Directory of Open Access Journals (Sweden)
Akihito Soeda
2010-06-01
Full Text Available We study how two pieces of localized quantum information can be delocalized across a composite Hilbert space when a global unitary operation is applied. We classify the delocalization power of global unitary operations on quantum information by investigating the possibility of relocalizing one piece of the quantum information without using any global quantum resource. We show that one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent of a controlled-unitary operation. The delocalization power turns out to reveal different aspect of the non-local properties of global unitary operations characterized by their entangling power.
Teleportation of M-Qubit Unitary Operations
Institute of Scientific and Technical Information of China (English)
郑亦庄; 顾永建; 郭光灿
2002-01-01
We discuss teleportation of unitary operations on a two-qubit in detail, then generalize the bidirectional state teleportation scheme from one-qubit to M-qubit unitary operations. The resources required for the optimal implementation of teleportation of an M-qubit unitary operation using a bidirectional state teleportation scheme are given.
A unitary correlation operator method
International Nuclear Information System (INIS)
Feldmeier, H.; Neff, T.; Roth, R.; Schnack, J.
1997-09-01
The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the repulsive core. By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given. The decomposition of correlated operators into irreducible n-body operators is discussed. The one- and two-body-irreducible parts are worked out explicitly and the contribution of three-body correlations is estimated to check convergence. Ground state energies of nuclei up to mass number A=48 are calculated with a spin-isospin-dependent potential and single Slater determinants as uncorrelated states. They show that the deduced energy-and mass-number-independent correlated two-body Hamiltonian reproduces all ''exact'' many-body calculations surprisingly well. (orig.)
Entanglement quantification by local unitary operations
Energy Technology Data Exchange (ETDEWEB)
Monras, A.; Giampaolo, S. M.; Gualdi, G.; Illuminati, F. [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, CNISM, Unita di Salerno, and INFN, Sezione di Napoli-Gruppo Collegato di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); Adesso, G.; Davies, G. B. [School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2011-07-15
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as ''mirror entanglement.'' They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the ''stellar mirror entanglement'' associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Entanglement quantification by local unitary operations
Monras, A.; Adesso, G.; Giampaolo, S. M.; Gualdi, G.; Davies, G. B.; Illuminati, F.
2011-07-01
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as “mirror entanglement.” They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the “stellar mirror entanglement” associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.76.042301 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Entanglement quantification by local unitary operations
International Nuclear Information System (INIS)
Monras, A.; Giampaolo, S. M.; Gualdi, G.; Illuminati, F.; Adesso, G.; Davies, G. B.
2011-01-01
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as ''mirror entanglement.'' They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the ''stellar mirror entanglement'' associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Multiple multicontrol unitary operations: Implementation and applications
Lin, Qing
2018-04-01
The efficient implementation of computational tasks is critical to quantum computations. In quantum circuits, multicontrol unitary operations are important components. Here, we present an extremely efficient and direct approach to multiple multicontrol unitary operations without decomposition to CNOT and single-photon gates. With the proposed approach, the necessary two-photon operations could be reduced from O( n 3) with the traditional decomposition approach to O( n), which will greatly relax the requirements and make large-scale quantum computation feasible. Moreover, we propose the potential application to the ( n- k)-uniform hypergraph state.
Random unitary operations and quantum Darwinism
International Nuclear Information System (INIS)
Balaneskovic, Nenad
2016-01-01
We study the behavior of Quantum Darwinism (Zurek, Nature Physics 5, 181-188 (2009)) within the iterative, random unitary operations qubit-model of pure decoherence (Novotn'y et al, New Jour. Phys. 13, 053052 (2011)). We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system from the point of view of its environment, is not a generic phenomenon, but depends on the specific form of initial states and on the type of system-environment interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial initial states of environment that allow to store information about an open system of interest and its pointer-basis with maximal efficiency. Furthermore, we investigate the behavior of Quantum Darwinism after introducing dissipation into the iterative random unitary qubit model with pure decoherence in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)) and reconstruct the corresponding dissipative attractor space. We conclude that in Zurek's qubit model Quantum Darwinism depends on the order in which pure decoherence and dissipation act upon an initial state of the entire system. We show explicitly that introducing dissipation into the random unitary evolution model in general suppresses Quantum Darwinism (regardless of the order in which decoherence and dissipation are applied) for all positive non-zero values of the dissipation strength parameter, even for those initial state configurations which, in Zurek's qubit model and in the random unitary model with pure decoherence, would lead to Quantum Darwinism. Finally, we discuss what happens with Quantum Darwinism after introducing into the iterative random unitary qubit model with pure decoherence (asymmetric) dissipation and dephasing, again in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)), and reconstruct the corresponding
Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach
Energy Technology Data Exchange (ETDEWEB)
Xia, Hui-Zhi; Li, Chao; Yang, Qing; Yang, Ming, E-mail: mingyang@ahu.edu.cn [Key Laboratory of Opto-electronic Information Acquisition and Manipulation, Ministry of Education, School of Physics and Material Science, Anhui University Hefei (China); Cao, Zhuo-Liang [School of Electronic Information Engineering, Hefei Normal University (China)
2012-08-15
The operator entanglement of two-qubit joint unitary operations is revisited. The Schmidt number, an important attribute of a two-qubit unitary operation, may have connection with the entanglement measure of the unitary operator. We find that the entanglement measure of a two-qubit unitary operators is classified by the Schmidt number of the unitary operators. We also discuss the exact relation between the operator entanglement and the parameters of the unitary operator. (author)
Efficient Nonlocal M-Control and N-Target Controlled Unitary Gate Using Non-symmetric GHZ States
Chen, Li-Bing; Lu, Hong
2018-03-01
Efficient local implementation of a nonlocal M-control and N-target controlled unitary gate is considered. We first show that with the assistance of two non-symmetric qubit(1)-qutrit(N) Greenberger-Horne-Zeilinger (GHZ) states, a nonlocal 2-control and N-target controlled unitary gate can be constructed from 2 local two-qubit CNOT gates, 2 N local two-qutrit conditional SWAP gates, N local qutrit-qubit controlled unitary gates, and 2 N single-qutrit gates. At each target node, the two third levels of the two GHZ target qutrits are used to expose one and only one initial computational state to the local qutrit-qubit controlled unitary gate, instead of being used to hide certain states from the conditional dynamics. This scheme can be generalized straightforwardly to implement a higher-order nonlocal M-control and N-target controlled unitary gate by using M non-symmetric qubit(1)-qutrit(N) GHZ states as quantum channels. Neither the number of the additional levels of each GHZ target particle nor that of single-qutrit gates needs to increase with M. For certain realistic physical systems, the total gate time may be reduced compared with that required in previous schemes.
Nonlocal Operational Calculi for Dunkl Operators
Directory of Open Access Journals (Sweden)
Ivan H. Dimovski
2009-03-01
Full Text Available The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusinski type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value problems for Dunkl functional-differential equations $P(D_ku = f$ with a given polynomial $P$ is proposed. The solution of these equations in mean-periodic functions reduces to such problems. Necessary and sufficient condition for existence of unique solution in mean-periodic functions is found.
Operator Spreading in Random Unitary Circuits
Nahum, Adam; Vijay, Sagar; Haah, Jeongwan
2018-04-01
Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1 +1 D and higher dimensions and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1 +1 D , we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC and determines the butterfly speed vB. We find that in 1 +1 D , the "front" of the OTOC broadens diffusively, with a width scaling in time as t1 /2. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front within a realization. Turning to higher dimensions, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a purely classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t1 /3 in 2 +1 D and as t0.240 in 3 +1 D (exponents of the Kardar-Parisi-Zhang universality class). We support our analytic argument with simulations in 2 +1 D . We point out that, in two or higher spatial dimensions, the shape of the spreading operator at late times is affected by underlying lattice symmetries and, in general, is not spherical. However, when full spatial rotational symmetry is present in 2 +1 D , our mapping implies an exact asymptotic form for the OTOC, in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1 +1 D , we map it to the partition function of an Ising-like statistical mechanics model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be
Implementing controlled-unitary operations over the butterfly network
Energy Technology Data Exchange (ETDEWEB)
Soeda, Akihito; Kinjo, Yoshiyuki; Turner, Peter S. [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo (Japan); Murao, Mio [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan and NanoQuine, The University of Tokyo, Tokyo (Japan)
2014-12-04
We introduce a multiparty quantum computation task over a network in a situation where the capacities of both the quantum and classical communication channels of the network are limited and a bottleneck occurs. Using a resource setting introduced by Hayashi [1], we present an efficient protocol for performing controlled-unitary operations between two input nodes and two output nodes over the butterfly network, one of the most fundamental networks exhibiting the bottleneck problem. This result opens the possibility of developing a theory of quantum network coding for multiparty quantum computation, whereas the conventional network coding only treats multiparty quantum communication.
Isometric and unitary phase operators: explaining the Villain transform
International Nuclear Information System (INIS)
Hemmen, J L van; Wreszinski, Walter F
2007-01-01
The Villain transform plays a key role in spin-wave theory, a bosonization of elementary excitations in a system of extensively many Heisenberg spins. Intuitively, it is a representation of the spin operators in terms of an angle and its canonically conjugate angular momentum operator and, as such, has a few nasty boundary-condition twists. We construct an isometric phase representation of spin operators that conveys a precise mathematical meaning to the Villain transform and is related to both classical mechanics and the Pegg-Barnett-Bialynicki-Birula boson (photon) phase operators by means of suitable limits. In contrast to the photon case, unitary extensions are inadequate because they describe the wrong physics. We also discuss in some detail the application to spin-wave theory, pointing out some examples in which the isometric representation is indispensable
Survey on nonlocal games and operator space theory
International Nuclear Information System (INIS)
Palazuelos, Carlos; Vidick, Thomas
2016-01-01
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 the nonlocality of different classes of entangled states
Survey on nonlocal games and operator space theory
Energy Technology Data Exchange (ETDEWEB)
Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)
2016-01-15
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 the nonlocality of different classes of entangled states.
Nonclassicality by Local Gaussian Unitary Operations for Gaussian States
Directory of Open Access Journals (Sweden)
Yangyang Wang
2018-04-01
Full Text Available A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 -mode Gaussian states and an estimate of N for ( n + m -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.
Energy Technology Data Exchange (ETDEWEB)
Akibue, Seiseki [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo (Japan); Murao, Mio [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan and NanoQuine, The University of Tokyo, Tokyo (Japan)
2014-12-04
We investigate distributed implementation of two-qubit unitary operations over two primitive networks, the butterfly network and the ladder network, as a first step to apply network coding for quantum computation. By classifying two-qubit unitary operations in terms of the Kraus-Cirac number, the number of non-zero parameters describing the global part of two-qubit unitary operations, we analyze which class of two-qubit unitary operations is implementable over these networks with free classical communication. For the butterfly network, we show that two classes of two-qubit unitary operations, which contain all Clifford, controlled-unitary and matchgate operations, are implementable over the network. For the ladder network, we show that two-qubit unitary operations are implementable over the network if and only if their Kraus-Cirac number do not exceed the number of the bridges of the ladder.
International Nuclear Information System (INIS)
Akibue, Seiseki; Murao, Mio
2014-01-01
We investigate distributed implementation of two-qubit unitary operations over two primitive networks, the butterfly network and the ladder network, as a first step to apply network coding for quantum computation. By classifying two-qubit unitary operations in terms of the Kraus-Cirac number, the number of non-zero parameters describing the global part of two-qubit unitary operations, we analyze which class of two-qubit unitary operations is implementable over these networks with free classical communication. For the butterfly network, we show that two classes of two-qubit unitary operations, which contain all Clifford, controlled-unitary and matchgate operations, are implementable over the network. For the ladder network, we show that two-qubit unitary operations are implementable over the network if and only if their Kraus-Cirac number do not exceed the number of the bridges of the ladder
Multiple-Trace Operators and Non-Local String Theories
International Nuclear Information System (INIS)
Silverstein, Eva M.
2001-01-01
We propose that a novel deformation of string perturbation theory, involving non-local interactions between strings, is required to describe the gravity duals of field theories deformed by multiple-trace operators. The new perturbative expansion involves a new parameter, which is neither the string coupling nor the coefficient of a vertex operator on the worldsheet. We explore some of the properties of this deformation, focusing on a special case where the deformation in the field theory is exactly marginal
International Nuclear Information System (INIS)
Malik, R. P.; Srinivas, N.; Bhanja, T.
2016-01-01
We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator and its Hermitian conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor and modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of the dual unitary operators and corresponding (anti-)dual-BRST symmetries are completely novel results in our present investigation.
Unitary-model-operator approach to Λ17O and lambda-nucleon effective interaction
International Nuclear Information System (INIS)
Fujii, Shinichiro; Okamoto, Ryoji; Suzuki, Kenji
1998-01-01
The unitary-model-operator approach (UMOA) is applied to Λ 17 O. A lambda-nucleon effective interaction is derived, taking the coupling of the sigma-nucleon channel into account. The lambda single-particle energies are calculated for the Os 1/2 , Op 3/2 and Op 1/2 states employing the Nijmegen soft-core potential. (author)
Matrix elements and few-body calculations within the unitary correlation operator method
International Nuclear Information System (INIS)
Roth, R.; Hergert, H.; Papakonstantinou, P.
2005-01-01
We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges. (orig.)
Matrix elements and few-body calculations within the unitary correlation operator method
International Nuclear Information System (INIS)
Roth, R.; Hergert, H.; Papakonstantinou, P.; Neff, T.; Feldmeier, H.
2005-01-01
We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges
Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio
2007-10-01
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1×M bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a , uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.
International Nuclear Information System (INIS)
Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio
2007-01-01
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1xM bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a, uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes
Entanglement Capacity of Two-Qubit Unitary Operator with the Help of Auxiliary System
International Nuclear Information System (INIS)
Hu Baolin; Di Yaomin
2007-01-01
The entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From the results the condition for perfect entangler, α 1 = α 2 = π/4, is obtained. Contrary to the case without auxiliary system, the parameter α 3 may play active role to the entanglement capacity when auxiliary systems are allowed.
Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (I)-Formalism
Institute of Scientific and Technical Information of China (English)
DAI Lian-Rong; PAN Feng
2001-01-01
The tensor algebraic method is used to derive general one- and two-body operator matrix elements within the Un representations, which are useful in the unitary group approach to the configuration interaction problems of quantum many-body systems.
Realization of a unique time evolution unitary operator in Klein Gordon theory
International Nuclear Information System (INIS)
Balasubramanian, T.S.; Bhatia, S.Kr.
1986-01-01
The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hilbert space L 2 (R 3 ) and the Einstein's relativistic equation in the space L 2 (R 3 ,dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hilbert space L 2 (R 3 ) with the help of unique symmetric symplectic operator, the time evolution unitary operator U(t) has been fixed for the Klein Gordon eqution, incorporating either the positive or negative frequencies, in the infinite dimensional Hilbert space L 2 (R 3 ). (author)
International Nuclear Information System (INIS)
Kiritsis, E.B.
1987-01-01
N = 2 superconformal-invariant theories are studied and their general structure is analyzed. The geometry of N = 2 complex superspace is developed as a tool to study the correlation functions of the theories above. The Ward identities of the global N = 2 superconformal symmetry are solved, to restrict the form of correlation functions. Advantage is taken of the existence of the degenerate operators to derive the ''fusion'' rules for the unitary minimal systems with c<1. In particular, the closure of the operator algebra for such systems is shown. The c = (1/3 minimal system is analyzed and its two-, three-, and four-point functions as well as its operator algebra are calculated explicitly
International Nuclear Information System (INIS)
Du, Qiang; Yang, Jiang
2017-01-01
This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.
International Nuclear Information System (INIS)
Krasnikov, N.V.
1987-01-01
Nonlocal gauge theories including gravity are considered. It is shown that the introduction of the additional nonlocal interaction makes γ 5 -anomalous theories meaningful. The introduction of such interaction leads to macrocausal unitary theory, which describes the interaction of massive vector fields with fermion fields. It is shown that nonlocal gauge theories with nonlocal scale Λ nl ≤(1-10) TeV can solve the gauge hierarchy problem. An example of nonlinear grand unified gauge model in which topologically nontrivial finite energy monopole solutions are absent is found
Stability issues of black hole in non-local gravity
Myung, Yun Soo; Park, Young-Jai
2018-04-01
We discuss stability issues of Schwarzschild black hole in non-local gravity. It is shown that the stability analysis of black hole for the unitary and renormalizable non-local gravity with γ2 = - 2γ0 cannot be performed in the Lichnerowicz operator approach. On the other hand, for the unitary and non-renormalizable case with γ2 = 0, the black hole is stable against the metric perturbations. For non-unitary and renormalizable local gravity with γ2 = - 2γ0 = const (fourth-order gravity), the small black holes are unstable against the metric perturbations. This implies that what makes the problem difficult in stability analysis of black hole is the simultaneous requirement of unitarity and renormalizability around the Minkowski spacetime.
Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter
2015-01-01
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.
Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter
2015-01-01
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581
Nehari manifold for non-local elliptic operator with concave–convex ...
Indian Academy of Sciences (India)
Introduction. We consider the following p-fractional Laplace equation ... ators of elliptic type due to concrete real world applications in finance, thin obstacle .... Due to the non-localness of the operator LK, we define the linear space as follows:.
Non-self-adjoint Schrödinger operators with nonlocal one-point interactions
Czech Academy of Sciences Publication Activity Database
Kuzhel, S.; Znojil, Miloslav
2017-01-01
Roč. 11, č. 4 (2017), s. 923-944 ISSN 1735-8787 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : 1-dimensional Schrodinger operator * nonlocal one-point interactions * boundary triplet Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 0.833, year: 2016
Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2014-01-01
Full Text Available The nonlocal boundary value problem for the parabolic differential equation v'(t+A(tv(t=f(t (0≤t≤T, v(0=v(λ+φ, 0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β of all Eα-β-valued continuous functions φ(t on [0,T] satisfying a Hölder condition with a weight (t+τγ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.
Bipartite separability and nonlocal quantum operations on graphs
Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.
2016-07-01
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.
Closure of the operator product expansion in the non-unitary bootstrap
Energy Technology Data Exchange (ETDEWEB)
Esterlis, Ilya [Stanford Institute for Theoretical Physics, Stanford University,Via Pueblo, Stanford, CA 94305 (United States); Fitzpatrick, A. Liam [Department of Physics, Boston University,Commonwealth Ave, Boston, MA, 02215 (United States); Ramirez, David M. [Stanford Institute for Theoretical Physics, Stanford University,Via Pueblo, Stanford, CA 94305 (United States)
2016-11-07
We use the numerical conformal bootstrap in two dimensions to search for finite, closed sub-algebras of the operator product expansion (OPE), without assuming unitarity. We find the minimal models as special cases, as well as additional lines of solutions that can be understood in the Coulomb gas formalism. All the solutions we find that contain the vacuum in the operator algebra are cases where the external operators of the bootstrap equation are degenerate operators, and we argue that this follows analytically from the expressions in http://arxiv.org/abs/1202.4698 for the crossing matrices of Virasoro conformal blocks. Our numerical analysis is a special case of the “Gliozzi” bootstrap method, and provides a simpler setting in which to study technical challenges with the method. In the supplementary material, we provide a Mathematica notebook that automates the calculation of the crossing matrices and OPE coefficients for degenerate operators using the formulae of Dotsenko and Fateev.
The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain
Directory of Open Access Journals (Sweden)
Natalya V. Zaitseva
2016-12-01
Full Text Available We consider a boundary value problem for a hyperbolic equation with Bessel differential operator in a rectangular domain with integral nonlocal boundary value condition of the first kind. The equivalence between boundary value problem with integral nonlocal condition of the first kind and a local boundary value problem with mixed boundary conditions of the first and third kinds is proved. The existence and uniqueness of solution of the equivalent problem are established by means of the spectral method. At the uniqueness proof the completeness of the eigenfunction system of the spectral problem is used . At the existence proof the assessment of coefficients of series, the asymptotic formula for Bessel function of the first kind and asymptotic formula for eigenvalues are used. Sufficient conditions on the functions defining initial data of the problem are received. The solution of the problem is obtained in explicit form. The solution is obtained in the form of the Fourier–Bessel series. Its convergence is proved in the class of regular solutions.
Finite-volume effects due to spatially non-local operators arXiv
Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J.
Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work, we estimate finite-volume effects for matrix elements of non-local operators, composed of two currents displaced in a spatial direction by a distance $\\xi$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $ e^{-m_\\pi (L- \\xi)} $, where $m_\\pi$ is the mass of the light state. For heavier external states the usual $e^{- m_\\pi L}$ form is recovered, but with a polynomial prefactor of the form $L^m/|L - \\xi|^n$ that can lead to enhanced volume effects. These ...
International Nuclear Information System (INIS)
Quesne, C.
1986-01-01
In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 1 +n/2> encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the unitary-operator coherent states, as defined by Klauder, Perelomov, and Gilmore. These states are parametrized by the points of the coset space Sp(2d,R)/H, where H is the stability group of the Sp(2d,R) irreducible representation lowest weight state, chosen as the reference state, and depends upon the relative values of lambda 1 ,...,lambda/sub d/, subject to the conditions lambda 1 > or =lambda 2 > or = x x x > or =lambda/sub d/> or =0. A parametrization of Sp(2d,R)/H corresponding to a factorization of the latter into a product of coset spaces Sp(2d,R)/U(d) and U(d)/H is chosen. The overlap of two coherent states is calculated, the action of the Sp(2d,R) generators on the coherent states is determined, and the explicit form of the unity resolution relation satisfied by the coherent states in the representation space of the irreducible representation is obtained. The Hilbert space of analytic functions arising from the coherent state representation is studied in detail. Finally, some applications of the formalism developed in the present paper are outlined
Directory of Open Access Journals (Sweden)
Shu-Ya Chen
2009-01-01
Full Text Available A nonlocal observation operator has been developed to assimilate GPS radio occultation (RO refractivity with WRF 3DVAR. For simplicity, in the past GPS RO refractivity was often assimilated using a local observation operator with the assumption that the GPS RO observation was representative of amodel local point. Such an operator did not take into account the effects of horizontal inhomogeneity on the derived GPS RO refractivity. In order to more accurately model the observables, Sokolovskiy et al. (2005a developed a nonlocal observation operator, which would take into account the effects of horizontal inhomogeneity on GPS RO measurements. This nonlocal observation operator calculates the integrated amount of the model refractivity along the ray paths centered at the perigee points. For comparative purposes, the nonlocal observation operator can be simplified by limiting the length of integration near the RO point. This is called the "local operator variant", which is equivalent to the original local operator except that the original one is performed with fixed tangent points at observation levels. For computational efficiency, assimilation using both the nonlocal operator and local operator variant now is performed with smear tangent points at the mean height of each model vertical level. In this study, the statistics of observation errors using both local and nonlocal operators were estimated based on WRF simulations. The observation errors produced by the nonlocal operator are about two times smaller than those generated by the local operator and in agreement with Sokolovskiy et al. (2005b.
Well-posedness of nonlocal parabolic differential problems with dependent operators.
Ashyralyev, Allaberen; Hanalyev, Asker
2014-01-01
The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.
A generalized nonlocal vector calculus
Alali, Bacim; Liu, Kuo; Gunzburger, Max
2015-10-01
A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.
Mashhoon, Bahram
2017-01-01
Relativity theory is based on a postulate of locality, which means that the past history of the observer is not directly taken into account. This book argues that the past history should be taken into account. In this way, nonlocality---in the sense of history dependence---is introduced into relativity theory. The deep connection between inertia and gravitation suggests that gravity could be nonlocal, and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein's theory of gravitation has recently been developed. A significant consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. According to nonlocal gravity theory, what astronomers attribute to dark matter should instead be due to the nonlocality of gravitation. Nonlocality dominates on the scale of galaxies and beyond. Memory fades with time; therefore, the nonlocal aspect of gravity becomes wea...
Entanglement-continuous unitary transformations
Energy Technology Data Exchange (ETDEWEB)
Sahin, Serkan; Orus, Roman [Institute of Physics, Johannes Gutenberg University, 55099 Mainz (Germany)
2016-07-01
In this talk we present a new algorithm for quantum many-body systems using continuous unitary transformations (CUT) and tensor networks (TNs). With TNs we are able to approximate the solution to the flow equations that lie at the heart of continuous unitary transformations. We call this method Entanglement-Continuous Unitary Transformations (eCUT). It allows us to compute expectation values of local observables as well as tensor network representations of ground states and low-energy excited states. An implementation of the method is shown for 1d systems using matrix product operators. We show preliminary results for the 1d transverse-field Ising model to demonstrate the feasibility of the method.
International Nuclear Information System (INIS)
Bergmann, P.G.
1980-01-01
A problem of construction of the unitary field theory is discussed. The preconditions of the theory are briefly described. The main attention is paid to the geometrical interpretation of physical fields. The meaning of the conceptions of diversity and exfoliation is elucidated. Two unitary field theories are described: the Weyl conformic geometry and Calitzy five-dimensioned theory. It is proposed to consider supersymmetrical theories as a new approach to the problem of a unitary field theory. It is noted that the supergravitational theories are really unitary theories, since the fields figuring there do not assume invariant expansion
Directory of Open Access Journals (Sweden)
David A. Grandy
2007-08-01
Full Text Available Nonlocality is a puzzling issue in modern physics. I propose that, aside from the experimental determination of nonlocality, the concept of atomistic lightmdash;discrete, self-bounded photonsmdash;breaks down toward something like nonlocality when subjected to philosophical scrutiny. Louis de Broglie made a similar argument regarding the material atom: the concept of the classical atom, when interrogated, collapses upon itself to offer a glimpse of wave-particle duality. Light atoms or photons, I argue, similarly collapse toward the contradictory possibility of nonlocality.
Multipartite nonlocality distillation
International Nuclear Information System (INIS)
Hsu, Li-Yi; Wu, Keng-Shuo
2010-01-01
The stronger nonlocality than that allowed in quantum theory can provide an advantage in information processing and computation. Since quantum entanglement is distillable, can nonlocality be distilled in the nonsignalling condition? The answer is positive in the bipartite case. In this article the distillability of the multipartite nonlocality is investigated. We propose a distillation protocol solely exploiting xor operations on output bits. The probability-distribution vectors and matrix are introduced to tackle the correlators. It is shown that only the correlators with extreme values can survive the distillation process. As the main result, the amplified nonlocality cannot maximally violate any Bell-type inequality. Accordingly, a distillability criterion in the postquantum region is proposed.
A Generalized Nonlocal Calculus with Application to the Peridynamics Model for Solid Mechanics
Alali, Bacim; Liu, Kuo; Gunzburger, Max
2014-01-01
A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal...
Leptonic unitary triangles and boomerangs
International Nuclear Information System (INIS)
Dueck, Alexander; Rodejohann, Werner; Petcov, Serguey T.
2010-01-01
We review the idea of leptonic unitary triangles and extend the concept of the recently proposed unitary boomerangs to the lepton sector. Using a convenient parametrization of the lepton mixing, we provide approximate expressions for the side lengths and the angles of the six different triangles and give examples of leptonic unitary boomerangs. Possible applications of the leptonic unitary boomerangs are also briefly discussed.
Consciousness, intentionality, and community: Unitary perspectives and research.
Zahourek, Rothlyn P; Larkin, Dorothy M
2009-01-01
Consciousness and intentionality often have been related and studied together. These concepts also are readily viewed and understood for practice, research, and education in a unitary paradigm. How these ideas relate to community is less known. Considering the expansion of our capacity for communication through the World Wide Web and other technologic advances and appreciating recent research on the nonlocal character of intentionality and consciousness, it is more apparent how concepts of community can be seen in the same unitary context. The authors address these issues and review relevant nursing research.
