising. In this paper, we propose a novel distance measurement and build a time series classification algorithm hybridizing nearest neighbor and long short term memory (LSTM) neural network. More specifically, first we propose a new distance measurement termed as local time warping (LTW), which utilizes a user-specified index set for local warping, and is designed to be noncommutative and nondynamic programming. Second, we hybridize the 1-nearest neighbor (1NN)-LTW and LSTM together. In particular, we combine the prediction probability vector of 1NN-LTW and LSTM to determine the label of the test cases. Finally, using the power consumption data from a real data center, we show that the proposed LTW can improve the classification accuracy of dynamic time warping (DTW) from about 84% to 90%. Our experimental results prove that the proposed LTW is competitive on our data set compared with existed DTW variants and its noncommutative feature is indeed beneficial. We also test a linear version of LTW and find out that it can perform similar to state-of-the-art DTW-based method while it runs as fast as the linear runtime lower bound methods like LB_Keogh for our problem. With the hybrid algorithm, for the power series classification task we achieve an accuracy up to about 93%. Our research can inspire more studies on time series distance measurement and the hybrid of the deep learning models with other traditional models.

Spectral action models of gravity on packed swiss cheese cosmology

NASA Astrophysics Data System (ADS)

Ball, Adam; Marcolli, Matilde

2016-06-01

We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the packed swiss cheese cosmology models. As the action functional for gravity we consider the spectral action of noncommutative geometry, and we compute its expansion on a space obtained as an Apollonian packing of three-dimensional spheres inside a four-dimensional ball. Using information from the zeta function of the Dirac operator of the spectral triple, we compute the leading terms in the asymptotic expansion of the spectral action. They consist of a zeta regularization of the divergent sum of the leading terms of the spectral actions of the individual spheres in the packing. This accounts for the contribution of points 1 and 3 in the dimension spectrum (as in the case of a 3-sphere). There is an additional term coming from the residue at the additional point in the real dimension spectrum that corresponds to the packing constant, as well as a series of fluctuations coming from log-periodic oscillations, created by the points of the dimension spectrum that are off the real line. These terms detect the fractality of the residue set of the sphere packing. We show that the presence of fractality influences the shape of the slow-roll potential for inflation, obtained from the spectral action. We also discuss the effect of truncating the fractal structure at a certain scale related to the energy scale in the spectral action.

A quantum-like model of homeopathy clinical trials: importance of in situ randomization and unblinding.

PubMed

Beauvais, Francis

2013-04-01

The randomized controlled trial (RCT) is the 'gold standard' of modern clinical pharmacology. However, for many practitioners of homeopathy, blind RCTs are an inadequate research tool for testing complex therapies such as homeopathy. Classical probabilities used in biological sciences and in medicine are only a special case of the generalized theory of probability used in quantum physics. I describe homeopathy trials using a quantum-like statistical model, a model inspired by quantum physics and taking into consideration superposition of states, non-commuting observables, probability interferences, contextuality, etc. The negative effect of blinding on success of homeopathy trials and the 'smearing effect' ('specific' effects of homeopathy medicine occurring in the placebo group) are described by quantum-like probabilities without supplementary ad hoc hypotheses. The difference of positive outcome rates between placebo and homeopathy groups frequently vanish in centralized blind trials. The model proposed here suggests a way to circumvent such problems in masked homeopathy trials by incorporating in situ randomization/unblinding. In this quantum-like model of homeopathy clinical trials, success in open-label setting and failure with centralized blind RCTs emerge logically from the formalism. This model suggests that significant differences between placebo and homeopathy in blind RCTs would be found more frequently if in situ randomization/unblinding was used. Copyright © 2013. Published by Elsevier Ltd.

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

Pramanik, Souvik, E-mail: souvick.in@gmail.com; Ghosh, Subir, E-mail: subir_ghosh2@rediffmail.com; Pal, Probir, E-mail: probirkumarpal@rediffmail.com

In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative κ-Minkowski space–time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard–Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of κ-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac frameworkmore » of Hamiltonian constraint analysis.« less

Building non-commutative spacetimes at the Planck length for Friedmann flat cosmologies

NASA Astrophysics Data System (ADS)

Tomassini, Luca; Viaggiu, Stefano

2014-09-01

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we construct a concrete realization of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space. In loving memory of Francesco Saverio de Blasi, mathematician and friend.

Phase space quantum mechanics - Direct

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

Nasiri, S.; Sobouti, Y.; Taati, F.

2006-09-15

Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of themore » formalism are demonstrated throughout the text.« less

The square cat

NASA Astrophysics Data System (ADS)

Putterman, E.; Raz, O.

2008-11-01

We present a simple two-dimensional model of a "cat"—a body with zero angular momentum that can rotate itself with no external forces. The model is used to explain the nature of a gauge theory and to illustrate the importance of noncommutative operators. We compare the free-space cat in Newtonian mechanics and the same problem in Aristotelian mechanics at low Reynolds numbers (with the velocity proportional to the force rather than to the acceleration). This example shows the analogy between (angular) momentum in Newtonian mechanics and (torque) force in Aristotelian mechanics. We discuss a topological invariant common to the model in free space and at low Reynolds number.

Deterministic nonlinear phase gates induced by a single qubit

NASA Astrophysics Data System (ADS)

Park, Kimin; Marek, Petr; Filip, Radim

2018-05-01

We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.

Center-of-Mass Tomography and Wigner Function for Multimode Photon States

NASA Astrophysics Data System (ADS)

Dudinets, Ivan V.; Man'ko, Vladimir I.

2018-06-01

Tomographic probability representation of multimode electromagnetic field states in the scheme of center-of-mass tomography is reviewed. Both connection of the field state Wigner function and observable Weyl symbols with the center-of-mass tomograms as well as connection of the Grönewold kernel with the center-of-mass tomographic kernel determining the noncommutative product of the tomograms are obtained. The dual center-of-mass tomogram of the photon states are constructed and the dual tomographic kernel is obtained. The models of other generalized center-of-mass tomographies are discussed. Example of two-mode even and odd Schrödinger cat states is presented in details.

Continuous quantum measurement with independent detector cross correlations.

PubMed

Jordan, Andrew N; Büttiker, Markus

2005-11-25

We investigate the advantages of using two independent, linear detectors for continuous quantum measurement. For single-shot measurement, the detection process may be quantum limited if the detectors are twins. For weak continuous measurement, cross correlations allow a violation of the Korotkov-Averin bound for the detector's signal-to-noise ratio. The joint weak measurement of noncommuting observables is also investigated, and we find the cross correlation changes sign as a function of frequency, reflecting a crossover from incoherent relaxation to coherent, out of phase oscillations. Our results are applied to a double quantum-dot charge qubit, simultaneously measured by two quantum point contacts.

Generation and control of Greenberger-Horne-Zeilinger entanglement in superconducting circuits.

PubMed

Wei, L F; Liu, Yu-xi; Nori, Franco

2006-06-23

Going beyond the entanglement of microscopic objects (such as photons, spins, and ions), here we propose an efficient approach to produce and control the quantum entanglement of three macroscopic coupled superconducting qubits. By conditionally rotating, one by one, selected Josephson-charge qubits, we show that their Greenberger-Horne-Zeilinger (GHZ) entangled states can be deterministically generated. The existence of GHZ correlations between these qubits could be experimentally demonstrated by effective single-qubit operations followed by high-fidelity single-shot readouts. The possibility of using the prepared GHZ correlations to test the macroscopic conflict between the noncommutativity of quantum mechanics and the commutativity of classical physics is also discussed.

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

Stoilova, N. I.

Generalized quantum statistics, such as paraboson and parafermion statistics, are characterized by triple relations which are related to Lie (super)algebras of type B. The correspondence of the Fock spaces of parabosons, parafermions as well as the Fock space of a system of parafermions and parabosons to irreducible representations of (super)algebras of type B will be pointed out. Example of generalized quantum statistics connected to the basic classical Lie superalgebra B(1|1) ≡ osp(3|2) with interesting physical properties, such as noncommutative coordinates, will be given. Therefore the article focuses on the question, addressed already in 1950 by Wigner: do the equation ofmore » motion determine the quantum mechanical commutation relation?.« less

Exact partition functions for gauge theories on Rλ3

NASA Astrophysics Data System (ADS)

Wallet, Jean-Christophe

2016-11-01

The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.

Hyperunified field theory and gravitational gauge-geometry duality

NASA Astrophysics Data System (ADS)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.

Global-to-local incompatibility, monogamy of entanglement, and ground-state dimerization: Theory and observability of quantum frustration in systems with competing interactions

NASA Astrophysics Data System (ADS)

Giampaolo, S. M.; Hiesmayr, B. C.; Illuminati, F.

2015-10-01

Frustration in quantum many-body systems is quantified by the degree of incompatibility between the local and global orders associated, respectively, with the ground states of the local interaction terms and the global ground state of the total many-body Hamiltonian. This universal measure is bounded from below by the ground-state bipartite block entanglement. For many-body Hamiltonians that are sums of two-body interaction terms, a further inequality relates quantum frustration to the pairwise entanglement between the constituents of the local interaction terms. This additional bound is a consequence of the limits imposed by monogamy on entanglement shareability. We investigate the behavior of local pair frustration in quantum spin models with competing interactions on different length scales and show that valence bond solids associated with exact ground state dimerization correspond to a transition from generic frustration, i.e., geometric, common to classical and quantum systems alike, to genuine quantum frustration, i.e., solely due to the noncommutativity of the different local interaction terms. We discuss how such frustration transitions separating genuinely quantum orders from classical-like ones are detected by observable quantities such as the static structure factor and the interferometric visibility.

Fractals, Coherence and Brain Dynamics

NASA Astrophysics Data System (ADS)

Vitiello, Giuseppe

2010-11-01

I show that the self-similarity property of deterministic fractals provides a direct connection with the space of the entire analytical functions. Fractals are thus described in terms of coherent states in the Fock-Bargmann representation. Conversely, my discussion also provides insights on the geometrical properties of coherent states: it allows to recognize, in some specific sense, fractal properties of coherent states. In particular, the relation is exhibited between fractals and q-deformed coherent states. The connection with the squeezed coherent states is also displayed. In this connection, the non-commutative geometry arising from the fractal relation with squeezed coherent states is discussed and the fractal spectral properties are identified. I also briefly discuss the description of neuro-phenomenological data in terms of squeezed coherent states provided by the dissipative model of brain and consider the fact that laboratory observations have shown evidence that self-similarity characterizes the brain background activity. This suggests that a connection can be established between brain dynamics and the fractal self-similarity properties on the basis of the relation discussed in this report between fractals and squeezed coherent states. Finally, I do not consider in this paper the so-called random fractals, namely those fractals obtained by randomization processes introduced in their iterative generation. Since self-similarity is still a characterizing property in many of such random fractals, my conjecture is that also in such cases there must exist a connection with the coherent state algebraic structure. In condensed matter physics, in many cases the generation by the microscopic dynamics of some kind of coherent states is involved in the process of the emergence of mesoscopic/macroscopic patterns. The discussion presented in this paper suggests that also fractal generation may provide an example of emergence of global features, namely long range correlation at mesoscopic/macroscopic level, from microscopic local deformation processes. In view of the wide spectrum of application of both, fractal studies and coherent state physics, spanning from solid state physics to laser physics, quantum optics, complex dynamical systems and biological systems, the results presented in the present report may lead to interesting practical developments in many research sectors.

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.

Anomalous Hall resistance in bilayer quantum Hall systems

NASA Astrophysics Data System (ADS)

Ezawa, Z. F.; Suzuki, S.; Tsitsishvili, G.

2007-07-01

We present a microscopic theory of the Hall current in the bilayer quantum Hall system on the basis of noncommutative geometry. By analyzing the Heisenberg equation of motion and the continuity equation of charge, we demonstrate the emergence of the phase current in a system where the interlayer phase coherence develops spontaneously. The phase current arranges itself to minimize the total energy of the system, as it induces certain anomalous behaviors in the Hall current in the counterflow geometry and also in the drag experiment. They explain the recent experimental data for anomalous Hall resistances due to Kellogg [Phys. Rev. Lett. 88, 126804 (2002); 93, 036801 (2004)] and Tutuc [Phys. Rev. Lett. 93, 036802 (2004)] at ν=1 .

Quasi-normal modes from non-commutative matrix dynamics

NASA Astrophysics Data System (ADS)

Aprile, Francesco; Sanfilippo, Francesco

2017-09-01

We explore similarities between the process of relaxation in the BMN matrix model and the physics of black holes in AdS/CFT. Focusing on Dyson-fluid solutions of the matrix model, we perform numerical simulations of the real time dynamics of the system. By quenching the equilibrium distribution we study quasi-normal oscillations of scalar single trace observables, we isolate the lowest quasi-normal mode, and we determine its frequencies as function of the energy. Considering the BMN matrix model as a truncation of N=4 SYM, we also compute the frequencies of the quasi-normal modes of the dual scalar fields in the AdS5-Schwarzschild background. We compare the results, and we finda surprising similarity.

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.

Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter

NASA Astrophysics Data System (ADS)

Degasperis, A.; Lebedev, D.; Olshanetsky, M.; Pakuliak, S.; Perelomov, A.; Santini, P. M.

1992-11-01

The simplest generalization of the intermediate long-wave hierarchy (ILW) is considered to show how to extend the Zakharov-Shabat dressing method to nonlocal, i.e., integro-partial differential, equations. The purpose is to give a procedure of constructing the zero-curvature representation of this class of equations. This result obtains by combining the Drinfeld-Sokolov formalism together with the introduction of an operator-valued spectral parameter, namely, a spectral parameter that does not commute with the space variable x. This extension provides a connection between the ILWk hierarchy and the Saveliev-Vershik continuum graded Lie algebras. In the case of ILW2 the Fairlie-Zachos sinh-algebra was found.

Measuring Incompatible Observables by Exploiting Sequential Weak Values.

PubMed

Piacentini, F; Avella, A; Levi, M P; Gramegna, M; Brida, G; Degiovanni, I P; Cohen, E; Lussana, R; Villa, F; Tosi, A; Zappa, F; Genovese, M

2016-10-21

One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.

Measuring Incompatible Observables by Exploiting Sequential Weak Values

NASA Astrophysics Data System (ADS)

Piacentini, F.; Avella, A.; Levi, M. P.; Gramegna, M.; Brida, G.; Degiovanni, I. P.; Cohen, E.; Lussana, R.; Villa, F.; Tosi, A.; Zappa, F.; Genovese, M.

2016-10-01

One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.

Modeling some two-dimensional relativistic phenomena using an educational interactive graphics software

NASA Astrophysics Data System (ADS)

Sastry, G. P.; Ravuri, Tushar R.

1990-11-01

This paper describes several relativistic phenomena in two spatial dimensions that can be modeled using the collision program of Spacetime Software. These include the familiar aberration, the Doppler effect, the headlight effect, and the invariance of the speed of light in vacuum, in addition to the rather unfamiliar effects like the dragging of light in a moving medium, reflection at moving mirrors, Wigner rotation of noncommuting boosts, and relativistic rotation of shrinking and expanding rods. All these phenomena are exhibited by tracings of composite computer printouts of the collision movie. It is concluded that an interactive educational graphics software with pleasing visuals can have considerable investigative power packed within it.

Fractal spectral triples on Kellendonk's C∗-algebra of a substitution tiling

NASA Astrophysics Data System (ADS)

Mampusti, Michael; Whittaker, Michael F.

2017-02-01

We introduce a new class of noncommutative spectral triples on Kellendonk's C∗-algebra associated with a nonperiodic substitution tiling. These spectral triples are constructed from fractal trees on tilings, which define a geodesic distance between any two tiles in the tiling. Since fractals typically have infinite Euclidean length, the geodesic distance is defined using Perron-Frobenius theory, and is self-similar with scaling factor given by the Perron-Frobenius eigenvalue. We show that each spectral triple is θ-summable, and respects the hierarchy of the substitution system. To elucidate our results, we construct a fractal tree on the Penrose tiling, and explicitly show how it gives rise to a collection of spectral triples.

Inflationary universe in deformed phase space scenario

NASA Astrophysics Data System (ADS)

Rasouli, S. M. M.; Saba, Nasim; Farhoudi, Mehrdad; Marto, João; Moniz, P. V.

2018-06-01

We consider a noncommutative (NC) inflationary model with a homogeneous scalar field minimally coupled to gravity. The particular NC inflationary setting herein proposed, produces entirely new consequences as summarized in what follows. We first analyze the free field case and subsequently examine the situation where the scalar field is subjected to a polynomial and exponential potentials. We propose to use a canonical deformation between momenta, in a spatially flat Friedmann-Lemaî tre-Robertson-Walker (FLRW) universe, and while the Friedmann equation (Hamiltonian constraint) remains unaffected the Friedmann acceleration equation (and thus the Klein-Gordon equation) is modified by an extra term linear in the NC parameter. This concrete noncommutativity on the momenta allows interesting dynamics that other NC models seem not to allow. Let us be more precise. This extra term behaves as the sole explicit pressure that under the right circumstances implies a period of accelerated expansion of the universe. We find that in the absence of the scalar field potential, and in contrast with the commutative case, in which the scale factor always decelerates, we obtain an inflationary phase for small negative values of the NC parameter. Subsequently, the period of accelerated expansion is smoothly replaced by an appropriate deceleration phase providing an interesting model regarding the graceful exit problem in inflationary models. This last property is present either in the free field case or under the influence of the scalar field potentials considered here. Moreover, in the case of the free scalar field, we show that not only the horizon problem is solved but also there is some resemblance between the evolution equation of the scale factor associated to our model and that for the R2 (Starobinsky) inflationary model. Therefore, our herein NC model not only can be taken as an appropriate scenario to get a successful kinetic inflation, but also is a convenient setting to obtain inflationary universe possessing the graceful exit when scalar field potentials are present.