Li, Dafa
2018-06-01
We construct ℓ -spin-flipping matrices from the coefficient matrices of pure states of n qubits and show that the ℓ -spin-flipping matrices are congruent and unitary congruent whenever two pure states of n qubits are SLOCC and LU equivalent, respectively. The congruence implies the invariance of ranks of the ℓ -spin-flipping matrices under SLOCC and then permits a reduction of SLOCC classification of n qubits to calculation of ranks of the ℓ -spin-flipping matrices. The unitary congruence implies the invariance of singular values of the ℓ -spin-flipping matrices under LU and then permits a reduction of LU classification of n qubits to calculation of singular values of the ℓ -spin-flipping matrices. Furthermore, we show that the invariance of singular values of the ℓ -spin-flipping matrices Ω 1^{(n)} implies the invariance of the concurrence for even n qubits and the invariance of the n-tangle for odd n qubits. Thus, the concurrence and the n-tangle can be used for LU classification and computing the concurrence and the n-tangle only performs additions and multiplications of coefficients of states.
More about the comparison of local and non-local NN interaction models
International Nuclear Information System (INIS)
Amghar, A.; Desplanques, B.
2003-01-01
The effect of non-locality in the NN interaction with an off-energy shell character has been studied in the past in relation with the possibility that some models could be approximately phase-shifts equivalent. This work is extended to a non-locality implying terms that involve an anticommutator with the operator p 2 . It includes both scalar and tensor components. The most recent 'high accuracy' models are considered in the analysis. After studying the deuteron wave functions, electromagnetic properties of various models are compared with the idea that these ones differ by their non-locality but are equivalent up to a unitary transformation. It is found that the extra non-local tensor interaction considered in this work tends to re-enforce the role of the term considered in previous works, allowing one to explain almost completely the difference in the deuteron D-state probabilities evidenced by the comparison of the Bonn-QB and Paris models for instance. Conclusions for the effect of the non-local scalar interaction are not so clear. In many cases, it was found that these terms could explain part of the differences that the comparison of predictions for various models evidences but cases where they could not were also found. Some of these last ones have been analyzed in order to pointing out the origin of the failure
Nonlocal higher order evolution equations
Rossi, Julio D.; Schö nlieb, Carola-Bibiane
2010-01-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove
Unitary unified field theories
International Nuclear Information System (INIS)
Sudarshan, E.C.G.
1976-01-01
This is an informal exposition of some recent developments. Starting with an examination of the universality of electromagnetic and weak interactions, the attempts at their unification are outlined. The theory of unitary renormalizable self-coupled vector mesons with dynamical sources is formulated for a general group. With masses introduced as variable parameters it is shown that the theory so defined is indeed unitary. Diagrammatic rules are developed in terms of a chosen set of fictitious particles. A number of special examples are outlined including a theory with strongly interacting vector and axial vector mesons and weak mesons. Applications to weak interactions of strange particles is briefly outlined. (Auth.)
International Nuclear Information System (INIS)
Audenaert, Koenraad M R; Scheel, Stefan
2008-01-01
In this paper, we provide necessary and sufficient conditions for a completely positive trace-preserving (CPT) map to be decomposable into a convex combination of unitary maps. Additionally, we set out to define a proper distance measure between a given CPT map and the set of random unitary maps, and methods for calculating it. In this way one could determine whether non-classical error mechanisms such as spontaneous decay or photon loss dominate over classical uncertainties, for example, in a phase parameter. The present paper is a step towards achieving this goal
Qubit transport model for unitary black hole evaporation without firewalls*
Osuga, Kento; Page, Don N.
2018-03-01
We give an explicit toy qubit transport model for transferring information from the gravitational field of a black hole to the Hawking radiation by a continuous unitary transformation of the outgoing radiation and the black hole gravitational field. The model has no firewalls or other drama at the event horizon, and it avoids a counterargument that has been raised for subsystem transfer models as resolutions of the firewall paradox. Furthermore, it fits the set of six physical constraints that Giddings has proposed for models of black hole evaporation. It does utilize nonlocal qubits for the gravitational field but assumes that the radiation interacts locally with these nonlocal qubits, so in some sense the nonlocality is confined to the gravitational sector. Although the qubit model is too crude to be quantitatively correct for the detailed spectrum of Hawking radiation, it fits qualitatively with what is expected.
General operator form of the non-local three-nucleon force
Energy Technology Data Exchange (ETDEWEB)
Topolnicki, K. [Jagiellonian University, M. Smoluchowski Institute of Physics, Krakow (Poland)
2017-09-15
This paper describes a procedure to obtain the general form of the three-nucleon force. The result is an operator form where the momentum space matrix element of the three-nucleon potential is written as a linear combination of 320 isospin-spin-momentum operators and scalar functions of momenta. Any spatial and isospin rotation invariant three-nucleon force can be written in this way and in order for the potential to be Hermitian, symmetric under parity inversion, time reversal and particle exchange, the scalar functions must have definite transformation properties under these discrete operations. A complete list of the isospin-spin-momentum operators and scalar function transformation properties is given. (orig.)
Equivalence of quantum states under local unitary transformations
International Nuclear Information System (INIS)
Fei Shaoming; Jing Naihuan
2005-01-01
In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational criterion for the equivalence of two such mixed bipartite states under local unitary transformations is presented
The nonlocal operator expansion for structure functions of e+e- annihilation
International Nuclear Information System (INIS)
Balitsky, I.I.; Braun, V.M.
1989-01-01
The Wilson operator expansion is generalized to inclusive particle production in e + e - annihilation. This turns out to be possible at the price of doubling the number of quantum quark and gluon fields in a similar fashion that gives rise to the Keldysh technique for nonequilibrium processes. Well-known results on the leading logarithmic contributions to inclusive production are reproduced as the one-loop evolution of the string operator of the leading twist. The general structure of the power corrections 1/Q 2 is outlined. (orig.)
A mapping from the unitary to doubly stochastic matrices and symbols on a finite set
Karabegov, Alexander V.
2008-11-01
We prove that the mapping from the unitary to doubly stochastic matrices that maps a unitary matrix (ukl) to the doubly stochastic matrix (|ukl|2) is a submersion at a generic unitary matrix. The proof uses the framework of operator symbols on a finite set.
Evenly distributed unitaries: On the structure of unitary designs
International Nuclear Information System (INIS)
Gross, D.; Audenaert, K.; Eisert, J.
2007-01-01
We clarify the mathematical structure underlying unitary t-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any tth order polynomial over the design equals the average over the entire unitary group. We present a simple necessary and sufficient criterion for deciding if a set of matrices constitutes a design. Lower bounds for the number of elements of 2-designs are derived. We show how to turn mutually unbiased bases into approximate 2-designs whose cardinality is optimal in leading order. Designs of higher order are discussed and an example of a unitary 5-design is presented. We comment on the relation between unitary and spherical designs and outline methods for finding designs numerically or by searching character tables of finite groups. Further, we sketch connections to problems in linear optics and questions regarding typical entanglement
International Nuclear Information System (INIS)
Namsrai, Kh.; Nyamtseren, N.
1994-09-01
A model of the extended electron is constructed by using definition of the d-operation. Gauge invariance of the nonlocal theory is proved. We use the Efimov approach to describe the nonlocal interaction of quantized fields. (author). 4 refs
Unitary evolution between pure and mixed states
International Nuclear Information System (INIS)
Reznik, B.
1996-01-01
We propose an extended quantum mechanical formalism that is based on a wave operator d, which is related to the ordinary density matrix via ρ=dd degree . This formalism allows a (generalized) unitary evolution between pure and mixed states. It also preserves much of the connection between symmetries and conservation laws. The new formalism is illustrated for the case of a two-level system. copyright 1996 The American Physical Society
Unitary Transformation in Quantum Teleportation
International Nuclear Information System (INIS)
Wang Zhengchuan
2006-01-01
In the well-known treatment of quantum teleportation, the receiver should convert the state of his EPR particle into the replica of the unknown quantum state by one of four possible unitary transformations. However, the importance of these unitary transformations must be emphasized. We will show in this paper that the receiver cannot transform the state of his particle into an exact replica of the unknown state which the sender wants to transfer if he has not a proper implementation of these unitary transformations. In the procedure of converting state, the inevitable coupling between EPR particle and environment which is needed by the implementation of unitary transformations will reduce the accuracy of the replica.
Theory of the unitary representations of compact groups
International Nuclear Information System (INIS)
Burzynski, A.; Burzynska, M.
1979-01-01
An introduction contains some basic notions used in group theory, Lie group, Lie algebras and unitary representations. Then we are dealing with compact groups. For these groups we show the problem of reduction of unitary representation of Wigner's projection operators, Clebsch-Gordan coefficients and Wigner-Eckart theorem. We show (this is a new approach) the representations reduction formalism by using superoperators in Hilbert-Schmidt space. (author)
Non-unitary probabilistic quantum computing circuit and method
Williams, Colin P. (Inventor); Gingrich, Robert M. (Inventor)
2009-01-01
A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained.
About the unitary discretizations of Heisenberg equations of motion
International Nuclear Information System (INIS)
Vazquez, L.
1986-01-01
In a recent paper Bender et al. (1985) have used a unitary discretization of Heisenberg equations for a one-dimensional quantum system in order to obtain information about the spectrum of the underlying continuum theory. The method consists in comparing the matrix elements between adjacent Fock states of the operators and at two steps. At the same time a very simple variational approach must be made. The purpose of this paper is to show that with unitary schemes, accurate either to order τ or τ 2 , we obtain the same spectrum results in the framework of the above method. On the other hand the same eigenvalues are obtained with a non-unitary scheme (Section II). In Section III we discuss the construction of the Hamiltonian associated to the unitary discretizations. (orig.)
Closed sets of nonlocal correlations
International Nuclear Information System (INIS)
Allcock, Jonathan; Linden, Noah; Brunner, Nicolas; Popescu, Sandu; Skrzypczyk, Paul; Vertesi, Tamas
2009-01-01
We present a fundamental concept - closed sets of correlations - for studying nonlocal correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum nonlocality is limited, and for finding constraints on physical theories beyond quantum mechanics.
More nonlocality with less purity.
Bandyopadhyay, Somshubhro
2011-05-27
Quantum information is nonlocal in the sense that local measurements on a composite quantum system, prepared in one of many mutually orthogonal states, may not reveal in which state the system was prepared. It is shown that in the many copy limit this kind of nonlocality is fundamentally different for pure and mixed quantum states. In particular, orthogonal mixed states may not be distinguishable by local operations and classical communication, no matter how many copies are supplied, whereas any set of N orthogonal pure states can be perfectly discriminated with m copies, where miff the set is not conclusively locally distinguishable with multiple copies. © 2011 American Physical Society
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Piaget's Egocentrism: A Unitary Construct?
Ruthven, Avis J.; Cunningham, William L.
In order to determine whether egocentrism can be conceptualized as a unitary construct, 100 children (51 four-year-olds, 37 five-year-olds, and 12 six-year-olds) were administered a visual/spatial perspective task, a cognitive/communicative task, and an affective task. All tasks were designed to measure different facets of egocentrism. The 50…
Random unitary maps for quantum state reconstruction
International Nuclear Information System (INIS)
Merkel, Seth T.; Riofrio, Carlos A.; Deutsch, Ivan H.; Flammia, Steven T.
2010-01-01
We study the possibility of performing quantum state reconstruction from a measurement record that is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of a single random unitary map, U 0 . We show that while this single-parameter orbit in operator space is not informationally complete, it can be used to yield surprisingly high-fidelity reconstruction. For a d-dimensional Hilbert space with the initial observable in su(d), the measurement record lacks information about a matrix subspace of dimension ≥d-2 out of the total dimension d 2 -1. We determine the conditions on U 0 such that the bound is saturated, and show they are achieved by almost all pseudorandom unitary matrices. When we further impose the constraint that the physical density matrix must be positive, we obtain even higher fidelity than that predicted from the missing subspace. With prior knowledge that the state is pure, the reconstruction will be perfect (in the limit of vanishing noise) and for arbitrary mixed states, the fidelity is over 0.96, even for small d, and reaching F>0.99 for d>9. We also study the implementation of this protocol based on the relationship between random matrices and quantum chaos. We show that the Floquet operator of the quantum kicked top provides a means of generating the required type of measurement record, with implications on the relationship between quantum chaos and information gain.
Robust Learning Control Design for Quantum Unitary Transformations.
Wu, Chengzhi; Qi, Bo; Chen, Chunlin; Dong, Daoyi
2017-12-01
Robust control design for quantum unitary transformations has been recognized as a fundamental and challenging task in the development of quantum information processing due to unavoidable decoherence or operational errors in the experimental implementation of quantum operations. In this paper, we extend the systematic methodology of sampling-based learning control (SLC) approach with a gradient flow algorithm for the design of robust quantum unitary transformations. The SLC approach first uses a "training" process to find an optimal control strategy robust against certain ranges of uncertainties. Then a number of randomly selected samples are tested and the performance is evaluated according to their average fidelity. The approach is applied to three typical examples of robust quantum transformation problems including robust quantum transformations in a three-level quantum system, in a superconducting quantum circuit, and in a spin chain system. Numerical results demonstrate the effectiveness of the SLC approach and show its potential applications in various implementation of quantum unitary transformations.
Unitary Housing Regimes in Transition
DEFF Research Database (Denmark)
Bengtsson, Bo; Jensen, Lotte
2013-01-01
Path dependence is strong in housing institutions and policy. In both Denmark and Sweden, today’s universal and ‘unitary’ (Kemeny) housing regimes can be traced back to institutions that were introduced fifty years back in history or more. Recently, universal and unitary housing systems...... in Scandinavia, and elsewhere, are under challenge from strong political and economic forces. These challenges can be summarized as economic cutbacks, privatization and Europeanization. Although both the Danish and the Swedish housing system are universal and unitary in character, they differ considerably...... in institutional detail. Both systems have corporatist features, however in Denmark public housing is based on local tenant democracy and control, and in Sweden on companies owned and controlled by the municipalities, combined with a centralized system of rent negotiations. In the paper the present challenges...
Quantum Nonlocality and Reality
Bell, Mary; Gao, Shan
2016-09-01
Preface; Part I. John Stewart Bell: The Physicist: 1. John Bell: the Irish connection Andrew Whitaker; 2. Recollections of John Bell Michael Nauenberg; 3. John Bell: recollections of a great scientist and a great man Gian-Carlo Ghirardi; Part II. Bell's Theorem: 4. What did Bell really prove? Jean Bricmont; 5. The assumptions of Bell's proof Roderich Tumulka; 6. Bell on Bell's theorem: the changing face of nonlocality Harvey R. Brown and Christopher G. Timpson; 7. Experimental tests of Bell inequalities Marco Genovese; 8. Bell's theorem without inequalities: on the inception and scope of the GHZ theorem Olival Freire, Jr and Osvaldo Pessoa, Jr; 9. Strengthening Bell's theorem: removing the hidden-variable assumption Henry P. Stapp; Part III. Nonlocality: Illusions or Reality?: 10. Is any theory compatible with the quantum predictions necessarily nonlocal? Bernard d'Espagnat; 11. Local causality, probability and explanation Richard A. Healey; 12. Bell inequality and many-worlds interpretation Lev Vaidman; 13. Quantum solipsism and non-locality Travis Norsen; 14. Lessons of Bell's theorem: nonlocality, yes; action at a distance, not necessarily Wayne C. Myrvold; 15. Bell non-locality, Hardy's paradox and hyperplane dependence Gordon N. Fleming; 16. Some thoughts on quantum nonlocality and its apparent incompatibility with relativity Shan Gao; 17. A reasonable thing that just might work Daniel Rohrlich; 18. Weak values and quantum nonlocality Yakir Aharonov and Eliahu Cohen; Part IV. Nonlocal Realistic Theories: 19. Local beables and the foundations of physics Tim Maudlin; 20. John Bell's varying interpretations of quantum mechanics: memories and comments H. Dieter Zeh; 21. Some personal reflections on quantum non-locality and the contributions of John Bell Basil J. Hiley; 22. Bell on Bohm Sheldon Goldstein; 23. Interactions and inequality Philip Pearle; 24. Gravitation and the noise needed in objective reduction models Stephen L. Adler; 25. Towards an objective
Boundary fluxes for nonlocal diffusion
Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.
Temporal nonlocality in bistable perception
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.
Nonlocality in Bohmian mechanics
Ghafar, Zati Amalina binti Mohd Abdul; Radiman, Shahidan bin; Siong, Ch'ng Han
2018-04-01
The Einstein-Podolsky-Rosen (EPR) paradox demonstrates that entangled particles can interact in such a way that it is possible to measure both their position and momentum instantaneously. The position or momentum of one particle can be determined by measuring another identical particle that exists in another space. This instantaneous action is actually called nonlocality. The nonlocality has been proved by Bell's theorem that states that all quantum theories must be nonlocal. The Bell's theorem gives a strong support to the hidden variable theory, i.e. Bohmian mechanics. Using nonlocality, we present that the velocity field of one particle can be obtained by measuring the velocity of other particles. The trajectory of these particles is perhaps surrealistic trajectory due to the nonlocality.
Nonlocal teleparallel cosmology.
Bahamonde, Sebastian; Capozziello, Salvatore; Faizal, Mir; Nunes, Rafael C
2017-01-01
Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + [Formula: see text] observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction.
Nonlocal teleparallel cosmology
Energy Technology Data Exchange (ETDEWEB)
Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Capozziello, Salvatore [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Gran Sasso Science Institute, L' Aquila (Italy); Compl. Univ. di Monte S. Angelo, Naples (Italy); INFN, Napoli (Italy); Faizal, Mir [University of British Columbia - Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada); Nunes, Rafael C. [Universidade Federal de Juiz de Fora, Departamento de Fisica, Juiz de Fora, MG (Brazil)
2017-09-15
Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + H{sub 0} observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction. (orig.)
A remark on the unitary part of contractions
International Nuclear Information System (INIS)
Duggal, B.P.
1992-07-01
Considering operators on a complex infinite dimensional Hilbert space H and denoting by T * a construction with C .O completely non-unitary part, it is proved that A T is projection which commutes with T and H (u) T = A T H. 3 refs
On nonlocality in quantum physics
International Nuclear Information System (INIS)
Spasskij, B.I.; Moskovskij, A.V.
1984-01-01
The properties of nonlocality of quantum objects are considered on the example of the Aharonov-Bohm, effect Brown-Twiss effect, Einstein-Podolsky-Rosen paradox. These effects demonstrate inherent features of specific integrity in quantum objects. The term ''nonlocality'' is considered as a ''quantum analog'' of the notion of long range. Experiments on checking the Bell inequalities for fulfilment are described. The inequalities permit to solve which of the quantum mechanics interpretations is correct either the Einstein interpretation according to which the quantum system properties exist as elements of physical reality irrespective of their observation, or the Copenhagen one, according to which the microsystem properties described by noncommuting operators do not exist irrespective of measurement means
Nonlocal hidden variables and nonlocal gauge theories
International Nuclear Information System (INIS)
Boiteux, M.
1984-01-01
A possible unification of classical fundamental interactions together with quantum interactions is proposed, based on an extension of the concept of local gauge invariance to a nonlocal gauge invariance. As an example this new concept is developed for the particular case of the electromagnetic field. (Auth.)
Glazyrina, O. V.; Pavlova, M. F.
2016-11-01
We consider the parabolic inequality with monotone with respect to a gradient space operator, which is depended on integral with respect to space variables solution characteristic. We construct a two-layer differential scheme for this problem with use of penalty method, semidiscretization with respect to time variable method and the finite element method (FEM) with respect to space variables. We proved a convergence of constructed mothod.
Unitary Root Music and Unitary Music with Real-Valued Rank Revealing Triangular Factorization
2010-06-01
AFRL-RY-WP-TP-2010-1213 UNITARY ROOT MUSIC AND UNITARY MUSIC WITH REAL-VALUED RANK REVEALING TRIANGULAR FACTORIZATION (Postprint) Nizar...DATES COVERED (From - To) June 2010 Journal Article Postprint 08 September 2006 – 31 August 2009 4. TITLE AND SUBTITLE UNITARY ROOT MUSIC AND...UNITARY MUSIC WITH REAL-VALUED RANK REVEALING TRIANGULAR FACTORIZATION (Postprint) 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA8650-05-D-1912-0007 5c
Nonlocal continuum field theories
2002-01-01
Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...
Unitary Application of the Quantum Error Correction Codes
International Nuclear Information System (INIS)
You Bo; Xu Ke; Wu Xiaohua
2012-01-01
For applying the perfect code to transmit quantum information over a noise channel, the standard protocol contains four steps: the encoding, the noise channel, the error-correction operation, and the decoding. In present work, we show that this protocol can be simplified. The error-correction operation is not necessary if the decoding is realized by the so-called complete unitary transformation. We also offer a quantum circuit, which can correct the arbitrary single-qubit errors.
On Investigating GMRES Convergence using Unitary Matrices
Czech Academy of Sciences Publication Activity Database
Duintjer Tebbens, Jurjen; Meurant, G.; Sadok, H.; Strakoš, Z.
2014-01-01
Roč. 450, 1 June (2014), s. 83-107 ISSN 0024-3795 Grant - others:GA AV ČR(CZ) M100301201; GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : GMRES convergence * unitary matrices * unitary spectra * normal matrices * Krylov residual subspace * Schur parameters Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014
Unitary symmetry, combinatorics, and special functions
Energy Technology Data Exchange (ETDEWEB)
Louck, J.D.
1996-12-31
From 1967 to 1994, Larry Biedenham and I collaborated on 35 papers on various aspects of the general unitary group, especially its unitary irreducible representations and Wigner-Clebsch-Gordan coefficients. In our studies to unveil comprehensible structures in this subject, we discovered several nice results in special functions and combinatorics. The more important of these will be presented and their present status reviewed.
Quantum Entanglement Growth under Random Unitary Dynamics
Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haah, Jeongwan
2017-07-01
Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time )1/3 and are spatially correlated over a distance ∝(time )2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.
Quantum Entanglement Growth under Random Unitary Dynamics
Directory of Open Access Journals (Sweden)
Adam Nahum
2017-07-01
Full Text Available Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ equation. The mean entanglement grows linearly in time, while fluctuations grow like (time^{1/3} and are spatially correlated over a distance ∝(time^{2/3}. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i a stochastic model of a growing surface, (ii a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.
Positive-definite functions and unitary representations of locally compact groups in a Hilbert space
International Nuclear Information System (INIS)
Gali, I.M.; Okb el-Bab, A.S.; Hassan, H.M.
1977-08-01
It is proved that the necessary and sufficient condition for the existence of an integral representation of a group of unitary operators in a Hilbert space is that it is positive-definite and continuous in some topology
A remark on the unitary group of a tensor product of n finite ...
Indian Academy of Sciences (India)
By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on the tensor product H = H 1 ⊗ H 2 ⊗ … ⊗ H n can be expressed as a composition of a finite number of unitary operators living on ...
Quantum Nonlocality and Beyond: Limits from Nonlocal Computation
Linden, Noah; Popescu, Sandu; Short, Anthony J.; Winter, Andreas
2007-11-01
We address the problem of “nonlocal computation,” in which separated parties must compute a function without any individual learning anything about the inputs. Surprisingly, entanglement provides no benefit over local classical strategies for such tasks, yet stronger nonlocal correlations allow perfect success. This provides intriguing insights into the limits of quantum information processing, the nature of quantum nonlocality, and the differences between quantum and stronger-than-quantum nonlocal correlations.
Unitary 4-point correlators from classical geometries
Energy Technology Data Exchange (ETDEWEB)
Bombini, Alessandro; Galliani, Andrea; Giusto, Stefano [Universita di Padova, Dipartimento di Fisica ed Astronomia ' ' Galileo Galilei' ' , Padua (Italy); I.N.F.N. Sezione di Padova, Padua (Italy); Moscato, Emanuele; Russo, Rodolfo [Queen Mary University of London, Centre for Research in String Theory, School of Physics and Astronomy, London (United Kingdom)
2018-01-15
We compute correlators of two heavy and two light operators in the strong coupling and large c limit of the D1D5 CFT which is dual to weakly coupled AdS{sub 3} gravity. The light operators have dimension two and are scalar descendants of the chiral primaries considered in arXiv:1705.09250, while the heavy operators belong to an ensemble of Ramond-Ramond ground states. We derive a general expression for these correlators when the heavy states in the ensemble are close to the maximally spinning ground state. For a particular family of heavy states we also provide a result valid for any value of the spin. In all cases we find that the correlators depend non-trivially on the CFT moduli and are not determined by the symmetries of the theory; however, they have the properties expected for correlators among pure states in a unitary theory, in particular they do not decay at large Lorentzian times. (orig.)
Nonlocal diffusion and applications
Bucur, Claudia
2016-01-01
Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.
New unitary affine-Virasoro constructions
International Nuclear Information System (INIS)
Halpern, M.B.; Kiritsis, E.; Obers, N.A.; Poratti, M.; Yamron, J.P.
1990-01-01
This paper reports on a quasi-systematic investigation of the Virasoro master equation. The space of all affine-Virasoro constructions is organized by K-conjugation into affine-Virasoro nests, and an estimate of the dimension of the space shows that most solutions await discovery. With consistent ansatze for the master equation, large classes of new unitary nests are constructed, including quadratic deformation nests with continuous conformal weights, and unitary irrational central charge nests, which may dominate unitary rational central charge on compact g
Time-nonlocal kinetic equations, jerk and hyperjerk in plasmas and solar physics
El-Nabulsi, Rami Ahmad
2018-06-01
The simulation and analysis of nonlocal effects in fluids and plasmas is an inherently complicated problem due to the massive breadth of physics required to describe the nonlocal dynamics. This is a multi-physics problem that draws upon various miscellaneous fields, such as electromagnetism and statistical mechanics. In this paper we strive to focus on one narrow but motivating mathematical way: the derivation of nonlocal plasma-fluid equations from a generalized nonlocal Liouville derivative operator motivated from Suykens's nonlocal arguments. The paper aims to provide a guideline toward modeling nonlocal effects occurring in plasma-fluid systems by means of a generalized nonlocal Boltzmann equation. The generalized nonlocal equations of fluid dynamics are derived and their implications in plasma-fluid systems are addressed, discussed and analyzed. Three main topics were discussed: Landau damping in plasma electrodynamics, ideal MHD and solar wind. A number of features were revealed, analyzed and confronted with recent research results and observations.
On relevant boundary perturbations of unitary minimal models
International Nuclear Information System (INIS)
Recknagel, A.; Roggenkamp, D.; Schomerus, V.
2000-01-01
We consider unitary Virasoro minimal models on the disk with Cardy boundary conditions and discuss deformations by certain relevant boundary operators, analogous to tachyon condensation in string theory. Concentrating on the least relevant boundary field, we can perform a perturbative analysis of renormalization group fixed points. We find that the systems always flow towards stable fixed points which admit no further (non-trivial) relevant perturbations. The new conformal boundary conditions are in general given by superpositions of 'pure' Cardy boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Kimura, Tetsuji [Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan); Department of Physics, Tokyo Institute of Technology,Tokyo 152-8551 (Japan); Mazumdar, Anupam [Consortium for Fundamental Physics, Physics Department, Lancaster University,Lancaster LA1 4YB (United Kingdom); Kapteyn Astronomical Institute, University of Groningen,9700 AV Groningen (Netherlands); Noumi, Toshifumi [Institute for Advanced Study, Hong Kong University of Science and Technology,Clear Water Bay (Hong Kong); Department of Physics, Kobe University,Kobe 657-8501 (Japan); Yamaguchi, Masahide [Department of Physics, Tokyo Institute of Technology,Tokyo 152-8551 (Japan)
2016-10-05
We construct N=1 supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of Kähler potential and superpotential up to quadratic order. We derive the condition in which an auxiliary field remains non-dynamical, and the dynamical scalars and fermions are free from the ghost degrees of freedom. We also investigate the nonlocal effects on the supersymmetry breaking and find that supertrace (mass) formula is significantly modified even at the tree level.
Testing nonlocal realism with entangled coherent states
International Nuclear Information System (INIS)
Paternostro, Mauro; Jeong, Hyunseok
2010-01-01
We investigate the violation of nonlocal realism using entangled coherent states (ECSs) under nonlinear operations and homodyne measurements. We address recently proposed Leggett-type inequalities, including a class of optimized incompatibility inequalities proposed by Branciard et al. [Nature Phys. 4, 681 (2008)], and thoroughly assess the effects of detection inefficiency.
The unitary space of particle internal states
International Nuclear Information System (INIS)
Perjes, Z.
1978-09-01
A relativistic theory of particle internal properties has been developed. Suppressing space-time information, internal wave functions and -observables are constructed in a 3-complex-dimensional space. The quantum numbers of a spinning point particle in this unitary space correspond with those of a low-mass hadron. Unitary space physics is linked with space-time notions via the Penrose theory of twistors, where new flavors may be represented by many-twistor systems. It is shown here that a four-twistor particle fits into the unitary space picture as a system of two points with equal masses and oppositely pointing unitary spins. Quantum states fall into the ISU(3) irreducible representations discovered by Sparling and the author. Full details of the computation involving SU(3) recoupling techniques are given. (author)
Chiral unitary theory: Application to nuclear problems
Indian Academy of Sciences (India)
Chiral unitary theory: Application to nuclear problems ... Physics Department, Nara Women University, Nara, Japan. 5 ... RCNP, Osaka University, Osaka, Japan ...... We acknowledge partial financial support from the DGICYT under contract ...
Non-unitary probabilistic quantum computing
Gingrich, Robert M.; Williams, Colin P.
2004-01-01
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.
Quantum unitary dynamics in cosmological spacetimes
International Nuclear Information System (INIS)
Cortez, Jerónimo; Mena Marugán, Guillermo A.; Velhinho, José M.
2015-01-01
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.
Quantum unitary dynamics in cosmological spacetimes
Energy Technology Data Exchange (ETDEWEB)
Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Mena Marugán, Guillermo A., E-mail: mena@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: jvelhi@ubi.pt [Departamento de Física, Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã (Portugal)
2015-12-15
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.
Probabilistic implementation of Hadamard and unitary gates
International Nuclear Information System (INIS)
Song Wei; Yang Ming; Cao Zhuoliang
2004-01-01
We show that the Hadamard and unitary gates could be implemented by a unitary evolution together with a measurement for any unknown state chosen from a set A={ vertical bar Ψi>, vertical bar Ψ-bar i>} (i=1,2) if and only if vertical bar Ψ1>, vertical bar Ψ2>, vertical bar Ψ-bar 1>, vertical bar Ψ-bar 2> are linearly independent. We also derive the best transformation efficiencies
Unitary representations of basic classical Lie superalgebras
International Nuclear Information System (INIS)
Gould, M.D.; Zhang, R.B.
1990-01-01
We have obtained all the finite-dimensional unitary irreps of gl(mvertical stroken) and C(n), which also exhaust such irreps of all the basic classical Lie superalgebras. The lowest weights of such irreps are worked out explicitly. It is also shown that the contravariant and covariant tensor irreps of gl(mvertical stroken) are unitary irreps of type (1) and type (2) respectively, explaining the applicability of the Young diagram method to these two types of tensor irreps. (orig.)
Unitary transformations in solid state physics
International Nuclear Information System (INIS)
Wagner, M.
1986-01-01
The main emphasis of this book is on the practical application of unitary transformations to problems in solid state physics. This is a method used in the field of nonadiabatic electron-phonon phenomena where the Born-Oppenheimer approximation is no longer applicable. The book is intended as a tool for those who want to apply unitary transformations quickly and on a more elementary level and also for those who want to use this method for more involved problems. The book is divided into 6 chapters. The first three chapters are concerned with presenting quick applications of unitary transformations and chapter 4 presents a more systematic procedure. The last two chapters contain the major known examples of the utilization of unitary transformations in solid state physics, including such highlights as the Froehlich and the Fulton-Gouterman transformations. The book is supplemented by extended tables of unitary transformations, whose properties and peculiarities are also listed. This tabulated material is unique and will be of great practical use to those applying the method of unitary transformations in their work. (Auth.)
Optimal quantum learning of a unitary transformation
International Nuclear Information System (INIS)
Bisio, Alessandro; Chiribella, Giulio; D'Ariano, Giacomo Mauro; Facchini, Stefano; Perinotti, Paolo
2010-01-01
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary with maximum fidelity. Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine) and subsequently retrieving it. We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a 'measure-and-rotate' retrieving. Differing from the case of quantum cloning, where the incoherent 'measure-and-prepare' strategies are typically suboptimal, in the case of learning the 'measure-and-rotate' strategy is optimal even when the learning machine is asked to reproduce a single copy of the unknown unitary. We finally address the problem of the optimal inversion of an unknown unitary evolution, showing also in this case the optimality of the 'measure-and-rotate' strategies and applying our result to the optimal approximate realignment of reference frames for quantum communication.
Random unitary evolution model of quantum Darwinism with pure decoherence
Balanesković, Nenad
2015-10-01
We study the behavior of Quantum Darwinism [W.H. Zurek, Nat. Phys. 5, 181 (2009)] within the iterative, random unitary operations qubit-model of pure decoherence [J. Novotný, G. Alber, I. Jex, New J. Phys. 13, 053052 (2011)]. We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system S from the point of view of its environment E, is not a generic phenomenon, but depends on the specific form of input states and on the type of S-E-interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial input states of environment E that allow to store information about an open system S of interest with maximal efficiency.
The unitary conformal field theory behind 2D Asymptotic Safety
Energy Technology Data Exchange (ETDEWEB)
Nink, Andreas; Reuter, Martin [Institute of Physics, PRISMA & MITP, Johannes Gutenberg University Mainz,Staudingerweg 7, D-55099 Mainz (Germany)
2016-02-25
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in d>2 dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge c=25. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d>2 dimensions and Polyakov’s induced gravity action in two dimensions.
Entanglement entropy of non-unitary integrable quantum field theory
Directory of Open Access Journals (Sweden)
Davide Bianchini
2015-07-01
Full Text Available In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee–Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by ceff3logℓ where ceff is the effective central charge of the theory (a positive number related to the central charge and ℓ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum, it appears to be much more model-dependent for non-unitary models.
International Nuclear Information System (INIS)
Efimov, G.V.
1976-01-01
The basic ideas for creating the theory of nonlocal interactions of a scalar one-component field are presented. Lagrangian describing a non-interacting field is the ordinary one so that non-interacting particles are described by standard methods of the Fock space. Form factors introduced have been chosen from a class of analytic functionals and quantized. Conditions of microcausality have been considered in detail. The convergence of all integrals corresponding to the arbitrary Feynman diagrams in spinor electrodynamics is guaranteed in the frame of the rules formulated. It is noted in conclusion that the spinor electrodynamics with nonlocal interaction contains no ultraviolet divergencies and satisfies all the requirements of the quantum field theory; in this sense it is mathematically more consistent than its local version
Nonlocal transformation optics.
Castaldi, Giuseppe; Galdi, Vincenzo; Alù, Andrea; Engheta, Nader
2012-02-10
We show that the powerful framework of transformation optics may be exploited for engineering the nonlocal response of artificial electromagnetic materials. Relying on the form-invariant properties of coordinate-transformed Maxwell's equations in the spectral domain, we derive the general constitutive "blueprints" of transformation media yielding prescribed nonlocal field-manipulation effects and provide a physically incisive and powerful geometrical interpretation in terms of deformation of the equifrequency contours. In order to illustrate the potentials of our approach, we present an example of application to a wave-splitting refraction scenario, which may be implemented via a simple class of artificial materials. Our results provide a systematic and versatile framework which may open intriguing venues in dispersion engineering of artificial materials.
Configurable unitary transformations and linear logic gates using quantum memories.
Campbell, G T; Pinel, O; Hosseini, M; Ralph, T C; Buchler, B C; Lam, P K
2014-08-08
We show that a set of optical memories can act as a configurable linear optical network operating on frequency-multiplexed optical states. Our protocol is applicable to any quantum memories that employ off-resonant Raman transitions to store optical information in atomic spins. In addition to the configurability, the protocol also offers favorable scaling with an increasing number of modes where N memories can be configured to implement arbitrary N-mode unitary operations during storage and readout. We demonstrate the versatility of this protocol by showing an example where cascaded memories are used to implement a conditional cz gate.
International Nuclear Information System (INIS)
Partovi, M.H.
1982-01-01
From a generalization of the covariant derivative, nonlocal gauge theories are developed. These theories enjoy local gauge invariance and associated Ward identities, a corresponding locally conserved current, and a locally conserved energy-momentum tensor, with the Ward identities implying the masslessness of the gauge field as in local theories. Their ultraviolet behavior allows the presence as well as the absence of the Adler-Bell-Jackiw anomaly, the latter in analogy with lattice theories
Experimental many-pairs nonlocality
Poh, Hou Shun; Cerè, Alessandro; Bancal, Jean-Daniel; Cai, Yu; Sangouard, Nicolas; Scarani, Valerio; Kurtsiefer, Christian
2017-08-01
Collective measurements on large quantum systems together with a majority voting strategy can lead to a violation of the Clauser-Horne-Shimony-Holt Bell inequality. In the presence of many entangled pairs, this violation decreases quickly with the number of pairs and vanishes for some critical pair number that is a function of the noise present in the system. Here we show that a different binning strategy can lead to a more substantial Bell violation when the noise is sufficiently small. Given the relation between the critical pair number and the source noise, we then present an experiment where the critical pair number is used to quantify the quality of a high visibility photon pair source. Our results demonstrate nonlocal correlations using collective measurements operating on clusters of more than 40 photon pairs.
How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
Cortazar, C.; Elgueta, M.; Rossi, J. D.; Wolanski, N.
2006-01-01
We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.
Multipartite fully nonlocal quantum states
International Nuclear Information System (INIS)
Almeida, Mafalda L.; Cavalcanti, Daniel; Scarani, Valerio; Acin, Antonio
2010-01-01
We present a general method for characterizing the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully nonlocal according to a given partition, as well as being (genuinely) multipartite fully nonlocal, are derived. These conditions allow us to identify all completely connected graph states as multipartite fully nonlocal quantum states. Moreover, we show that this feature can also be observed in mixed states: the tensor product of five copies of the Smolin state, a biseparable and bound entangled state, is multipartite fully nonlocal.
Nonlocal gravity. Conceptual aspects and cosmological predictions
Belgacem, Enis; Dirian, Yves; Foffa, Stefano; Maggiore, Michele
2018-03-01
Even if the fundamental action of gravity is local, the corresponding quantum effective action, that includes the effect of quantum fluctuations, is a nonlocal object. These nonlocalities are well understood in the ultraviolet regime but much less in the infrared, where they could in principle give rise to important cosmological effects. Here we systematize and extend previous work of our group, in which it is assumed that a mass scale Λ is dynamically generated in the infrared, giving rise to nonlocal terms in the quantum effective action of gravity. We give a detailed discussion of conceptual aspects related to nonlocal gravity (including causality, degrees of freedom, ambiguities related to the boundary conditions of the nonlocal operator, scenarios for the emergence of a dynamical scale in the infrared) and of the cosmological consequences of these models. The requirement of providing a viable cosmological evolution severely restricts the form of the nonlocal terms, and selects a model (the so-called RR model) that corresponds to a dynamical mass generation for the conformal mode. For such a model: (1) there is a FRW background evolution, where the nonlocal term acts as an effective dark energy with a phantom equation of state, providing accelerated expansion without a cosmological constant. (2) Cosmological perturbations are well behaved. (3) Implementing the model in a Boltzmann code and comparing with observations we find that the RR model fits the CMB, BAO, SNe, structure formation data and local H0 measurements at a level statistically equivalent to ΛCDM. (4) Bayesian parameter estimation shows that the value of H0 obtained in the RR model is higher than in ΛCDM, reducing to 2.0σ the tension with the value from local measurements. (5) The RR model provides a prediction for the sum of neutrino masses that falls within the limits set by oscillation and terrestrial experiments (in contrast to ΛCDM, where letting the sum of neutrino masses vary as a free
Multiqubit Clifford groups are unitary 3-designs
Zhu, Huangjun
2017-12-01
Unitary t -designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum process tomography, and scrambling. Despite the intensive efforts of many researchers, little is known about unitary t -designs with t ≥3 in the literature. We show that the multiqubit Clifford group in any even prime-power dimension is not only a unitary 2-design, but also a 3-design. Moreover, it is a minimal 3-design except for dimension 4. As an immediate consequence, any orbit of pure states of the multiqubit Clifford group forms a complex projective 3-design; in particular, the set of stabilizer states forms a 3-design. In addition, our study is helpful in studying higher moments of the Clifford group, which are useful in many research areas ranging from quantum information science to signal processing. Furthermore, we reveal a surprising connection between unitary 3-designs and the physics of discrete phase spaces and thereby offer a simple explanation of why no discrete Wigner function is covariant with respect to the multiqubit Clifford group, which is of intrinsic interest in studying quantum computation.
Remarks on unitary representations of Poincare group
International Nuclear Information System (INIS)
Burzynski, A.
1979-01-01
In this paper the elementary review of methods and notions using in the theory of unitary representations of Poincare group is included. The Poincare group is a basic group for relativistic quantum mechanics. Our aim is to introduce the reader into some problems of quantum physics, which are difficult approachable for beginners. (author)
Generalized unitaries and the Picard group
Indian Academy of Sciences (India)
some explicit calculations of that type.) So the range of this .... when we restrict our attention to generalized unitaries and full modules, that is, to modules. E for which BE = B. For every ..... without dividing out equivalence classes. But there is no ...
Unitary information ether and its possible applications
International Nuclear Information System (INIS)
Horodecki, R.
1991-01-01
The idea of information ether as the unitary information field is developed. It rests on the assumption that the notion of information is a fundamental category in the description of reality and that it can be defined independently from the notion of probability itself. It is shown that the information ether provides a deterministic background for the nonlinear wave hypothesis and quantum cybernetics. (orig.)
Boundary fluxes for non-local diffusion
Cortazar, C.; Elgueta, M.; Rossi, J. D.; Wolanski, N.
2006-01-01
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.
Entanglement without nonlocality
International Nuclear Information System (INIS)
Hewitt-Horsman, C.; Vedral, V.
2007-01-01
We consider the characterization of entanglement from the perspective of a Heisenberg formalism. We derive a two-party generalized separability criterion, and from this describe a physical understanding of entanglement. We find that entanglement may be considered as fundamentally a local effect, and therefore as a separate computational resource from nonlocality. We show how entanglement differs from correlation physically, and explore the implications of this concept of entanglement for the notion of classicality. We find that this understanding of entanglement extends naturally to multipartite cases
Polynomial approximation of non-Gaussian unitaries by counting one photon at a time
Arzani, Francesco; Treps, Nicolas; Ferrini, Giulia
2017-05-01
In quantum computation with continuous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the laboratory. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.
Microscopic entropy and nonlocality
International Nuclear Information System (INIS)
Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.
2003-01-01
We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper
Extent of multiparticle quantum nonlocality
International Nuclear Information System (INIS)
Jones, Nick S.; Linden, Noah; Massar, Serge
2005-01-01
It is well known that entangled quantum states are nonlocal: the corrrelations between local measurements carried out on these states cannot be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are more nonlocal than bipartite ones in the sense that even some nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely, we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalizes work of Svetlichny and others in which it was showed that a particular class of classical nonlocal models, the 'separable' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition
Optimal unitary dilation for bosonic Gaussian channels
International Nuclear Information System (INIS)
Caruso, Filippo; Eisert, Jens; Giovannetti, Vittorio; Holevo, Alexander S.
2011-01-01
A general quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. In this paper the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multimode bosonic Gaussian channel is analyzed for both pure and mixed environments. We compute this quantity in the case of pure environment corresponding to the Stinespring representation and give an improved estimate in the case of mixed environment. The computations rely, on one hand, on the properties of the generalized Choi-Jamiolkowski state and, on the other hand, on an explicit construction of the minimal dilation for arbitrary bosonic Gaussian channel. These results introduce a new quantity reflecting ''noisiness'' of bosonic Gaussian channels and can be applied to address some issues concerning transmission of information in continuous variables systems.
Black hole thermodynamics based on unitary evolutions
International Nuclear Information System (INIS)
Feng, Yu-Lei; Chen, Yi-Xin
2015-01-01
In this paper, we try to construct black hole thermodynamics based on the fact that the formation and evaporation of a black hole can be described by quantum unitary evolutions. First, we show that the Bekenstein–Hawking entropy S BH may not be a Boltzmann or thermal entropy. To confirm this statement, we show that the original black hole's ‘first law’ may not simply be treated as the first law of thermodynamics formally, due to some missing metric perturbations caused by matter. Then, by including those (quantum) metric perturbations, we show that the black hole formation and evaporation can be described effectively in a unitary manner, through a quantum channel between the exterior and interior of the event horizon. In this way, the paradoxes of information loss and firewall can be resolved effectively. Finally, we show that black hole thermodynamics can be constructed in an ordinary way, by constructing statistical mechanics. (paper)
Li, Yanna; Gessner, Manuel; Li, Weidong; Smerzi, Augusto
2018-02-01
The controlled generation and identification of quantum correlations, usually encoded in either qubits or continuous degrees of freedom, builds the foundation of quantum information science. Recently, more sophisticated approaches, involving a combination of two distinct degrees of freedom, have been proposed to improve on the traditional strategies. Hyperentanglement describes simultaneous entanglement in more than one distinct degree of freedom, whereas hybrid entanglement refers to entanglement shared between a discrete and a continuous degree of freedom. In this work we propose a scheme that allows us to combine the two approaches, and to extend them to the strongest form of quantum correlations. Specifically, we show how two identical, initially separated particles can be manipulated to produce Bell nonlocality among their spins, among their momenta, as well as across their spins and momenta. We discuss possible experimental realizations with atomic and photonic systems.
Biased Monte Carlo algorithms on unitary groups
International Nuclear Information System (INIS)
Creutz, M.; Gausterer, H.; Sanielevici, S.
1989-01-01
We introduce a general updating scheme for the simulation of physical systems defined on unitary groups, which eliminates the systematic errors due to inexact exponentiation of algebra elements. The essence is to work directly with group elements for the stochastic noise. Particular cases of the scheme include the algorithm of Metropolis et al., overrelaxation algorithms, and globally corrected Langevin and hybrid algorithms. The latter are studied numerically for the case of SU(3) theory
International Nuclear Information System (INIS)
Klimko, G.T.; Luzanov, A.V.
1988-01-01
An analysis has been made of the problem of calculating one- and two-particle spin densities, which are needed in calculations of spin-orbit and spin-spin coupling. The proposed solution is oriented toward the application of computational algorithms using unitary group representations; the solution consists of explicit expressions for the matrix elements of spin density operators in terms of the means of products of spin-free generators. This has eliminated a serious problem encountered previously in determining spin characteristics of molecules within the framework of unitary formalism
How many invariant polynomials are needed to decide local unitary equivalence of qubit states?
International Nuclear Information System (INIS)
Maciążek, Tomasz; Oszmaniec, Michał; Sawicki, Adam
2013-01-01
Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure
Nonlocal heat transfer in nanostructures
International Nuclear Information System (INIS)
Kanavin, A.P.; Uryupin, S.A.
2008-01-01
Kinetics of electrons in a degenerate conductor heated up by absorption of a high-frequency field localized in a region of about hundred nanometers has been studied. A new law for nonlocal electron thermal flux has been predicted
Fundamental length, bubble electrons and non-local quantum electrodynamics
International Nuclear Information System (INIS)
Hsu, J.P.; Mac, E.
1977-06-01
Based on the concept of a bubble electron and the approach of Pais and Uhlenbeck, one constructs a finite quantum electrodynamics which is relativistically invariant, macro-causal and unitary. In this model, fields and their interaction are local, but the action function of free fields is nonlocal. The propagators are modified so that a fundamental length L is naturally introduced to physics. The modified static potential is given by V(r) = e/r for r greater than L and V(r) = 0 for r less than L, which is produced by the bubble source r -1 ddelta(r-L)/dr rather than a point source. It is found that L less than 4 x 10 -15 cm. Experimental consequences and modifications of strict causality at short distances, vertical bars 2 vertical bar approximately L 2 , are discussed
Nonlocal gravity simulates dark matter
Hehl, Friedrich W.; Mashhoon, Bahram
2009-01-01
A nonlocal generalization of Einstein's theory of gravitation is constructed within the framework of the translational gauge theory of gravity. In the linear approximation, the nonlocal theory can be interpreted as linearized general relativity but in the presence of "dark matter" that can be simply expressed as an integral transform of matter. It is shown that this approach can accommodate the Tohline-Kuhn treatment of the astrophysical evidence for dark matter.
Energy Technology Data Exchange (ETDEWEB)
Luis, Alfredo [Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, 28040 Madrid (Spain)
2003-01-10
In a recent paper in this journal Fan (Fan H 2002 J. Phys. A: Math. Gen.35 1007) discards the possibility of using a genuine phase-difference operator to investigate number-phase entanglement because of the lack of unitarity of the Susskind-Glogower phase operators. However, Fan overlooked the existence of a bona fide unitary operator exponential of the phase difference. Here we find the amplitude-phase maximally entangled states as the simultaneous eigenstates of the total number and the phase-difference operators. (comment)
Luis, A
2003-01-01
In a recent paper in this journal Fan (Fan H 2002 J. Phys. A: Math. Gen.35 1007) discards the possibility of using a genuine phase-difference operator to investigate number-phase entanglement because of the lack of unitarity of the Susskind-Glogower phase operators. However, Fan overlooked the existence of a bona fide unitary operator exponential of the phase difference. Here we find the amplitude-phase maximally entangled states as the simultaneous eigenstates of the total number and the phase-difference operators. (comment)
The virial equation of state for unitary fermion thermodynamics with non-Gaussian correlations
International Nuclear Information System (INIS)
Chen Jisheng; Li Jiarong; Wang Yanping; Xia Xiangjun
2008-01-01
We study the roles of the dynamical high order perturbation and statistically non-linear infrared fluctuation/correlation in the virial equation of state for the Fermi gas in the unitary limit. Incorporating the quantum level crossing rearrangement effects, the spontaneously generated entropy departing from the mean-field theory formalism leads to concise thermodynamical expressions. The dimensionless virial coefficients with complex non-local correlations are calculated up to the fourth order for the first time. The virial coefficients of unitary Fermi gas are found to be proportional to those of the ideal quantum gas with integer ratios through a general term formula. Counterintuitively, contrary to those of the ideal bosons (a (0) 2 =-(1/4√2)) or fermions (a (0) 2 =(1/4√2)), the second virial coefficient a 2 of Fermi gas at unitarity is found to be equal to zero. With the vanishing leading order quantum correction, the BCS–BEC crossover thermodynamics manifests the famous pure classical Boyle's law in the Boltzmann regime. The non-Gaussian correlation phenomena can be validated by studying the Joule–Thomson effect
Nonlocal Intracranial Cavity Extraction
Manjón, José V.; Eskildsen, Simon F.; Coupé, Pierrick; Romero, José E.; Collins, D. Louis; Robles, Montserrat
2014-01-01
Automatic and accurate methods to estimate normalized regional brain volumes from MRI data are valuable tools which may help to obtain an objective diagnosis and followup of many neurological diseases. To estimate such regional brain volumes, the intracranial cavity volume (ICV) is often used for normalization. However, the high variability of brain shape and size due to normal intersubject variability, normal changes occurring over the lifespan, and abnormal changes due to disease makes the ICV estimation problem challenging. In this paper, we present a new approach to perform ICV extraction based on the use of a library of prelabeled brain images to capture the large variability of brain shapes. To this end, an improved nonlocal label fusion scheme based on BEaST technique is proposed to increase the accuracy of the ICV estimation. The proposed method is compared with recent state-of-the-art methods and the results demonstrate an improved performance both in terms of accuracy and reproducibility while maintaining a reduced computational burden. PMID:25328511
Nonlocal Intracranial Cavity Extraction
Directory of Open Access Journals (Sweden)
José V. Manjón
2014-01-01
Full Text Available Automatic and accurate methods to estimate normalized regional brain volumes from MRI data are valuable tools which may help to obtain an objective diagnosis and followup of many neurological diseases. To estimate such regional brain volumes, the intracranial cavity volume (ICV is often used for normalization. However, the high variability of brain shape and size due to normal intersubject variability, normal changes occurring over the lifespan, and abnormal changes due to disease makes the ICV estimation problem challenging. In this paper, we present a new approach to perform ICV extraction based on the use of a library of prelabeled brain images to capture the large variability of brain shapes. To this end, an improved nonlocal label fusion scheme based on BEaST technique is proposed to increase the accuracy of the ICV estimation. The proposed method is compared with recent state-of-the-art methods and the results demonstrate an improved performance both in terms of accuracy and reproducibility while maintaining a reduced computational burden.
Quantum reading of unitary optical devices
International Nuclear Information System (INIS)
Dall'Arno, Michele; Bisio, Alessandro; D'Ariano, Giacomo Mauro
2014-01-01
We address the problem of quantum reading of optical memories, namely the retrieving of classical information stored in the optical properties of a media with minimum energy. We present optimal strategies for ambiguous and unambiguous quantum reading of unitary optical memories, namely when one's task is to minimize the probability of errors in the retrieved information and when perfect retrieving of information is achieved probabilistically, respectively. A comparison of the optimal strategy with coherent probes and homodyne detection shows that the former saves orders of magnitude of energy when achieving the same performances. Experimental proposals for quantum reading which are feasible with present quantum optical technology are reported
Towards LHC physics with nonlocal Standard Model
Energy Technology Data Exchange (ETDEWEB)
Biswas, Tirthabir, E-mail: tbiswas@loyno.edu [Department of Physics, Loyola University, 6363 St. Charles Avenue, Box 92, New Orleans, LA 70118 (United States); Okada, Nobuchika, E-mail: okadan@ua.edu [Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487-0324 (United States)
2015-09-15
We take a few steps towards constructing a string-inspired nonlocal extension of the Standard Model. We start by illustrating how quantum loop calculations can be performed in nonlocal scalar field theory. In particular, we show the potential to address the hierarchy problem in the nonlocal framework. Next, we construct a nonlocal abelian gauge model and derive modifications of the gauge interaction vertex and field propagators. We apply the modifications to a toy version of the nonlocal Standard Model and investigate collider phenomenology. We find the lower bound on the scale of nonlocality from the 8 TeV LHC data to be 2.5–3 TeV.
On the Activation of Quantum Nonlocality
Directory of Open Access Journals (Sweden)
Andrés Felipe Ducuara
2016-05-01
Full Text Available We report on some quantum properties of physical systems, namely, entanglement, nonlocality, k-copy nonlocality (superactivation of nonlocality, hidden nonlocality (activation of nonlocality through local filtering and the activation of nonlocality through tensoring and local filtering. The aim of this work is two-fold. First, we provide a review of the numerical procedures that must be followed in order to calculate the aforementioned properties, in particular, for any two-qubit system, and reproduce the bounds for two-qudit Werner states. Second, we use such numerical tools to calculate new bounds of these properties for two-qudit Isotropic states and two-qubit Hirsch states.
Unitary Transformations in 3 D Vector Representation of Qutrit States
2018-03-12
ARL-TR-8330 ● MAR 2018 US Army Research Laboratory Unitary Transformations in 3- D Vector Representation of Qutrit States by...return it to the originator. ARL-TR-8330 ● MAR 2018 US Army Research Laboratory Unitary Transformations in 3- D Vector...2018 2. REPORT TYPE Technical Report 3. DATES COVERED June–December 2017 4. TITLE AND SUBTITLE Unitary Transformations in 3- D Vector
Meditations on the unitary rhythm of dying-grieving.