Nonclassical properties of coherent light in a pair of coupled anharmonic oscillators

NASA Astrophysics Data System (ADS)

Alam, Nasir; Mandal, Swapan

2016-01-01

The Hamiltonian and hence the equations of motion involving the field operators of two anharmonic oscillators coupled through a linear one is framed. It is found that these equations of motion involving the non-commuting field operators are nonlinear and are coupled to each other and hence pose a great problem for getting the solutions. In order to investigate the dynamics and hence the nonclassical properties of the radiation fields, we obtain approximate analytical solutions of these coupled nonlinear differential equations involving the non-commuting field operators up to the second orders in anharmonic and coupling constants. These solutions are found useful for investigating the squeezing of pure and mixed modes, amplitude squared squeezing, principal squeezing, and the photon antibunching of the input coherent radiation field. With the suitable choice of the parameters (photon number in various field modes, anharmonic, and coupling constants, etc.), we calculate the second order variances of field quadratures of various modes and hence the squeezing, amplitude squared, and mixed mode squeezing of the input coherent light. In the absence of anharmonicities, it is found that these nonlinear nonclassical phenomena (squeezing of pure and mixed modes, amplitude squared squeezing and photon antibunching) are completely absent. The percentage of squeezing, mixed mode squeezing, amplitude squared squeezing increase with the increase of photon number and the dimensionless interaction time. The collapse and revival phenomena in squeezing, mixed mode squeezing and amplitude squared squeezing are exhibited. With the increase of the interaction time, the monotonic increasing nature of the squeezing effects reveal the presence of unwanted secular terms. It is established that the mere coupling of two oscillators through a third one does not produces the squeezing effects of input coherent light. However, the pure nonclassical phenomena of antibunching of photons in vacuum field modes are obtained through the mere coupling and hence the transfers of photons from the remaining coupled mode.

Self-quartic interaction for a scalar field in an extended DFR noncommutative space-time

NASA Astrophysics Data System (ADS)

Abreu, Everton M. C.; Neves, M. J.

2014-07-01

The framework of Dopliche-Fredenhagen-Roberts (DFR) for a noncommutative (NC) space-time is considered as an alternative approach to study the NC space-time of the early Universe. Concerning this formalism, the NC constant parameter, θ, is promoted to coordinate of the space-time and consequently we can describe a field theory in a space-time with extra-dimensions. We will see that there is a canonical momentum associated with this new coordinate in which the effects of a new physics can emerge in the propagation of the fields along the extra-dimensions. The Fourier space of this framework is automatically extended by the addition of the new momenta components. The main concept that we would like to emphasize from the outset is that the formalism demonstrated here will not be constructed by introducing a NC parameter in the system, as usual. It will be generated naturally from an already NC space. We will review that when the components of the new momentum are zero, the (extended) DFR approach is reduced to the usual (canonical) NC case, in which θ is an antisymmetric constant matrix. In this work we will study a scalar field action with self-quartic interaction ϕ4⋆ defined in the DFR NC space-time. We will obtain the Feynman rules in the Fourier space for the scalar propagator and vertex of the model. With these rules we are able to build the radiative corrections to one loop order of the model propagator. The consequences of the NC scale, as well as the propagation of the field in extra-dimensions, will be analyzed in the ultraviolet divergences scenario. We will investigate about the actual possibility that this kμν conjugate momentum has the property of healing the combination of IR/UV divergences that emerges in this recently new NC spacetime quantum field theory.

External quality assurance programs as a tool for verifying standardization of measurement procedures: Pilot collaboration in Europe.

PubMed

Perich, C; Ricós, C; Alvarez, V; Biosca, C; Boned, B; Cava, F; Doménech, M V; Fernández-Calle, P; Fernández-Fernández, P; García-Lario, J V; Minchinela, J; Simón, M; Jansen, R

2014-05-15

Current external quality assurance schemes have been classified into six categories, according to their ability to verify the degree of standardization of the participating measurement procedures. SKML (Netherlands) is a Category 1 EQA scheme (commutable EQA materials with values assigned by reference methods), whereas SEQC (Spain) is a Category 5 scheme (replicate analyses of non-commutable materials with no values assigned by reference methods). The results obtained by a group of Spanish laboratories participating in a pilot study organized by SKML are examined, with the aim of pointing out the improvements over our current scheme that a Category 1 program could provide. Imprecision and bias are calculated for each analyte and laboratory, and compared with quality specifications derived from biological variation. Of the 26 analytes studied, 9 had results comparable with those from reference methods, and 10 analytes did not have comparable results. The remaining 7 analytes measured did not have available reference method values, and in these cases, comparison with the peer group showed comparable results. The reasons for disagreement in the second group can be summarized as: use of non-standard methods (IFCC without exogenous pyridoxal phosphate for AST and ALT, Jaffé kinetic at low-normal creatinine concentrations and with eGFR); non-commutability of the reference material used to assign values to the routine calibrator (calcium, magnesium and sodium); use of reference materials without established commutability instead of reference methods for AST and GGT, and lack of a systematic effort by manufacturers to harmonize results. Results obtained in this work demonstrate the important role of external quality assurance programs using commutable materials with values assigned by reference methods to correctly monitor the standardization of laboratory tests with consequent minimization of risk to patients. Copyright © 2013 Elsevier B.V. All rights reserved.

Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states: Non-classical and non-Gaussian properties

NASA Astrophysics Data System (ADS)

Xu, Xue-Xiang; Yuan, Hong-Chun; Wang, Yan

2014-07-01

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q-parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.

Gaussification and entanglement distillation of continuous-variable systems: a unifying picture.

PubMed

Campbell, Earl T; Eisert, Jens

2012-01-13

Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.

Quantum-like microeconomics: Statistical model of distribution of investments and production

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2008-10-01

In this paper we demonstrate that the probabilistic quantum-like (QL) behavior-the Born’s rule, interference of probabilities, violation of Bell’s inequality, representation of variables by in general noncommutative self-adjoint operators, Schrödinger’s dynamics-can be exhibited not only by processes in the micro world, but also in economics. In our approach the QL-behavior is induced not by properties of systems. Here systems (commodities) are macroscopic. They could not be superpositions of two different states. In our approach the QL-behavior of economical statistics is a consequence of the organization of the process of production as well as investments. In particular, Hamiltonian (“financial energy”) is determined by rate of return.

Spectral distances on the doubled Moyal plane using Dirac eigenspinors

NASA Astrophysics Data System (ADS)

Kumar, Kaushlendra; Chakraborty, Biswajit

2018-04-01

We present here a novel method for computing spectral distances in the doubled Moyal plane in a noncommutative geometrical framework using Dirac eigenspinors, while solving the Lipschitz ball condition explicitly through matrices. The standard results of longitudinal, transverse, and hypotenuse distances between different pairs of pure states have been computed and the Pythagorean equality between them has been reproduced. The issue of the nonunital nature of the Moyal plane algebra is taken care of through a sequence of projection operators constructed from Dirac eigenspinors, which plays a crucial role throughout this paper. At the end, a toy model for a "Higgs field" has been constructed by fluctuating the Dirac operator and the variation on the transverse distance has been demonstrated, through an explicit computation.

Optimal feedback scheme and universal time scaling for Hamiltonian parameter estimation.

PubMed

Yuan, Haidong; Fung, Chi-Hang Fred

2015-09-11

Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.

Dirac Theory on a Space with Linear Lie Type Fuzziness

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Khorrami, Mohammad; Fatollahi, Amir H.

2012-08-01

A spinor theory on a space with linear Lie type noncommutativity among spatial coordinates is presented. The model is based on the Fourier space corresponding to spatial coordinates, as this Fourier space is commutative. When the group is compact, the real space exhibits lattice characteristics (as the eigenvalues of space operators are discrete), and the similarity of such a lattice with ordinary lattices is manifested, among other things, in a phenomenon resembling the famous fermion doubling problem. A projection is introduced to make the dynamical number of spinors equal to that corresponding to the ordinary space. The actions for free and interacting spinors (with Fermi-like interactions) are presented. The Feynman rules are extracted and 1-loop corrections are investigated.

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

Ni, Xiaotong; Van den Nest, Maarten; Buerschaper, Oliver

We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are tensor products of single-qubit operators drawn from the group 〈αI, X, S〉, where α = e{sup iπ/4} and S = diag(1, i). We provide techniques to efficiently compute various properties related to bipartite entanglement, expectation values of local observables, preparation by means of quantum circuits, parent Hamiltonians, etc. We also highlight significant differences compared to the Pauli stabilizer formalism. In particular, we give examplesmore » of states in our formalism which cannot arise in the Pauli stabilizer formalism, such as topological models that support non-Abelian anyons.« less

Twist for Snyder space

NASA Astrophysics Data System (ADS)

Meljanac, Daniel; Meljanac, Stjepan; Mignemi, Salvatore; Pikutić, Danijel; Štrajn, Rina

2018-03-01

We construct the twist operator for the Snyder space. Our starting point is a non-associative star product related to a Hermitian realisation of the noncommutative coordinates originally introduced by Snyder. The corresponding coproduct of momenta is non-coassociative. The twist is constructed using a general definition of the star product in terms of a bi-differential operator in the Hopf algebroid approach. The result is given by a closed analytical expression. We prove that this twist reproduces the correct coproducts of the momenta and the Lorentz generators. The twisted Poincaré symmetry is described by a non-associative Hopf algebra, while the twisted Lorentz symmetry is described by the undeformed Hopf algebra. This new twist might be important in the construction of different types of field theories on Snyder space.

Is quantum theory a form of statistical mechanics?

NASA Astrophysics Data System (ADS)

Adler, S. L.

2007-05-01

We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantum mechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.

The fourfold way of the genetic code.

PubMed

Jiménez-Montaño, Miguel Angel

2009-11-01

We describe a compact representation of the genetic code that factorizes the table in quartets. It represents a "least grammar" for the genetic language. It is justified by the Klein-4 group structure of RNA bases and codon doublets. The matrix of the outer product between the column-vector of bases and the corresponding row-vector V(T)=(C G U A), considered as signal vectors, has a block structure consisting of the four cosets of the KxK group of base transformations acting on doublet AA. This matrix, translated into weak/strong (W/S) and purine/pyrimidine (R/Y) nucleotide classes, leads to a code table with mixed and unmixed families in separate regions. A basic difference between them is the non-commuting (R/Y) doublets: AC/CA, GU/UG. We describe the degeneracy in the canonical code and the systematic changes in deviant codes in terms of the divisors of 24, employing modulo multiplication groups. We illustrate binary sub-codes characterizing mutations in the quartets. We introduce a decision-tree to predict the mode of tRNA recognition corresponding to each codon, and compare our result with related findings by Jestin and Soulé [Jestin, J.-L., Soulé, C., 2007. Symmetries by base substitutions in the genetic code predict 2' or 3' aminoacylation of tRNAs. J. Theor. Biol. 247, 391-394], and the rearrangements of the table by Delarue [Delarue, M., 2007. An asymmetric underlying rule in the assignment of codons: possible clue to a quick early evolution of the genetic code via successive binary choices. RNA 13, 161-169] and Rodin and Rodin [Rodin, S.N., Rodin, A.S., 2008. On the origin of the genetic code: signatures of its primordial complementarity in tRNAs and aminoacyl-tRNA synthetases. Heredity 100, 341-355], respectively.

Tripartite-to-Bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces

NASA Astrophysics Data System (ADS)

Li, Yinan; Qiao, Youming; Wang, Xin; Duan, Runyao

2018-03-01

We study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication (SLOCC). It is known that the tripartite-to-bipartite SLOCC convertibility is characterized by the maximal Schmidt rank of the given tripartite state, i.e. the largest Schmidt rank over those bipartite states lying in the support of the reduced density operator. In this paper, we further study this problem and exhibit novel results in both multi-copy and asymptotic settings, utilizing powerful results from the structure of matrix spaces. In the multi-copy regime, we observe that the maximal Schmidt rank is strictly super-multiplicative, i.e. the maximal Schmidt rank of the tensor product of two tripartite pure states can be strictly larger than the product of their maximal Schmidt ranks. We then provide a full characterization of those tripartite states whose maximal Schmidt rank is strictly super-multiplicative when taking tensor product with itself. Notice that such tripartite states admit strict advantages in tripartite-to-bipartite SLOCC transformation when multiple copies are provided. In the asymptotic setting, we focus on determining the tripartite-to-bipartite SLOCC entanglement transformation rate. Computing this rate turns out to be equivalent to computing the asymptotic maximal Schmidt rank of the tripartite state, defined as the regularization of its maximal Schmidt rank. Despite the difficulty caused by the super-multiplicative property, we provide explicit formulas for evaluating the asymptotic maximal Schmidt ranks of two important families of tripartite pure states by resorting to certain results of the structure of matrix spaces, including the study of matrix semi-invariants. These formulas turn out to be powerful enough to give a sufficient and necessary condition to determine whether a given tripartite pure state can be transformed to the bipartite maximally entangled state under SLOCC, in the asymptotic setting. Applying the recent progress on the non-commutative rank problem, we can verify this condition in deterministic polynomial time.

Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

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

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems ontomore » non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.« less

Repeatability of measurements: Non-Hermitian observables and quantum Coriolis force

DOE PAGES

Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh

2016-08-26

A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of non-Hermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that non-Hermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems ontomore » non-Hermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.« less

S-Duality, Deconstruction and Confinement for a Marginal Deformation of N=4 SUSY Yang-Mills

NASA Astrophysics Data System (ADS)

Dorey, Nick

2004-08-01

We study an exactly marginal deformation of Script N = 4 SUSY Yang-Mills with gauge group U(N) using field theory and string theory methods. The classical theory has a Higgs branch for rational values of the deformation parameter. We argue that the quantum theory also has an S-dual confining branch which cannot be seen classically. The low-energy effective theory on these branches is a six-dimensional non-commutative gauge theory with sixteen supercharges. Confinement of magnetic and electric charges, on the Higgs and confining branches respectively, occurs due to the formation of BPS-saturated strings in the low energy theory. The results also suggest a new way of deconstructing Little String Theory as a large-N limit of a confining gauge theory in four dimensions.

Open Quantum Walks with Noncommuting Jump Operators

NASA Astrophysics Data System (ADS)

Caballar, Roland Cristopher; Petruccione, Francesco; Sinayskiy, Ilya

2014-03-01

We examine homogeneous open quantum walks along a line, wherein each forward step is due to one quantum jump operator, and each backward step due to another quantum jump operator. We assume that these two quantum jump operators do not commute with each other. We show that if the system has N internal degrees of freedom, for particular forms of these quantum jump operators, we can obtain exact probability distributions which fall into two distinct classes, namely Gaussian distributions and solitonic distributions. We also show that it is possible for a maximum of 2 solitonic distributions to be present simultaneously in the system. Finally, we consider applications of these classes of jump operators in quantum state preparation and quantum information. We acknowledge support from the National Institute for Theoretical Physics (NITheP).

Hamiltonian purification

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

Orsucci, Davide; Burgarth, Daniel; Facchi, Paolo

The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. The notions of spanning-set purificationmore » and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.« less

Light on curved backgrounds

NASA Astrophysics Data System (ADS)

Batic, D.; Nelson, S.; Nowakowski, M.

2015-05-01

We consider the motion of light on different spacetime manifolds by calculating the deflection angle, lensing properties and by probing into the possibility of bound states. The metrics in which we examine the light motion include, among other items, a general relativistic dark matter metric, a dirty black hole, and a worm hole metric, the last two inspired by noncommutative geometry. The lensing in a holographic screen metric is discussed in detail. We study also the bending of light around naked singularities like, e.g., the Janis-Newman-Winicour metric and include other cases. A generic property of light behavior in these exotic metrics is pointed out. For the standard metric like the Schwarzschild and Schwarzschild-de Sitter cases, we improve the accuracy of the lensing results for the weak and strong regimes.

A review of the generalized uncertainty principle.

PubMed

Tawfik, Abdel Nasser; Diab, Abdel Magied

2015-12-01

Based on string theory, black hole physics, doubly special relativity and some 'thought' experiments, minimal distance and/or maximum momentum are proposed. As alternatives to the generalized uncertainty principle (GUP), the modified dispersion relation, the space noncommutativity, the Lorentz invariance violation, and the quantum-gravity-induced birefringence effects are summarized. The origin of minimal measurable quantities and the different GUP approaches are reviewed and the corresponding observations are analysed. Bounds on the GUP parameter are discussed and implemented in the understanding of recent PLANCK observations of cosmic inflation. The higher-order GUP approaches predict minimal length uncertainty with and without maximum momenta. Possible arguments against the GUP are discussed; for instance, the concern about its compatibility with the equivalence principles, the universality of gravitational redshift and the free fall and law of reciprocal action are addressed.