Malinski, Violet M
2012-07-01
When someone faces loss of a loved one, that person simultaneously grieves and dies a little, just as the one dying also grieves. The author's personal conceptualization of dying and grieving as a unitary rhythm is explored based primarily on her interpretation of Rogers' science of unitary human beings, along with selected examples from related nursing literature and from the emerging focus on continuing bonds in other disciplines. Examples from contemporary songwriters that depict such a unitary conceptualization are given along with personal examples. The author concludes with her description of the unitary rhythm of dying-grieving.
Moduli spaces of unitary conformal field theories
International Nuclear Information System (INIS)
Wendland, K.
2000-08-01
We investigate various features of moduli spaces of unitary conformal field theories. A geometric characterization of rational toroidal conformal field theories in arbitrary dimensions is presented and discussed in relation to singular tori and those with complex multiplication. We study the moduli space M 2 of unitary two-dimensional conformal field theories with central charge c = 2. All the 26 non-exceptional non-isolated irreducible components of M 2 are constructed that may be obtained by an orbifold procedure from toroidal theories. The parameter spaces and partition functions are calculated explicitly. All multicritical points and lines are determined, such that all but three of these 26 components are directly or indirectly connected to the space of toroidal theories in M 2 . Relating our results to those by Dixon, Ginsparg, Harvey on the classification of c = 3/2 superconformal field theories, we give geometric interpretations to all non-isolated orbifolds discussed by them and correct their statements on multicritical points within the moduli space of c = 3/2 superconformal field theories. In the main part of this work, we investigate the moduli space M of N = (4, 4) superconformal field theories with central charge c = 6. After a slight emendation of its global description we give generic partition functions for models contained in M. We explicitly determine the locations of various known models in the component of M associated to K3 surfaces
Electrovacuum solutions in nonlocal gravity
Fernandes, Karan; Mitra, Arpita
2018-05-01
We consider the coupling of the electromagnetic field to a nonlocal gravity theory comprising of the Einstein-Hilbert action in addition to a nonlocal R □-2R term associated with a mass scale m . We demonstrate that in the case of the minimally coupled electromagnetic field, real corrections about the Reissner-Nordström background only exist between the inner Cauchy horizon and the event horizon of the black hole. This motivates us to consider the modified coupling of electromagnetism to this theory via the Kaluza ansatz. The Kaluza reduction introduces nonlocal terms involving the electromagnetic field to the pure gravitational nonlocal theory. An iterative approach is provided to perturbatively solve the equations of motion to arbitrary order in m2 about any known solution of general relativity. We derive the first-order corrections and demonstrate that the higher order corrections are real and perturbative about the external background of a Reissner-Nordström black hole. We also discuss how the Kaluza reduced action, through the inclusion of nonlocal electromagnetic fields, could also be relevant in quantum effects on curved backgrounds with horizons.
Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble
Berggren, Tomas; Duits, Maurice
2017-09-01
In this paper we study the asymptotic behavior of mesoscopic fluctuations for the thinned Circular Unitary Ensemble. The effect of thinning is that the eigenvalues start to decorrelate. The decorrelation is stronger on the larger scales than on the smaller scales. We investigate this behavior by studying mesoscopic linear statistics. There are two regimes depending on the scale parameter and the thinning parameter. In one regime we obtain a CLT of a classical type and in the other regime we retrieve the CLT for CUE. The two regimes are separated by a critical line. On the critical line the limiting fluctuations are no longer Gaussian, but described by infinitely divisible laws. We argue that this transition phenomenon is universal by showing that the same transition and their laws appear for fluctuations of the thinned sine process in a growing box. The proofs are based on a Riemann-Hilbert problem for integrable operators.
Unitary pole approximations and expansions in few-body systems
International Nuclear Information System (INIS)
Casel, A.; Haberzettl, H.; Sandhas, W.
1982-01-01
The unitary pole approximations or expansions of the two-body subsystem operators are well known, and particularly efficient and practical, methods to reduce the three-body problem to an effective two-body theory. In the present investigation we develop generalizations of these approximation techniques to the subsystem amplitudes of problems with higher particle numbers. They are based on the expansion of effective potentials which, in contrast to the genuine two-body interactions, are now energy dependent. Despite this feature our generalizations require only energy independent form factors, thus preserving one of the essential advantages of the genuine two-body approach. The application of these techniques to the four-body case is discussed in detail
Nonlocal symmetries and nonlocal conservation laws of Maxwell's equations
International Nuclear Information System (INIS)
Anco, S.C.; Bluman, G.
1997-01-01
Nonlocal symmetries are obtained for Maxwell's equations in three space-time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the constants of motion arising from local conservation laws for space-time symmetries. These nine constants of motion represent additional conserved quantities for the electromagnetic field in three space endash time dimensions. copyright 1997 American Institute of Physics
Stable rotating dipole solitons in nonlocal media
DEFF Research Database (Denmark)
Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.
2006-01-01
We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons.......We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons....
Certifying the absence of quantum nonlocality
Miller, Carl A.; Shi, Yaoyun
2016-01-01
Quantum nonlocality is an inherently non-classical feature of quantum mechanics and manifests itself through violation of Bell inequalities for nonlocal games. We show that in a fairly general setting, a simple extension of a nonlocal game can certify instead the absence of quantum nonlocality. Through contraposition, our result implies that a super-classical performance for such a game ensures that a player's output is unpredictable to the other player. Previously such output unpredictabilit...
Non-locality of non-Abelian anyons
International Nuclear Information System (INIS)
Brennen, G K; Iblisdir, S; Pachos, J K; Slingerland, J K
2009-01-01
Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.
Non-locality of non-Abelian anyons
Brennen, G. K.; Iblisdir, S.; Pachos, J. K.; Slingerland, J. K.
2009-10-01
Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.
Bell inequality, nonlocality and analyticity
International Nuclear Information System (INIS)
Socolovsky, M.
2003-01-01
The Bell and the Clauser-Horne-Shimony-Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein-Podolsky-Rosen-Bohm experiments for spin ((1)/(2)) particles and photons, in both the deterministic and stochastic cases. Therefore, the theoretical and experimental violation of the inequalities by quantum mechanics excludes all hidden variables theories with that kind of nonlocality. In particular, real analyticity leads to negative definite correlations, in contradiction with quantum mechanics
Bell inequality, nonlocality and analyticity
Energy Technology Data Exchange (ETDEWEB)
Socolovsky, M
2003-09-15
The Bell and the Clauser-Horne-Shimony-Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein-Podolsky-Rosen-Bohm experiments for spin ((1)/(2)) particles and photons, in both the deterministic and stochastic cases. Therefore, the theoretical and experimental violation of the inequalities by quantum mechanics excludes all hidden variables theories with that kind of nonlocality. In particular, real analyticity leads to negative definite correlations, in contradiction with quantum mechanics.
Modulational instability in nonlocal nonlinear Kerr media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens
2001-01-01
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function. For a defoc...
Optical Beams in Nonlocal Nonlinear Media
DEFF Research Database (Denmark)
Królikowski, W.; Bang, Ole; Wyller, J.
2003-01-01
We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons....
On a nonlocal Cauchy problem for differential inclusions
Directory of Open Access Journals (Sweden)
Y. G. Sficas
2004-05-01
Full Text Available We establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values.
Perfect state transfer in unitary Cayley graphs over local rings
Directory of Open Access Journals (Sweden)
Yotsanan Meemark
2014-12-01
Full Text Available In this work, using eigenvalues and eigenvectors of unitary Cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing PST occurring in its unitary Cayley graph. Moreover, we have some developments when $R$ is a product of local rings.
Unitary Quantum Relativity. (Work in Progress)
Finkelstein, David Ritz
2017-01-01
A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.
Nonlocal Response in Plasmonic Nanostructures
DEFF Research Database (Denmark)
Wubs, Martijn; Mortensen, N. Asger
2016-01-01
After a brief overview of nanoplasmonics experiments that defy explanation with classical electrodynamics, we introduce nonlocal response as a main reason for non-classical effects. This concept is first introduced phenomenologically, and afterwards based on the semi-classical hydrodynamic Drude...
Quantum nonlocality does not exist.
Tipler, Frank J
2014-08-05
Quantum nonlocality is shown to be an artifact of the Copenhagen interpretation, in which each observed quantity has exactly one value at any instant. In reality, all physical systems obey quantum mechanics, which obeys no such rule. Locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the many-worlds interpretation (MWI). Using the MWI, I show that the quantum side of Bell's inequality, generally believed nonlocal, is really due to a series of three measurements (not two as in the standard, oversimplified analysis), all three of which have only local effects. Thus, experiments confirming "nonlocality" are actually confirming the MWI. The mistaken interpretation of nonlocality experiments depends crucially on a question-begging version of the Born interpretation, which makes sense only in "collapse" versions of quantum theory, about the meaning of the modulus of the wave function, so I use the interpretation based on the MWI, namely that the wave function is a world density amplitude, not a probability amplitude. This view allows the Born interpretation to be derived directly from the Schrödinger equation, by applying the Schrödinger equation to both the observed and the observer.
Nonlocal quasilinear damped differential inclusions
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2002-01-01
Full Text Available In this paper we investigate the existence of mild solutions to second order initial value problems for a class of damped differential inclusions with nonlocal conditions. By using suitable fixed point theorems, we study the case when the multivalued map has convex and nonconvex values.
Nonlocal interactions and Bell's inequality
International Nuclear Information System (INIS)
Garuccio, A.; Selleri, F.
1976-01-01
It is shown that natural extensions of the local hidden variable theories to include nonlocal effects still lead to a full validity of Bell's inequality. It is conjectured that the essential point expressed by this inequality is not locality, but the wave-particle dualism
Extreme nonlocality with one photon
Energy Technology Data Exchange (ETDEWEB)
Heaney, Libby; Vedral, Vlatko [Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU (United Kingdom); Cabello, Adan [Departamento de Fisica Aplicada II, Universidad de Sevilla, E-41012 Sevilla (Spain); Santos, Marcelo Franca, E-mail: l.heaney1@physics.ox.ac.uk, E-mail: adan@us.es [Departamento de Fisica, Universidade Federal de Minas Gerais, Belo Horizonte, Caixa Postal 702, 30123-970, MG (Brazil)
2011-05-15
Quantum nonlocality is typically assigned to systems of two or more well-separated particles, but nonlocality can also exist in systems consisting of just a single particle when one considers the subsystems to be distant spatial field modes. Single particle nonlocality has been confirmed experimentally via a bipartite Bell inequality. In this paper, we introduce an N-party Hardy-like proof of the impossibility of local elements of reality and a Bell inequality for local realistic theories in the case of a single particle superposed symmetrically over N spatial field modes (i.e. N qubit W state). We show that, in the limit of large N, the Hardy-like proof effectively becomes an all-versus-nothing (or Greenberger-Horne-Zeilinger (GHZ)-like) proof, and the quantum-classical gap of the Bell inequality tends to be the same as that in a three-particle GHZ experiment. We describe how to test the nonlocality in realistic systems.
Global existence of weak solutions to dissipative transport equations with nonlocal velocity
Bae, Hantaek; Granero-Belinchón, Rafael; Lazar, Omar
2018-04-01
We consider 1D dissipative transport equations with nonlocal velocity field: where is a nonlocal operator given by a Fourier multiplier. We especially consider two types of nonlocal operators: (1) , the Hilbert transform, (2) . In this paper, we show several global existence of weak solutions depending on the range of γ, δ and α. When , we take initial data having finite energy, while we take initial data in weighted function spaces (in the real variables or in the Fourier variables), which have infinite energy, when .
Directory of Open Access Journals (Sweden)
Dhakne Machindra B.
2017-04-01
Full Text Available In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.
Prats, J. M.; Lopez-Aguilar, F.
1996-01-01
Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged excitations. In this way, we obtain an effective Hamiltonian which, for small couplings, consists in a kinetic term for conduction electrons and holes, an RKKY-like term, and a renormalized Kondo interaction. The physical picture of the system implied by this ...
2016 CIME Course on Nonlocal and Nonlinear Diffusions and Interactions : New Methods and Directions
Grillo, Gabriele
2017-01-01
Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.
Fractional diffusion models of nonlocal transport
International Nuclear Information System (INIS)
Castillo-Negrete, D. del
2006-01-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments
Constructing a unitary title regime for the European Patent System
Rodriguez, V.F.
2011-01-01
The European Patent System without any unitary title allows Member States to retain institutional arrangements within their borders and to prevent any moves to delegate responsibility outside the national sphere. This intergovernmental patent regime suffers from fragmentation due to national
Elegant Coercion and Iran: Beyond the Unitary Actor Model
National Research Council Canada - National Science Library
Moss, J. C
2005-01-01
.... At its core, then, coercion is about state decision-making. Most theories of coercion describe states as if they were unitary actors whose decision-making results from purely rational cost-benefit calculations...
On a class of nonlocal wave equations from applications
Beyer, Horst Reinhard; Aksoylu, Burak; Celiker, Fatih
2016-06-01
We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form a system of nonlocal wave equations. We take a novel approach by applying operator theory methods in a systematic way. On the unbounded domain ℝn, we present three main results. As main result 1, we find that the governing operator is a bounded function of the governing operator of classical elasticity. As main result 2, a consequence of main result 1, we prove that the peridynamic solutions strongly converge to the classical solutions by utilizing, for the first time, strong resolvent convergence. In addition, main result 1 allows us to incorporate local boundary conditions, in particular, into peridynamics. This avenue of research is developed in companion papers, providing a remedy for boundary effects. As main result 3, employing spherical Bessel functions, we give a new practical series representation of the solution which allows straightforward numerical treatment with symbolic computation.
Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering
International Nuclear Information System (INIS)
Jones, S. J.; Wiseman, H. M.; Doherty, A. C.
2007-01-01
In a recent work [Phys. Rev. Lett. 98, 140402 (2007)] we defined 'steering', a type of quantum nonlocality that is logically distinct from both nonseparability and Bell nonlocality. In the bipartite setting, it hinges on the question of whether Alice can affect Bob's state at a distance through her choice of measurement. More precisely and operationally, it hinges on the question of whether Alice, with classical communication, can convince Bob that they share an entangled state under the circumstances that Bob trusts nothing that Alice says. We argue that if she can, then this demonstrates the nonlocal effect first identified in the famous Einstein-Podolsky-Rosen paper [Phys. Rev. 47, 777 (1935)] as a universal effect for pure entangled states. This ability of Alice to remotely prepare Bob's state was subsequently called steering by Schroedinger, whose terminology we adopt. The phenomenon of steering has been largely overlooked, and prior to our work had not even been given a rigorous definition that is applicable to mixed states as well as pure states. Armed with our rigorous definition, we proved that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. In this work we expand on these results and provide further examples of steerable states. We also elaborate on the connection with the original EPR paradox
Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering
Jones, S. J.; Wiseman, H. M.; Doherty, A. C.
2007-11-01
In a recent work [Phys. Rev. Lett. 98, 140402 (2007)] we defined “steering,” a type of quantum nonlocality that is logically distinct from both nonseparability and Bell nonlocality. In the bipartite setting, it hinges on the question of whether Alice can affect Bob’s state at a distance through her choice of measurement. More precisely and operationally, it hinges on the question of whether Alice, with classical communication, can convince Bob that they share an entangled state under the circumstances that Bob trusts nothing that Alice says. We argue that if she can, then this demonstrates the nonlocal effect first identified in the famous Einstein-Podolsky-Rosen paper [Phys. Rev. 47, 777 (1935)] as a universal effect for pure entangled states. This ability of Alice to remotely prepare Bob’s state was subsequently called steering by Schrödinger, whose terminology we adopt. The phenomenon of steering has been largely overlooked, and prior to our work had not even been given a rigorous definition that is applicable to mixed states as well as pure states. Armed with our rigorous definition, we proved that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. In this work we expand on these results and provide further examples of steerable states. We also elaborate on the connection with the original EPR paradox.
Nonlocal transport in the presence of transport barriers
Del-Castillo-Negrete, D.
2013-10-01
There is experimental, numerical, and theoretical evidence that transport in plasmas can, under certain circumstances, depart from the standard local, diffusive description. Examples include fast pulse propagation phenomena in perturbative experiments, non-diffusive scaling in L-mode plasmas, and non-Gaussian statistics of fluctuations. From the theoretical perspective, non-diffusive transport descriptions follow from the relaxation of the restrictive assumptions (locality, scale separation, and Gaussian/Markovian statistics) at the foundation of diffusive models. We discuss an alternative class of models able to capture some of the observed non-diffusive transport phenomenology. The models are based on a class of nonlocal, integro-differential operators that provide a unifying framework to describe non- Fickian scale-free transport, and non-Markovian (memory) effects. We study the interplay between nonlocality and internal transport barriers (ITBs) in perturbative transport including cold edge pulses and power modulation. Of particular interest in the nonlocal ``tunnelling'' of perturbations through ITBs. Also, flux-gradient diagrams are discussed as diagnostics to detect nonlocal transport processes in numerical simulations and experiments. Work supported by the US Department of Energy.
Hyperbolic metamaterial lens with hydrodynamic nonlocal response
Yan, Wei; Mortensen, N. Asger; Wubs, Martijn
2013-01-01
We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion cu...
Frustrated Brownian Motion of Nonlocal Solitary Waves
International Nuclear Information System (INIS)
Folli, V.; Conti, C.
2010-01-01
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.
International Nuclear Information System (INIS)
Santos, Marcelo Franca
2005-01-01
We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state
Steering, Entanglement, Nonlocality, and the EPR Paradox
Wiseman, Howard; Jones, Steve; Andrew, Doherty
2007-06-01
The concept of steering was introduced by Schroedinger in 1935 as a generalization of the EPR paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and Isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell-nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original EPR paradox.
DEFF Research Database (Denmark)
Wubs, Martijn; Yan, Wei; Amooghorban, Ehsan
2013-01-01
A well-known challenge for fabricating metamaterials is to make unit cells significantly smaller than the operating wavelength of light, so one can be sure that effective-medium theories apply. But do they apply? Here we show that nonlocal response in the metal constituents of the metamaterial...... leads to modified effective parameters for strongly subwavelength unit cells. For infinite hyperbolic metamaterials, nonlocal response gives a very large finite upper bound to the optical density of states that otherwise would diverge. Moreover, for finite hyperbolic metamaterials we show that nonlocal...... response affects their operation as superlenses, and interestingly that sometimes nonlocal theory predicts the better imaging. Finally, we discuss how to describe metamaterials effectively in quantum optics. Media with loss or gain have associated quantum noise, and the question is whether the effective...
Unified criteria for multipartite quantum nonlocality
Energy Technology Data Exchange (ETDEWEB)
Cavalcanti, E. G. [Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111 (Australia); He, Q. Y.; Reid, M. D. [Centre for Atom Optics and Ultrafast Spectroscopy and Centre for Quantum-Atom Optics (Australian Research Council), Swinburne University of Technology, Melbourne (Australia); Wiseman, H. M. [Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111 (Australia); Centre for Quantum Computation and Communication Technology (Australian Research Council), Griffith University, Brisbane, Queensland 4111 (Australia)
2011-09-15
Wiseman and co-workers [H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402, (2007)] proposed a distinction among the nonlocality classes of Bell's nonlocality, Einstein-Podolsky-Rosen (EPR) paradox or steering, and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.
Unified criteria for multipartite quantum nonlocality
International Nuclear Information System (INIS)
Cavalcanti, E. G.; He, Q. Y.; Reid, M. D.; Wiseman, H. M.
2011-01-01
Wiseman and co-workers [H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402, (2007)] proposed a distinction among the nonlocality classes of Bell's nonlocality, Einstein-Podolsky-Rosen (EPR) paradox or steering, and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.
Robustness of multiparty nonlocality to local decoherence
International Nuclear Information System (INIS)
Jang, Sung Soon; Cheong, Yong Wook; Kim, Jaewan; Lee, Hai-Woong
2006-01-01
We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystem. To be specific, we consider an N-qubit Greenberger-Horne-Zeilinger (GHZ) state under a depolarization, dephasing, or dissipation channel, and examine nonlocality by testing violation of the Mermin-Klyshko inequality, which is one of Bell's inequalities for multiqubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an N-qubit GHZ state with even N is extremely persistent against dephasing
Non-Local Effects in Kaonic Atoms
International Nuclear Information System (INIS)
Lutz, M.; Florkowski, W.
2000-01-01
Optical potentials with non-local (gradient) terms are used to describe the spectra of kaonic atoms. The strength of the non-local terms is determined from a many-body calculation of the kaon self energy in nuclear matter. We find that the non-local terms are quantitatively important and the results depend strongly on the way the gradient terms are arranged. Phenomenologically successful description is obtained for p-wave like optical potentials. It is suggested that the microscopic form of the non-local interaction terms is obtained systematically by means of a semi-classical expansion of the nucleus structure. (author)
The solution space of the unitary matrix model string equation and the Sato Grassmannian
International Nuclear Information System (INIS)
Anagnostopoulos, K.N.; Bowick, M.J.; Schwarz, A.
1992-01-01
The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equations is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P, 2 - ]=1, with P and 2 - 2x2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints L n (n≥0), where L n annihilate the two modified-KdV τ-functions whose product gives the partition function of the Unitary Matrix Model. (orig.)
On Properties of Class A(n and n-Paranormal Operators
Directory of Open Access Journals (Sweden)
Xiaochun Li
2014-01-01
both non-zero operators; secondly we consider the properties for n-paranormal operators, showing that a n-paranormal contraction is the direct sum of a unitary and a C.0 completely non-unitary contraction.
Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry
International Nuclear Information System (INIS)
Afshar, Hamid; Creutzig, Thomas; Grumiller, Daniel; Hikida, Yasuaki; Rønne, Peter B.
2014-01-01
We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Semikhatov W_n"("2")-algebra. This algebra is conjecturally a quantum Hamiltonian reduction corresponding to a non-principal nilpotent element. We conjecture that this algebra admits a unitary real form for even n. Our main result is that this conjecture is consistent with the known part of the operator product algebra, and especially it is true for n=2 and n=4. Moreover, we find certain ranges of allowed levels where a positive definite inner product is possible. We also find a unitary conformal field theory for every even n at the special level k+n=(n+1)/(n−1). At these points, the W_n"("2")-algebra is nothing but a compactified free boson. This family of W-algebras admits an ’t Hooft limit. Further, in the case of n=4, we reproduce the algebra from the higher spin gravity point of view. In general, gravity computations allow us to reproduce some leading coefficients of the operator product.
International Nuclear Information System (INIS)
Wang Yu; Su Xiaolong; Shen Heng; Tan Aihong; Xie Changde; Peng Kunchi
2010-01-01
One-way quantum computation based on measurement and multipartite cluster entanglement offers the ability to perform a variety of unitary operations only through different choices of measurement bases. Here we present an experimental study toward demonstrating the controlled-X operation, a two-mode gate in which continuous variable (CV) four-partite cluster states of optical modes are utilized. Two quantum teleportation elements are used for achieving the gate operation of the quantum state transformation from input target and control states to output states. By means of the optical cluster state prepared off-line, the homodyne detection and electronic feeding forward, the information carried by the input control state is transformed to the output target state. The presented scheme of the controlled-X operation based on teleportation can be implemented nonlocally and deterministically. The distortion of the quantum information resulting from the imperfect cluster entanglement is estimated with the fidelity.
Nonlocal structures: bilocal photon
International Nuclear Information System (INIS)
Clapp, R.E.
1980-01-01
It is postulated that all particles and fields are built from a single primitive field, a massless fermion with a σ spin of one-half. Two helicities are embodied in a tau spin of one-half. The vacuum is an open Fermi sea whose height is a wave number kappa. Elementary particles are structures having the form of standing-wave systems floating on the vacuum sea. A bilocal photon starts with a function describing two primitive quanta with parallel σ spin and opposite tau spin. A centroid-time wave equation then couples-in and infinite set of orthogonal functions. The introduction of an operator Qlambda permits the reduction of the infinite secular determinant to finite six-by-six determinant. Solutions are obtained describing photons with right-handed and left-handed polarizations. Electric and magnetic field vectors satisfying the vacuum Maxwell equations, are obtained from a bilocal Hertz vector. (author)
Conformal symmetry and nonlinear extensions of nonlocal gravity
Cusin, Giulia; Maggiore, Michele; Mancarella, Michele
2016-01-01
We study two nonlinear extensions of the nonlocal $R\\,\\Box^{-2}R$ gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing $\\Box^{-2}$ with $(-\\Box + R/6)^{-2}$, which is the operator that enters the action for a conformally-coupled scalar field, or replacing $\\Box^{-2}$ with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly. We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state today $w_{\\rm DE}\\simeq -1.01$, which very closely mimics $\\Lambda$CDM and evolves asymptotically into a de Sitter solution. The model based on the Paneitz operator seems instead excluded by the comparison with observations. We also review some issues about the causality of nonlocal theories, and we point out that these nonlocal models can be modified so to nicely interpolate between Starobinski inflation in the primordia...
Crypto-Unitary Forms of Quantum Evolution Operators
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav
2013-01-01
Roč. 52, č. 6 (2013), s. 2038-2045 ISSN 0020-7748 R&D Projects: GA ČR GAP203/11/1433 Institutional support: RVO:61389005 Keywords : PT-symmetric quantum mechanics * time-dependent Schrödinger equation * manifestly time-dependent Hermitian Hamiltonians * Manifestly time-dependent Dyson maps * equivalent time-independent non-Hermitian Hamiltonians Subject RIV: BE - Theoretical Physics Impact factor: 1.188, year: 2013 http://link.springer.com/content/pdf/10.1007%2Fs10773-012-1451-9.pdf
On the compatible weakly nonlocal Poisson brackets of hydrodynamic type
Directory of Open Access Journals (Sweden)
Andrei Ya. Maltsev
2002-01-01
of hydrodynamic type (Ferapontov brackets and the corresponding integrable hierarchies. We show that, under the requirement of the nondegeneracy of the corresponding first pseudo-Riemannian metric g(0 νμ and also some nondegeneracy requirement for the nonlocal part, it is possible to introduce a canonical set of integrable hierarchies based on the Casimirs, momentum functional and some canonical Hamiltonian functions. We prove also that all the higher positive Hamiltonian operators and the negative symplectic forms have the weakly nonlocal form in this case. The same result is also true for negative Hamiltonian operators and positive symplectic structures in the case when both pseudo-Riemannian metrics g(0 νμ and g(1 νμ are nondegenerate.
Unitary Evolution as a Uniqueness Criterion
Cortez, J.; Mena Marugán, G. A.; Olmedo, J.; Velhinho, J. M.
2015-01-01
It is well known that the process of quantizing field theories is plagued with ambiguities. First, there is ambiguity in the choice of basic variables describing the system. Second, once a choice of field variables has been made, there is ambiguity concerning the selection of a quantum representation of the corresponding canonical commutation relations. The natural strategy to remove these ambiguities is to demand positivity of energy and to invoke symmetries, namely by requiring that classical symmetries become unitarily implemented in the quantum realm. The success of this strategy depends, however, on the existence of a sufficiently large group of symmetries, usually including time-translation invariance. These criteria are therefore generally insufficient in non-stationary situations, as is typical for free fields in curved spacetimes. Recently, the criterion of unitary implementation of the dynamics has been proposed in order to select a unique quantization in the context of manifestly non-stationary systems. Specifically, the unitarity criterion, together with the requirement of invariance under spatial symmetries, has been successfully employed to remove the ambiguities in the quantization of linearly polarized Gowdy models as well as in the quantization of a scalar field with time varying mass, propagating in a static background whose spatial topology is either of a d-sphere (with d = 1, 2, 3) or a three torus. Following Ref. 3, we will see here that the symmetry and unitarity criteria allows for a complete removal of the ambiguities in the quantization of scalar fields propagating in static spacetimes with compact spatial sections, obeying field equations with an explicitly time-dependent mass, of the form ddot φ - Δ φ + s(t)φ = 0 . These results apply in particular to free fields in spacetimes which, like e.g. in the closed FRW models, are conformal to a static spacetime, by means of an exclusively time-dependent conformal factor. In fact, in such
A nonlocal inhomogeneous dispersal process
Cortázar, C.; Coville, J.; Elgueta, M.; Martínez, S.