Finite-time quantum entanglement in propagating squeezed microwaves.

PubMed

Fedorov, K G; Pogorzalek, S; Las Heras, U; Sanz, M; Yard, P; Eder, P; Fischer, M; Goetz, J; Xie, E; Inomata, K; Nakamura, Y; Di Candia, R; Solano, E; Marx, A; Deppe, F; Gross, R

2018-04-23

Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of non-commuting observables between two subsystems. At the same time, these subsystems themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental dephasing process of quantum cross-correlations in continuous-variable propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain the insight into finite-time entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.

The Ponzano-Regge Model and Parametric Representation

NASA Astrophysics Data System (ADS)

Li, Dan

2014-04-01

We give a parametric representation of the effective noncommutative field theory derived from a -deformation of the Ponzano-Regge model and define a generalized Kirchhoff polynomial with -correction terms, obtained in a -linear approximation. We then consider the corresponding graph hypersurfaces and the question of how the presence of the correction term affects their motivic nature. We look in particular at the tetrahedron graph, which is the basic case of relevance to quantum gravity. With the help of computer calculations, we verify that the number of points over finite fields of the corresponding hypersurface does not fit polynomials with integer coefficients, hence the hypersurface of the tetrahedron is not polynomially countable. This shows that the correction term can change significantly the motivic properties of the hypersurfaces, with respect to the classical case.

Continuous Variable Quantum Key Distribution Using Polarized Coherent States

NASA Astrophysics Data System (ADS)

Vidiella-Barranco, A.; Borelli, L. F. M.

We discuss a continuous variables method of quantum key distribution employing strongly polarized coherent states of light. The key encoding is performed using the variables known as Stokes parameters, rather than the field quadratures. Their quantum counterpart, the Stokes operators Ŝi (i=1,2,3), constitute a set of non-commuting operators, being the precision of simultaneous measurements of a pair of them limited by an uncertainty-like relation. Alice transmits a conveniently modulated two-mode coherent state, and Bob randomly measures one of the Stokes parameters of the incoming beam. After performing reconciliation and privacy amplification procedures, it is possible to distill a secret common key. We also consider a non-ideal situation, in which coherent states with thermal noise, instead of pure coherent states, are used for encoding.

State dragging using the quantum Zeno effect

NASA Astrophysics Data System (ADS)

Hacohen-Gourgy, Shay; Martin, Leigh; GarcíA-Pintos, Luis Pedro; Dressel, Justin; Siddiqi, Irfan

The quantum Zeno effect is the suppression of Hamiltonian evolution by continuous measurement. It arises as a consequence of the quantum back-action pushing the state towards an eigenstate of the measurement operator. Rotating the operator at a rate much slower than the measurement rate will effectively drag the state with it. We use our recently developed scheme, which enables dynamic control of the measurement operator, to demonstrate this dragging effect on a superconducting transmon qubit. Since the system is continuously measured, the deterministic trajectory can be monitored, and quantum jumps can be detected in real-time. Furthermore, we perform this with two observables that are set to be either commuting or non-commuting, demonstrating new quantum dynamics. This work was supported by the Army Research Office and the Air Force Research Laboratory.

Semiclassical theory of Hall viscosity

NASA Astrophysics Data System (ADS)

Biswas, Rudro

2014-03-01

Hall viscosity is an intriguing stress response in quantum Hall systems and is predicted to be observable via the conductivity in an inhomogeneous electric field. This has been studied extensively using a range of techniques, such as adiabatic transport, effective field theories, and Kubo formulae. All of these are, however, agnostic as to the distinction between strongly correlated quantum Hall states and non-interacting ones, where the effect arises due to the fundamental non-commuting nature of velocities and orbit positions in a magnetic field. In this talk I shall develop the semiclassical theory of quantized cyclotron orbits drifting in an applied inhomogeneous electric field and use it to provide a clear physical picture of how single particle properties in a magnetic field contribute to the Hall viscosity-dependence of the conductivity.

It is the Theory Which Decides What We Can Observe (Einstein)

NASA Astrophysics Data System (ADS)

Filk, Thomas

In this chapter I will give examples for three types of contextuality: theory as context, a theory of measurement as context, and environmental and internal conditions as context. In particular, I will argue that depending on which theory of measurements we attribute to Bohmian mechanics, this theory may be called a classical theory or a quantum theory. Furthermore, I will show that for neural networks one can define in a natural way two different theories of measurements which can be compared with scanner-type measurements on the one hand and psychological experiments on the other hand. The later theory of measurements for neural networks leads to non-commutativity and even quantum-like contextuality. It is shown that very simple neural networks can violate Bell-type inequalities.

LOCC indistinguishable orthogonal product quantum states

NASA Astrophysics Data System (ADS)

Zhang, Xiaoqian; Tan, Xiaoqing; Weng, Jian; Li, Yongjun

2016-07-01

We construct two families of orthogonal product quantum states that cannot be exactly distinguished by local operation and classical communication (LOCC) in the quantum system of 2k+i ⊗ 2l+j (i, j ∈ {0, 1} and i ≥ j ) and 3k+i ⊗ 3l+j (i, j ∈ {0, 1, 2}). And we also give the tiling structure of these two families of quantum product states where the quantum states are unextendible in the first family but are extendible in the second family. Our construction in the quantum system of 3k+i ⊗ 3l+j is more generalized than the other construction such as Wang et al.’s construction and Zhang et al.’s construction, because it contains the quantum system of not only 2k ⊗ 2l and 2k+1 ⊗ 2l but also 2k ⊗ 2l+1 and 2k+1 ⊗ 2l+1. We calculate the non-commutativity to quantify the quantumness of a quantum ensemble for judging the local indistinguishability. We give a general method to judge the indistinguishability of orthogonal product states for our two constructions in this paper. We also extend the dimension of the quantum system of 2k ⊗ 2l in Wang et al.’s paper. Our work is a necessary complement to understand the phenomenon of quantum nonlocality without entanglement.

INFORMATION-THEORETIC INEQUALITIES ON UNIMODULAR LIE GROUPS

PubMed Central

Chirikjian, Gregory S.

2010-01-01

Classical inequalities used in information theory such as those of de Bruijn, Fisher, Cramér, Rao, and Kullback carry over in a natural way from Euclidean space to unimodular Lie groups. These are groups that possess an integration measure that is simultaneously invariant under left and right shifts. All commutative groups are unimodular. And even in noncommutative cases unimodular Lie groups share many of the useful features of Euclidean space. The rotation and Euclidean motion groups, which are perhaps the most relevant Lie groups to problems in geometric mechanics, are unimodular, as are the unitary groups that play important roles in quantum computing. The extension of core information theoretic inequalities defined in the setting of Euclidean space to this broad class of Lie groups is potentially relevant to a number of problems relating to information gathering in mobile robotics, satellite attitude control, tomographic image reconstruction, biomolecular structure determination, and quantum information theory. In this paper, several definitions are extended from the Euclidean setting to that of Lie groups (including entropy and the Fisher information matrix), and inequalities analogous to those in classical information theory are derived and stated in the form of fifteen small theorems. In all such inequalities, addition of random variables is replaced with the group product, and the appropriate generalization of convolution of probability densities is employed. An example from the field of robotics demonstrates how several of these results can be applied to quantify the amount of information gained by pooling different sensory inputs. PMID:21113416

Connes distance function on fuzzy sphere and the connection between geometry and statistics

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

Devi, Yendrembam Chaoba, E-mail: chaoba@bose.res.in; Chakraborty, Biswajit, E-mail: biswajit@bose.res.in; Prajapat, Shivraj, E-mail: shraprajapat@gmail.com

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which ismore » shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2.« less

Open Quantum Random Walks on the Half-Line: The Karlin-McGregor Formula, Path Counting and Foster's Theorem

NASA Astrophysics Data System (ADS)

Jacq, Thomas S.; Lardizabal, Carlos F.

2017-11-01

In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative version of the gambler's ruin is studied by obtaining the probability of reaching a certain fortune and the mean time to reach a fortune or ruin in terms of generating functions. In the case of the Hadamard coin, a counting technique for boundary restricted paths in a lattice is also presented. We discuss an open quantum version of Foster's Theorem for the expected return time together with applications.

Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Fadel, Matteo; Zibold, Tilman; Décamps, Boris; Treutlein, Philipp

2018-04-01

Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks.

BRST technique for the cosmological density matrix

NASA Astrophysics Data System (ADS)

Barvinsky, A. O.

2013-10-01

The microcanonical density matrix in closed cosmology has a natural definition as a projector on the space of solutions of Wheeler-DeWitt equations, which is motivated by the absence of global non-vanishing charges and energy in spatially closed gravitational systems. Using the BRST/BFV formalism in relativistic phase space of gauge and ghost variables we derive the path integral representation for this projector and the relevant statistical sum. This derivation circumvents the difficulties associated with the open algebra of noncommutative quantum Dirac constraints and the construction/regularization of the physical inner product in the subspace of BRS singlets. This inner product is achieved via the Batalin-Marnelius gauge fixing in the space of BRS-invariant states, which in its turn is shown to be a result of truncation of the BRST/BFV formalism to the "matter" sector of relativistic phase space.

Doe Research and Development Report

NASA Astrophysics Data System (ADS)

Gell-Mann, Murray

Forty years ago, I arrived at M.I.T. as a graduate student. I was discouraged at having been rejected by Princeton and granted insufficient financial aid by Harvard. The only really friendly letter that I received from a graduate school in physics was one from M.I.T. welcoming me as a potential student and as a research assistant in theoretical physics to a certain Professor Weisskopf, of whom I had never heard, but who added a personal letter of invitation of his own. I have described elsewhere how that letter arrived as I was contemplating suicide, as befits someone rejected by the Ivy League. It occurred to me however, (and it is an interesting example of non-commutation of operators) that I could try M.I.T. first and kill myself later, while the reverse order of events was impossible…

Repelling Point Bosons

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

McGuire, J. B.

2011-12-01

There is a body of conventional wisdom that holds that a solvable quantum problem, by virtue of its solvability, is pathological and thus irrelevant. It has been difficult to refute this view owing to the paucity of theoretical constructs and experimental results. Recent experiments involving equivalent ions trapped in a spatial conformation of extreme anisotropic confinement (longitudinal extension tens, hundreds or even thousands of times transverse extension) have modified the view of relevancy, and it is now possible to consider systems previously thought pathological, in particular point Bosons that repel in one dimension. It has been difficult for the experimentalistsmore » to utilize existing theory, mainly due to long-standing theoretical misunderstanding of the relevance of the permutation group, in particular the non-commutativity of translations (periodicity) and transpositions (permutation). This misunderstanding is most easily rectified in the case of repelling Bosons.« less

Constituting objectivity: Transcendental perspectives on modern physics

NASA Astrophysics Data System (ADS)

Everett, Jonathan

2012-05-01

There is increasing interest in exploring Kantian approaches in the study of the history and philosophy of physics. The most well-known examples of this trend-Friedman's (2001), Ryckman's (2005) and DiSalle's (2006)-focus on Kantianism in the context of the development of the general theory of relativity. The edited collection Constituting Objectivity seeks to develop key Kantian insights-in the most part-in the context of later developments in physics: as well as discussing relativity the volume also provides Kantian interpretations of Bohr's development of quantum theory and continues to provide Kantian insight from later interpretations of quantum mechanics all the way through to considering noncommutative geometry and loop quantum gravity. The volume contains papers on a wide variety of subjects and offers an essential introduction to the breadth of Kantian trends in modern physics.

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

NASA Astrophysics Data System (ADS)

Campos, P.; Martins, M. G. R.; Fernandes, M. C. B.; Vianna, J. D. M.

2018-03-01

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

Supersymmetric symplectic quantum mechanics

NASA Astrophysics Data System (ADS)

de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

2018-02-01

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

Noninvasive Quantum Measurement of Arbitrary Operator Order by Engineered Non-Markovian Detectors

NASA Astrophysics Data System (ADS)

Bülte, Johannes; Bednorz, Adam; Bruder, Christoph; Belzig, Wolfgang

2018-04-01

The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, nonisolated quantum systems. In general, a permanent coupling of detectors to a quantum system leads to memory effects that have to be taken into account in interpreting the measurement results. We analyze a generic setup of two detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit that interpolates between an instantaneous (text-book type) and almost continuous—detector dynamics-dependent—measurement. A quantum memory effect that we term "system-mediated detector-detector interaction" is crucial to observe noncommuting observables simultaneously. Finally, we propose a mesoscopic double-dot detector setup in which the memory effect is tunable and that can be used to explore the transition to non-Markovian quantum measurements experimentally.

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

Ahuatzin, G.; Bautista, I.; Hernandez-Lopez, J. A.

A constant antisymmetric 2-tensor can arise in general relativity with spontaneous symmetry breaking or in field theories formulated in a noncommutative space-time. In this work, the one-loop contribution of a nonstandard WW{gamma} vertex on the flavor violating quark transition q{sub i}{yields}q{sub j}{gamma} is studied in the context of the electroweak Yang-Mills sector extended with a Lorentz-violating constant 2-tensor. An exact analytical expression for the on-shell case is presented. It is found that the loop amplitude is gauge independent, electromagnetic gauge invariant, and free of ultraviolet divergences. The dipolar contribution to the b{yields}s{gamma} transition together with the experimental data on themore » B{yields}X{sub s{gamma}} decay is used to derive the constraint {Lambda}{sub LV}>1.96 TeV on the Lorentz-violating scale.« less

Highly effective action from large N gauge fields

NASA Astrophysics Data System (ADS)

Yang, Hyun Seok

2014-10-01

Recently Schwarz put forward a conjecture that the world-volume action of a probe D3-brane in an AdS5×S5 background of type IIB superstring theory can be reinterpreted as the highly effective action (HEA) of four-dimensional N =4 superconformal field theory on the Coulomb branch. We argue that the HEA can be derived from the noncommutative (NC) field theory representation of the AdS/CFT correspondence and the Seiberg-Witten (SW) map defining a spacetime field redefinition between ordinary and NC gauge fields. It is based only on the well-known facts that the master fields of large N matrices are higher-dimensional NC U(1) gauge fields and the SW map is a local coordinate transformation eliminating U(1) gauge fields known as the Darboux theorem in symplectic geometry.

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

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

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energymore » for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.« less

Measurements and mathematical formalism of quantum mechanics

NASA Astrophysics Data System (ADS)

Slavnov, D. A.

2007-03-01

A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.

A note on derivations of Murray-von Neumann algebras.

PubMed

Kadison, Richard V; Liu, Zhe

2014-02-11

A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray-von Neumann algebras. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer's seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements.

Template-based structure modeling of protein-protein interactions

PubMed Central

Szilagyi, Andras; Zhang, Yang

2014-01-01

The structure of protein-protein complexes can be constructed by using the known structure of other protein complexes as a template. The complex structure templates are generally detected either by homology-based sequence alignments or, given the structure of monomer components, by structure-based comparisons. Critical improvements have been made in recent years by utilizing interface recognition and by recombining monomer and complex template libraries. Encouraging progress has also been witnessed in genome-wide applications of template-based modeling, with modeling accuracy comparable to high-throughput experimental data. Nevertheless, bottlenecks exist due to the incompleteness of the proteinprotein complex structure library and the lack of methods for distant homologous template identification and full-length complex structure refinement. PMID:24721449

In Silico Analysis for the Study of Botulinum Toxin Structure

NASA Astrophysics Data System (ADS)

Suzuki, Tomonori; Miyazaki, Satoru

2010-01-01

Protein-protein interactions play many important roles in biological function. Knowledge of protein-protein complex structure is required for understanding the function. The determination of protein-protein complex structure by experimental studies remains difficult, therefore computational prediction of protein structures by structure modeling and docking studies is valuable method. In addition, MD simulation is also one of the most popular methods for protein structure modeling and characteristics. Here, we attempt to predict protein-protein complex structure and property using some of bioinformatic methods, and we focus botulinum toxin complex as target structure.

Evaluation of protein-protein docking model structures using all-atom molecular dynamics simulations combined with the solution theory in the energy representation

NASA Astrophysics Data System (ADS)

Takemura, Kazuhiro; Guo, Hao; Sakuraba, Shun; Matubayasi, Nobuyuki; Kitao, Akio

2012-12-01

We propose a method to evaluate binding free energy differences among distinct protein-protein complex model structures through all-atom molecular dynamics simulations in explicit water using the solution theory in the energy representation. Complex model structures are generated from a pair of monomeric structures using the rigid-body docking program ZDOCK. After structure refinement by side chain optimization and all-atom molecular dynamics simulations in explicit water, complex models are evaluated based on the sum of their conformational and solvation free energies, the latter calculated from the energy distribution functions obtained from relatively short molecular dynamics simulations of the complex in water and of pure water based on the solution theory in the energy representation. We examined protein-protein complex model structures of two protein-protein complex systems, bovine trypsin/CMTI-1 squash inhibitor (PDB ID: 1PPE) and RNase SA/barstar (PDB ID: 1AY7), for which both complex and monomer structures were determined experimentally. For each system, we calculated the energies for the crystal complex structure and twelve generated model structures including the model most similar to the crystal structure and very different from it. In both systems, the sum of the conformational and solvation free energies tended to be lower for the structure similar to the crystal. We concluded that our energy calculation method is useful for selecting low energy complex models similar to the crystal structure from among a set of generated models.

Evaluation of protein-protein docking model structures using all-atom molecular dynamics simulations combined with the solution theory in the energy representation.

PubMed

Takemura, Kazuhiro; Guo, Hao; Sakuraba, Shun; Matubayasi, Nobuyuki; Kitao, Akio

2012-12-07

We propose a method to evaluate binding free energy differences among distinct protein-protein complex model structures through all-atom molecular dynamics simulations in explicit water using the solution theory in the energy representation. Complex model structures are generated from a pair of monomeric structures using the rigid-body docking program ZDOCK. After structure refinement by side chain optimization and all-atom molecular dynamics simulations in explicit water, complex models are evaluated based on the sum of their conformational and solvation free energies, the latter calculated from the energy distribution functions obtained from relatively short molecular dynamics simulations of the complex in water and of pure water based on the solution theory in the energy representation. We examined protein-protein complex model structures of two protein-protein complex systems, bovine trypsin/CMTI-1 squash inhibitor (PDB ID: 1PPE) and RNase SA/barstar (PDB ID: 1AY7), for which both complex and monomer structures were determined experimentally. For each system, we calculated the energies for the crystal complex structure and twelve generated model structures including the model most similar to the crystal structure and very different from it. In both systems, the sum of the conformational and solvation free energies tended to be lower for the structure similar to the crystal. We concluded that our energy calculation method is useful for selecting low energy complex models similar to the crystal structure from among a set of generated models.

Relationships between structural complexity, coral traits, and reef fish assemblages

NASA Astrophysics Data System (ADS)

Darling, Emily S.; Graham, Nicholas A. J.; Januchowski-Hartley, Fraser A.; Nash, Kirsty L.; Pratchett, Morgan S.; Wilson, Shaun K.

2017-06-01

With the ongoing loss of coral cover and the associated flattening of reef architecture, understanding the links between coral habitat and reef fishes is of critical importance. Here, we investigate whether considering coral traits and functional diversity provides new insights into the relationship between structural complexity and reef fish communities, and whether coral traits and community composition can predict structural complexity. Across 157 sites in Seychelles, Maldives, the Chagos Archipelago, and Australia's Great Barrier Reef, we find that structural complexity and reef zone are the strongest and most consistent predictors of reef fish abundance, biomass, species richness, and trophic structure. However, coral traits, diversity, and life histories provided additional predictive power for models of reef fish assemblages, and were key drivers of structural complexity. Our findings highlight that reef complexity relies on living corals—with different traits and life histories—continuing to build carbonate skeletons, and that these nuanced relationships between coral assemblages and habitat complexity can affect the structure of reef fish assemblages. Seascape-level estimates of structural complexity are rapid and cost effective with important implications for the structure and function of fish assemblages, and should be incorporated into monitoring programs.

Spin wave Feynman diagram vertex computation package

NASA Astrophysics Data System (ADS)

Price, Alexander; Javernick, Philip; Datta, Trinanjan

Spin wave theory is a well-established theoretical technique that can correctly predict the physical behavior of ordered magnetic states. However, computing the effects of an interacting spin wave theory incorporating magnons involve a laborious by hand derivation of Feynman diagram vertices. The process is tedious and time consuming. Hence, to improve productivity and have another means to check the analytical calculations, we have devised a Feynman Diagram Vertex Computation package. In this talk, we will describe our research group's effort to implement a Mathematica based symbolic Feynman diagram vertex computation package that computes spin wave vertices. Utilizing the non-commutative algebra package NCAlgebra as an add-on to Mathematica, symbolic expressions for the Feynman diagram vertices of a Heisenberg quantum antiferromagnet are obtained. Our existing code reproduces the well-known expressions of a nearest neighbor square lattice Heisenberg model. We also discuss the case of a triangular lattice Heisenberg model where non collinear terms contribute to the vertex interactions.

On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems

NASA Astrophysics Data System (ADS)

Tessarotto, Massimo; Cremaschini, Claudio; Mond, Michael; Asci, Claudio; Soranzo, Alessandro; Tironi, Gino

2018-03-01

The problem is posed of the prescription of the so-called Boltzmann-Grad limit operator (L_{BG}) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator L_{BG}, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is "no time-asymmetric ingredient" in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the "ab initio" axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.

“Stringy” coherent states inspired by generalized uncertainty principle

NASA Astrophysics Data System (ADS)

Ghosh, Subir; Roy, Pinaki

2012-05-01

Coherent States with Fractional Revival property, that explicitly satisfy the Generalized Uncertainty Principle (GUP), have been constructed in the context of Generalized Harmonic Oscillator. The existence of such states is essential in motivating the GUP based phenomenological results present in the literature which otherwise would be of purely academic interest. The effective phase space is Non-Canonical (or Non-Commutative in popular terminology). Our results have a smooth commutative limit, equivalent to Heisenberg Uncertainty Principle. The Fractional Revival time analysis yields an independent bound on the GUP parameter. Using this and similar bounds obtained here, we derive the largest possible value of the (GUP induced) minimum length scale. Mandel parameter analysis shows that the statistics is Sub-Poissonian. Correspondence Principle is deformed in an interesting way. Our computational scheme is very simple as it requires only first order corrected energy values and undeformed basis states.

More nonlocality with less entanglement in Clauser-Horne-Shimony-Holt experiments using inefficient detectors

NASA Astrophysics Data System (ADS)

Dilley, Daniel; Chitambar, Eric

2018-06-01

It is well-known that in certain scenarios weakly entangled states can generate stronger nonlocal effects than their maximally entangled counterparts. In this paper, we consider violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality when one party has inefficient detectors, a scenario known as an asymmetric Bell experiment. For any fixed detection efficiency, we derive a simple upper bound on the entanglement needed to violate the inequality by more than some specified amount κ ≥0 . When κ =0 , the amount of entanglement in all states violating the inequality goes to zero as the detection efficiency approaches 50 % from above. We finally consider the scenario in which detection inefficiency arises for only one choice of local measurement. In this case, it is shown that the CHSH inequality can always be violated for any nonzero detection efficiency and any choice of noncommuting measurements.

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.

Toward the classification of differential calculi on κ-Minkowski space and related field theories

NASA Astrophysics Data System (ADS)

Jurić, Tajron; Meljanac, Stjepan; Pikutić, Danijel; Štrajn, Rina

2015-07-01

Classification of differential forms on κ-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the κ-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to κ-Poincaré Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications.

Historical remarks on exponential product and quantum analysis

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

Suzuki, Masuo

2015-03-10

The exponential product formula [1, 2] was substantially introduced in physics by the present author [2]. Its systematic applications to quantum Monte Carlo Methods [3] were preformed [4, 5] first in 1977. Many interesting applications [6] of the quantum-classical correspondence (namely S-T transformation) have been reported. Systematic higher-order decomposition formulae were also discovered by the present author [7-11], using the recursion scheme [7, 9]. Physically speaking, these exponential product formulae play a conceptual role of separation of procedures [3,14]. Mathematical aspects of these formulae have been integrated in quantum analysis [15], in which non-commutative differential calculus is formulated and amore » general quantum Taylor expansion formula is given. This yields many useful operator expansion formulae such as the Feynman expansion formula and the resolvent expansion. Irreversibility and entropy production are also studied using quantum analysis [15].« less

Quantized mode of a leaky cavity

NASA Astrophysics Data System (ADS)

Dutra, S. M.; Nienhuis, G.

2000-12-01

We use Thomson's classical concept of mode of a leaky cavity to develop a quantum theory of cavity damping. This theory generalizes the conventional system-reservoir theory of high-Q cavity damping to arbitrary Q. The small system now consists of damped oscillators corresponding to the natural modes of the leaky cavity rather than undamped oscillators associated with the normal modes of a fictitious perfect cavity. The formalism unifies semiclassical Fox-Li modes and the normal modes traditionally used for quantization. It also lays the foundations for a full quantum description of excess noise. The connection with Siegman's semiclassical work is straightforward. In a wider context, this theory constitutes a radical departure from present models of dissipation in quantum mechanics: unlike conventional models, system and reservoir operators no longer commute with each other. This noncommutability is an unavoidable consequence of having to use natural cavity modes rather than normal modes of a fictitious perfect cavity.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

T-branes through 3d mirror symmetry

NASA Astrophysics Data System (ADS)

Collinucci, Andrés; Giacomelli, Simone; Savelli, Raffaele; Valandro, Roberto

2016-07-01

T-branes are exotic bound states of D-branes, characterized by mutually non-commuting vacuum expectation values for the worldvolume scalars. The M/F-theory geometry lifting D6/D7-brane configurations is blind to the T-brane data. In this paper, we make this data manifest, by probing the geometry with an M2-brane. We find that the effect of a T-brane is to deform the membrane worldvolume superpotential with monopole operators, which partially break the three-dimensional flavor symmetry, and reduce super-symmetry from {N} = 4 to {N} = 2. Our main tool is 3d mirror symmetry. Through this language, a very concrete framework is developed for understanding T-branes in M-theory. This leads us to uncover a new class of {N} = 2 quiver gauge theories, whose Higgs branches mimic those of membranes at ADE singularities, but whose Coulomb branches differ from their {N} = 4 counterparts.

Quantumness-generating capability of quantum dynamics

NASA Astrophysics Data System (ADS)

Li, Nan; Luo, Shunlong; Mao, Yuanyuan

2018-04-01

We study quantumness-generating capability of quantum dynamics, where quantumness refers to the noncommutativity between the initial state and the evolving state. In terms of the commutator of the square roots of the initial state and the evolving state, we define a measure to quantify the quantumness-generating capability of quantum dynamics with respect to initial states. Quantumness-generating capability is absent in classical dynamics and hence is a fundamental characteristic of quantum dynamics. For qubit systems, we present an analytical form for this measure, by virtue of which we analyze several prototypical dynamics such as unitary dynamics, phase damping dynamics, amplitude damping dynamics, and random unitary dynamics (Pauli channels). Necessary and sufficient conditions for the monotonicity of quantumness-generating capability are also identified. Finally, we compare these conditions for the monotonicity of quantumness-generating capability with those for various Markovianities and illustrate that quantumness-generating capability and quantum Markovianity are closely related, although they capture different aspects of quantum dynamics.

Ensembles and Experiments in Classical and Quantum Physics

NASA Astrophysics Data System (ADS)

Neumaier, Arnold

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the ''probability via expectation'' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

A note on derivations of Murray–von Neumann algebras

PubMed Central

Kadison, Richard V.; Liu, Zhe

2014-01-01

A Murray–von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray–von Neumann algebras. We show that the “extended derivations” of a Murray–von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray–von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer’s seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements. PMID:24469831

Mixed-state fidelity susceptibility through iterated commutator series expansion

NASA Astrophysics Data System (ADS)

Tonchev, N. S.

2014-11-01

We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provide an analytical expression for the MFS as a formal expansion in terms of the thermodynamic mean values of successively higher commutators of the Hamiltonian with the operator involved through the control parameter. That expression is naturally divided into two parts: the usual isothermal susceptibility and a constituent in the form of an infinite series of thermodynamic mean values which encodes the noncommutativity in the problem. If the symmetry properties of the Hamiltonian are given in terms of the generators of some (finite-dimensional) algebra, the obtained expansion may be evaluated in a closed form. This issue is tested on several popular models, for which it is shown that the calculations are much simpler if they are based on the properties from the representation theory of the Heisenberg or SU(1, 1) Lie algebra.

High-order noise filtering in nontrivial quantum logic gates.

PubMed

Green, Todd; Uys, Hermann; Biercuk, Michael J

2012-07-13

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.

Energy absorption capabilities of complex thin walled structures

NASA Astrophysics Data System (ADS)

Tarlochan, F.; AlKhatib, Sami

2017-10-01

Thin walled structures have been used in the area of energy absorption during an event of a crash. A lot of work has been done on tubular structures. Due to limitation of manufacturing process, complex geometries were dismissed as potential solutions. With the advancement in metal additive manufacturing, complex geometries can be realized. As a motivation, the objective of this study is to investigate computationally the crash performance of complex tubular structures. Five designs were considered. In was found that complex geometries have better crashworthiness performance than standard tubular structures used currently.

Syntheses, crystal structures and properties of novel copper(II) complexes obtained by reactions of copper(II) sulfate pentahydrate with tripodal ligands.

PubMed

Zhao, Wei; Fan, Jian; Song, You; Kawaguchi, Hiroyuki; Okamura, Taka-aki; Sun, Wei-Yin; Ueyama, Norikazu

2005-04-21

Three novel metal-organic frameworks (MOFs), [Cu(1)SO4].H2O (4), [Cu2(2)2(SO4)2].4H2O (5) and [Cu(3)(H2O)]SO4.5.5H2O (6), were obtained by hydrothermal reactions of CuSO4.5H2O with the corresponding ligands, which have different flexibility. The structures of the synthesized complexes were determined by single-crystal X-ray diffraction analyses. Complex 4 has a 2D network structure with two types of metallacycles. Complex 5 also has a 2D network structure in which each independent 2D sheet contains two sub-layers bridged by oxygen atoms of the sulfate anions. Complex 6 has a 2D puckered structure in which the sulfate anions serve as counter anions, which are different from those in complexes 4 (terminators) and 5 (bridges). The different structures of complexes 4, 5 and 6 indicate that the nature of organic ligands affected the structures of the assemblies greatly. The magnetic behavior of complex 5 and anion-exchange properties of complex 6 were investigated.

Solving a meiotic LEGO puzzle: transverse filaments and the assembly of the synaptonemal complex in Caenorhabditis elegans.

PubMed

Hawley, R Scott

2011-10-01

The structure of the meiosis-specific synaptonemal complex, which is perhaps the central visible characteristic of meiotic prophase, has been a matter of intense interest for decades. Although a general picture of the interactions between the transverse filament proteins that create this structure has emerged from studies in a variety of organisms, a recent analysis of synaptonemal complex structure in Caenorhabditis elegans by Schild-Prüfert et al. (2011) has provided the clearest picture of the structure of the architecture of a synaptonemal complex to date. Although the transverse filaments of the worm synaptonemal complex are assembled differently then those observed in yeast, mammalian, and Drosophila synaptonemal complexes, a comparison of the four assemblies shows that achieving the overall basic structure of the synaptonemal complex is far more crucial than conserving the structures of the individual transverse filaments.

The effect of structural complexity, prey density, and "predator-free space" on prey survivorship at created oyster reef mesocosms

USGS Publications Warehouse

Humphries, Austin T.; La Peyre, Megan K.; Decossas, Gary A.

2011-01-01

Interactions between predators and their prey are influenced by the habitat they occupy. Using created oyster (Crassostrea virginica) reef mesocosms, we conducted a series of laboratory experiments that created structure and manipulated complexity as well as prey density and “predator-free space” to examine the relationship between structural complexity and prey survivorship. Specifically, volume and spatial arrangement of oysters as well as prey density were manipulated, and the survivorship of prey (grass shrimp, Palaemonetes pugio) in the presence of a predator (wild red drum, Sciaenops ocellatus) was quantified. We found that the presence of structure increased prey survivorship, and that increasing complexity of this structure further increased survivorship, but only to a point. This agrees with the theory that structural complexity may influence predator-prey dynamics, but that a threshold exists with diminishing returns. These results held true even when prey density was scaled to structural complexity, or the amount of “predator-free space” was manipulated within our created reef mesocosms. The presence of structure and its complexity (oyster shell volume) were more important in facilitating prey survivorship than perceived refugia or density-dependent prey effects. A more accurate indicator of refugia might require “predator-free space” measures that also account for the available area within the structure itself (i.e., volume) and not just on the surface of a structure. Creating experiments that better mimic natural conditions and test a wider range of “predator-free space” are suggested to better understand the role of structural complexity in oyster reefs and other complex habitats.

Structure, recognition and adaptive binding in RNA aptamer complexes.

PubMed

Patel, D J; Suri, A K; Jiang, F; Jiang, L; Fan, P; Kumar, R A; Nonin, S

1997-10-10

Novel features of RNA structure, recognition and discrimination have been recently elucidated through the solution structural characterization of RNA aptamers that bind cofactors, aminoglycoside antibiotics, amino acids and peptides with high affinity and specificity. This review presents the solution structures of RNA aptamer complexes with adenosine monophosphate, flavin mononucleotide, arginine/citrulline and tobramycin together with an example of hydrogen exchange measurements of the base-pair kinetics for the AMP-RNA aptamer complex. A comparative analysis of the structures of these RNA aptamer complexes yields the principles, patterns and diversity associated with RNA architecture, molecular recognition and adaptive binding associated with complex formation.

Principles of assembly reveal a periodic table of protein complexes.

PubMed

Ahnert, Sebastian E; Marsh, Joseph A; Hernández, Helena; Robinson, Carol V; Teichmann, Sarah A

2015-12-11

Structural insights into protein complexes have had a broad impact on our understanding of biological function and evolution. In this work, we sought a comprehensive understanding of the general principles underlying quaternary structure organization in protein complexes. We first examined the fundamental steps by which protein complexes can assemble, using experimental and structure-based characterization of assembly pathways. Most assembly transitions can be classified into three basic types, which can then be used to exhaustively enumerate a large set of possible quaternary structure topologies. These topologies, which include the vast majority of observed protein complex structures, enable a natural organization of protein complexes into a periodic table. On the basis of this table, we can accurately predict the expected frequencies of quaternary structure topologies, including those not yet observed. These results have important implications for quaternary structure prediction, modeling, and engineering. Copyright © 2015, American Association for the Advancement of Science.