This article in devoted to the study of the nonlocal dispersal equation u(x,t)=∫R J({x-y}/{g(y)}){u(y,t)}/{g(y)} dy-u(x,t) in R×[0,∞), and its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on g and J, we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as t→∞, showing that they converge locally to zero.
Attraction of nonlocal dark optical solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, Dragomir; Krolikowski, Wieslaw
2004-01-01
We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states...
Nonlocality and localizability in quantum mechanics
International Nuclear Information System (INIS)
Matsuno, K.
1989-01-01
Nonlocality of simultaneous spatial correlation of a quantum phenomenon as demonstrated in various versions of Einstein-Podolsky-Rosen type experiment reduces to nonlocality of the measurement apparatus in the sense that the eigen-wavefunctions for the apparatus are completely specified in a manner of being independent of whatever object it may measure. Nonlocality of the measurement apparatus however serves as no more than a good approximation to reality at best. The theoretical imposition of nonlocality of the measurement apparatus as an approximation is compatible with the actual locality of quantum mechanics that dispenses with an agent claiming globally simultaneous specifiability of boundary conditions, though the genuine locality of quantum mechanics has to be examined without employing the nonlocality of the measurement apparatus. The actual locality of quantum mechanics is intrinsically irreversible in its development
Hyperbolic metamaterial lens with hydrodynamic nonlocal response
DEFF Research Database (Denmark)
Yan, Wei; Mortensen, N. Asger; Wubs, Martijn
2013-01-01
We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves...... of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens...... in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we...
Nonlocal Galileons and self-acceleration
Energy Technology Data Exchange (ETDEWEB)
Gabadadze, Gregory; Yu, Siqing, E-mail: sy1430@nyu.edu
2017-05-10
A certain class of nonlocal theories eliminates an arbitrary cosmological constant (CC) from a universe that can be perceived as our world. Dark energy then cannot be explained by a CC; it could however be due to massive gravity. We calculate the new corrections, which originate from the nonlocal terms that eliminate the CC, to the decoupling limit Lagrangian of massive gravity. The new nonlocal terms also have internal field space Galilean symmetry and are referred here as “nonlocal Galileons.” We then study a self-accelerated solution and show that the new nonlocal terms change the perturbative stability analysis. In particular, small fluctuations are now stable and non-superluminal for some simple parameter choices, whereas for the same choices the pure massive gravity fluctuations are unstable. We also study stable spherically symmetric solutions on this background.
Virial Theorem in Nonlocal Newtonian Gravity
Directory of Open Access Journals (Sweden)
Bahram Mashhoon
2016-05-01
Full Text Available Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter D 0 —namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.
Hyperbolic metamaterial lens with hydrodynamic nonlocal response.
Yan, Wei; Mortensen, N Asger; Wubs, Martijn
2013-06-17
We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we propose to measure the near-field distribution of a hyperbolic metamaterial lens.
Non-local effects in kaonic atoms
International Nuclear Information System (INIS)
Lutz, M.; Florkowski, W.
2000-04-01
Optical potentials with non-local (gradient) terms are used to describe the spectra of kaonic atoms. The strength of the non-local terms is determined from a many-body calculation of the kaon self-energy in nuclear matter. The optical potentials show strong non-linearities in the nucleon density and sizeable non-local terms. We find that the non-local terms are quantitatively important and the results depend strongly on the way the gradient terms are arranged. Phenomenologically successful fits are obtained for p-wave like optical potentials. It is suggested that the microscopic form of the non-local interaction terms is obtained systematically by means of a semi-classical expansion of the nucleus structure. We conclude that a microscopic description of kaonic atom data requires further detailed studies of the microscopic K - nuclear dynamics. (orig.)
Nonlocal Quantum Effects in Cosmology
Directory of Open Access Journals (Sweden)
Yurii V. Dumin
2014-01-01
Full Text Available Since it is commonly believed that the observed large-scale structure of the universe is an imprint of quantum fluctuations existing at the very early stage of its evolution, it is reasonable to pose the question: do the effects of quantum nonlocality, which are well established now by the laboratory studies, manifest themselves also in the early universe? We try to answer this question by utilizing the results of a few experiments, namely, with the superconducting multi-Josephson-junction loops and the ultracold gases in periodic potentials. Employing a close analogy between the above-mentioned setups and the simplest one-dimensional Friedmann-Robertson-Walker cosmological model, we show that the specific nonlocal correlations revealed in the laboratory studies might be of considerable importance also in treating the strongly nonequilibrium phase transitions of Higgs fields in the early universe. Particularly, they should substantially reduce the number of topological defects (e.g., domain walls expected due to independent establishment of the new phases in the remote spatial regions. This gives us a hint on resolving a long-standing problem of the excessive concentration of topological defects, inconsistent with observational constraints. The same effect may be also relevant to the recent problem of the anomalous behavior of cosmic microwave background fluctuations at large angular scales.
Lehoucq, R B; Sears, Mark P
2011-09-01
The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.
Joule-Thomson Coefficient for Strongly Interacting Unitary Fermi Gas
International Nuclear Information System (INIS)
Liao Kai; Chen Jisheng; Li Chao
2010-01-01
The Joule-Thomson effect reflects the interaction among constituent particles of macroscopic system. For classical ideal gas, the corresponding Joule-Thomson coefficient is vanishing while it is non-zero for ideal quantum gas due to the quantum degeneracy. In recent years, much attention is paid to the unitary Fermi gas with infinite two-body scattering length. According to universal analysis, the thermodynamical law of unitary Fermi gas is similar to that of non-interacting ideal gas, which can be explored by the virial theorem P = 2E/3V. Based on previous works, we further study the unitary Fermi gas properties. The effective chemical potential is introduced to characterize the nonlinear levels crossing effects in a strongly interacting medium. The changing behavior of the rescaled Joule-Thomson coefficient according to temperature manifests a quite different behavior from that for ideal Fermi gas. (general)
Maximum nonlocality and minimum uncertainty using magic states
Howard, Mark
2015-04-01
We prove that magic states from the Clifford hierarchy give optimal solutions for tasks involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both the nonlocality and uncertainty tasks, stabilizer states are the worst possible pure states, so our solutions have an operational interpretation as being highly nonstabilizer. The optimal strategy for a qudit version of the Clauser-Horne-Shimony-Holt game in prime dimensions is achieved by measuring maximally entangled states that are isomorphic to single-qudit magic states. These magic states have an appealingly simple form, and our proof shows that they are "balanced" with respect to all but one of the mutually unbiased stabilizer bases. Of all equatorial qudit states, magic states minimize the average entropic uncertainties for collision entropy and also, for small prime dimensions, min-entropy, a fact that may have implications for cryptography.
Cogeneration Power Plants: a Proposed Methodology for Unitary Production Cost
International Nuclear Information System (INIS)
Metalli, E.
2009-01-01
A new methodology to evaluate unitary energetic production costs in the cogeneration power plants is proposed. This methodology exploits the energy conversion factors fixed by Italian Regulatory Authority for Electricity and Gas. So it allows to settle such unitary costs univocally for a given plant, without assigning them a priori subjective values when there are two or more energy productions at the same time. Moreover the proposed methodology always ensures positive values for these costs, complying with the total generation cost balance equation. [it
Can EPR non-locality be geometrical?
International Nuclear Information System (INIS)
Ne'eman, Y.
1995-01-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3
Bell's theorem, accountability and nonlocality
International Nuclear Information System (INIS)
Vona, Nicola; Liang, Yeong-Cherng
2014-01-01
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)
Ring vortex solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Briedis, D.; Petersen, D.E.; Edmundson, D.
2005-01-01
We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single...... or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....
DU and UD-invariants of unitary groups
International Nuclear Information System (INIS)
Aguilera-Navarro, M.C.K.
1977-01-01
Four distint ways of obtaining the eigenvalues of unitary groups, in any irreducible representation, are presented. The invariants are defined according to two different contraction conventions. Their eigenvalue can be given in terms of two classes of special partial hooks associated with the young diagram characterizing the irreducible representation considered
Establishing the Unitary Classroom: Organizational Change and School Culture.
Eddy, Elizabeth M.; True, Joan H.
1980-01-01
This paper examines the organizational changes introduced in two elementary schools to create unitary (desegregated) classrooms. The different models adopted by the two schools--departmentalization and team teaching--are considered as expressions of their patterns of interaction, behavior, and values. (Part of a theme issue on educational…
Microscopic description and excitation of unitary analog states
Energy Technology Data Exchange (ETDEWEB)
Kisslinger, L S [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA); Van Giai, N [Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
1977-12-05
A microscopic investigation in a self-consistent particle-hole model reveals approximate unitary analog states in spite of large symmetry breaking. The K-nucleus elastic scattering and (K/sup -/, ..pi../sup -/) excitation of these states are studied, showing strong surface effects.
Subquantum nonlocal correlations induced by the background random field
Energy Technology Data Exchange (ETDEWEB)
Khrennikov, Andrei, E-mail: Andrei.Khrennikov@lnu.s [International Center for Mathematical Modelling in Physics and Cognitive Sciences, Linnaeus University, Vaexjoe (Sweden); Institute of Information Security, Russian State University for Humanities, Moscow (Russian Federation)
2011-10-15
We developed a purely field model of microphenomena-prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction-the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology-for Gaussian random fields with covariance operators corresponding to factorizable quantum states).
Subquantum nonlocal correlations induced by the background random field
International Nuclear Information System (INIS)
Khrennikov, Andrei
2011-01-01
We developed a purely field model of microphenomena-prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction-the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology-for Gaussian random fields with covariance operators corresponding to factorizable quantum states).
Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions
Ablowitz, Mark J.
2009-09-01
Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.
Reassessment of the nonlocality of correlation boxes
Energy Technology Data Exchange (ETDEWEB)
Costa, A.P.; Parisio, Fernando, E-mail: parisio@df.ufpe.br
2017-01-15
Correlation boxes are hypothetical systems usually designed to produce the maximal algebraic violation of a Bell inequality, beyond the quantum bound and without superluminal signalling. The fact that these systems show stronger correlations than those presented by maximally entangled quantum states, as the spin singlet, has been regarded as a demonstration that the former are more nonlocal than the latter. By applying an alternative, consistent measure of nonlocality to a family of correlation boxes, we show that this conclusion is not necessarily true. Complementarily, we define a class of systems displaying subquantum correlations which, nevertheless, are more nonlocal than the singlet state, showing that the extent of the numeric violation of an inequality may have little to do with the degree of nonlocality, especially in the case of correlation boxes.
Unified criteria for multipartite quantum nonlocality
Cavalcanti, E. G.; He, Q. Y.; Reid, M. D.; Wiseman, H. M.
2011-09-01
Wiseman and co-workers [H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.140402 98, 140402, (2007)] proposed a distinction among the nonlocality classes of Bell's nonlocality, Einstein-Podolsky-Rosen (EPR) paradox or steering, and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.
Revealing Hidden Einstein-Podolsky-Rosen Nonlocality
Walborn, S. P.; Salles, A.; Gomes, R. M.; Toscano, F.; Souto Ribeiro, P. H.
2011-04-01
Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid’s EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.
Nanoplasmonics: Exploring nonlocal and quantum effects
DEFF Research Database (Denmark)
Mortensen, N. Asger
2016-01-01
Plasmonics is commonly understood within classical electrodynamics with local-response constitutive relations. However, possibilities for nonlocal dynamics and quantum effects emerge with strong spatial confinement in plasmonic nanostructures. This talks reviews recent theory and experiments...
Some generalizations of the nonlocal transformations approach
Directory of Open Access Journals (Sweden)
V. A. Tychynin
2015-02-01
Full Text Available Some generalizations of a method of nonlocal transformations are proposed: a connection of given equations via prolonged nonlocal transformations and finding of an adjoint solution to the solutions of initial equation are considered. A concept of nonlocal transformation with additional variables is introduced, developed and used for searching symmetries of differential equations. A problem of inversion of the nonlocal transformation with additional variables is investigated and in some cases solved. Several examples are presented. Derived technique is applied for construction of the algorithms and formulae of generation of solutions. The formulae derived are used for construction of exact solutions of some nonlinear equations.
Employee Travel Data (Non-Local)
Montgomery County of Maryland — ‘This dataset provides information regarding the total approved actual expenses incurred by Montgomery County government employees traveling non-locally (over 75...
Plasmonic nanostructures: local versus nonlocal response
DEFF Research Database (Denmark)
Toscano, Giuseppe; Wubs, Martijn; Xiao, Sanshui
2010-01-01
, and hence it is sensitive to possible narrow resonances that may arise due to strong electronic quantum confinement in the metal. This feature allows us to accurately determine which geometries are strongly affected by nonlocal response, for example regarding applications based on electric field enhancement......We study the importance of taking the nonlocal optical response of metals into account for accurate determination of optical properties of nanoplasmonic structures. Here we focus on the computational physics aspects of this problem, and in particular we report on the nonlocal-response package...... that we wrote for state-of the art numerical software, enabling us to take into account the nonlocal material response of metals for any arbitrarily shaped nanoplasmonic structures, without much numerical overhead as compared to the standard local response. Our method is a frequency-domain method...
Black hole information, unitarity, and nonlocality
Giddings, Steven B.
2006-01-01
The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. The leading contender is nonlocality. Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. Suggestions that such dynamics arises from ultra-planckian modes in Hawking's derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. However, no simul...
Gauging Non-local Quark Models
International Nuclear Information System (INIS)
Broniowski, W.
1999-09-01
The gauge effective quark model with non-local interactions is considered. It is shown how this approach regularize the theory in such a way that the anomalies are preserved and charges are properly quantized. With non-local interactions the effective action is finite to all orders in the loop expansion and there is no need to introduce the quark momentum cut-off parameter
Nonlinear unitary quantum collapse model with self-generated noise
Geszti, Tamás
2018-04-01
Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.
Robust non-local median filter
Matsuoka, Jyohei; Koga, Takanori; Suetake, Noriaki; Uchino, Eiji
2017-04-01
This paper describes a novel image filter with superior performance on detail-preserving removal of random-valued impulse noise superimposed on natural gray-scale images. The non-local means filter is in the limelight as a way of Gaussian noise removal with superior performance on detail preservation. By referring the fundamental concept of the non-local means, we had proposed a non-local median filter as a specialized way for random-valued impulse noise removal so far. In the non-local processing, the output of a filter is calculated from pixels in blocks which are similar to the block centered at a pixel of interest. As a result, aggressive noise removal is conducted without destroying the detailed structures in an original image. However, the performance of non-local processing decreases enormously in the case of high noise occurrence probability. A cause of this problem is that the superimposed noise disturbs accurate calculation of the similarity between the blocks. To cope with this problem, we propose an improved non-local median filter which is robust to the high level of corruption by introducing a new similarity measure considering possibility of being the original signal. The effectiveness and validity of the proposed method are verified in a series of experiments using natural gray-scale images.
Dang, Cai-Ping; Braeken, Johan; Ferrer, Emilio; Liu, Chang
2012-01-01
This study explored the controversy surrounding working memory: whether it is a unitary system providing general purpose resources or a more differentiated system with domain-specific sub-components. A total of 348 participants completed a set of 6 working memory tasks that systematically varied in storage target contents and type of information…
Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity
DEFF Research Database (Denmark)
Raza, Søren; Christensen, Thomas; Wubs, Martijn
2013-01-01
the Thomas-Fermi internal kinetic energy of the free electrons in the metal. We derive the nonlocal dispersion relations of the three waveguide structures taking into account also retardation and interband effects, and examine the delicate interplay between nonlocal response and absorption losses...
Instantaneous Non-Local Computation of Low T-Depth Quantum Circuits
DEFF Research Database (Denmark)
Speelman, Florian
2016-01-01
-depth of a quantum circuit, able to perform non-local computation of quantum circuits with a (poly-)logarithmic number of layers of T gates with quasi-polynomial entanglement. Our proofs combine ideas from blind and delegated quantum computation with the garden-hose model, a combinatorial model of communication......Instantaneous non-local quantum computation requires multiple parties to jointly perform a quantum operation, using pre-shared entanglement and a single round of simultaneous communication. We study this task for its close connection to position-based quantum cryptography, but it also has natural...... applications in the context of foundations of quantum physics and in distributed computing. The best known general construction for instantaneous non-local quantum computation requires a pre-shared state which is exponentially large in the number of qubits involved in the operation, while efficient...
International Nuclear Information System (INIS)
Maltsev, A Ya
2005-01-01
We consider the special type of field-theoretical symplectic structures called weakly nonlocal. The structures of this type are, in particular, very common for integrable systems such as KdV or NLS. We introduce here the special class of weakly nonlocal symplectic structures which we call weakly nonlocal symplectic structures of hydrodynamic type. We investigate then the connection of such structures with the Whitham averaging method and propose the procedure of 'averaging' the weakly nonlocal symplectic structures. The averaging procedure gives the weakly nonlocal symplectic structure of hydrodynamic type for the corresponding Whitham system. The procedure also gives 'action variables' corresponding to the wave numbers of m-phase solutions of the initial system which give the additional conservation laws for the Whitham system
Nonlocality and entanglement in qubit systems
Energy Technology Data Exchange (ETDEWEB)
Batle, J [Departament de Fisica, Universitat de les Illes Balears, 07122 Palma de Mallorca (Spain); Casas, M, E-mail: vdfsjbv4@uib.es [Departament de Fisica and IFISC-CSIC, Universitat de les Illes Balears, 07122 Palma de Mallorca (Spain)
2011-11-04
Nonlocality and quantum entanglement constitute two special aspects of the quantum correlations existing in quantum systems, which are of paramount importance in quantum-information theory. Traditionally, they have been regarded as identical (equivalent, in fact, for pure two qubit states, that is, Gisin's Theorem), yet they constitute different resources. Describing nonlocality by means of the violation of several Bell inequalities, we obtain by direct optimization those states of two qubits that maximally violate a Bell inequality, in terms of their degree of mixture as measured by either their participation ratio R = 1/Tr({rho}{sup 2}) or their maximum eigenvalue {lambda}{sub max}. This optimum value is obtained as well, which coincides with previous results. Comparison with entanglement is performed too. An example of an application is given in the XY model. In this novel approximation, we also concentrate on the nonlocality for linear combinations of pure states of two qubits, providing a closed form for their maximal nonlocality measure. The case of Bell diagonal mixed states of two qubits is also extensively studied. Special attention concerning the connection between nonlocality and entanglement for mixed states of two qubits is paid to the so-called maximally entangled mixed states. Additional aspects for the case of two qubits are also described in detail. Since we deal with qubit systems, we will perform an analogous study for three qubits, employing similar tools. Relation between distillability and nonlocality is explored quantitatively for the whole space of states of three qubits. We finally extend our analysis to four-qubit systems, where nonlocality for generalized Greenberger-Horne-Zeilinger states of arbitrary number of parties is computed. (paper)
Unitary group representations in Fock spaces with generalized exchange properties
International Nuclear Information System (INIS)
Liguori, A.
1994-09-01
The notion of second R-quantization is investigated, - a suitable deformation of the standard second quantization which properly takes into account the non-trivial exchange properties characterizing generalized statistics. The R-quantization of a class of unitary one-particle representations relevant for the description of symmetries is also performed. The Euclidean covariance of anyons is analyzed in this context. (author). 11 refs
Prenominal and postnominal reduced relative clauses: arguments against unitary analyses
Directory of Open Access Journals (Sweden)
Petra Sleeman
2007-01-01
Full Text Available These last years, several analyses have been proposed in which prenominal and postnominal reduced relatives are merged in the same position. Kayne (1994 claims that both types of reduced relative clauses are the complement of the determiner. More recently, Cinque (2005 has proposed that both types are merged in the functional projections of the noun, at the left edge of the modifier system. In this paper, I argue against a unitary analysis of prenominal and postnominal participial reduced relatives.
Effective hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Avramenko, V.I.; Blokhin, A.L.
1989-01-01
Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs
Unitary-matrix models as exactly solvable string theories
Periwal, Vipul; Shevitz, Danny
1990-01-01
Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.
Complex projection of unitary dynamics of quaternionic pure states
International Nuclear Information System (INIS)
Asorey, M.; Scolarici, G.; Solombrino, L.
2007-01-01
Quaternionic quantum mechanics has been revealed to be a very useful framework to describe quantum phenomena. In the case of two qubit compound systems we show that the complex projection of quaternionic pure states and quaternionic unitary maps permits the description of interesting phenomena such as decoherence and optimal entanglement generation. The approach, however, presents severe limitations for the case of multipartite or higher dimensional bipartite quantum systems as we point out
Information-disturbance tradeoff in estimating a unitary transformation
International Nuclear Information System (INIS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Chiribella, Giulio
2010-01-01
We address the problem of the information-disturbance tradeoff associated to the estimation of a quantum transformation and show how the extraction of information about a black box causes a perturbation of the corresponding input-output evolution. In the case of a black box performing a unitary transformation, randomly distributed according to the invariant measure, we give a complete solution of the problem, deriving the optimal tradeoff curve and presenting an explicit construction of the optimal quantum network.
Primary fields in a unitary representation of Virasoro algebras
International Nuclear Information System (INIS)
Sasaki, R.; Yamanaka, I.
1985-08-01
A unitary representation of Virasoro algebras with the central charge c = 1 - 6/(N + 1)(N + 2) is constructed explicitly in terms of a colored (two color) coset space (the complex projective space CP sup(N-1)) quark model. By utilizing the explicit forms of the Virasoro generators Lsub(m), we derive a general method of constructing the primary fields (fields with well-defined conformal transformation properties) of the above Virasoro algebras. (author)
Efficient learning algorithm for quantum perceptron unitary weights
Seow, Kok-Leong; Behrman, Elizabeth; Steck, James
2015-01-01
For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must meet the non-trivial task of integrating the unitary dynamics of quantum computing and the dissipative dynamics of neural computing. At the core of quantum computing and neural computing lies the qubit and perceptron, respectively. We see that past implementat...
Higher dimensional unitary braid matrices: Construction, associated structures and entanglements
International Nuclear Information System (INIS)
Abdesselam, B.; Chakrabarti, A.; Dobrev, V.K.; Mihov, S.G.
2007-03-01
We construct (2n) 2 x (2n) 2 unitary braid matrices R-circumflex for n ≥ 2 generalizing the class known for n = 1. A set of (2n) x (2n) matrices (I, J,K,L) are defined. R-circumflex is expressed in terms of their tensor products (such as K x J), leading to a canonical formulation for all n. Complex projectors P ± provide a basis for our real, unitary R-circumflex. Baxterization is obtained. Diagonalizations and block- diagonalizations are presented. The loss of braid property when R-circumflex (n > 1) is block-diagonalized in terms of R-circumflex (n = 1) is pointed out and explained. For odd dimension (2n + 1) 2 x (2n + 1) 2 , a previously constructed braid matrix is complexified to obtain unitarity. R-circumflexLL- and R-circumflexTT- algebras, chain Hamiltonians, potentials for factorizable S-matrices, complex non-commutative spaces are all studied briefly in the context of our unitary braid matrices. Turaev construction of link invariants is formulated for our case. We conclude with comments concerning entanglements. (author)
Constraining generalized non-local cosmology from Noether symmetries.
Bahamonde, Sebastian; Capozziello, Salvatore; Dialektopoulos, Konstantinos F
2017-01-01
We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory.
Constraining generalized non-local cosmology from Noether symmetries
Energy Technology Data Exchange (ETDEWEB)
Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Capozziello, Salvatore [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Gran Sasso Science Institute, L' Aquila (Italy); Complesso di Monte Sant' Angelo, Naples (Italy); INFN Sezione di Napoli, Naples (Italy); Dialektopoulos, Konstantinos F. [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Complesso di Monte Sant' Angelo, Naples (Italy); INFN Sezione di Napoli, Naples (Italy)
2017-11-15
We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory. (orig.)
NLOM - a program for nonlocal optical model calculations
International Nuclear Information System (INIS)
Kim, B.T.; Kyum, M.C.; Hong, S.W.; Park, M.H.; Udagawa, T.
1992-01-01
A FORTRAN program NLOM for nonlocal optical model calculations is described. It is based on a method recently developed by Kim and Udagawa, which utilizes the Lanczos technique for solving integral equations derived from the nonlocal Schroedinger equation. (orig.)
Coupling of nonlocal and local continuum models by the Arlequinapproach
Han, Fei; Lubineau, Gilles
2011-01-01
for the 'fine scale' description in which nonlocal interactions are considered to have non-negligible effects. Classical continuum mechanics only involving local contact forces is introduced for the rest of the structure where these nonlocal effects can
Accurate nonlocal theory for cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey
2007-01-01
We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
2018-06-01
Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.
Black hole information, unitarity, and nonlocality
International Nuclear Information System (INIS)
Giddings, Steven B.
2006-01-01
The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. The leading contender is nonlocality. Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. Suggestions that such dynamics arise from ultra-Planckian modes in Hawking's derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. However, no simultaneous description of modes that have fallen into the black hole and outgoing Hawking modes can be given without appearance of a large kinematic invariant, or other dependence on ultra-Planckian physics. This indicates that a reliable argument for information loss has not been constructed, and that strong gravitational dynamics is important. Such dynamics has been argued to be fundamentally nonlocal in extreme situations, such as those required to investigate the fate of information
International Nuclear Information System (INIS)
Yao, Yao
2015-01-01
The deep sub-Ohmic spin–boson model shows a longstanding non-Markovian coherence at low temperature. Motivating to quench this robust coherence, the thermal effect is unitarily incorporated into the time evolution of the model, which is calculated by the adaptive time-dependent density matrix renormalization group algorithm combined with the orthogonal polynomials theory. Via introducing a unitary heating operator to the bosonic bath, the bath is heated up so that a majority portion of the bosonic excited states is occupied. It is found in this situation the coherence of the spin is quickly quenched even in the coherent regime, in which the non-Markovian feature dominates. With this finding we come up with a novel way to implement the unitary equilibration, the essential term of the eigenstate-thermalization hypothesis, through a short-time evolution of the model
Spiraling solitons and multipole localized modes in nonlocal nonlinear media
International Nuclear Information System (INIS)
Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.; Bang, Ole; Krolikowski, Wieslaw; Kivshar, Yuri S.
2007-01-01
We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form
Spiralling solitons and multipole localized modes in nonlocal nonlinear media
DEFF Research Database (Denmark)
Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan
2007-01-01
We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form....
Unitary Supermultiplets of $OSp(8^{*}|4)$ and the $AdS_{7}/CFT_{6}$ Duality
Günaydin, M; Gunaydin, Murat; Takemae, Seiji
2000-01-01
We study the unitary supermultiplets of the N=4 d=7 anti-de Sitter (AdS_7) superalgebra OSp(8^*|4), with the even subalgebra SO(6,2) X USp(4), which is the symmetry superalgebra of M-theory on AdS_7 X S^4. We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8^*|4) . The ultra-short doubleton supermultiplets do not have a Poincaré limit in AdS_7 and correspond to superconformal field theories on the boundary of AdS_7 which can be identified with d=6 Minkowski space. We show that the six dimensional Poincare mass operator vanishes identically for the doubleton representations. By going from the compact U(4) basis of SO^*(8)=SO(6,2) to the noncompact basis SU^*(4)XD (d=6 Lorentz group times dilatations) one can associate the positive (conformal) energy representations of SO^*(8) with conformal fields transforming covariantly under the Lorentz group in d=6. The oscillator method used for the construction of the unitary supermultiplets of OSp(8^*|4) can be given ...
Purely non-local Hamiltonian formalism, Kohno connections and ∨-systems
International Nuclear Information System (INIS)
Arsie, Alessandro; Lorenzoni, Paolo
2014-01-01
In this paper, we extend purely non-local Hamiltonian formalism to a class of Riemannian F-manifolds, without assumptions on the semisimplicity of the product ○ or on the flatness of the connection ∇. In the flat case, we show that the recurrence relations for the principal hierarchy can be re-interpreted using a local and purely non-local Hamiltonian operators and in this case they split into two Lenard-Magri chains, one involving the even terms, the other involving the odd terms. Furthermore, we give an elementary proof that the Kohno property and the ∨-system condition are equivalent under suitable assumptions and we show how to associate a purely non-local Hamiltonian structure to any ∨-system, including degenerate ones
Reversed rainbow with a nonlocal metamaterial
Energy Technology Data Exchange (ETDEWEB)
Morgado, Tiago A., E-mail: tiago.morgado@co.it.pt; Marcos, João S.; Silveirinha, Mário G., E-mail: mario.silveirinha@co.it.pt [Department of Electrical Engineering, Instituto de Telecomunicações, University of Coimbra, 3030 Coimbra (Portugal); Costa, João T. [CST AG, Bad Nauheimer Strasse 19, 64289 Darmstadt (Germany); Costa, Jorge R. [Instituto de Telecomunicações and Instituto Universitário de Lisboa (ISCTE-IUL), 1649-026 Lisboa (Portugal); Fernandes, Carlos A. [Instituto de Telecomunicações, and Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa (Portugal)
2014-12-29
One of the intriguing potentials of metamaterials is the possibility to realize a nonlocal electromagnetic reaction, such that the effective medium response at a given point is fundamentally entangled with the macroscopic field distribution at long distances. Here, it is experimentally and numerically verified that a microwave nonlocal metamaterial formed by crossed metallic wires enables a low-loss broadband anomalous material response such that the refractive index decreases with frequency. Notably, it is shown that an electromagnetic beam refracted by our metamaterial prism creates a reversed microwave rainbow.
On nonlocal modeling in continuum mechanics
Directory of Open Access Journals (Sweden)
Adam Martowicz
2018-01-01
Full Text Available The objective of the paper is to provide an overview of nonlocal formulations for models of elastic solids. The author presents the physical foundations for nonlocal theories of continuum mechanics, followed by various analytical and numerical techniques. The characteristics and range of practical applications for the presented approaches are discussed. The results of numerical simulations for the selected case studies are provided to demonstrate the properties of the described methods. The paper is illustrated with outcomes from peridynamic analyses. Fatigue and axial stretching were simulated to show the capabilities of the developed numerical tools.
Hyperbolic metamaterials: Nonlocal response regularizes broadband supersingularity
DEFF Research Database (Denmark)
Yan, Wei; Wubs, Martijn; Mortensen, N. Asger
2012-01-01
We study metamaterials known as hyperbolic media that in the usual local-response approximation exhibit hyperbolic dispersion and an associated broadband singularity in the density of states. Instead, from the more microscopic hydrodynamic Drude theory we derive qualitatively different optical...... properties of these metamaterials, due to the free-electron nonlocal optical response of their metal constituents. We demonstrate that nonlocal response gives rise to a large-wavevector cutoff in the dispersion that is inversely proportional to the Fermi velocity of the electron gas, but also for small...
Classification of scalar and dyadic nonlocal optical response models
DEFF Research Database (Denmark)
Wubs, Martijn
2015-01-01
Nonlocal optical response is one of the emerging effects on the nanoscale for particles made of metals or doped semiconductors. Here we classify and compare both scalar and tensorial nonlocal response models. In the latter case the nonlocality can stem from either the longitudinal response...
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality...
Directory of Open Access Journals (Sweden)
Zuomao Yan
2012-01-01
Full Text Available In this paper, we discuss the existence results for a class of nnlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques.
Planting nonlocal seed sources of loblolly pine - managing benefits and risks
Clem Lambeth; Steve Mckeand; Randy Rousseau; Ron Schmidtling
2005-01-01
Seed source testing of loblolly pine (Pinus taeda), which began in the 1920s, has allowed large realized genetic gains from using nonlocal seed sources in operational plantations. Seed source testing continues, and deployment guidlines are being refined. some general effects of seed source movement can be described, but there are still gaps in (1)...
DEFF Research Database (Denmark)
Möllers, Jan
2013-01-01
(\\pi)\\subseteq\\mathfrak{p}_{\\mathbb{C}}^*$. The associated variety $Ass(\\pi)$ is the closure of a single nilpotent $K_{\\mathbb{C}}$-orbit $\\mathcal{O}^{K_{\\mathbb{C}}}\\subseteq\\mathfrak{p}_{\\mathbb{C}}^*$ which corresponds by the Kostant-Sekiguchi correspondence to a nilpotent coadjoint $G$-orbit $\\mathcal{O}^G\\subseteq\\mathfrak{g}^*$. The known Schr\\"odinger...... model of $\\pi$ is a realization on $L^2(\\mathcal{O})$, where $\\mathcal{O}\\subseteq\\mathcal{O}^G$ is a Lagrangian submanifold. We construct an intertwining operator from the Schr\\"odinger model to the new Fock model, the generalized Segal-Bargmann transform, which gives a geometric quantization...... and as integral kernel of the Segal-Bargmann transform. As a corollary to our construction we also obtain the integral kernel of the unitary inversion operator in the Schr\\"odinger model in terms of a multivariable $J$-Bessel function....
DEFF Research Database (Denmark)
Esbensen, B.K.; Bache, Morten; Krolikowski, W.
2012-01-01
We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description...... this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions....
Directory of Open Access Journals (Sweden)
Reem A. Al-Omair
2009-03-01
Full Text Available In this paper we prove the existence of a mild solution for a semilinear evolution differential inclusion with nonlocal condition and governed by a family of linear operators, not necessarily bounded or closed, in a Banach space. No compactness assumption is assumed on the evolution operator generated by the family operators. Also, we prove that the set of mild solutions is compact.
Nonlocality, Entanglement Witnesses and Supra-correlations
2012-04-01
quantum non-locality, non-signaling theories, Popescu-Rohrlich boxes, EPR 1. INTRODUCTION Physics imposes limits on the correlations that can be...References [1] J.S. Bell, “On the Einstein Podolsky Rosen paradox ,” Physics 1, 195 (1964). [2] B. Tsirelson, “Quantum Generalizations of Bell’s
Energy dependence of nonlocal optical potentials
Lovell, A. E.; Bacq, P.-L.; Capel, P.; Nunes, F. M.; Titus, L. J.
2017-11-01
Recently, a variety of studies have shown the importance of including nonlocality in the description of reactions. The goal of this work is to revisit the phenomenological approach to determining nonlocal optical potentials from elastic scattering. We perform a χ2 analysis of neutron elastic scattering data off 40Ca, 90Zr, and 208Pb at energies E ≈5 -40 MeV, assuming a Perey and Buck [Nucl. Phys. 32, 353 (1962), 10.1016/0029-5582(62)90345-0] or Tian et al. [Int. J. Mod. Phys. E 24, 1550006 (2015), 10.1142/S0218301315500068] nonlocal form for the optical potential. We introduce energy and asymmetry dependencies in the imaginary part of the potential and refit the data to obtain a global parametrization. Independently of the starting point in the minimization procedure, an energy dependence in the imaginary depth is required for a good description of the data across the included energy range. We present two parametrizations, both of which represent an improvement over the original potentials for the fitted nuclei as well as for other nuclei not included in our fit. Our results show that, even when including the standard Gaussian nonlocality in optical potentials, a significant energy dependence is required to describe elastic-scattering data.
Nonlocal study of ultimate plasmon hybridization
DEFF Research Database (Denmark)
Raza, Søren; Wubs, Martijn; Bozhevolnyi, Sergey I.
2015-01-01
the transition from separated dimers via touching dimers to finally overlapping dimers. In particular, we focus on the touching case, showing a fundamental limit on the hybridization of the bonding plasmon modes due to nonlocality. Using transformation optics, we determine a simple analytical equation...
The statistical strength of nonlocality proofs
Dam, van W.; Gill, R.D.; Grünwald, P.D.
2005-01-01
There exist numerous proofs of Bell's theorem, stating that quantum mechanics is incompatible with local realistic theories of nature. Here the strength of such nonlocality proofs is defined in terms of the amount of evidence against local realism provided by the corresponding experiments.
Quantum Nonlocality with Spins in Diamond
Hensen, B.J.
2016-01-01
In this thesis we experimentally investigate quantum nonlocality: entangled states of spatially separated objects. Entanglement is one of the most striking consequences of the quantum formalism developed in the 1920's; the predicted outcomes of independent measurements on entangled objects reveal
Local and nonlocal space-time singularities
International Nuclear Information System (INIS)
Konstantinov, M.Yu.
1985-01-01
The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established
Multiscale differential phase contrast analysis with a unitary detector
Lopatin, Sergei; Ivanov, Yurii P.; Kosel, Jü rgen; Chuvilin, Andrey
2015-01-01
A new approach to generate differential phase contrast (DPC) images for the visualization and quantification of local magnetic fields in a wide range of modern nano materials is reported. In contrast to conventional DPC methods our technique utilizes the idea of a unitary detector under bright field conditions, making it immediately usable by a majority of modern transmission electron microscopes. The approach is put on test to characterize the local magnetization of cylindrical nanowires and their 3D ordered arrays, revealing high sensitivity of our method in a combination with nanometer-scale spatial resolution.
Introduction to orthogonal, symplectic and unitary representations of finite groups
Riehm, Carl R
2011-01-01
Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics-linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms-and thus inherit some of the characteristics of both. This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the "classical" fields-algebraically closed, rea
Deformations of polyhedra and polygons by the unitary group
Energy Technology Data Exchange (ETDEWEB)
Livine, Etera R. [Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Allée d' Italie, Lyon 69007, France and Perimeter Institute, 31 Caroline St N, Waterloo, Ontario N2L 2Y5 (Canada)
2013-12-15
We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient C{sup 2N}//SU(2). A framed polyhedron is then parametrized by N spinors living in C{sup 2} satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N−2)). We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in
A model of diffraction scattering with unitary corrections
International Nuclear Information System (INIS)
Etim, E.; Malecki, A.; Satta, L.
1989-01-01
The inability of the multiple scattering model of Glauber and similar geometrical picture models to fit data at Collider energies, to fit low energy data at large momentum transfers and to explain the absence of multiple diffraction dips in the data is noted. It is argued and shown that a unitary correction to the multiple scattering amplitude gives rise to a better model and allows to fit all available data on nucleon-nucleon and nucleus-nucleus collisions at all energies and all momentum transfers. There are no multiple diffraction dips
Non-unitary neutrino propagation from neutrino decay
Energy Technology Data Exchange (ETDEWEB)
Berryman, Jeffrey M., E-mail: jeffreyberryman2012@u.northwestern.edu [Northwestern University, Department of Physics & Astronomy, 2145 Sheridan Road, Evanston, IL 60208 (United States); Gouvêa, André de; Hernández, Daniel [Northwestern University, Department of Physics & Astronomy, 2145 Sheridan Road, Evanston, IL 60208 (United States); Oliveira, Roberto L.N. [Northwestern University, Department of Physics & Astronomy, 2145 Sheridan Road, Evanston, IL 60208 (United States); Instituto de Física Gleb Wataghin Universidade Estadual de Campinas, UNICAMP 13083-970, Campinas, São Paulo (Brazil)
2015-03-06
Neutrino propagation in space-time is not constrained to be unitary if very light states – lighter than the active neutrinos – exist into which neutrinos may decay. If this is the case, neutrino flavor-change is governed by a handful of extra mixing and “oscillation” parameters, including new sources of CP-invariance violation. We compute the transition probabilities in the two- and three-flavor scenarios and discuss the different phenomenological consequences of the new physics. These are qualitatively different from other sources of unitarity violation discussed in the literature.
Non-unitary neutrino propagation from neutrino decay
International Nuclear Information System (INIS)
Berryman, Jeffrey M.; Gouvêa, André de; Hernández, Daniel; Oliveira, Roberto L.N.
2015-01-01
Neutrino propagation in space-time is not constrained to be unitary if very light states – lighter than the active neutrinos – exist into which neutrinos may decay. If this is the case, neutrino flavor-change is governed by a handful of extra mixing and “oscillation” parameters, including new sources of CP-invariance violation. We compute the transition probabilities in the two- and three-flavor scenarios and discuss the different phenomenological consequences of the new physics. These are qualitatively different from other sources of unitarity violation discussed in the literature
Experiments with Highly-Ionized Atoms in Unitary Penning Traps
Directory of Open Access Journals (Sweden)
Shannon Fogwell Hoogerheide
2015-08-01
Full Text Available Highly-ionized atoms with special properties have been proposed for interesting applications, including potential candidates for a new generation of optical atomic clocks at the one part in 1019 level of precision, quantum information processing and tests of fundamental theory. The proposed atomic systems are largely unexplored. Recent developments at NIST are described, including the isolation of highly-ionized atoms at low energy in unitary Penning traps and the use of these traps for the precise measurement of radiative decay lifetimes (demonstrated with a forbidden transition in Kr17+, as well as for studying electron capture processes.
A Unitary-Transformative Nursing Science: From Angst to Appreciation.
Cowling, W Richard
2017-10-01
The discord within nursing regarding the definition of nursing science has created great angst, particularly for those who view nursing science as a body of knowledge derived from theories specific to its unique concerns. The purpose of this brief article is to suggest a perspective and process grounded in appreciation of wholeness that may offer a way forward for proponents of a unitary-transformative nursing science that transcends the discord. This way forward is guided by principles of fostering dissent without contempt, generating a well-imagined future, and garnering appreciatively inspired action for change.
Multiscale differential phase contrast analysis with a unitary detector
Lopatin, Sergei
2015-12-30
A new approach to generate differential phase contrast (DPC) images for the visualization and quantification of local magnetic fields in a wide range of modern nano materials is reported. In contrast to conventional DPC methods our technique utilizes the idea of a unitary detector under bright field conditions, making it immediately usable by a majority of modern transmission electron microscopes. The approach is put on test to characterize the local magnetization of cylindrical nanowires and their 3D ordered arrays, revealing high sensitivity of our method in a combination with nanometer-scale spatial resolution.
Global unitary fixing and matrix-valued correlations in matrix models
International Nuclear Information System (INIS)
Adler, Stephen L.; Horwitz, Lawrence P.
2003-01-01
We consider the partition function for a matrix model with a global unitary invariant energy function. We show that the averages over the partition function of global unitary invariant trace polynomials of the matrix variables are the same when calculated with any choice of a global unitary fixing, while averages of such polynomials without a trace define matrix-valued correlation functions, that depend on the choice of unitary fixing. The unitary fixing is formulated within the standard Faddeev-Popov framework, in which the squared Vandermonde determinant emerges as a factor of the complete Faddeev-Popov determinant. We give the ghost representation for the FP determinant, and the corresponding BRST invariance of the unitary-fixed partition function. The formalism is relevant for deriving Ward identities obeyed by matrix-valued correlation functions
Nonlocal astrophysics dark matter, dark energy and physical vacuum
Alexeev, Boris V
2017-01-01
Non-Local Astrophysics: Dark Matter, Dark Energy and Physical Vacuum highlights the most significant features of non-local theory, a highly effective tool for solving many physical problems in areas where classical local theory runs into difficulties. The book provides the fundamental science behind new non-local astrophysics, discussing non-local kinetic and generalized hydrodynamic equations, non-local parameters in several physical systems, dark matter, dark energy, black holes and gravitational waves. Devoted to the solution of astrophysical problems from the position of non-local physics Provides a solution for dark matter and dark energy Discusses cosmological aspects of the theory of non-local physics Includes a solution for the problem of the Hubble Universe expansion, and of the dependence of the orbital velocity from the center of gravity
International Nuclear Information System (INIS)
Dragunov, Yu.G.; Banyuk, G.F.; Denisov, V.P.; Sorokin, S.R.; Safonova, M.A.; Prodon, D.G.
2002-01-01
The texts of the reports at the Conference of the young specialists of the Federal State Unitary Enterprise GIDROPRESS Special Designers' Office (January 24-25, 2002, Podolsk) are presented. The subject field of the reports is related to the 0NPPs designing and operation. In particular, the following problems are discussed: the operational safety of the reactors and containers for the radioactive waste storage and transport; the analysis of the WWER-type reactor behavior under different emergency situations; the possibilities of increasing the service life of the reactors at the NPPs [ru
Zhou, Junhe; Wu, Jianjie; Hu, Qinsong
2018-02-05
In this paper, we propose a novel tunable unitary transformer, which can achieve arbitrary discrete unitary transforms. The unitary transformer is composed of multiple sections of multi-core fibers with closely aligned coupled cores. Phase shifters are inserted before and after the sections to control the phases of the waves in the cores. A simple algorithm is proposed to find the optimal phase setup for the phase shifters to realize the desired unitary transforms. The proposed device is fiber based and is particularly suitable for the mode division multiplexing systems. A tunable mode MUX/DEMUX for a three-mode fiber is designed based on the proposed structure.
On the equivalence of massive qed with renormalizable and in unitary gauge
International Nuclear Information System (INIS)
Abdalla, E.
1978-03-01
In the framework of BPHZ renormalization procedure, we discuss the equivalence between 4-dimensional renormalizable massive quantum electrodynamics (Stueckelberg lagrangian), and massive QED in the unitary gauge
The universal sound velocity formula for the strongly interacting unitary Fermi gas
International Nuclear Information System (INIS)
Liu Ke; Chen Ji-Sheng
2011-01-01
Due to the scale invariance, the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas. For example, the virial theorem between pressure and energy density of the ideal gas P = 2E/3V is still satisfied by the unitary Fermi gas. This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation. For comparison, the sound velocities for the ideal Boltzmann, Bose and Fermi gas are also given. Quite interestingly, the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions. (general)
First unitary, then divided: the temporal dynamics of dividing attention.
Jefferies, Lisa N; Witt, Joseph B
2018-04-24
Whether focused visual attention can be divided has been the topic of much investigation, and there is a compelling body of evidence showing that, at least under certain conditions, attention can be divided and deployed as two independent foci. Three experiments were conducted to examine whether attention can be deployed in divided form from the outset, or whether it is first deployed as a unitary focus before being divided. To test this, we adapted the methodology of Jefferies, Enns, and Di Lollo (Journal of Experimental Psychology: Human Perception and Performance 40: 465, 2014), who used a dual-stream Attentional Blink paradigm and two letter-pair targets. One aspect of the AB, Lag-1 sparing, has been shown to occur only if the second target pair appears within the focus of attention. By presenting the second target pair at various spatial locations and assessing the magnitude of Lag-1 sparing, we probed the spatial distribution of attention. By systematically manipulating the stimulus-onset-asynchrony between the targets, we also tracked changes to the spatial distribution of attention over time. The results showed that even under conditions which encourage the division of attention, the attentional focus is first deployed in unitary form before being divided. It is then maintained in divided form only briefly before settling on a single location.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories
Buican, Matthew; Laczko, Zoltan
2018-02-01
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.
Buican, Matthew; Laczko, Zoltan
2018-02-23
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Nonlocal hyperconcentration on entangled photons using photonic module system
Energy Technology Data Exchange (ETDEWEB)
Cao, Cong; Wang, Tie-Jun; Mi, Si-Chen [School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China); State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Zhang, Ru [School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China); State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Ethnic Minority Education, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Wang, Chuan, E-mail: wangchuan@bupt.edu.cn [School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China); State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2016-06-15
Entanglement distribution will inevitably be affected by the channel and environment noise. Thus distillation of maximal entanglement nonlocally becomes a crucial goal in quantum information. Here we illustrate that maximal hyperentanglement on nonlocal photons could be distilled using the photonic module and cavity quantum electrodynamics, where the photons are simultaneously entangled in polarization and spatial-mode degrees of freedom. The construction of the photonic module in a photonic band-gap structure is presented, and the operation of the module is utilized to implement the photonic nondestructive parity checks on the two degrees of freedom. We first propose a hyperconcentration protocol using two identical partially hyperentangled initial states with unknown coefficients to distill a maximally hyperentangled state probabilistically, and further propose a protocol by the assistance of an ancillary single photon prepared according to the known coefficients of the initial state. In the two protocols, the total success probability can be improved greatly by introducing the iteration mechanism, and only one of the remote parties is required to perform the parity checks in each round of iteration. Estimates on the system requirements and recent experimental results indicate that our proposal is realizable with existing or near-further technologies.
A non-local computational boundary condition for duct acoustics
Zorumski, William E.; Watson, Willie R.; Hodge, Steve L.
1994-01-01
A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.
Nonlocal hyperconcentration on entangled photons using photonic module system
International Nuclear Information System (INIS)
Cao, Cong; Wang, Tie-Jun; Mi, Si-Chen; Zhang, Ru; Wang, Chuan
2016-01-01
Entanglement distribution will inevitably be affected by the channel and environment noise. Thus distillation of maximal entanglement nonlocally becomes a crucial goal in quantum information. Here we illustrate that maximal hyperentanglement on nonlocal photons could be distilled using the photonic module and cavity quantum electrodynamics, where the photons are simultaneously entangled in polarization and spatial-mode degrees of freedom. The construction of the photonic module in a photonic band-gap structure is presented, and the operation of the module is utilized to implement the photonic nondestructive parity checks on the two degrees of freedom. We first propose a hyperconcentration protocol using two identical partially hyperentangled initial states with unknown coefficients to distill a maximally hyperentangled state probabilistically, and further propose a protocol by the assistance of an ancillary single photon prepared according to the known coefficients of the initial state. In the two protocols, the total success probability can be improved greatly by introducing the iteration mechanism, and only one of the remote parties is required to perform the parity checks in each round of iteration. Estimates on the system requirements and recent experimental results indicate that our proposal is realizable with existing or near-further technologies.
Notes on nonlocal projective measurements in relativistic systems
International Nuclear Information System (INIS)
Lin, Shih-Yuin
2014-01-01
In quantum mechanical bipartite systems, naive extensions of von Neumann’s projective measurement to nonlocal variables can produce superluminal signals and thus violate causality. We analyze the projective quantum nondemolition state-verification in a two-spin system and see how the projection introduces nonlocality without entanglement. For the ideal measurements of “R-nonlocal” variables, we argue that causality violation can be resolved by introducing further restrictions on the post-measurement states, which makes the measurement “Q-nonlocal”. After we generalize these ideas to quantum mechanical harmonic oscillators, we look into the projective measurements of the particle number of a single mode or a wave-packet of a relativistic quantum field in Minkowski space. It turns out that the causality-violating terms in the expectation values of the local operators, generated either by the ideal measurement of the “R-nonlocal” variable or the quantum nondemolition verification of a Fock state, are all suppressed by the IR and UV cutoffs of the theory. Thus relativistic quantum field theories with such projective measurements are effectively causal
Entanglement, nonlocality and multi-particle quantum correlations
Reid, Margaret D.
2018-04-01
This paper contributes to the proceedings of the Latin-American School of Physics (ELAF-2017) on Quantum Correlations, and is a brief review of quantum entanglement and nonlocality. In such a brief review, only some topics can be covered. The emphasis is on those topics relevant that may be relevant to detecting multi-particle quantum correlations arising in atomic and Bose-Einstein condensate (BEC) experiments. The paper is divided into five sections. In the first section, the historical papers of Einstein-Podolsky-Rosen (EPR), Bell, Schrodinger and Greenberger-Zeilinger-Horne (GHZ) are described in a tutorial fashion. This is followed by an introduction to entanglement and density operators. A discussion of the classes of nonlocality is given in the third section, including the modern interpretation of the correlations of the EPR paradox experiments, known as EPR steering correlations. The fourth section covers the detection and generation of so-called continuous variable entanglement and EPR steering. Various known criteria are derived with the details of the proofs given for tutorial purposes. The final section focuses on the criteria and methods that have been useful to detect quantum correlation in BEC or atomic systems. Recent results relating spin squeezing with quantum correlations, including entanglement and EPR steering, are summarised.
Unitary input DEA model to identify beef cattle production systems typologies
Directory of Open Access Journals (Sweden)
Eliane Gonçalves Gomes
2012-08-01
Full Text Available The cow-calf beef production sector in Brazil has a wide variety of operating systems. This suggests the identification and the characterization of homogeneous regions of production, with consequent implementation of actions to achieve its sustainability. In this paper we attempted to measure the performance of 21 livestock modal production systems, in their cow-calf phase. We measured the performance of these systems, considering husbandry and production variables. The proposed approach is based on data envelopment analysis (DEA. We used unitary input DEA model, with apparent input orientation, together with the efficiency measurements generated by the inverted DEA frontier. We identified five modal production systems typologies, using the isoefficiency layers approach. The results showed that the knowledge and the processes management are the most important factors for improving the efficiency of beef cattle production systems.
Greenberger-Horne-Zeilinger nonlocality for continuous-variable systems
International Nuclear Information System (INIS)
Chen Zengbing; Zhang Yongde
2002-01-01
As a development of our previous work, this paper is concerned with the Greenberger-Horne-Zeilinger (GHZ) nonlocality for continuous-variable cases. The discussion is based on the introduction of a pseudospin operator, which has the same algebra as the Pauli operator, for each of the N modes of a light field. Then the Bell-Clauser-Horne-Shimony-Holt inequality is presented for the N modes, each of which has a continuous degree of freedom. Following Mermin's argument, it is demonstrated that for N-mode parity-entangled GHZ states (in an infinite-dimensional Hilbert space) of the light field, the contradictions between quantum mechanics and local realism grow exponentially with N, similarly to the usual N-spin cases
Compactifications of the Heterotic string with unitary bundles
Energy Technology Data Exchange (ETDEWEB)
Weigand, T.
2006-05-23
In this thesis we investigate a large new class of four-dimensional supersymmetric string vacua defined as compactifications of the E{sub 8} x E{sub 8} and the SO(32) heterotic string on smooth Calabi-Yau threefolds with unitary gauge bundles and heterotic five-branes. The first part of the thesis discusses the implementation of this idea into the E{sub 8} x E{sub 8} heterotic string. After specifying a large class of group theoretic embeddings featuring unitary bundles, we analyse the effective four-dimensional N=1 supergravity upon compactification. From the gauge invariant Kaehler potential for the moduli fields we derive a modification of the Fayet-Iliopoulos D-terms arising at one-loop in string perturbation theory. From this we conjecture a one-loop deformation of the Hermitian Yang-Mills equation and introduce the idea of {lambda}-stability as the perturbatively correct stability concept generalising the notion of Mumford stability valid at tree-level. We then proceed to a definition of SO(32) heterotic vacua with unitary gauge bundles in the presence of heterotic five-branes and find agreement of the resulting spectrum with the S-dual framework of Type I/Type IIB orientifolds. A similar analysis of the effective four-dimensional supergravity is performed. Further evidence for the proposed one-loop correction to the stability condition is found by identifying the heterotic corrections as the S-dual of the perturbative part of {pi}-stability as the correct stability concept in Type IIB theory. After reviewing the construction of holomorphic stable vector bundles on elliptically fibered Calabi-Yau manifolds via spectral covers, we provide semi-realistic examples for SO(32) heterotic vacua with Pati-Salam and MSSM-like gauge sectors. We finally discuss the construction of realistic vacua with flipped SU(5) GUT and MSSM gauge group within the E{sub 8} x E{sub 8} framework, based on the embedding of line bundles into both E{sub 8} factors. Some of the appealing
Nonlocal inhomogeneous broadening in plasmonic nanoparticle ensembles
DEFF Research Database (Denmark)
Tserkezis, Christos; Maack, Johan Rosenkrantz; Liu, Z.
Nonclassical effects are increasingly more relevant in plasmonics as modern nanofabrication techniques rapidly approach the extreme nanoscale limits, for which departing from classical electrodynamics becomes important. One of the largest-scale necessary corrections towards this direction...... is to abandon the local response approximation (LRA) and take the nonlocal response of the metal into account, typically through the simple hydrodynamic Drude model (HDM), which predicts a sizedependent deviation of plasmon modes from the quasistatic (QS) limit. While this behaviour has been explored for simple...... metallic nanoparticles (NPs) or NP dimers, the possibility of inhomogeneous resonance broadening due to size variation in a large NP collection and the resulting spectral overlap of modes (as depicted in Fig. 1), has been so far overlooked. Here we study theoretically the effect of nonlocality on ensemble...