Structural investigation of the β-cyclodextrin complexes with chiral bicyclic monoterpenes - Influence of the functionality group on the host-guest stoichiometry

NASA Astrophysics Data System (ADS)

Ceborska, Magdalena

2017-10-01

The crystal structures of the complexes of β-cyclodextrin with (+)- and (-)-camphors are presented. The comparison of the obtained crystal structures with available data for other complexes of β-cyclodextrin with chiral bicyclic monoterpenes (hydrocarbon (+)-fenchene and alcohols: (-)-isopinocampheol, and (+)-, and (-)-borneols) obtained from Cambridge Structural Database (CSD) shows the trend of alcohols to form dimeric complexes of 2:3 stoichiometry, while hydrocarbons and ketones prefer to form 2:2 host-guest inclusion complexes.

Changes in habitat complexity negatively affect diverse gastropod assemblages in coralline algal turf.

PubMed

Kelaher, B P

2003-05-01

The physical structure of a habitat generally has a strong influence on the diversity and abundance of associated organisms. I investigated the role of coralline algal turf structure in determining spatial variation of gastropod assemblages at different tidal heights of a rocky shore near Sydney, Australia. The structural characteristics of algal turf tested were frond density (or structural complexity) and frond length (the vertical scale over which structural complexity was measured). This definition of structural complexity assumes that complexity of the habitat increases with increasing frond density. While frond length was unrelated to gastropod community structure, I found significant correlations between density of fronds and multivariate and univariate measures of gastropod assemblages, indicating the importance of structural complexity. In contrast to previous studies, here there were negative relationships between the density of fronds and the richness and abundance of gastropods. Artificial habitat mimics were used to manipulate the density of fronds to test the hypothesis that increasing algal structural complexity decreases the richness and abundance of gastropods. As predicted, there were significantly more species of gastropods in loosely packed than in tightly packed turf at both low- and mid-shore levels. Despite large differences between gastropod assemblages at different tidal heights, the direction and magnitude of these negative effects were similar at low- and mid-shore levels and, therefore, relatively independent of local environmental conditions. These novel results extend our previous understanding of the ecological effects of habitat structure because they demonstrate possible limitations of commonly used definitions of structural complexity, as well as distinct upper thresholds in the relationship between structural complexity and faunal species richness.

Habitat Complexity in Aquatic Microcosms Affects Processes Driven by Detritivores

PubMed Central

Flores, Lorea; Bailey, R. A.; Elosegi, Arturo; Larrañaga, Aitor; Reiss, Julia

2016-01-01

Habitat complexity can influence predation rates (e.g. by providing refuge) but other ecosystem processes and species interactions might also be modulated by the properties of habitat structure. Here, we focussed on how complexity of artificial habitat (plastic plants), in microcosms, influenced short-term processes driven by three aquatic detritivores. The effects of habitat complexity on leaf decomposition, production of fine organic matter and pH levels were explored by measuring complexity in three ways: 1. as the presence vs. absence of habitat structure; 2. as the amount of structure (3 or 4.5 g of plastic plants); and 3. as the spatial configuration of structures (measured as fractal dimension). The experiment also addressed potential interactions among the consumers by running all possible species combinations. In the experimental microcosms, habitat complexity influenced how species performed, especially when comparing structure present vs. structure absent. Treatments with structure showed higher fine particulate matter production and lower pH compared to treatments without structures and this was probably due to higher digestion and respiration when structures were present. When we explored the effects of the different complexity levels, we found that the amount of structure added explained more than the fractal dimension of the structures. We give a detailed overview of the experimental design, statistical models and R codes, because our statistical analysis can be applied to other study systems (and disciplines such as restoration ecology). We further make suggestions of how to optimise statistical power when artificially assembling, and analysing, ‘habitat complexity’ by not confounding complexity with the amount of structure added. In summary, this study highlights the importance of habitat complexity for energy flow and the maintenance of ecosystem processes in aquatic ecosystems. PMID:27802267

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

Meng, Jiang Ping; Yan, Zhi Shuo; Long, Ji Ying

By using a rigid dicarboxylate ligand, 4,5-di(4′-carboxylphenyl)benzene (H{sub 2}L), two complexes formulated as SrL(DMF)(H{sub 2}O)·(CH{sub 3}CN) (DMF=N,N′-dimethylformamide) (1) and BaL(H{sub 2}O){sub 2} (2) were solvothermally synthesized and structurally characterized by single-crystal X-ray diffraction. Complexes 1 and 2 display two-dimensional (2D) layer structures. The two complexes exhibit different electrochemical and photoelectrochemical properties. Their thermal stabilities, cyclic voltammograms, UV–vis absorption and diffuse reflectance spectra and photoluminescence properties have been investigated. The band structures, the total density of states (TDOS) and partial density of states (PDOS) of the two complexes were calculated by CASTEP program. Complex 2 exhibits much higher photocurrent density thanmore » complex 1. The Mott–Schottky plots reveal that complexes 1 and 2 both are p-type semiconductors, which are in agreement with their band structure calculations. - Graphical abstract: Two alkaline earth metal(II) complexes with 2D layer structures are p-type semiconductors, they possess different band structures and density of states. And the Ba(II) complex 2 exhibits much higher photocurrent density than the Sr(II) complex 1.« less

Complexity in language learning and treatment.

PubMed

Thompson, Cynthia K

2007-02-01

To introduce a Clinical Forum focused on the Complexity Account of Treatment Efficacy (C. K. Thompson, L. P. Shapiro, S. Kiran, & J. Sobecks, 2003), a counterintuitive but effective approach for treating language disorders. This approach espouses training complex structures to promote generalized improvement of simpler, linguistically related structures. Three articles are included, addressing complexity in treatment of phonology, lexical-semantics, and syntax. Complexity hierarchies based on models of normal language representation and processing are discussed in each language domain. In addition, each article presents single-subject controlled experimental studies examining the complexity effect. By counterbalancing treatment of complex and simple structures across participants, acquisition and generalization patterns are examined as they emerge. In all language domains, cascading generalization occurs from more to less complex structures; however, the opposite pattern is rarely seen. The results are robust, with replication within and across participants. The construct of complexity appears to be a general principle that is relevant to treating a range of language disorders in both children and adults. While challenging the long-standing clinical notion that treatment should begin with simple structures, mounting evidence points toward the facilitative effects of using more complex structures as a starting point for treatment.

Crystal structure of mitochondrial respiratory membrane protein complex II.

PubMed

Sun, Fei; Huo, Xia; Zhai, Yujia; Wang, Aojin; Xu, Jianxing; Su, Dan; Bartlam, Mark; Rao, Zihe

2005-07-01

The mitochondrial respiratory Complex II or succinate:ubiquinone oxidoreductase (SQR) is an integral membrane protein complex in both the tricarboxylic acid cycle and aerobic respiration. Here we report the first crystal structure of Complex II from porcine heart at 2.4 A resolution and its complex structure with inhibitors 3-nitropropionate and 2-thenoyltrifluoroacetone (TTFA) at 3.5 A resolution. Complex II is comprised of two hydrophilic proteins, flavoprotein (Fp) and iron-sulfur protein (Ip), and two transmembrane proteins (CybL and CybS), as well as prosthetic groups required for electron transfer from succinate to ubiquinone. The structure correlates the protein environments around prosthetic groups with their unique midpoint redox potentials. Two ubiquinone binding sites are discussed and elucidated by TTFA binding. The Complex II structure provides a bona fide model for study of the mitochondrial respiratory system and human mitochondrial diseases related to mutations in this complex.

Structure-Based Characterization of Multiprotein Complexes

PubMed Central

Wiederstein, Markus; Gruber, Markus; Frank, Karl; Melo, Francisco; Sippl, Manfred J.

2014-01-01

Summary Multiprotein complexes govern virtually all cellular processes. Their 3D structures provide important clues to their biological roles, especially through structural correlations among protein molecules and complexes. The detection of such correlations generally requires comprehensive searches in databases of known protein structures by means of appropriate structure-matching techniques. Here, we present a high-speed structure search engine capable of instantly matching large protein oligomers against the complete and up-to-date database of biologically functional assemblies of protein molecules. We use this tool to reveal unseen structural correlations on the level of protein quaternary structure and demonstrate its general usefulness for efficiently exploring complex structural relationships among known protein assemblies. PMID:24954616

Effects of Chain Length and Degree of Unsaturation of Fatty Acids on Structure and in Vitro Digestibility of Starch-Protein-Fatty Acid Complexes.

PubMed

Zheng, Mengge; Chao, Chen; Yu, Jinglin; Copeland, Les; Wang, Shuo; Wang, Shujun

2018-02-28

The effects of chain length and degree of unsaturation of fatty acids (FAs) on structure and in vitro digestibility of starch-protein-FA complexes were investigated in model systems. Studies with the rapid visco analyzer (RVA) showed that the formation of ternary complex resulted in higher viscosities than those of binary complex during the cooling and holding stages. The results of differential scanning calorimetry (DSC), Raman, and X-ray diffraction (XRD) showed that the structural differences for ternary complexes were much less than those for binary complexes. Starch-protein-FA complexes presented lower in vitro enzymatic digestibility compared with starch-FAs complexes. We conclude that shorter chain and lower unsaturation FAs favor the formation of ternary complexes but decrease the thermal stability of these complexes. FAs had a smaller effect on the ordered structures of ternary complexes than on those of binary complexes and little effect on enzymatic digestibility of both binary and ternary complexes.

Conformational Transitions upon Ligand Binding: Holo-Structure Prediction from Apo Conformations

PubMed Central

Seeliger, Daniel; de Groot, Bert L.

2010-01-01

Biological function of proteins is frequently associated with the formation of complexes with small-molecule ligands. Experimental structure determination of such complexes at atomic resolution, however, can be time-consuming and costly. Computational methods for structure prediction of protein/ligand complexes, particularly docking, are as yet restricted by their limited consideration of receptor flexibility, rendering them not applicable for predicting protein/ligand complexes if large conformational changes of the receptor upon ligand binding are involved. Accurate receptor models in the ligand-bound state (holo structures), however, are a prerequisite for successful structure-based drug design. Hence, if only an unbound (apo) structure is available distinct from the ligand-bound conformation, structure-based drug design is severely limited. We present a method to predict the structure of protein/ligand complexes based solely on the apo structure, the ligand and the radius of gyration of the holo structure. The method is applied to ten cases in which proteins undergo structural rearrangements of up to 7.1 Å backbone RMSD upon ligand binding. In all cases, receptor models within 1.6 Å backbone RMSD to the target were predicted and close-to-native ligand binding poses were obtained for 8 of 10 cases in the top-ranked complex models. A protocol is presented that is expected to enable structure modeling of protein/ligand complexes and structure-based drug design for cases where crystal structures of ligand-bound conformations are not available. PMID:20066034

Multi-frequency complex network from time series for uncovering oil-water flow structure.

PubMed

Gao, Zhong-Ke; Yang, Yu-Xuan; Fang, Peng-Cheng; Jin, Ning-De; Xia, Cheng-Yi; Hu, Li-Dan

2015-02-04

Uncovering complex oil-water flow structure represents a challenge in diverse scientific disciplines. This challenge stimulates us to develop a new distributed conductance sensor for measuring local flow signals at different positions and then propose a novel approach based on multi-frequency complex network to uncover the flow structures from experimental multivariate measurements. In particular, based on the Fast Fourier transform, we demonstrate how to derive multi-frequency complex network from multivariate time series. We construct complex networks at different frequencies and then detect community structures. Our results indicate that the community structures faithfully represent the structural features of oil-water flow patterns. Furthermore, we investigate the network statistic at different frequencies for each derived network and find that the frequency clustering coefficient enables to uncover the evolution of flow patterns and yield deep insights into the formation of flow structures. Current results present a first step towards a network visualization of complex flow patterns from a community structure perspective.

Modeling the assembly order of multimeric heteroprotein complexes

PubMed Central

Esquivel-Rodriguez, Juan; Terashi, Genki; Christoffer, Charles; Shin, Woong-Hee

2018-01-01

Protein-protein interactions are the cornerstone of numerous biological processes. Although an increasing number of protein complex structures have been determined using experimental methods, relatively fewer studies have been performed to determine the assembly order of complexes. In addition to the insights into the molecular mechanisms of biological function provided by the structure of a complex, knowing the assembly order is important for understanding the process of complex formation. Assembly order is also practically useful for constructing subcomplexes as a step toward solving the entire complex experimentally, designing artificial protein complexes, and developing drugs that interrupt a critical step in the complex assembly. There are several experimental methods for determining the assembly order of complexes; however, these techniques are resource-intensive. Here, we present a computational method that predicts the assembly order of protein complexes by building the complex structure. The method, named Path-LzerD, uses a multimeric protein docking algorithm that assembles a protein complex structure from individual subunit structures and predicts assembly order by observing the simulated assembly process of the complex. Benchmarked on a dataset of complexes with experimental evidence of assembly order, Path-LZerD was successful in predicting the assembly pathway for the majority of the cases. Moreover, when compared with a simple approach that infers the assembly path from the buried surface area of subunits in the native complex, Path-LZerD has the strong advantage that it can be used for cases where the complex structure is not known. The path prediction accuracy decreased when starting from unbound monomers, particularly for larger complexes of five or more subunits, for which only a part of the assembly path was correctly identified. As the first method of its kind, Path-LZerD opens a new area of computational protein structure modeling and will be an indispensable approach for studying protein complexes. PMID:29329283

Modeling the assembly order of multimeric heteroprotein complexes.

PubMed

Peterson, Lenna X; Togawa, Yoichiro; Esquivel-Rodriguez, Juan; Terashi, Genki; Christoffer, Charles; Roy, Amitava; Shin, Woong-Hee; Kihara, Daisuke

2018-01-01

Protein-protein interactions are the cornerstone of numerous biological processes. Although an increasing number of protein complex structures have been determined using experimental methods, relatively fewer studies have been performed to determine the assembly order of complexes. In addition to the insights into the molecular mechanisms of biological function provided by the structure of a complex, knowing the assembly order is important for understanding the process of complex formation. Assembly order is also practically useful for constructing subcomplexes as a step toward solving the entire complex experimentally, designing artificial protein complexes, and developing drugs that interrupt a critical step in the complex assembly. There are several experimental methods for determining the assembly order of complexes; however, these techniques are resource-intensive. Here, we present a computational method that predicts the assembly order of protein complexes by building the complex structure. The method, named Path-LzerD, uses a multimeric protein docking algorithm that assembles a protein complex structure from individual subunit structures and predicts assembly order by observing the simulated assembly process of the complex. Benchmarked on a dataset of complexes with experimental evidence of assembly order, Path-LZerD was successful in predicting the assembly pathway for the majority of the cases. Moreover, when compared with a simple approach that infers the assembly path from the buried surface area of subunits in the native complex, Path-LZerD has the strong advantage that it can be used for cases where the complex structure is not known. The path prediction accuracy decreased when starting from unbound monomers, particularly for larger complexes of five or more subunits, for which only a part of the assembly path was correctly identified. As the first method of its kind, Path-LZerD opens a new area of computational protein structure modeling and will be an indispensable approach for studying protein complexes.

3D Complex: A Structural Classification of Protein Complexes

PubMed Central

Levy, Emmanuel D; Pereira-Leal, Jose B; Chothia, Cyrus; Teichmann, Sarah A

2006-01-01

Most of the proteins in a cell assemble into complexes to carry out their function. It is therefore crucial to understand the physicochemical properties as well as the evolution of interactions between proteins. The Protein Data Bank represents an important source of information for such studies, because more than half of the structures are homo- or heteromeric protein complexes. Here we propose the first hierarchical classification of whole protein complexes of known 3-D structure, based on representing their fundamental structural features as a graph. This classification provides the first overview of all the complexes in the Protein Data Bank and allows nonredundant sets to be derived at different levels of detail. This reveals that between one-half and two-thirds of known structures are multimeric, depending on the level of redundancy accepted. We also analyse the structures in terms of the topological arrangement of their subunits and find that they form a small number of arrangements compared with all theoretically possible ones. This is because most complexes contain four subunits or less, and the large majority are homomeric. In addition, there is a strong tendency for symmetry in complexes, even for heteromeric complexes. Finally, through comparison of Biological Units in the Protein Data Bank with the Protein Quaternary Structure database, we identified many possible errors in quaternary structure assignments. Our classification, available as a database and Web server at http://www.3Dcomplex.org, will be a starting point for future work aimed at understanding the structure and evolution of protein complexes. PMID:17112313

Structural Characterization by Cross-linking Reveals the Detailed Architecture of a Coatomer-related Heptameric Module from the Nuclear Pore Complex*

PubMed Central

Shi, Yi; Fernandez-Martinez, Javier; Tjioe, Elina; Pellarin, Riccardo; Kim, Seung Joong; Williams, Rosemary; Schneidman-Duhovny, Dina; Sali, Andrej; Rout, Michael P.; Chait, Brian T.