Nonlocal synchronization in nearest neighbour coupled oscillators
International Nuclear Information System (INIS)
El-Nashar, H.F.; Elgazzar, A.S.; Cerdeira, H.A.
2002-02-01
We investigate a system of nearest neighbour coupled oscillators. We show that the nonlocal frequency synchronization, that might appear in such a system, occurs as a consequence of the nearest neighbour coupling. The power spectra of nonadjacent oscillators shows that there is no complete coincidence between all frequency peaks of the oscillators in the nonlocal cluster, while the peaks for neighbouring oscillators approximately coincide even if they are not yet in a cluster. It is shown that nonadjacent oscillators closer in frequencies, share slow modes with their adjacent oscillators which are neighbours in space. It is also shown that when a direct coupling between non-neighbours oscillators is introduced explicitly, the peaks of the spectra of the frequencies of those non-neighbours coincide. (author)
Evidence and concepts for nonlocal transport
International Nuclear Information System (INIS)
Callen, J.D.; Kissick, M.W.
1997-08-01
Up until a few years ago, most transient transport studies observed primarily diffusive plasma transport responses to fast, localized perturbations. Recently, a number of experiments have, in addition, observed nonlocal electron heat responses. Most remarkably, in cold pulse experiments the abrupt edge cooling via radiative processes can induce both a diffusive cooling response moving in from the edge, and simultaneously a rising electron temperature in the central core of tokamak plasmas--an opposite response even before the diffusive cooling from the edge reaches the center. These and other nonlocal electron heat transport conundrums from recent experiments are reviewed. Also, models and physical processes being advanced to explain these puzzling phenomena are discussed. The importance of resolving this transport enigma is emphasized
Nonlocal transport in hot plasma. Part I
International Nuclear Information System (INIS)
Brantov, A. V.; Bychenkov, V. Yu.
2013-01-01
The problem of describing charged particle transport in hot plasma under the conditions in which the ratio of the electron mean free path to the gradient length is not too small is one of the key problems of plasma physics. However, up to now, there was a deficit of the systematic interpretation of the current state of this problem, which, in most studies, is formulated as the problem of nonlocal transport. In this review, we fill this gap by presenting a self-consistent linear theory of nonlocal transport for small plasma perturbations and an arbitrary collisionality from the classical highly collisional hydrodynamic regime to the collisionless regime. We describe a number of nonlinear transport models and demonstrate the application of the nonclassical transport theory to the solution of some problems of plasma physics, first of all for plasmas produced by nanosecond laser pulses with intensities of 10 13 –10 16 W/cm 2
Nonlocality and short-range wetting phenomena.
Parry, A O; Romero-Enrique, J M; Lazarides, A
2004-08-20
We propose a nonlocal interfacial model for 3D short-range wetting at planar and nonplanar walls. The model is characterized by a binding-potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tubelike fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong nonperturbative influence of nonlocality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.
Nonlocality and Short-Range Wetting Phenomena
Parry, A. O.; Romero-Enrique, J. M.; Lazarides, A.
2004-08-01
We propose a nonlocal interfacial model for 3D short-range wetting at planar and nonplanar walls. The model is characterized by a binding-potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tubelike fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong nonperturbative influence of nonlocality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.
EPR paradox, quantum nonlocality and physical reality
International Nuclear Information System (INIS)
Kupczynski, M
2016-01-01
Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are
EPR paradox, quantum nonlocality and physical reality
Kupczynski, M.
2016-03-01
Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced
Using nonlocal coherence to quantify quantum correlation
Pei, Pei; Wang, Wei; Li, Chong; Song, He-Shan
2010-01-01
We reexamine quantum correlation from the fundamental perspective of its consanguineous quantum property, the coherence. We emphasize the importance of specifying the tensor product structure of the total state space before discussing quantum correlation. A measure of quantum correlation for arbitrary dimension bipartite states using nonlocal coherence is proposed, and it can be easily generalized to the multipartite case. The quantification of non-entangled component within quantum correlati...
Nonlocal Boltzmann theory of plasma channels
International Nuclear Information System (INIS)
Yu, S.S.; Melendez, R.E.
1983-01-01
The mathematical framework for the LLNL code NUTS is developed. This code is designed to study the evolution of an electron-beam-generated plasma channel at all pressures. The Boltzmann treatment of the secondary electrons presented include all inertial, nonlocal, electric and magnetic effects, as well as effects of atomic collisions. Field equations are advanced simultaneously and self-consistently with the evolving plasma currents
Hartman effect and nonlocality in quantum networks
International Nuclear Information System (INIS)
Bandopadhyay, Swarnali; Jayannavar, A.M.
2005-01-01
We study the phase time for various quantum mechanical networks having potential barriers in their arms to find the generic presence of Hartman effect. In such systems it is possible to control the 'super arrival' time in one of the arms by changing parameters on another, spatially separated from it. This is yet another quantum nonlocal effect. Negative time delays (time advancement) and 'ultra Hartman effect' with negative saturation times have been observed in some parameter regimes
Switching non-local vector median filter
Matsuoka, Jyohei; Koga, Takanori; Suetake, Noriaki; Uchino, Eiji
2016-04-01
This paper describes a novel image filtering method that removes random-valued impulse noise superimposed on a natural color image. In impulse noise removal, it is essential to employ a switching-type filtering method, as used in the well-known switching median filter, to preserve the detail of an original image with good quality. In color image filtering, it is generally preferable to deal with the red (R), green (G), and blue (B) components of each pixel of a color image as elements of a vectorized signal, as in the well-known vector median filter, rather than as component-wise signals to prevent a color shift after filtering. By taking these fundamentals into consideration, we propose a switching-type vector median filter with non-local processing that mainly consists of a noise detector and a noise removal filter. Concretely, we propose a noise detector that proactively detects noise-corrupted pixels by focusing attention on the isolation tendencies of pixels of interest not in an input image but in difference images between RGB components. Furthermore, as the noise removal filter, we propose an extended version of the non-local median filter, we proposed previously for grayscale image processing, named the non-local vector median filter, which is designed for color image processing. The proposed method realizes a superior balance between the preservation of detail and impulse noise removal by proactive noise detection and non-local switching vector median filtering, respectively. The effectiveness and validity of the proposed method are verified in a series of experiments using natural color images.
Nonlocal Gravity and Structure in the Universe
Energy Technology Data Exchange (ETDEWEB)
Dodelson, Scott [Chicago U., Astron. Astrophys. Ctr.; Park, Sohyun [Penn State U., University Park, IGC
2014-08-26
The observed acceleration of the Universe can be explained by modifying general relativity. One such attempt is the nonlocal model of Deser and Woodard. Here we fix the background cosmology using results from the Planck satellite and examine the predictions of nonlocal gravity for the evolution of structure in the universe, confronting the model with three tests: gravitational lensing, redshift space distortions, and the estimator of gravity $E_G$. Current data favor general relativity (GR) over nonlocal gravity: fixing primordial cosmology with the best fit parameters from Planck leads to weak lensing results favoring GR by 5.9 sigma; redshift space distortions measurements of the growth rate preferring GR by 7.8 sigma; and the single measurement of $E_G$ favoring GR, but by less than 1-sigma. The significance holds up even after the parameters are allowed to vary within Planck limits. The larger lesson is that a successful modified gravity model will likely have to suppress the growth of structure compared to general relativity.
The Schur algorithm for generalized Schur functions III : J-unitary matrix polynomials on the circle
Alpay, Daniel; Azizov, Tomas; Dijksma, Aad; Langer, Heinz
2003-01-01
The main result is that for J = ((1)(0) (0)(-1)) every J-unitary 2 x 2-matrix polynomial on the unit circle is an essentially unique product of elementary J-unitary 2 x 2-matrix polynomials which are either of degree 1 or 2k. This is shown by means of the generalized Schur transformation introduced
An Informal Overview of the Unitary Group Approach
International Nuclear Information System (INIS)
Sonnad, V.; Escher, J.; Kruse, M.; Baker, R.
2016-01-01
The Unitary Groups Approach (UGA) is an elegant and conceptually unified approach to quantum structure calculations. It has been widely used in molecular structure calculations, and holds the promise of a single computational approach to structure calculations in a variety of different fields. We explore the possibility of extending the UGA to computations in atomic and nuclear structure as a simpler alternative to traditional Racah algebra-based approaches. We provide a simple introduction to the basic UGA and consider some of the issues in using the UGA with spin-dependent, multi-body Hamiltonians requiring multi-shell bases adapted to additional symmetries. While the UGA is perfectly capable of dealing with such problems, it is seen that the complexity rises dramatically, and the UGA is not at this time, a simpler alternative to Racah algebra-based approaches.
The SNARC effect is not a unitary phenomenon.
Basso Moro, Sara; Dell'Acqua, Roberto; Cutini, Simone
2018-04-01
Models of the spatial-numerical association of response codes (SNARC) effect-faster responses to small numbers using left effectors, and the converse for large numbers-diverge substantially in localizing the root cause of this effect along the numbers' processing chain. One class of models ascribes the cause of the SNARC effect to the inherently spatial nature of the semantic representation of numerical magnitude. A different class of models ascribes the effect's cause to the processing dynamics taking place during response selection. To disentangle these opposing views, we devised a paradigm combining magnitude comparison and stimulus-response switching in order to monitor modulations of the SNARC effect while concurrently tapping both semantic and response-related processing stages. We observed that the SNARC effect varied nonlinearly as a function of both manipulated factors, a result that can hardly be reconciled with a unitary cause of the SNARC effect.
Construction of unitary matrices from observable transition probabilities
International Nuclear Information System (INIS)
Peres, A.
1989-01-01
An ideal measuring apparatus defines an orthonormal basis vertical strokeu m ) in Hilbert space. Another apparatus defines another basis vertical strokeυ μ ). Both apparatuses together allow to measure the transition probabilities P mμ =vertical stroke(u m vertical strokeυ μ )vertical stroke 2 . The problem is: Given all the elements of a doubly stochastic matrix P mμ , find a unitary matrix U mμ such that P mμ =vertical strokeU mμ vertical stroke 2 . The number of unknown nontrivial phases is equal to the number of independent equations to satisfy. The problem can therefore be solved provided that the values of the P mμ satisfy some inequalities. (orig.)
The Science of Unitary Human Beings in a Creative Perspective.
Caratao-Mojica, Rhea
2015-10-01
In moving into a new kind of world, nurses are encouraged to look ahead and be innovative by transcending to new ways of using nursing knowledge while embracing a new worldview. "We need to recognize that we're going to have to use our imagination more and more" (Rogers, 1994). On that note, the author in this paper explicates Rogers' science of unitary human beings in a creative way relating it to painting. In addition, the author also explores works derived from Rogers' science such as Butcher's (1993) and Cowling's (1997), which are here discussed in light of an artwork. A painting is presented with the unpredictability, creativity, and the "dance of color and light" (Butcher, 1993) is appreciated through comprehending essence, pandimensionality, and wholeness. © The Author(s) 2015.
Territory in the Constitutional Standards of Unitary States
Directory of Open Access Journals (Sweden)
Marina V. Markhgeym
2017-06-01
Full Text Available The article is based on the analysis of the constitutions of seven European countries (Albania, Hungary, Greece, Spain, Malta, Poland, Sweden. The research allows to reveal general and specific approaches to consolidation of norms on territories in a state and give the characteristic of the corresponding constitutional norms. Given the authors ' comprehensive approach to the definition of the territory of the state declared constitutional norms were assessed from the perspective of the fundamental principles and constituent elements of the territory. Considering the specifics of the constitutional types of state territories authors suggest typical and variative models and determine the constitutions of unitary states, distinguished by their originality in the declared group of legal relations. The original constitutional language areas associated with the introduction at the state level, these types of areas that are not typical for other countries.
Gap solitons under competing local and nonlocal nonlinearities
International Nuclear Information System (INIS)
Kuo, Kuan-Hsien; Lin Yuanyao; Lee, Ray-Kuang; Malomed, Boris A.
2011-01-01
We analyze the existence, bifurcations, and shape transformations of one-dimensional gap solitons (GSs) in the first finite band gap induced by a periodic potential built into materials with local self-focusing and nonlocal self-defocusing nonlinearities. Originally stable on-site GS modes become unstable near the upper edge of the band gap with the introduction of the nonlocal self-defocusing nonlinearity with a small nonlocality radius. Unstable off-site GSs bifurcate into a new branch featuring single-humped, double-humped, and flat-top modes due to the competition between local and nonlocal nonlinearities. The mechanism underlying the complex bifurcation pattern and cutoff effects (termination of some bifurcation branches) is illustrated in terms of the shape transformation under the action of the varying degree of the nonlocality. The results of this work suggest a possibility of optical-signal processing by means of the competing nonlocal and local nonlinearities.
International Nuclear Information System (INIS)
Colombant, Denis; Manheimer, Wallace
2010-01-01
Flux limitation and preheat are important processes in electron transport occurring in laser produced plasmas. The proper calculation of both of these has been a subject receiving much attention over the entire lifetime of the laser fusion project. Where nonlocal transport (instead of simple single flux limit) has been modeled, it has always been with what we denote the equivalent diffusion solution, namely treating the transport as only a diffusion process. We introduce here a new approach called the nonlocal source solution and show it is numerically viable for laser produced plasmas. It turns out that the equivalent diffusion solution generally underestimates preheat. Furthermore, the advance of the temperature front, and especially the preheat, can be held up by artificial 'thermal barriers'. The nonlocal source method of solution, on the other hand more accurately describes preheat and can stably calculate the solution for the temperature even if the heat flux is up the gradient.
Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing.
Elmoataz, Abderrahim; Lezoray, Olivier; Bougleux, Sébastien
2008-07-01
We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach considers the problem as a variational one, which consists of minimizing a weighted sum of two energy terms: a regularization one that uses a discrete weighted p-Dirichlet energy and an approximation one. This is the discrete analogue of recent continuous Euclidean nonlocal regularization functionals. The proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted p-Laplace operator, parameterized by the degree p of regularity, the graph structure and the graph weight function. These discrete processing methods provide a graph-based version of recently proposed semi-local or nonlocal processing methods used in image and mesh processing, such as the bilateral filter, the TV digital filter or the nonlocal means filter. It works with equal ease on regular 2-D and 3-D images, manifolds or any data. We illustrate the abilities of the approach by applying it to various types of images, meshes, manifolds, and data represented as graphs.
Experimental demonstration of conflicting interest nonlocal games using superconducting qubits
Situ, Haozhen; Li, Lvzhou; Huang, Zhiming; He, Zhimin; Zhang, Cai
2018-06-01
Conflicting interest nonlocal games are special Bayesian games played by noncooperative players without communication. In recent years, some conflicting interest nonlocal games have been proposed where quantum advice can help players to obtain higher payoffs. In this work we perform an experiment of six conflicting interest nonlocal games using the IBM quantum computer made up of five superconducting qubits. The experimental results demonstrate quantum advantage in four of these games, whereas the other two games fail to showcase quantum advantage in the experiment.
Modulational instability and nonlocality management in coupled NLS systems
International Nuclear Information System (INIS)
Doktorov, Evgeny V; Molchan, Maxim A
2007-01-01
The modulational instability of two interacting waves in a nonlocal Kerr-type medium is considered analytically and numerically. For a generic choice of wave amplitudes, we give a complete description of stable/unstable regimes for zero group-velocity mismatch. It is shown that nonlocality suppresses considerably the growth rate and bandwidth of instability. For nonzero group-velocity mismatch we perform a geometrical analysis of a nonlocality management which can provide stability of waves otherwise unstable in a local medium
Occurrence of exact R{sup 2} inflation in non-local UV-complete gravity
Energy Technology Data Exchange (ETDEWEB)
Koshelev, Alexey S. [Departamento de Física and Centro de Matemática e Aplicações (CMA-UBI),Universidade da Beira Interior, 6200 Covilhã (Portugal); Theoretische Natuurkunde, Vrije Universiteit Brussel, and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Modesto, Leonardo [Department of Physics, Southern University of Science and Technology, Shenzhen 518055 (China); Department of Physics & Center for Field Theory and Particle Physics, Fudan University,200433 Shanghai (China); Rachwał, Lesław [Department of Physics & Center for Field Theory and Particle Physics, Fudan University,200433 Shanghai (China); Starobinsky, Alexei A. [L.D. Landau Institute for Theoretical Physics RAS, Moscow 119334 (Russian Federation); Kazan Federal University, Kazan 420008, Republic of Tatarstan (Russian Federation)
2016-11-10
The R+R{sup 2}, shortly named “R{sup 2}” (“Starobinsky”) inflationary model, represents a fully consistent example of a one-parameter inflationary scenario. This model has a “graceful exit” from inflation and provides a mechanism for subsequent creation and final thermalization of the standard matter. Moreover, it produces a very good fit of the observed spectrum of primordial perturbations. In the present paper we show explicitly that the R{sup 2} inflationary spacetime is an exact solution of a range of weakly non-local (quasi-polynomial) gravitational theories, which provide an ultraviolet completion of the R{sup 2} theory. These theories are ghost-free, super-renormalizable or finite at quantum level, and perturbatively unitary. Their spectrum consists of the graviton and the scalaron that is responsible for driving the inflation. Notably, any further extension of the spectrum leads to propagating ghost degrees of freedom. We are aimed at presenting a detailed construction of such theories in the so called Weyl basis. Further, we give a special account to the cosmological implications of this theory by considering perturbations during inflation. The highlight of the non-local model is the prediction of a modified, in comparison to a local R{sup 2} model, value for the ratio of tensor and scalar power spectra r, depending on the parameters of the theory. The relevant parameters are under control to be successfully confronted with existing observational data. Furthermore, the modified r can surely meet future observational constraints.
Explicit solution for a wave equation with nonlocal condition
Bazhlekova, Emilia; Dimovski, Ivan
2012-11-01
An initial-boundary value problem with a nonlocal boundary condition for one-dimensional wave equation is studied. Applying spectral projections, we find a series solution of the problem. The character of the solution found shows that the oscillation amplitude of the system described by this equation increases with time at any fixed x in absence of external forces. To find a representation of the solution more convenient for numerical calculation we develop a two-dimensional operational calculus for the problem. The solution is expressed as a sum of non-classical convolution products of particular solutions and the arbitrary initial functions. This result is an extension of the classical Duhamel principle for the space variable. The representation is used successfully for numerical computation and visualization of the solution. Numerical results obtained for specific test problems with known exact solutions indicate that the present technique provides accurate numerical solutions.
Sign-changing solutions for non-local elliptic equations
Directory of Open Access Journals (Sweden)
Huxiao Luo
2017-07-01
Full Text Available This article concerns the existence of sign-changing solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions, $$\\displaylines{ -\\mathcal{L}_Ku=f(x,u,\\quad x\\in \\Omega, \\cr u=0,\\quad x\\in \\mathbb{R}^n\\setminus\\Omega, }$$ where $\\Omega\\subset\\mathbb{R}^n\\; (n\\geq2$ is a bounded, smooth domain and the nonlinear term f satisfies suitable growth assumptions. By using Brouwer's degree theory and Deformation Lemma and arguing as in [2], we prove that there exists a least energy sign-changing solution. Our results generalize and improve some results obtained in [27
Local and nonlocal order parameters in the Kitaev chain
Chitov, Gennady Y.
2018-02-01
We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs) defined via the correlation functions of the Majorana string operators. The SOPs are mapped onto the local order parameters of some dual Hamiltonians and easily calculated. We have shown that the phase diagram of the interacting dimerized chain comprises the phases with the conventional local order as well as the phases with nonlocal SOPs. From the results for the critical indices, we infer the two-dimensional Ising universality class of criticality at the particular symmetry point where the model is exactly solvable.
International Nuclear Information System (INIS)
Kaganovich, Igor D.; Polomarov, Oleg
2003-01-01
In low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially non-local. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the non-local conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, non-uniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the non-uniform plasma density profile on both the current density profile and the EEDF is demonstrated
Nonlocal effects on dynamic damage accumulation in brittle solids
Energy Technology Data Exchange (ETDEWEB)
Chen, E.P.
1995-12-01
This paper presents a nonlocal analysis of the dynamic damage accumulation processes in brittle solids. A nonlocal formulation of a microcrack based continuum damage model is developed and implemented into a transient dynamic finite element computer code. The code is then applied to the study of the damage accumulation process in a concrete plate with a central hole and subjected to the action of a step tensile pulse applied at opposite edges of the plate. Several finite element discretizations are used to examine the mesh size effect. Comparisons between calculated results based on local and nonlocal formulations are made and nonlocal effects are discussed.
Alpay, D.; Dijksma, A.; Langer, H.
2004-01-01
We prove that a 2 × 2 matrix polynomial which is J-unitary on the real line can be written as a product of normalized elementary J-unitary factors and a J-unitary constant. In the second part we give an algorithm for this factorization using an analog of the Schur transformation.
Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm
Directory of Open Access Journals (Sweden)
Wang Rong-Nian
2011-01-01
Full Text Available Abstract In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered. Mathematics subject classification (2000 26A33, 34G10, 34G20
Greenberger-Horne-Zeilinger argument of nonlocality without inequalities for mixed states
International Nuclear Information System (INIS)
Ghirardi, Gian Carlo; Marinatto, Luca
2006-01-01
We generalize the Greenberger-Horne-Zeilinger nonlocality without inequalities argument to cover the case of arbitrary mixed statistical operators associated to three-qubits quantum systems. More precisely, we determine the radius of a ball (in the trace distance topology) surrounding the pure GHZ state and containing arbitrary mixed statistical operators which cannot be described by any local and realistic hidden variable model and which are, as a consequence, noncompletely separable. As a practical application, we focus on certain one-parameter classes of mixed states which are commonly considered in the experimental realization of the original GHZ argument and which result from imperfect preparations of the pure GHZ state. In these cases we determine for which values of the parameter measuring the noise a nonlocality argument can still be exhibited, despite the mixedness of the considered states. Moreover, the effect of the imperfect nature of measurement processes is discussed
Local unitary versus local Clifford equivalence of stabilizer and graph states
International Nuclear Information System (INIS)
Zeng, Bei; Chung, Hyeyoun; Cross, Andrew W.; Chuang, Isaac L.
2007-01-01
The equivalence of stabilizer states under local transformations is of fundamental interest in understanding properties and uses of entanglement. Two stabilizer states are equivalent under the usual stochastic local operations and classical communication criterion if and only if they are equivalent under local unitary (LU) operations. More surprisingly, under certain conditions, two LU-equivalent stabilizer states are also equivalent under local Clifford (LC) operations, as was shown by Van den Nest et al. [Phys. Rev. A 71, 062323 (2005)]. Here, we broaden the class of stabilizer states for which LU equivalence implies LC equivalence (LU LC) to include all stabilizer states represented by graphs with cycles of length neither 3 nor 4. To compare our result with Van den Nest et al.'s, we show that any stabilizer state of distance δ=2 is beyond their criterion. We then further prove that LU LC holds for a more general class of stabilizer states of δ=2. We also explicitly construct graphs representing δ>2 stabilizer states which are beyond their criterion: we identify all 58 graphs with up to 11 vertices and construct graphs with 2 m -1 (m≥4) vertices using quantum error-correcting codes which have non-Clifford transversal gates
Directory of Open Access Journals (Sweden)
Tomas eVeloz
2015-11-01
Full Text Available Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked.In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. %Moreover, we show that each representation is unique up to change of basis. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.
Veloz, Tomas; Desjardins, Sylvie
2015-01-01
Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.
Energy Technology Data Exchange (ETDEWEB)
Green, Jeremy; Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2017-07-15
Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.
International Nuclear Information System (INIS)
Green, Jeremy; Jansen, Karl; Steffens, Fernanda
2017-07-01
Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.
Well-posedness and exponential stability for a wave equation with nonlocal time-delay condition
Directory of Open Access Journals (Sweden)
Carlos Alberto Raposo
2017-11-01
Full Text Available Well-posedness and exponential stability of nonlocal time-delayed of a wave equation with a integral conditions of the 1st kind forms the center of this work. Through semigroup theory we prove the well-posedness by the Hille-Yosida theorem and the exponential stability exploring the dissipative properties of the linear operator associated to damped model using the Gearhart-Huang-Pruss theorem.
Tensor Norms and the Classical Communication Complexity of Nonlocal Quantum Measurement
Shi, Yaoyun; Zhu, Yufan
2005-01-01
We initiate the study of quantifying nonlocalness of a bipartite measurement by the minimum amount of classical communication required to simulate the measurement. We derive general upper bounds, which are expressed in terms of certain tensor norms of the measurement operator. As applications, we show that (a) If the amount of communication is constant, quantum and classical communication protocols with unlimited amount of shared entanglement or shared randomness compute the same set of funct...
Directory of Open Access Journals (Sweden)
Mingqi Xiang
2013-04-01
Full Text Available In this article, we study a class of nonlocal quasilinear parabolic variational inequality involving $p(x$-Laplacian operator and gradient constraint on a bounded domain. Choosing a special penalty functional according to the gradient constraint, we transform the variational inequality to a parabolic equation. By means of Galerkin's approximation method, we obtain the existence of weak solutions for this equation, and then through a priori estimates, we obtain the weak solutions of variational inequality.
The nonlocal elastomagnetoelectrostatics of disordered micropolar media
International Nuclear Information System (INIS)
Kabychenkov, A. F.; Lisiovskii, F. V.
2016-01-01
The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.
Some loopholes to save quantum nonlocality
Accardi, Luigi
2005-02-01
The EPR-chameleon experiment has closed a long standing debate between the supporters of quantum nonlocality and the thesis of quantum probability according to which the essence of the quantum pecularity is non Kolmogorovianity rather than non locality. The theory of adaptive systems (symbolized by the chameleon effect) provides a natural intuition for the emergence of non-Kolmogorovian statistics from classical deterministic dynamical systems. These developments are quickly reviewed and in conclusion some comments are introduced on recent attempts to "reconstruct history" on the lines described by Orwell in "1984".
Pion polarizability in nonlocal quark model
International Nuclear Information System (INIS)
Efimov, G.V.; Okhlopkova, V.A.
1978-01-01
The γγ→ππ amplitude was calculated in nonlocal quark model in the fourth order on the perturbation theory. The coefficients of electric[a) and magnetic polarizability (β) determined are equal in magnitude and opposite in sign αsub(π+-)=βsub(π+-)=+0.014α/msub(π)sup(3), αsub(πsup(0))=-βsub(πsup(0))=-0.07α/msub(π)sup(3). The results have been compared with calculations in other models
Non-local Effects of Conformal Anomaly
Meissner, Krzysztof A.; Nicolai, Hermann
2018-03-01
It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein's equations. The fact that Einstein's general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein's theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in D=4 for both the C^2 invariant and the Euler (Gauss-Bonnet) invariant can only be achieved for N-extended supergravity multiplets with N ≥ 5.
Spectral tunneling of lattice nonlocal solitons
International Nuclear Information System (INIS)
Kartashov, Yaroslav V.; Torner, Lluis; Vysloukh, Victor A.
2010-01-01
We address spectral tunneling of walking spatial solitons in photorefractive media with nonlocal diffusion component of the nonlinear response and an imprinted shallow optical lattice. In contrast to materials with local nonlinearities, where solitons traveling across the lattice close to the Bragg angle suffer large radiative losses, in photorefractive media with diffusion nonlinearity resulting in self-bending, solitons survive when their propagation angle approaches and even exceeds the Bragg angle. In the spatial frequency domain this effect can be considered as tunneling through the band of spatial frequencies centered around the Bragg frequency where the spatial group velocity dispersion is positive.
Hyperspherical effective interaction for nonlocal potentials
International Nuclear Information System (INIS)
Barnea, N.; Leidemann, W.; Orlandini, G.