2014-01-01

Most cellular processes are orchestrated by macromolecular complexes. However, structural elucidation of these endogenous complexes can be challenging because they frequently contain large numbers of proteins, are compositionally and morphologically heterogeneous, can be dynamic, and are often of low abundance in the cell. Here, we present a strategy for the structural characterization of such complexes that has at its center chemical cross-linking with mass spectrometric readout. In this strategy, we isolate the endogenous complexes using a highly optimized sample preparation protocol and generate a comprehensive, high-quality cross-linking dataset using two complementary cross-linking reagents. We then determine the structure of the complex using a refined integrative method that combines the cross-linking data with information generated from other sources, including electron microscopy, X-ray crystallography, and comparative protein structure modeling. We applied this integrative strategy to determine the structure of the native Nup84 complex, a stable hetero-heptameric assembly (∼600 kDa), 16 copies of which form the outer rings of the 50-MDa nuclear pore complex (NPC) in budding yeast. The unprecedented detail of the Nup84 complex structure reveals previously unseen features in its pentameric structural hub and provides information on the conformational flexibility of the assembly. These additional details further support and augment the protocoatomer hypothesis, which proposes an evolutionary relationship between vesicle coating complexes and the NPC, and indicates a conserved mechanism by which the NPC is anchored in the nuclear envelope. PMID:25161197

Effects of sentence-structure complexity on speech initiation time and disfluency.

PubMed

Tsiamtsiouris, Jim; Cairns, Helen Smith

2013-03-01

There is general agreement that stuttering is caused by a variety of factors, and language formulation and speech motor control are two important factors that have been implicated in previous research, yet the exact nature of their effects is still not well understood. Our goal was to test the hypothesis that sentences of high structural complexity would incur greater processing costs than sentences of low structural complexity and these costs would be higher for adults who stutter than for adults who do not stutter. Fluent adults and adults who stutter participated in an experiment that required memorization of a sentence classified as low or high structural complexity followed by production of that sentence upon a visual cue. Both groups of speakers initiated most sentences significantly faster in the low structural complexity condition than in the high structural complexity condition. Adults who stutter were over-all slower in speech initiation than were fluent speakers, but there were no significant interactions between complexity and group. However, adults who stutter produced significantly more disfluencies in sentences of high structural complexity than in those of low complexity. After reading this article, the learner will be able to: (a) identify integral parts of all well-known models of adult sentence production; (b) summarize the way that sentence structure might negatively influence the speech production processes; (c) discuss whether sentence structure influences speech initiation time and disfluencies. Copyright © 2012 Elsevier Inc. All rights reserved.

Tomographic inversion of P-wave velocity and Q structures beneath the Kirishima volcanic complex, Southern Japan, based on finite difference calculations of complex traveltimes

USGS Publications Warehouse

Tomatsu, T.; Kumagai, H.; Dawson, P.B.

2001-01-01

We estimate the P-wave velocity and attenuation structures beneath the Kirishima volcanic complex, southern Japan, by inverting the complex traveltimes (arrival times and pulse widths) of waveform data obtained during an active seismic experiment conducted in 1994. In this experiment, six 200-250 kg shots were recorded at 163 temporary seismic stations deployed on the volcanic complex. We use first-arrival times for the shots, which were hand-measured interactively. The waveform data are Fourier transformed into the frequency domain and analysed using a new method based on autoregressive modelling of complex decaying oscillations in the frequency domain to determine pulse widths for the first-arrival phases. A non-linear inversion method is used to invert 893 first-arrival times and 325 pulse widths to estimate the velocity and attenuation structures of the volcanic complex. Wavefronts for the inversion are calculated with a finite difference method based on the Eikonal equation, which is well suited to estimating the complex traveltimes for the structures of the Kirishima volcano complex, where large structural heterogeneities are expected. The attenuation structure is derived using ray paths derived from the velocity structure. We obtain 3-D velocity and attenuation structures down to 1.5 and 0.5 km below sea level, respectively. High-velocity pipe-like structures with correspondingly low attenuation are found under the summit craters. These pipe-like structures are interpreted as remnant conduits of solidified magma. No evidence of a shallow magma chamber is visible in the tomographic images.

(PS)2: protein structure prediction server version 3.0.

PubMed

Huang, Tsun-Tsao; Hwang, Jenn-Kang; Chen, Chu-Huang; Chu, Chih-Sheng; Lee, Chi-Wen; Chen, Chih-Chieh

2015-07-01

Protein complexes are involved in many biological processes. Examining coupling between subunits of a complex would be useful to understand the molecular basis of protein function. Here, our updated (PS)(2) web server predicts the three-dimensional structures of protein complexes based on comparative modeling; furthermore, this server examines the coupling between subunits of the predicted complex by combining structural and evolutionary considerations. The predicted complex structure could be indicated and visualized by Java-based 3D graphics viewers and the structural and evolutionary profiles are shown and compared chain-by-chain. For each subunit, considerations with or without the packing contribution of other subunits cause the differences in similarities between structural and evolutionary profiles, and these differences imply which form, complex or monomeric, is preferred in the biological condition for the subunit. We believe that the (PS)(2) server would be a useful tool for biologists who are interested not only in the structures of protein complexes but also in the coupling between subunits of the complexes. The (PS)(2) is freely available at http://ps2v3.life.nctu.edu.tw/. © The Author(s) 2015. Published by Oxford University Press on behalf of Nucleic Acids Research.

Structure-based characterization of multiprotein complexes.

PubMed

Wiederstein, Markus; Gruber, Markus; Frank, Karl; Melo, Francisco; Sippl, Manfred J

2014-07-08

Multiprotein complexes govern virtually all cellular processes. Their 3D structures provide important clues to their biological roles, especially through structural correlations among protein molecules and complexes. The detection of such correlations generally requires comprehensive searches in databases of known protein structures by means of appropriate structure-matching techniques. Here, we present a high-speed structure search engine capable of instantly matching large protein oligomers against the complete and up-to-date database of biologically functional assemblies of protein molecules. We use this tool to reveal unseen structural correlations on the level of protein quaternary structure and demonstrate its general usefulness for efficiently exploring complex structural relationships among known protein assemblies. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Structure of complexes between aluminum chloride and other chlorides, 2: Alkali-(chloroaluminates). Gaseous complexes

NASA Technical Reports Server (NTRS)

Hargittai, M.

1980-01-01

The structural chemistry of complexes between aluminum chloride and other metal chlorides is important both for practice and theory. Condensed-phase as well as vapor-phase complexes are of interest. Structural information on such complexes is reviewed. The first emphasis is given to the molten state because of its practical importance. Aluminum chloride forms volatile complexes with other metal chlorides and these vapor-phase complexes are dealt with in the second part. Finally, the variations in molecular shape and geometrical parameters are summarized.

Hierarchical coordinate systems for understanding complexity and its evolution, with applications to genetic regulatory networks.

PubMed

Egri-Nagy, Attila; Nehaniv, Chrystopher L

2008-01-01

Beyond complexity measures, sometimes it is worthwhile in addition to investigate how complexity changes structurally, especially in artificial systems where we have complete knowledge about the evolutionary process. Hierarchical decomposition is a useful way of assessing structural complexity changes of organisms modeled as automata, and we show how recently developed computational tools can be used for this purpose, by computing holonomy decompositions and holonomy complexity. To gain insight into the evolution of complexity, we investigate the smoothness of the landscape structure of complexity under minimal transitions. As a proof of concept, we illustrate how the hierarchical complexity analysis reveals symmetries and irreversible structure in biological networks by applying the methods to the lac operon mechanism in the genetic regulatory network of Escherichia coli.

Architecture of the pontin/reptin complex, essential in the assembly of several macromolecular complexes

PubMed Central

Torreira, Eva; Jha, Sudhakar; López-Blanco, José R.; Arias-Palomo, Ernesto; Chacón, Pablo; Cañas, Cristina; Ayora, Sylvia; Dutta, Anindya; Llorca, Oscar

2008-01-01

Summary Pontin and reptin belong to the AAA+ family and they are essential for the structural integrity and catalytic activity of several chromatin remodeling complexes. They are also indispensable for the assembly of several ribonucleoprotein complexes, including telomerase. Here, we propose a structural model of the yeast pontin/reptin complex based on a cryo-electron microscopy reconstruction at 13 Å. Pontin/reptin hetero-dodecamers were purified from in vivo assembled complexes forming a double ring. Two rings interact through flexible domains projecting from each hexamer, constituting an atypical asymmetric form of oligomerization. These flexible domains and the AAA+ cores reveal significant conformational changes when compared to the crystal structure of human pontin that generate enlarged channels. This structure of endogenously assembled pontin/reptin complexes is different to previously described structures, suggesting that pontin and reptin could acquire distinct structural states to regulate their broad functions as molecular motors and scaffolds for nucleic acids and proteins. PMID:18940606

An overview of the structures of protein-DNA complexes

PubMed Central

Luscombe, Nicholas M; Austin, Susan E; Berman , Helen M; Thornton, Janet M

2000-01-01

On the basis of a structural analysis of 240 protein-DNA complexes contained in the Protein Data Bank (PDB), we have classified the DNA-binding proteins involved into eight different structural/functional groups, which are further classified into 54 structural families. Here we present this classification and review the functions, structures and binding interactions of these protein-DNA complexes. PMID:11104519

Structural Insights into the Molecular Design of Flutolanil Derivatives Targeted for Fumarate Respiration of Parasite Mitochondria.

PubMed

Inaoka, Daniel Ken; Shiba, Tomoo; Sato, Dan; Balogun, Emmanuel Oluwadare; Sasaki, Tsuyoshi; Nagahama, Madoka; Oda, Masatsugu; Matsuoka, Shigeru; Ohmori, Junko; Honma, Teruki; Inoue, Masayuki; Kita, Kiyoshi; Harada, Shigeharu

2015-07-07

Recent studies on the respiratory chain of Ascaris suum showed that the mitochondrial NADH-fumarate reductase system composed of complex I, rhodoquinone and complex II plays an important role in the anaerobic energy metabolism of adult A. suum. The system is the major pathway of energy metabolism for adaptation to a hypoxic environment not only in parasitic organisms, but also in some types of human cancer cells. Thus, enzymes of the pathway are potential targets for chemotherapy. We found that flutolanil is an excellent inhibitor for A. suum complex II (IC50 = 0.058 μM) but less effectively inhibits homologous porcine complex II (IC50 = 45.9 μM). In order to account for the specificity of flutolanil to A. suum complex II from the standpoint of structural biology, we determined the crystal structures of A. suum and porcine complex IIs binding flutolanil and its derivative compounds. The structures clearly demonstrated key interactions responsible for its high specificity to A. suum complex II and enabled us to find analogue compounds, which surpass flutolanil in both potency and specificity to A. suum complex II. Structures of complex IIs binding these compounds will be helpful to accelerate structure-based drug design targeted for complex IIs.

Structural Insights into the Molecular Design of Flutolanil Derivatives Targeted for Fumarate Respiration of Parasite Mitochondria

PubMed Central

Inaoka, Daniel Ken; Shiba, Tomoo; Sato, Dan; Balogun, Emmanuel Oluwadare; Sasaki, Tsuyoshi; Nagahama, Madoka; Oda, Masatsugu; Matsuoka, Shigeru; Ohmori, Junko; Honma, Teruki; Inoue, Masayuki; Kita, Kiyoshi; Harada, Shigeharu

2015-01-01

Recent studies on the respiratory chain of Ascaris suum showed that the mitochondrial NADH-fumarate reductase system composed of complex I, rhodoquinone and complex II plays an important role in the anaerobic energy metabolism of adult A. suum. The system is the major pathway of energy metabolism for adaptation to a hypoxic environment not only in parasitic organisms, but also in some types of human cancer cells. Thus, enzymes of the pathway are potential targets for chemotherapy. We found that flutolanil is an excellent inhibitor for A. suum complex II (IC50 = 0.058 μM) but less effectively inhibits homologous porcine complex II (IC50 = 45.9 μM). In order to account for the specificity of flutolanil to A. suum complex II from the standpoint of structural biology, we determined the crystal structures of A. suum and porcine complex IIs binding flutolanil and its derivative compounds. The structures clearly demonstrated key interactions responsible for its high specificity to A. suum complex II and enabled us to find analogue compounds, which surpass flutolanil in both potency and specificity to A. suum complex II. Structures of complex IIs binding these compounds will be helpful to accelerate structure-based drug design targeted for complex IIs. PMID:26198225

Atomic structure of the Y complex of the nuclear pore

DOE PAGES

Kelley, Kotaro; Knockenhauer, Kevin E.; Kabachinski, Greg; ...

2015-03-30

The nuclear pore complex (NPC) is the principal gateway for transport into and out of the nucleus. Selectivity is achieved through the hydrogel-like core of the NPC. The structural integrity of the NPC depends on ~15 architectural proteins, which are organized in distinct subcomplexes to form the >40-MDa ring-like structure. In this paper, we present the 4.1-Å crystal structure of a heterotetrameric core element ('hub') of the Y complex, the essential NPC building block, from Myceliophthora thermophila. Using the hub structure together with known Y-complex fragments, we built the entire ~0.5-MDa Y complex. Our data reveal that the conserved coremore » of the Y complex has six rather than seven members. Finally, evolutionarily distant Y-complex assemblies share a conserved core that is very similar in shape and dimension, thus suggesting that there are closely related architectural codes for constructing the NPC in all eukaryotes.« less

Magnitude and nature of carbohydrate-aromatic interactions in fucose-phenol and fucose-indole complexes: CCSD(T) level interaction energy calculations.

PubMed

Tsuzuki, Seiji; Uchimaru, Tadafumi; Mikami, Masuhiro

2011-10-20

The CH/π contact structures of the fucose-phenol and fucose-indole complexes and the stabilization energies by formation of the complexes (E(form)) were studied by ab initio molecular orbital calculations. The three types of interactions (CH/π and OH/π interactions and OH/O hydrogen bonds) were compared and evaluated in a single molecular system and at the same level of theory. The E(form) calculated for the most stable CH/π contact structure of the fucose-phenol complex at the CCSD(T) level (-4.9 kcal/mol) is close to that for the most stable CH/π contact structure of the fucose-benzene complex (-4.5 kcal/mol). On the other hand the most stable CH/π contact structure of the fucose-indole complex has substantially larger E(form) (-6.5 kcal/mol). The dispersion interaction is the major source of the attraction in the CH/π contact structures of the fucose-phenol and fucose-indole complexes as in the case of the fucose-benzene complex. The electrostatic interactions in the CH/π contact structures are small (less than 1.5 kcal/mol). The nature of the interactions between the nonpolar surface of the carbohydrate and aromatic rings is completely different from that of the conventional hydrogen bonds where the electrostatic interaction is the major source of the attraction. The distributed multipole analysis and DFT-SATP analysis show that the dispersion interactions in the CH/π contact structure of fucose-indole complex are substantially larger than those in the CH/π contact structures of fucose-benzene and fucose-phenol complexes. The large dispersion interactions are responsible for the large E(form) for the fucose-indole complex.

Structural characterization by cross-linking reveals the detailed architecture of a coatomer-related heptameric module from the nuclear pore complex.

PubMed

Shi, Yi; Fernandez-Martinez, Javier; Tjioe, Elina; Pellarin, Riccardo; Kim, Seung Joong; Williams, Rosemary; Schneidman-Duhovny, Dina; Sali, Andrej; Rout, Michael P; Chait, Brian T

2014-11-01

Most cellular processes are orchestrated by macromolecular complexes. However, structural elucidation of these endogenous complexes can be challenging because they frequently contain large numbers of proteins, are compositionally and morphologically heterogeneous, can be dynamic, and are often of low abundance in the cell. Here, we present a strategy for the structural characterization of such complexes that has at its center chemical cross-linking with mass spectrometric readout. In this strategy, we isolate the endogenous complexes using a highly optimized sample preparation protocol and generate a comprehensive, high-quality cross-linking dataset using two complementary cross-linking reagents. We then determine the structure of the complex using a refined integrative method that combines the cross-linking data with information generated from other sources, including electron microscopy, X-ray crystallography, and comparative protein structure modeling. We applied this integrative strategy to determine the structure of the native Nup84 complex, a stable hetero-heptameric assembly (∼ 600 kDa), 16 copies of which form the outer rings of the 50-MDa nuclear pore complex (NPC) in budding yeast. The unprecedented detail of the Nup84 complex structure reveals previously unseen features in its pentameric structural hub and provides information on the conformational flexibility of the assembly. These additional details further support and augment the protocoatomer hypothesis, which proposes an evolutionary relationship between vesicle coating complexes and the NPC, and indicates a conserved mechanism by which the NPC is anchored in the nuclear envelope. © 2014 by The American Society for Biochemistry and Molecular Biology, Inc.

Structural changes of homodimers in the PDB.

PubMed

Koike, Ryotaro; Amemiya, Takayuki; Horii, Tatsuya; Ota, Motonori

2018-04-01

Protein complexes are involved in various biological phenomena. These complexes are intrinsically flexible, and structural changes are essential to their functions. To perform a large-scale automated analysis of the structural changes of complexes, we combined two original methods. An application, SCPC, compares two structures of protein complexes and decides the match of binding mode. Another application, Motion Tree, identifies rigid-body motions in various sizes and magnitude from the two structural complexes with the same binding mode. This approach was applied to all available homodimers in the Protein Data Bank (PDB). We defined two complex-specific motions: interface motion and subunit-spanning motion. In the former, each subunit of a complex constitutes a rigid body, and the relative movement between subunits occurs at the interface. In the latter, structural parts from distinct subunits constitute a rigid body, providing the relative movement spanning subunits. All structural changes were classified and examined. It was revealed that the complex-specific motions were common in the homodimers, detected in around 40% of families. The dimeric interfaces were likely to be small and flat for interface motion, while large and rugged for subunit-spanning motion. Interface motion was accompanied by a drastic change in contacts at the interface, while the change in the subunit-spanning motion was moderate. These results indicate that the interface properties of homodimers correlated with the type of complex-specific motion. The study demonstrates that the pipeline of SCPC and Motion Tree is useful for the massive analysis of structural change of protein complexes. Copyright © 2017 Elsevier Inc. All rights reserved.

Complexity and dynamics of topological and community structure in complex networks

NASA Astrophysics Data System (ADS)

Berec, Vesna

2017-07-01

Complexity is highly susceptible to variations in the network dynamics, reflected on its underlying architecture where topological organization of cohesive subsets into clusters, system's modular structure and resulting hierarchical patterns, are cross-linked with functional dynamics of the system. Here we study connection between hierarchical topological scales of the simplicial complexes and the organization of functional clusters - communities in complex networks. The analysis reveals the full dynamics of different combinatorial structures of q-th-dimensional simplicial complexes and their Laplacian spectra, presenting spectral properties of resulting symmetric and positive semidefinite matrices. The emergence of system's collective behavior from inhomogeneous statistical distribution is induced by hierarchically ordered topological structure, which is mapped to simplicial complex where local interactions between the nodes clustered into subcomplexes generate flow of information that characterizes complexity and dynamics of the full system.

Supramolecular structure of glibenclamide and β-cyclodextrins complexes.

PubMed

Lucio, David; Irache, Juan Manuel; Font, María; Martínez-Ohárriz, María Cristina

2017-09-15

Glibenclamide is an antidiabetic drug showing low bioavailability as consequence of its low solubility. To solve this drawback, the interaction with cyclodextrins has been proposed. The formation of GB-βCDs inclusion complexes was carried out using different methods, βCD derivatives and drug-to-cyclodextrin ratios. The structures of the corresponding complexes have been studied by molecular modelling, X-ray diffraction and differential thermal analysis. The dissolution behavior of inclusion complexes has been compared to that of pure GB. Dimeric inclusion complexes were obtained with different CD disposals, head-to-head for βCD and head-to-tail for HPβCD and RMβCD. Amorphous inclusion complexes were obtained by employing methods of freeze-drying or coevaporation in ammonia-water. However, crystalline structures were formed by kneading and coevaporation in ethanol/water in the case of GB-βCD complexes. The arrangement of these structures depended on the GB:βCD ratio, yielding cage type structures for 1:3 and 1:5 ratios and channel-type structures for higher GB contents. The amount of GB released and its dissolution rate was considerably increased by the use of amorphous inclusion complexes; whereas, slower GB release rates were found from crystalline inclusion complexes formed by kneading or coevaporation in ethanol/water. In addition, it was found that the porous structure strongly conditioned the GB dissolution rate from crystalline products. Copyright © 2017 Elsevier B.V. All rights reserved.

Identification of Complex Carbon Nanotube Structures

NASA Technical Reports Server (NTRS)

Han, Jie; Saini, Subhash (Technical Monitor)

1998-01-01

A variety of complex carbon nanotube (CNT) structures have been observed experimentally. These include sharp bends, branches, tori, and helices. They are believed to be formed by using topological defects such as pentagons and heptagons to connect different CNT. The effects of type, number, and arrangement (separation and orientation) of defects on atomic structures and energetics of complex CNT are investigated using topology, quantum mechanics and molecular mechanics calculations. Energetically stable models are derived for identification of observed complex CNT structures.

Complex band structure and electronic transmission eigenchannels

NASA Astrophysics Data System (ADS)

Jensen, Anders; Strange, Mikkel; Smidstrup, Søren; Stokbro, Kurt; Solomon, Gemma C.; Reuter, Matthew G.

2017-12-01

It is natural to characterize materials in transport junctions by their conductance length dependence, β. Theoretical estimations of β are made employing two primary theories: complex band structure and density functional theory (DFT) Landauer transport. It has previously been shown that the β value derived from total Landauer transmission can be related to the β value from the smallest |ki| complex band; however, it is an open question whether there is a deeper relationship between the two. Here we probe the details of the relationship between transmission and complex band structure, in this case individual eigenchannel transmissions and different complex bands. We present calculations of decay constants for the two most conductive states as determined by complex band structure and standard DFT Landauer transport calculations for one semi-conductor and two molecular junctions. The molecular junctions show that both the length dependence of the total transmission and the individual transmission eigenvalues can be, almost always, found through the complex band structure. The complex band structure of the semi-conducting material, however, does not predict the length dependence of the total transmission but only of the individual channels, at some k-points, due to multiple channels contributing to transmission. We also observe instances of vertical bands, some of which are the smallest |ki| complex bands, that do not contribute to transport. By understanding the deeper relationship between complex bands and individual transmission eigenchannels, we can make a general statement about when the previously accepted wisdom linking transmission and complex band structure will fail, namely, when multiple channels contribute significantly to the transmission.

Insectivorous bats respond to vegetation complexity in urban green spaces.

PubMed

Suarez-Rubio, Marcela; Ille, Christina; Bruckner, Alexander

2018-03-01

Structural complexity is known to determine habitat quality for insectivorous bats, but how bats respond to habitat complexity in highly modified areas such as urban green spaces has been little explored. Furthermore, it is uncertain whether a recently developed measure of structural complexity is as effective as field-based surveys when applied to urban environments. We assessed whether image-derived structural complexity (MIG) was as/more effective than field-based descriptors in this environment and evaluated the response of insectivorous bats to structural complexity in urban green spaces. Bat activity and species richness were assessed with ultrasonic devices at 180 locations within green spaces in Vienna, Austria. Vegetation complexity was assessed using 17 field-based descriptors and by calculating the mean information gain (MIG) using digital images. Total bat activity and species richness decreased with increasing structural complexity of canopy cover, suggesting maneuverability and echolocation (sensorial) challenges for bat species using the canopy for flight and foraging. The negative response of functional groups to increased complexity was stronger for open-space foragers than for edge-space foragers. Nyctalus noctula , a species foraging in open space, showed a negative response to structural complexity, whereas Pipistrellus pygmaeus , an edge-space forager, was positively influenced by the number of trees. Our results show that MIG is a useful, time- and cost-effective tool to measure habitat complexity that complemented field-based descriptors. Response of insectivorous bats to structural complexity was group- and species-specific, which highlights the need for manifold management strategies (e.g., increasing or reinstating the extent of ground vegetation cover) to fulfill different species' requirements and to conserve insectivorous bats in urban green spaces.

Systematic bioinformatics and experimental validation of yeast complexes reduces the rate of attrition during structural investigations.

PubMed

Brooks, Mark A; Gewartowski, Kamil; Mitsiki, Eirini; Létoquart, Juliette; Pache, Roland A; Billier, Ysaline; Bertero, Michela; Corréa, Margot; Czarnocki-Cieciura, Mariusz; Dadlez, Michal; Henriot, Véronique; Lazar, Noureddine; Delbos, Lila; Lebert, Dorothée; Piwowarski, Jan; Rochaix, Pascal; Böttcher, Bettina; Serrano, Luis; Séraphin, Bertrand; van Tilbeurgh, Herman; Aloy, Patrick; Perrakis, Anastassis; Dziembowski, Andrzej

2010-09-08

For high-throughput structural studies of protein complexes of composition inferred from proteomics data, it is crucial that candidate complexes are selected accurately. Herein, we exemplify a procedure that combines a bioinformatics tool for complex selection with in vivo validation, to deliver structural results in a medium-throughout manner. We have selected a set of 20 yeast complexes, which were predicted to be feasible by either an automated bioinformatics algorithm, by manual inspection of primary data, or by literature searches. These complexes were validated with two straightforward and efficient biochemical assays, and heterologous expression technologies of complex components were then used to produce the complexes to assess their feasibility experimentally. Approximately one-half of the selected complexes were useful for structural studies, and we detail one particular success story. Our results underscore the importance of accurate target selection and validation in avoiding transient, unstable, or simply nonexistent complexes from the outset. Copyright © 2010 Elsevier Ltd. All rights reserved.

Structural basis of DNA folding and recognition in an AMP-DNA aptamer complex: distinct architectures but common recognition motifs for DNA and RNA aptamers complexed to AMP.

PubMed

Lin, C H; Patel, D J

1997-11-01

Structural studies by nuclear magnetic resonance (NMR) of RNA and DNA aptamer complexes identified through in vitro selection and amplification have provided a wealth of information on RNA and DNA tertiary structure and molecular recognition in solution. The RNA and DNA aptamers that target ATP (and AMP) with micromolar affinity exhibit distinct binding site sequences and secondary structures. We report below on the tertiary structure of the AMP-DNA aptamer complex in solution and compare it with the previously reported tertiary structure of the AMP-RNA aptamer complex in solution. The solution structure of the AMP-DNA aptamer complex shows, surprisingly, that two AMP molecules are intercalated at adjacent sites within a rectangular widened minor groove. Complex formation involves adaptive binding where the asymmetric internal bubble of the free DNA aptamer zippers up through formation of a continuous six-base mismatch segment which includes a pair of adjacent three-base platforms. The AMP molecules pair through their Watson-Crick edges with the minor groove edges of guanine residues. These recognition G.A mismatches are flanked by sheared G.A and reversed Hoogsteen G.G mismatch pairs. The AMP-DNA aptamer and AMP-RNA aptamer complexes have distinct tertiary structures and binding stoichiometries. Nevertheless, both complexes have similar structural features and recognition alignments in their binding pockets. Specifically, AMP targets both DNA and RNA aptamers by intercalating between purine bases and through identical G.A mismatch formation. The recognition G.A mismatch stacks with a reversed Hoogsteen G.G mismatch in one direction and with an adenine base in the other direction in both complexes. It is striking that DNA and RNA aptamers selected independently from libraries of 10(14) molecules in each case utilize identical mismatch alignments for molecular recognition with micromolar affinity within binding-site pockets containing common structural elements.

Characterization of measurement errors using structure-from-motion and photogrammetry to measure marine habitat structural complexity.

PubMed

Bryson, Mitch; Ferrari, Renata; Figueira, Will; Pizarro, Oscar; Madin, Josh; Williams, Stefan; Byrne, Maria

2017-08-01

Habitat structural complexity is one of the most important factors in determining the makeup of biological communities. Recent advances in structure-from-motion and photogrammetry have resulted in a proliferation of 3D digital representations of habitats from which structural complexity can be measured. Little attention has been paid to quantifying the measurement errors associated with these techniques, including the variability of results under different surveying and environmental conditions. Such errors have the potential to confound studies that compare habitat complexity over space and time. This study evaluated the accuracy, precision, and bias in measurements of marine habitat structural complexity derived from structure-from-motion and photogrammetric measurements using repeated surveys of artificial reefs (with known structure) as well as natural coral reefs. We quantified measurement errors as a function of survey image coverage, actual surface rugosity, and the morphological community composition of the habitat-forming organisms (reef corals). Our results indicated that measurements could be biased by up to 7.5% of the total observed ranges of structural complexity based on the environmental conditions present during any particular survey. Positive relationships were found between measurement errors and actual complexity, and the strength of these relationships was increased when coral morphology and abundance were also used as predictors. The numerous advantages of structure-from-motion and photogrammetry techniques for quantifying and investigating marine habitats will mean that they are likely to replace traditional measurement techniques (e.g., chain-and-tape). To this end, our results have important implications for data collection and the interpretation of measurements when examining changes in habitat complexity using structure-from-motion and photogrammetry.

Diversity and Phylogenetic Structure of Two Complex Marine Microbial Communities

DTIC Science & Technology

2004-09-01

Science 190 and Engineering DOCTORAL DISSERTATION Diversity and Phylogenetic Structure of Two Complex Marine Microbial Communities by Vanja Klepac-Ceraj...Two Complex Marine Microbial Communities by Vanja Klepac-Ceraj Massachusetts Institute of Technology Cambridge, Massachusetts 02139 and Woods Hole...Phylogenetic Structure of Two Complex Marine Microbial Communities. Ph.D. Thesis. MIT/WHOI, 2004-11. Approved for publication; distribution unlimited

Aggregation behavior and complex structure between triblock copolymer and anionic surfactants

NASA Astrophysics Data System (ADS)

Li, Yiming; Bao, Mutai; Wang, Zhining; Zhang, Haixia; Xu, Guiying

2011-01-01

The aggregation behavior and complex structure of ABA triblock copolymer EO 76PO 30EO 76 (F68) with sodium dodecyl sulfate (SDS) and sodium bis(2-ethylhexyl)sulfonate (AOT) in aqueous solution were investigated by surface tension, fluorescence techniques and dynamic light-scattering (DLS) measurements. It is revealed that in certain regions of binding, surfactant/F68 complexes are formed. Structural informations and size of complexes are evaluated. When F68 is present in its nonassociated state, F68/micellar SDS complexes are formed at SDS concentrations above its critical aggregation concentration (cac). The cac is well below the critical micellar concentration (cmc) of pure SDS, and a model suggesting how complexes are formed at the cac in the presence of F68 is described. Experimental results show that SDS interacts with F68 mainly through hydrophobic forces, polypropylene oxide (PPO) groups of F68 are solubilized into SDS micellar cores and poly(ethylene oxide) (PEO) groups interact with SDS micelles. This interaction mechanism results in a "pearl-necklace" complex structure. However, a different structure occurs for F68/AOT complex at lower F68 concentrations, as nonassociated F68 interacts with AOT mainly through ion-dipole interactions. Complexes with a "wrapping" structure at lower F68 concentrations are formed.

Choosing the Best Enzyme Complex Structure Made Easy.

PubMed

Das, Sayoni; Orengo, Christine

2018-04-03

In this issue of Structure, Tyzack et al. (2018) present a study of enzyme-ligand complexes in the PDB and show that the molecular similarity of bound and cognate ligands can be used to choose the most biologically appropriate complex structure for analysis when multiple structures are available. Copyright © 2018 Elsevier Ltd. All rights reserved.

RNACompress: Grammar-based compression and informational complexity measurement of RNA secondary structure.

PubMed

Liu, Qi; Yang, Yu; Chen, Chun; Bu, Jiajun; Zhang, Yin; Ye, Xiuzi

2008-03-31

With the rapid emergence of RNA databases and newly identified non-coding RNAs, an efficient compression algorithm for RNA sequence and structural information is needed for the storage and analysis of such data. Although several algorithms for compressing DNA sequences have been proposed, none of them are suitable for the compression of RNA sequences with their secondary structures simultaneously. This kind of compression not only facilitates the maintenance of RNA data, but also supplies a novel way to measure the informational complexity of RNA structural data, raising the possibility of studying the relationship between the functional activities of RNA structures and their complexities, as well as various structural properties of RNA based on compression. RNACompress employs an efficient grammar-based model to compress RNA sequences and their secondary structures. The main goals of this algorithm are two fold: (1) present a robust and effective way for RNA structural data compression; (2) design a suitable model to represent RNA secondary structure as well as derive the informational complexity of the structural data based on compression. Our extensive tests have shown that RNACompress achieves a universally better compression ratio compared with other sequence-specific or common text-specific compression algorithms, such as Gencompress, winrar and gzip. Moreover, a test of the activities of distinct GTP-binding RNAs (aptamers) compared with their structural complexity shows that our defined informational complexity can be used to describe how complexity varies with activity. These results lead to an objective means of comparing the functional properties of heteropolymers from the information perspective. A universal algorithm for the compression of RNA secondary structure as well as the evaluation of its informational complexity is discussed in this paper. We have developed RNACompress, as a useful tool for academic users. Extensive tests have shown that RNACompress is a universally efficient algorithm for the compression of RNA sequences with their secondary structures. RNACompress also serves as a good measurement of the informational complexity of RNA secondary structure, which can be used to study the functional activities of RNA molecules.

RNACompress: Grammar-based compression and informational complexity measurement of RNA secondary structure

PubMed Central

Liu, Qi; Yang, Yu; Chen, Chun; Bu, Jiajun; Zhang, Yin; Ye, Xiuzi

2008-01-01

Background With the rapid emergence of RNA databases and newly identified non-coding RNAs, an efficient compression algorithm for RNA sequence and structural information is needed for the storage and analysis of such data. Although several algorithms for compressing DNA sequences have been proposed, none of them are suitable for the compression of RNA sequences with their secondary structures simultaneously. This kind of compression not only facilitates the maintenance of RNA data, but also supplies a novel way to measure the informational complexity of RNA structural data, raising the possibility of studying the relationship between the functional activities of RNA structures and their complexities, as well as various structural properties of RNA based on compression. Results RNACompress employs an efficient grammar-based model to compress RNA sequences and their secondary structures. The main goals of this algorithm are two fold: (1) present a robust and effective way for RNA structural data compression; (2) design a suitable model to represent RNA secondary structure as well as derive the informational complexity of the structural data based on compression. Our extensive tests have shown that RNACompress achieves a universally better compression ratio compared with other sequence-specific or common text-specific compression algorithms, such as Gencompress, winrar and gzip. Moreover, a test of the activities of distinct GTP-binding RNAs (aptamers) compared with their structural complexity shows that our defined informational complexity can be used to describe how complexity varies with activity. These results lead to an objective means of comparing the functional properties of heteropolymers from the information perspective. Conclusion A universal algorithm for the compression of RNA secondary structure as well as the evaluation of its informational complexity is discussed in this paper. We have developed RNACompress, as a useful tool for academic users. Extensive tests have shown that RNACompress is a universally efficient algorithm for the compression of RNA sequences with their secondary structures. RNACompress also serves as a good measurement of the informational complexity of RNA secondary structure, which can be used to study the functional activities of RNA molecules. PMID:18373878

EXAFS characterisation of metal bonding in highly luminescent, UV stable, water-soluble and biocompatible lanthanide complexes

NASA Astrophysics Data System (ADS)

Kalyakina, A.; Utochnikova, V.; Trigub, A.; Zubavichus, Y.; Kuzmina, N.; Bräse, S.

2016-05-01

The combination of X-ray diffraction with EXAFS was employed to assess the coordination environment of lanthanide complexes in solutions. This method is based on the assumption that the local structure of lanthanide complexes in solution combines elements of the crystal structure of the complex in the solid state (single- or polycrystalline) and the elements of the local structure of a lanthanide salt, completely dissociated in the solvent (usually chlorides). The success of this approach is demonstrated with the lanthanide (III) 2,3,4,5,6-pentafluorobenzoate complexes, where the local structure in aqueous and methanol solutions were estimated. Moreover, the dissociation degree of the complexes in aqueous and methanol solutions was evaluated.

Family Structure and Child Well-Being: Integrating Family Complexity

PubMed Central

Brown, Susan L.; Manning, Wendy D.; Stykes, J. Bart

2014-01-01

Although children’s family lives are diverse, the measurement of children’s living arrangements has lagged, focusing on the relationships of children to parents while largely ignoring sibling composition. Using data from the 2008 Survey of Income and Program Participation (N = 23,985) the authors documented patterns of family complexity among a nationally representative sample of children ages 0–17 living in a range of family structures. They also examined the independent and joint associations of family structure and family complexity on child economic well-being. Family complexity was independently related to economic disadvantage, namely, a lower income-to-needs ratio and a higher likelihood of public assistance receipt. The role of family complexity was partially contingent on family structure, with the positive association between family complexity and receipt of public assistance more pronounced for children in families with 2 married biological parents. This study demonstrates the utility of integrating family structure and family complexity in studies of children’s well-being. PMID:25620810

Modeling of protein binary complexes using structural mass spectrometry data

PubMed Central

Kamal, J.K. Amisha; Chance, Mark R.

2008-01-01

In this article, we describe a general approach to modeling the structure of binary protein complexes using structural mass spectrometry data combined with molecular docking. In the first step, hydroxyl radical mediated oxidative protein footprinting is used to identify residues that experience conformational reorganization due to binding or participate in the binding interface. In the second step, a three-dimensional atomic structure of the complex is derived by computational modeling. Homology modeling approaches are used to define the structures of the individual proteins if footprinting detects significant conformational reorganization as a function of complex formation. A three-dimensional model of the complex is constructed from these binary partners using the ClusPro program, which is composed of docking, energy filtering, and clustering steps. Footprinting data are used to incorporate constraints—positive and/or negative—in the docking step and are also used to decide the type of energy filter—electrostatics or desolvation—in the successive energy-filtering step. By using this approach, we examine the structure of a number of binary complexes of monomeric actin and compare the results to crystallographic data. Based on docking alone, a number of competing models with widely varying structures are observed, one of which is likely to agree with crystallographic data. When the docking steps are guided by footprinting data, accurate models emerge as top scoring. We demonstrate this method with the actin/gelsolin segment-1 complex. We also provide a structural model for the actin/cofilin complex using this approach which does not have a crystal or NMR structure. PMID:18042684

Online Sentence Reading in People With Aphasia: Evidence From Eye Tracking

PubMed Central

Knilans, Jessica

2015-01-01

Purpose There is a lot of evidence that people with aphasia have more difficulty understanding structurally complex sentences (e.g., object clefts) than simpler sentences (subject clefts). However, subject clefts also occur more frequently in English than object clefts. Thus, it is possible that both structural complexity and frequency affect how people with aphasia understand these structures. Method Nine people with aphasia and 8 age-matched controls participated in the study. The stimuli consisted of 24 object cleft and 24 subject cleft sentences. The task was eye tracking during reading, which permits a more fine-grained analysis of reading performance than measures such as self-paced reading. Results As expected, controls had longer reading times for critical regions in object cleft sentences compared with subject cleft sentences. People with aphasia showed the predicted effects of structural frequency. Effects of structural complexity in people with aphasia did not emerge on their first pass through the sentence but were observed when they were rereading critical regions of complex sentences. Conclusions People with aphasia are sensitive to both structural complexity and structural frequency when reading. However, people with aphasia may use different reading strategies than controls when confronted with relatively infrequent and complex sentence structures. PMID:26383779

Online Sentence Reading in People With Aphasia: Evidence From Eye Tracking.

PubMed

Knilans, Jessica; DeDe, Gayle

2015-11-01

There is a lot of evidence that people with aphasia have more difficulty understanding structurally complex sentences (e.g., object clefts) than simpler sentences (subject clefts). However, subject clefts also occur more frequently in English than object clefts. Thus, it is possible that both structural complexity and frequency affect how people with aphasia understand these structures. Nine people with aphasia and 8 age-matched controls participated in the study. The stimuli consisted of 24 object cleft and 24 subject cleft sentences. The task was eye tracking during reading, which permits a more fine-grained analysis of reading performance than measures such as self-paced reading. As expected, controls had longer reading times for critical regions in object cleft sentences compared with subject cleft sentences. People with aphasia showed the predicted effects of structural frequency. Effects of structural complexity in people with aphasia did not emerge on their first pass through the sentence but were observed when they were rereading critical regions of complex sentences. People with aphasia are sensitive to both structural complexity and structural frequency when reading. However, people with aphasia may use different reading strategies than controls when confronted with relatively infrequent and complex sentence structures.

A novel complexity-to-diversity strategy for the diversity-oriented synthesis of structurally diverse and complex macrocycles from quinine.

PubMed

Ciardiello, J J; Stewart, H L; Sore, H F; Galloway, W R J D; Spring, D R

2017-06-01

Recent years have witnessed a global decline in the productivity and advancement of the pharmaceutical industry. A major contributing factor to this is the downturn in drug discovery successes. This can be attributed to the lack of structural (particularly scaffold) diversity and structural complexity exhibited by current small molecule screening collections. Macrocycles have been shown to exhibit a diverse range of biological properties, with over 100 natural product-derived examples currently marketed as FDA-approved drugs. Despite this, synthetic macrocycles are widely considered to be a poorly explored structural class within drug discovery, which can be attributed to their synthetic intractability. Herein we describe a novel complexity-to-diversity strategy for the diversity-oriented synthesis of novel, structurally complex and diverse macrocyclic scaffolds from natural product starting materials. This approach exploits the inherent structural (including functional) and stereochemical complexity of natural products in order to rapidly generate diversity and complexity. Readily-accessible natural product-derived intermediates serve as structural templates which can be divergently functionalized with different building blocks to generate a diverse range of acyclic precursors. Subsequent macrocyclisation then furnishes compounds that are each based around a distinct molecular scaffold. Thus, high levels of library scaffold diversity can be rapidly achieved. In this proof-of-concept study, the natural product quinine was used as the foundation for library synthesis, and six novel structurally diverse, highly complex and functionalized macrocycles were generated. Copyright © 2017 Elsevier Ltd. All rights reserved.

Integrative structure and functional anatomy of a nuclear pore complex

NASA Astrophysics Data System (ADS)

Kim, Seung Joong; Fernandez-Martinez, Javier; Nudelman, Ilona; Shi, Yi; Zhang, Wenzhu; Raveh, Barak; Herricks, Thurston; Slaughter, Brian D.; Hogan, Joanna A.; Upla, Paula; Chemmama, Ilan E.; Pellarin, Riccardo; Echeverria, Ignacia; Shivaraju, Manjunatha; Chaudhury, Azraa S.; Wang, Junjie; Williams, Rosemary; Unruh, Jay R.; Greenberg, Charles H.; Jacobs, Erica Y.; Yu, Zhiheng; de La Cruz, M. Jason; Mironska, Roxana; Stokes, David L.; Aitchison, John D.; Jarrold, Martin F.; Gerton, Jennifer L.; Ludtke, Steven J.; Akey, Christopher W.; Chait, Brian T.; Sali, Andrej; Rout, Michael P.

2018-03-01

Nuclear pore complexes play central roles as gatekeepers of RNA and protein transport between the cytoplasm and nucleoplasm. However, their large size and dynamic nature have impeded a full structural and functional elucidation. Here we determined the structure of the entire 552-protein nuclear pore complex of the yeast Saccharomyces cerevisiae at sub-nanometre precision by satisfying a wide range of data relating to the molecular arrangement of its constituents. The nuclear pore complex incorporates sturdy diagonal columns and connector cables attached to these columns, imbuing the structure with strength and flexibility. These cables also tie together all other elements of the nuclear pore complex, including membrane-interacting regions, outer rings and RNA-processing platforms. Inwardly directed anchors create a high density of transport factor-docking Phe-Gly repeats in the central channel, organized into distinct functional units. This integrative structure enables us to rationalize the architecture, transport mechanism and evolutionary origins of the nuclear pore complex.

Integrative structure and functional anatomy of a nuclear pore complex.

PubMed

Kim, Seung Joong; Fernandez-Martinez, Javier; Nudelman, Ilona; Shi, Yi; Zhang, Wenzhu; Raveh, Barak; Herricks, Thurston; Slaughter, Brian D; Hogan, Joanna A; Upla, Paula; Chemmama, Ilan E; Pellarin, Riccardo; Echeverria, Ignacia; Shivaraju, Manjunatha; Chaudhury, Azraa S; Wang, Junjie; Williams, Rosemary; Unruh, Jay R; Greenberg, Charles H; Jacobs, Erica Y; Yu, Zhiheng; de la Cruz, M Jason; Mironska, Roxana; Stokes, David L; Aitchison, John D; Jarrold, Martin F; Gerton, Jennifer L; Ludtke, Steven J; Akey, Christopher W; Chait, Brian T; Sali, Andrej; Rout, Michael P

2018-03-22

Nuclear pore complexes play central roles as gatekeepers of RNA and protein transport between the cytoplasm and nucleoplasm. However, their large size and dynamic nature have impeded a full structural and functional elucidation. Here we determined the structure of the entire 552-protein nuclear pore complex of the yeast Saccharomyces cerevisiae at sub-nanometre precision by satisfying a wide range of data relating to the molecular arrangement of its constituents. The nuclear pore complex incorporates sturdy diagonal columns and connector cables attached to these columns, imbuing the structure with strength and flexibility. These cables also tie together all other elements of the nuclear pore complex, including membrane-interacting regions, outer rings and RNA-processing platforms. Inwardly directed anchors create a high density of transport factor-docking Phe-Gly repeats in the central channel, organized into distinct functional units. This integrative structure enables us to rationalize the architecture, transport mechanism and evolutionary origins of the nuclear pore complex.

Ink composition for making a conductive silver structure

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

Walker, Steven B.; Lewis, Jennifer A.

An ink composition for making a conductive silver structure comprises a silver salt and a complex of (a) a complexing agent and a short chain carboxylic acid or (b) a complexing agent and a salt of a short chain carboxylic acid, according to one embodiment. A method for making a silver structure entails combining a silver salt and a complexing agent, and then adding a short chain carboxylic acid or a salt of the short chain carboxylic acid to the combined silver salt and a complexing agent to form an ink composition. A concentration of the complexing agent in themore » ink composition is reduced to form a concentrated formulation, and the silver salt is reduced to form a conductive silver structure, where the concentrated formulation and the conductive silver structure are formed at a temperature of about 120.degree. C. or less.« less

Spectroscopic and structural study of the newly synthesized heteroligand complex of copper with creatinine and urea.

PubMed

Gangopadhyay, Debraj; Singh, Sachin Kumar; Sharma, Poornima; Mishra, Hirdyesh; Unnikrishnan, V K; Singh, Bachcha; Singh, Ranjan K

2016-02-05

Study of copper complex of creatinine and urea is very important in life science and medicine. In this paper, spectroscopic and structural study of a newly synthesized heteroligand complex of copper with creatinine and urea has been discussed. Structural studies have been carried out using DFT calculations and spectroscopic analyses were carried out by FT-IR, Raman, UV-vis absorption and fluorescence techniques. The copper complex of creatinine and the heteroligand complex were found to have much increased water solubility as compared to pure creatinine. The analysis of FT-IR and Raman spectra helps to understand the coordination properties of the two ligands and to determine the probable structure of the heteroligand complex. The LIBS spectra of the heteroligand complex reveal that the complex is free from other metal impurities. UV-visible absorption spectra and the fluorescence emission spectra of the aqueous solution of Cu-Crn-urea heteroligand complex at different solute concentrations have been analyzed and the complex is found to be rigid and stable in its monomeric form at very low concentrations. Copyright © 2015 Elsevier B.V. All rights reserved.

On the Cohomology of Almost Complex Manifolds

NASA Astrophysics Data System (ADS)

Fino, Anna; Tomassini, Adriano

2010-07-01

We review some properties of two special types of almost complex structures, introduced by T.-J. Li and W. Zhang in [11], in relation to the existence of compatible symplectic structures and to the Hard Lefschetz condition. The two types of almost complex structures are defined respectively in terms of differential forms and currents. The paper is based on the results obtained in [9]. We give a new example of an 8-dimensional compact solvmanifold endowed with a C∞ pure and full almost complex structure calibrated by a symplectic form satisfying the Hard Lefschetz condition.

Structural study of surfactant-dependent interaction with protein

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

Mehan, Sumit; Aswal, Vinod K., E-mail: vkaswal@barc.gov.in; Kohlbrecher, Joachim

2015-06-24

Small-angle neutron scattering (SANS) has been used to study the complex structure of anionic BSA protein with three different (cationic DTAB, anionic SDS and non-ionic C12E10) surfactants. These systems form very different surfactant-dependent complexes. We show that the structure of protein-surfactant complex is initiated by the site-specific electrostatic interaction between the components, followed by the hydrophobic interaction at high surfactant concentrations. It is also found that hydrophobic interaction is preferred over the electrostatic interaction in deciding the resultant structure of protein-surfactant complexes.

Structural study of surfactant-dependent interaction with protein

NASA Astrophysics Data System (ADS)

Mehan, Sumit; Aswal, Vinod K.; Kohlbrecher, Joachim

2015-06-01

Small-angle neutron scattering (SANS) has been used to study the complex structure of anionic BSA protein with three different (cationic DTAB, anionic SDS and non-ionic C12E10) surfactants. These systems form very different surfactant-dependent complexes. We show that the structure of protein-surfactant complex is initiated by the site-specific electrostatic interaction between the components, followed by the hydrophobic interaction at high surfactant concentrations. It is also found that hydrophobic interaction is preferred over the electrostatic interaction in deciding the resultant structure of protein-surfactant complexes.

Identifying three-dimensional structures of autophosphorylation complexes in crystals of protein kinases

PubMed Central

Xu, Qifang; Malecka, Kimberly L.; Fink, Lauren; Jordan, E. Joseph; Duffy, Erin; Kolander, Samuel; Peterson, Jeffrey; Dunbrack, Roland L.

2016-01-01

Protein kinase autophosphorylation is a common regulatory mechanism in cell signaling pathways. Crystal structures of several homomeric protein kinase complexes have a serine, threonine, or tyrosine autophosphorylation site of one kinase monomer located in the active site of another monomer, a structural complex that we call an “autophosphorylation complex.” We developed and applied a structural bioinformatics method to identify all such autophosphorylation kinase complexes in X-ray crystallographic structures in the Protein Data Bank (PDB). We identified 15 autophosphorylation complexes in the PDB, of which 5 complexes had not previously been described in the publications describing the crystal structures. These 5 consist of tyrosine residues in the N-terminal juxtamembrane regions of colony stimulating factor 1 receptor (CSF1R, Tyr561) and EPH receptor A2 (EPHA2, Tyr594), tyrosine residues in the activation loops of the SRC kinase family member LCK (Tyr394) and insulin-like growth factor 1 receptor (IGF1R, Tyr1166), and a serine in a nuclear localization signal region of CDC-like kinase 2 (CLK2, Ser142). Mutations in the complex interface may alter autophosphorylation activity and contribute to disease; therefore we mutated residues in the autophosphorylation complex interface of LCK and found that two mutations impaired autophosphorylation (T445V and N446A) and mutation of Pro447 to Ala, Gly, or Leu increased autophosphorylation. The identified autophosphorylation sites are conserved in many kinases, suggesting that, by homology, these complexes may provide insight into autophosphorylation complex interfaces of kinases that are relevant drug targets. PMID:26628682