2010-01-01
The effective interaction hyperspherical-harmonics method, formulated for local forces, is generalized to accommodate nonlocal interactions. As for local potentials this formulation retains the separation of the hyper-radial part leading solely to a hyperspherical effective interaction. By applying the method to study ground-state properties of 4 He with a modern effective-field-theory nucleon-nucleon potential model (Idaho-N3LO), one finds a substantial acceleration in the convergence rate of the hyperspherical-harmonics series. Also studied are the binding energies of the six-body nuclei 6 He and 6 Li with the JISP16 nuclear force. Again an excellent convergence is observed.
Non-local modeling of materials
DEFF Research Database (Denmark)
Niordson, Christian Frithiof
2002-01-01
Numerical studies of non-local plasticity effects on different materials and problems are carried out. Two different theories are used. One is of lower order in that it retains the structure of a conventional plasticity boundary value problem, while the other is of higher order and employs higher...... order stresses as work conjugates to higher order strains and uses higher order boundary conditions. The influence of internal material length parameters is studied, and the effects of higher order boundary conditions are analyzed. The focus of the thesis is on metal-matrix composites, and non...
A nonlocal model of chiral dynamics
International Nuclear Information System (INIS)
Holdom, B.; Terning, J.; Verbeek, K.
1989-01-01
We consider a nonlocal generalization of the nonlinear σ model. Our chirally symmetric model couples quarks with self-energy Σ(p) to Goldstone bosons (GBs). By integrating out the quarks we obtain a chiral lagrangian, the parameters of which are finite integrals of Σ(p). We find that chiral symmetry is not sufficient to derive the well-known Pagels-Stokar formula for the GB decay constant. We reproduce the Wess-Zumino term and we illustrate the dependence of other four derivative coefficients on Σ(p). (orig.)
Quantum circuits cannot control unknown operations
International Nuclear Information System (INIS)
Araújo, Mateus; Feix, Adrien; Costa, Fabio; Brukner, Časlav
2014-01-01
One of the essential building blocks of classical computer programs is the ‘if’ clause, which executes a subroutine depending on the value of a control variable. Similarly, several quantum algorithms rely on applying a unitary operation conditioned on the state of a control system. Here we show that this control cannot be performed by a quantum circuit if the unitary is completely unknown. The task remains impossible even if we allow the control to be done modulo a global phase. However, this no-go theorem does not prevent implementing quantum control of unknown unitaries in practice, as any physical implementation of an unknown unitary provides additional information that makes the control possible. We then argue that one should extend the quantum circuit formalism to capture this possibility in a straightforward way. This is done by allowing unknown unitaries to be applied to subspaces and not only to subsystems. (paper)
Non-local matrix generalizations of W-algebras
International Nuclear Information System (INIS)
Bilal, A.
1995-01-01
There is a standard way to define two symplectic (hamiltonian) structures, the first and second Gelfand-Dikii brackets, on the space of ordinary m th -order linear differential operators L=-d m +U 1 d m-1 +U 2 d m-2 +..+U m . In this paper, I consider in detail the case where the U k are nxn-matrix-valued functions, with particular emphasis on the (more interesting) second Gelfand-Dikii bracket. Of particular interest is the reduction to the symplectic submanifold U 1 =0. This reduction gives rise to matrix generalizations of (the classical version of) the non-linear W m -algebras, called V n,m -algebras. The non-commutativity of the matrices leads to non-local terms in these V n,m -algebras. I show that these algebras contain a conformal Virasoro subalgebra and that combinations W k of the U k can be formed that are nxn-matrices of conformally primary fields of spin k, in analogy with the scalar case n=1. In general however, the V m,n -algebras have a much richer structure than the W m -algebras as can be seen on the examples of the non-linear and non-local Poisson brackets {(U 2 ) ab (σ),(U 2 ) cd (σ')}, {(U 2 ) ab (σ),(W 3 ) cd (σ')} and {(W 3 ) ab (σ),(W 3 ) cd (σ')} which I work out explicitly for all m and n. A matrix Miura transformation is derived, mapping these complicated (second Gelfand-Dikii) brackets of the U k to a set of much simpler Poisson brackets, providing the analogue of the free-field representation of the W m -algebras. (orig.)
Koithan, Mary S; Kreitzer, Mary Jo; Watson, Jean
2017-07-01
The principles of integrative nursing and caring science align with the unitary paradigm in a way that can inform and shape nursing knowledge, patient care delivery across populations and settings, and new healthcare policy. The proposed policies may transform the healthcare system in a way that supports nursing praxis and honors the discipline's unitary paradigm. This call to action provides a distinct and hopeful vision of a healthcare system that is accessible, equitable, safe, patient-centered, and affordable. In these challenging times, it is the unitary paradigm and nursing wisdom that offer a clear path forward.
Symmetric mixed states of n qubits: Local unitary stabilizers and entanglement classes
Energy Technology Data Exchange (ETDEWEB)
Lyons, David W.; Walck, Scott N. [Lebanon Valley College, Annville, Pennsylvania 17003 (United States)
2011-10-15
We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states of n qubits into six classes. These include the stabilizer types of the Werner states, the Greenberger-Horne-Zeilinger state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.
Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.
Jin, Leisheng; Li, Lijie
2017-12-01
In this work, nonlinear dynamics of silicon nanowire resonator considering nonlocal effect has been investigated. For the first time, dynamical parameters (e.g., resonant frequency, Duffing coefficient, and the damping ratio) that directly influence the nonlinear dynamics of the nanostructure have been derived. Subsequently, by calculating their response with the varied nonlocal coefficient, it is unveiled that the nonlocal effect makes more obvious impacts at the starting range (from zero to a small value), while the impact of nonlocal effect becomes weaker when the nonlocal term reaches to a certain threshold value. Furthermore, to characterize the role played by nonlocal effect in exerting influence on nonlinear behaviors such as bifurcation and chaos (typical phenomena in nonlinear dynamics of nanoscale devices), we have calculated the Lyapunov exponents and bifurcation diagram with and without nonlocal effect, and results shows the nonlocal effect causes the most significant effect as the device is at resonance. This work advances the development of nanowire resonators that are working beyond linear regime.
Discussion record of the workshop on nonlocal transport
International Nuclear Information System (INIS)
Itoh, K.; Itoh, S.-I.; Stroth, U.; Iwasaki, T.; Yagi, M.; Fukuyama, A.
1997-06-01
The discussion on the problem of the transient response and nonlocal transport is reported. Problem of the transient response is surveyed, and several approaches are reviewed. The formulation based on the nonlocal transport is discussed. Example of the analysis is presented. Future study is identified. (author)
Greenberger-Horne-Zeilinger nonlocality in arbitrary even dimensions
International Nuclear Information System (INIS)
Lee, Jinhyoung; Lee, Seung-Woo; Kim, M. S.
2006-01-01
We generalize Greenberger-Horne-Zeilinger (GHZ) nonlocality to every even-dimensional and odd-partite system. For the purpose we employ concurrent observables that are incompatible and nevertheless have a common eigenstate. It is remarkable that a tripartite system can exhibit the genuinely high-dimensional GHZ nonlocality
On nonlocal symmetries of some shallow water equations
Energy Technology Data Exchange (ETDEWEB)
Reyes, Enrique G [Departamento de Matematicas y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2 Santiago (Chile)
2007-04-27
A recent construction of nonlocal symmetries for the Korteweg-de Vries, Camassa-Holm and Hunter-Saxton equations is reviewed, and it is pointed out that-in the Camassa-Holm and Hunter-Saxton case-these symmetries can be considered as (nonlocal) symmetries of integro-differential equations.
Directory of Open Access Journals (Sweden)
Diem Dang Huan
2015-12-01
Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.
International Nuclear Information System (INIS)
Oppenheim, Jonathan; Horodecki, Karol; Horodecki, Michal; Horodecki, Ryszard; Horodecki, Pawel
2003-01-01
Complex physical systems contain information which, under some well-defined processes can differentiate between local and nonlocal information. Both these fundamental aspects of information are defined operationally. Local information is locally accessible and allows one to perform processes, such as physical work, while nonlocal information allows one to perform processes such as teleportation. It is shown that these two kinds of information are complementary in the sense that two parties can either gain access to the nonlocal information or to the local information but not both. This complementarity has a form similar to that expressed by entropic uncertainty relations. For pure states, the entanglement plays the role of Planck's constant. We also find another class of complementarity relations which applies to operators and is induced when two parties can only perform local operations and communicate classical (LOCC). In particular, observables such as the parity and phase of two qubits commute but under LOCC, they are complementary observables. It is also found this complementarity is pure in the sense that it can be ''decoupled'' from the uncertainty principle. It is suggested that these complementarities represent an essential extension of Bohr's complementarity to complex (distributed) systems which are entangled
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Hutchinson, John; Stojkovic, Dejan
2016-01-01
We examine the basic assumptions in the original setup of the firewall paradox. The main claim is that a single mode of the lathe radiation is maximally entangled with the mode inside the horizon and simultaneously with the modes of early Hawking radiation. We argue that this situation never happens during the evolution of a black hole. Quantum mechanics tells us that while the black hole exists, unitary evolution maximally entangles a late mode located just outside the horizon with a combination of early radiation and black hole states, instead of either of them separately. One of the reasons for this is that the black hole radiation is not random and strongly depends on the geometry and charge of the black hole, as detailed numerical calculations of Hawking evaporation clearly show. As a consequence, one can not factor out the state of the black hole. However, this extended entanglement between the black hole and modes of early and late radiation indicates that, as the black hole ages, the local Rindler horizon is modified out to macroscopic distances from the black hole. Fundamentally non-local physics nor firewalls are not necessary to explain this result. We propose an infrared mechanism called icezone that is mediated by low energy interacting modes and acts near any event horizon to entangle states separated by long distances. These interactions at first provide small corrections to the thermal Hawking radiation. At the end of evaporation however the effect of interactions is as large as the Hawking radiation and information is recovered for an outside observer. We verify this in an explicit construction and calculation of the density matrix of a spin model. (paper)
Hutchinson, John; Stojkovic, Dejan
2016-07-01
We examine the basic assumptions in the original setup of the firewall paradox. The main claim is that a single mode of the lathe radiation is maximally entangled with the mode inside the horizon and simultaneously with the modes of early Hawking radiation. We argue that this situation never happens during the evolution of a black hole. Quantum mechanics tells us that while the black hole exists, unitary evolution maximally entangles a late mode located just outside the horizon with a combination of early radiation and black hole states, instead of either of them separately. One of the reasons for this is that the black hole radiation is not random and strongly depends on the geometry and charge of the black hole, as detailed numerical calculations of Hawking evaporation clearly show. As a consequence, one can not factor out the state of the black hole. However, this extended entanglement between the black hole and modes of early and late radiation indicates that, as the black hole ages, the local Rindler horizon is modified out to macroscopic distances from the black hole. Fundamentally non-local physics nor firewalls are not necessary to explain this result. We propose an infrared mechanism called icezone that is mediated by low energy interacting modes and acts near any event horizon to entangle states separated by long distances. These interactions at first provide small corrections to the thermal Hawking radiation. At the end of evaporation however the effect of interactions is as large as the Hawking radiation and information is recovered for an outside observer. We verify this in an explicit construction and calculation of the density matrix of a spin model.
A unitary model of the black hole evaporation
Feng, Yu-Lei; Chen, Yi-Xin
2014-12-01
A unitary effective field model of the black hole evaporation is proposed to satisfy almost the four postulates of the black hole complementarity (BHC). In this model, we enlarge a black hole-scalar field system by adding an extra radiation detector that couples with the scalar field. After performing a partial trace over the scalar field space, we obtain an effective entanglement between the black hole and the detector (or radiation in it). As the whole system evolves, the S-matrix formula can be constructed formally step by step. Without local quantum measurements, the paradoxes of the information loss and AMPS's firewall can be resolved. However, the information can be lost due to quantum decoherence, as long as some local measurement has been performed on the detector to acquire the information of the radiation in it. But unlike Hawking's completely thermal spectrum, some residual correlations can be found in the radiations. All these considerations can be simplified in a qubit model that provides a modified quantum teleportation to transfer the information via an EPR pairs.
The unitary-group formulation of quantum chemistry
International Nuclear Information System (INIS)
Campbell, L.L.
1990-01-01
The major part of this dissertation establishes group theoretical techniques that are applicable to the quantum-mechanical many-body atomic and molecular problems. Several matrix element evaluation methods for many-body states are developed. The generator commutation method using generator states is presented for the first time as a complete algorithm, and a computer implementation of the method is developed. A major result of this work is the development of a new method of calculation called the freeon tensor product (FTP) method. This method is much simpler and for many purposes superior to the GUGA procedure (graphical unitary group approach), widely used in configuration interaction calculations. This dissertation is also concerned with the prediction of atomic spectra. In principle spectra can be computed by the methods of ab initio quantum chemistry. In practice these computations are difficult, expensive, time consuming, and not uniformly successful. In this dissertation, the author employs a semi-empirical group theoretical analysis of discrete spectra is the exact analog of the Fourier analysis of continuous functions. In particular, he focuses on the spectra of atoms with incomplete p, d, and f shells. The formulas and techniques are derived in a fashion that apply equally well for more complex systems, as well as the isofreeon model of spherical nuclei
Conditional mutual information of bipartite unitaries and scrambling
Energy Technology Data Exchange (ETDEWEB)
Ding, Dawei; Hayden, Patrick; Walter, Michael [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-12-28
One way to diagnose chaos in bipartite unitary channels is via the tripartite information of the corresponding Choi state, which for certain choices of the subsystems reduces to the negative conditional mutual information (CMI). We study this quantity from a quantum information-theoretic perspective to clarify its role in diagnosing scrambling. When the CMI is zero, we find that the channel has a special normal form consisting of local channels between individual inputs and outputs. However, we find that arbitrarily low CMI does not imply arbitrary proximity to a channel of this form, although it does imply a type of approximate recoverability of one of the inputs. When the CMI is maximal, we find that the residual channel from an individual input to an individual output is completely depolarizing when the other input is maximally mixed. However, we again find that this result is not robust. We also extend some of these results to the multipartite case and to the case of Haar-random pure input states. Finally, we look at the relationship between tripartite information and its Rényi-2 version which is directly related to out-of-time-order correlation functions. In particular, we demonstrate an arbitrarily large gap between the two quantities.
Correlation functions in unitary minimal Liouville gravity and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Belavin, V. [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky prospect 53, 119991 Moscow (Russian Federation); Department of Quantum Physics, Institute for Information Transmission Problems,Bolshoy Karetny per. 19, 127994 Moscow (Russian Federation); Department of Theoretical Physics, National Research Nuclear University MEPhI,Kashirskoe shosse 31, 115409 Moscow (Russian Federation)
2015-02-10
We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the A{sub q} integrable hierarchy via the resonance transformations, which are in turn fixed by conformal selection rules. One of the main problems in this approach is to choose the solution of the Douglas string equation that is relevant for MLG. The appropriate solution was recently found using connection with the Frobenius manifolds. We use this solution to investigate three- and four-point correlators in the unitary MLG models. We find an agreement with the results of the original approach in the region of the parameters where both methods are applicable. In addition, we find that only part of the selection rules can be satisfied using the resonance transformations. The physical meaning of the nonzero correlators, which before coupling to Liouville gravity are forbidden by the selection rules, and also the modification of the dual formulation that takes this effect into account remains to be found.
A new treatment of nonlocality in scattering process
Upadhyay, N. J.; Bhagwat, A.; Jain, B. K.
2018-01-01
Nonlocality in the scattering potential leads to an integro-differential equation. In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schrödinger equation is usually handled by approximating r,{r}{\\prime }-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method is accurate and valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off 12C, 56Fe and 100Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in reasonable accord with the experiments.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators.
Belenchia, Alessio; Benincasa, Dionigi M T; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-22
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Protecting nonlocality of multipartite states by feed-forward control
Li, Xiao-Gang; Zou, Jian; Shao, Bin
2018-06-01
Nonlocality is a useful resource in quantum communication and quantum information processing. In practical quantum communication, multipartite entangled states must be distributed between different users in different places through a channel. However, the channel is usually inevitably disturbed by the environment in quantum state distribution processing and then the nonlocality of states will be weakened and even lost. In this paper, we use a feed-forward control scheme to protect the nonlocality of the Bell and GHZ states against dissipation. We find that this protection scheme is very effective, specifically, for the Bell state, we can increase the noise threshold from 0.5 to 0.98, and for GHZ state from 0.29 to 0.96. And we also find that entanglement is relatively easier to be protected than nonlocality. For our scheme, protecting entanglement is equivalent to protecting the state in the case of Bell state, while protecting nonlocality is not.
Nonlocal nonlinear coupling of kinetic sound waves
Directory of Open Access Journals (Sweden)
O. Lyubchyk
2014-11-01
Full Text Available We study three-wave resonant interactions among kinetic-scale oblique sound waves in the low-frequency range below the ion cyclotron frequency. The nonlinear eigenmode equation is derived in the framework of a two-fluid plasma model. Because of dispersive modifications at small wavelengths perpendicular to the background magnetic field, these waves become a decay-type mode. We found two decay channels, one into co-propagating product waves (forward decay, and another into counter-propagating product waves (reverse decay. All wavenumbers in the forward decay are similar and hence this decay is local in wavenumber space. On the contrary, the reverse decay generates waves with wavenumbers that are much larger than in the original pump waves and is therefore intrinsically nonlocal. In general, the reverse decay is significantly faster than the forward one, suggesting a nonlocal spectral transport induced by oblique sound waves. Even with low-amplitude sound waves the nonlinear interaction rate is larger than the collisionless dissipation rate. Possible applications regarding acoustic waves observed in the solar corona, solar wind, and topside ionosphere are briefly discussed.
Buonomano against Bell: Nonergodicity or nonlocality?
Khrennikov, Andrei
The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell’s arguments, one cannot distinguish two hypotheses: (a) quantum mechanics is nonlocal, (b) quantum mechanics is nonergodic. Therefore, experimental violations of Bell’s inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements are nonergodic. The latter hypothesis was discussed actively by Buonomano since 1980. However, in contrast to Bell’s hypothesis on nonlocality, it did not attract so much attention. The only experiment testing the hypothesis on nonergodicity was performed in neutron interferometry (by Summhammer, in 1989). This experiment can be considered as rejecting this hypothesis. However, it cannot be considered as a decisive experiment. New experiments are badly needed. We point out that a nonergodic model can be realistic, i.e. the distribution of hidden (local!) variables is well-defined. We also discuss coupling of violation of the Bell inequality with violation of the condition of weak mixing for ergodic dynamical systems.
Feature-Based Nonlocal Polarimetric SAR Filtering
Directory of Open Access Journals (Sweden)
Xiaoli Xing
2017-10-01
Full Text Available Polarimetric synthetic aperture radar (PolSAR images are inherently contaminated by multiplicative speckle noise, which complicates the image interpretation and image analyses. To reduce the speckle effect, several adaptive speckle filters have been developed based on the weighted average of the similarity measures commonly depending on the model or probability distribution, which are often affected by the distribution parameters and modeling texture components. In this paper, a novel filtering method introduces the coefficient of variance ( CV and Pauli basis (PB to measure the similarity, and the two features are combined with the framework of the nonlocal mean filtering. The CV is used to describe the complexity of various scenes and distinguish the scene heterogeneity; moreover, the Pauli basis is able to express the polarimetric information in PolSAR image processing. This proposed filtering combines the CV and Pauli basis to improve the estimation accuracy of the similarity weights. Then, the similarity of the features is deduced according to the test statistic. Subsequently, the filtering is proceeded by using the nonlocal weighted estimation. The performance of the proposed filter is tested with the simulated images and real PolSAR images, which are acquired by AIRSAR system and ESAR system. The qualitative and quantitative experiments indicate the validity of the proposed method by comparing with the widely-used despeckling methods.
All unitary ray representations of the conformal group SU(2,2) with positive energy
International Nuclear Information System (INIS)
Mack, G.
1975-12-01
We find all those unitary irreducible representations of the infinitely - sheeted covering group G tilde of the conformal group SU(2,2)/Z 4 which have positive energy P 0 >= O. They are all finite component field representations and are labelled by dimension d and a finite dimensional irreducible representation (j 1 , j 2 ) of the Lorentz group SL(2C). They all decompose into a finite number of unitary irreducible representations of the Poincare subgroup with dilations. (orig.) [de
Zhang, Li-qiang; Ma, Ting-ting; Yu, Chang-shui
2018-03-01
The computability of the quantifier of a given quantum resource is the essential challenge in the resource theory and the inevitable bottleneck for its application. Here we focus on the measurement-induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement-induced nonlocality and has analytic expressions for pure states, (2 ⊗d )-dimensional quantum states, and some particular high-dimensional quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost-analytic expressions for any quantum state, which can also shed light on other aspects in physics. To illustrate applications as well as demonstrate the validity of the algorithm, we compare the analytic and numerical expressions of various examples and show their perfect consistency.
Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane
Hu, Wenjie; Duan, Yueliang
2018-04-01
We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.
International Nuclear Information System (INIS)
Gunaydin, Murat; Pavlyk, Oleksandr
2005-01-01
We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E 8(-24) in SU*(8) as well as SU(6,2) covariant bases. E 8(-24) has E 7 x SU(2) as its maximal compact subgroup and is the U-duality group of the exceptional supergravity theory in d=3. For the corresponding U-duality group E 8(8) of the maximal supergravity theory the minimal realization was given. The minimal unitary realizations of all the lower rank noncompact exceptional groups can be obtained by truncation of those of E 8(-24) and E 8(8) . By further truncation one can obtain the minimal unitary realizations of all the groups of the 'Magic Triangle'. We give explicitly the minimal unitary realizations of the exceptional subgroups of E 8(-24) as well as other physically interesting subgroups. These minimal unitary realizations correspond, in general, to the quantization of their geometric actions as quasi-conformal groups. (author)
Unitary three-body calculation of nucleon-nucleon scattering
International Nuclear Information System (INIS)
Tanabe, H.; Ohta, K.
1986-07-01
We calculate nucleon-nucleon elastic scattering phase parameters based on a unitary, relativistic, pion-exchange model. The results are highly dependent on the off-shell amplitudes of πN scattering. The isobar-dominated model for the P 33 interaction leads to too small pion production rates owing to its strong suppression of off-shell pions. We propose to expand the idea of the Δ-isobar model in such a manner as to incorporate a background (non-pole) interaction. The two-potential model, which was first applied to the P 11 partial wave by Mizutani and Koltun, is applied also to the P 33 wave. Our phenomenological model for πN interaction in the P 33 partial wave differs from the conventional model only in its off-shell extrapolation, and has two different variants for the πN → Δ vertex. The three-body approach of Kloet and Silbar is extended such that the background interactions can be included straightfowardly. We make detailed comparisons of the new model with the conventional one and find that our model adequately reproduces the 1 D 2 phase parameters as well as those of peripheral partial waves. We also find that the longitudinal total cross section difference Δσ L (pp → NNπ) comes closer to the data compared to Kloet and Silbar. We discuss about the backward pion propagation in the three-body calculation, and the Pauli-principle violating states for the background P 11 interaction. (author)
Mermin Non-Locality in Abstract Process Theories
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Stefano Gogioso
2015-11-01
Full Text Available The study of non-locality is fundamental to the understanding of quantum mechanics. The past 50 years have seen a number of non-locality proofs, but its fundamental building blocks, and the exact role it plays in quantum protocols, has remained elusive. In this paper, we focus on a particular flavour of non-locality, generalising Mermin's argument on the GHZ state. Using strongly complementary observables, we provide necessary and sufficient conditions for Mermin non-locality in abstract process theories. We show that the existence of more phases than classical points (aka eigenstates is not sufficient, and that the key to Mermin non-locality lies in the presence of certain algebraically non-trivial phases. This allows us to show that fRel, a favourite toy model for categorical quantum mechanics, is Mermin local. We show Mermin non-locality to be the key resource ensuring the device-independent security of the HBB CQ (N,N family of Quantum Secret Sharing protocols. Finally, we challenge the unspoken assumption that the measurements involved in Mermin-type scenarios should be complementary (like the pair X,Y, opening the doors to a much wider class of potential experimental setups than currently employed. In short, we give conditions for Mermin non-locality tests on any number of systems, where each party has an arbitrary number of measurement choices, where each measurement has an arbitrary number of outcomes and further, that works in any abstract process theory.
Nonlocal kinetic-energy-density functionals
International Nuclear Information System (INIS)
Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E.
1996-01-01
In this paper we present nonlocal kinetic-energy functionals T[n] within the average density approximation (ADA) framework, which do not require any extra input when applied to any electron system and recover the exact kinetic energy and the linear response function of a homogeneous system. In contrast with previous ADA functionals, these present good behavior of the long-range tail of the exact weight function. The averaging procedure for the kinetic functional (averaging the Fermi momentum of the electron gas, instead of averaging the electron density) leads to a functional without numerical difficulties in the calculation of extended systems, and it gives excellent results when applied to atoms and jellium surfaces. copyright 1996 The American Physical Society
Certainty relations between local and nonlocal observables
International Nuclear Information System (INIS)
Diaz, R Garcia; Romero, J L; Bjoerk, G; Bourennane, M
2005-01-01
We point out that for an arbitrary number of identical particles, each defined on a Hilbert space of arbitrary dimension, there exists a whole ladder of relations of complementarity between certain local and nonlocal measurements corresponding to every conceivable grouping of the particles, e.g., the more accurately we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite-entangled state), the less accurate some other property, local to the three qubits, becomes. We investigate the relation between these complementarity relations and a similar relation based on interference visibilities. We also show that the complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces
Switching non-local median filter
Matsuoka, Jyohei; Koga, Takanori; Suetake, Noriaki; Uchino, Eiji
2015-06-01
This paper describes a novel image filtering method for removal of random-valued impulse noise superimposed on grayscale images. Generally, it is well known that switching-type median filters are effective for impulse noise removal. In this paper, we propose a more sophisticated switching-type impulse noise removal method in terms of detail-preserving performance. Specifically, the noise detector of the proposed method finds out noise-corrupted pixels by focusing attention on the difference between the value of a pixel of interest (POI) and the median of its neighboring pixel values, and on the POI's isolation tendency from the surrounding pixels. Furthermore, the removal of the detected noise is performed by the newly proposed median filter based on non-local processing, which has superior detail-preservation capability compared to the conventional median filter. The effectiveness and the validity of the proposed method are verified by some experiments using natural grayscale images.
The quantum handshake entanglement, nonlocality and transactions
Cramer, John G
2016-01-01
This book shines bright light into the dim recesses of quantum theory, where the mysteries of entanglement, nonlocality, and wave collapse have motivated some to conjure up multiple universes, and others to adopt a "shut up and calculate" mentality. After an extensive and accessible introduction to quantum mechanics and its history, the author turns attention to his transactional model. Using a quantum handshake between normal and time-reversed waves, this model provides a clear visual picture explaining the baffling experimental results that flow daily from the quantum physics laboratories of the world. To demonstrate its powerful simplicity, the transactional model is applied to a collection of counter-intuitive experiments and conceptual problems.
Relativistic dynamical reduction models and nonlocality
International Nuclear Information System (INIS)
Ghirardi, G.C.; Grassi, R.
1990-09-01
We discuss some features of continuous dynamical models yielding state vector reduction and we briefly sketch some recent attempts to get a relativistic generalization of them. Within the relativistic context we analyze in detail the local an nonlocal features of the reduction mechanism and we investigate critically the possibility of attributing objective properties to individual systems in the micro and macroscopic cases. At the nonrelativistic level, two physically equivalent versions of continuous reduction mechanisms have been presented. However, only one of them can be taken as a starting point for the above considered relativistic generalization. By resorting to counterfactual arguments we show that the reason for this lies in the fact that the stochasticity involved in the two approaches has different conceptual implications. (author). 7 refs, 4 figs
Graphene plasmons: Impurities and nonlocal effects
Viola, Giovanni; Wenger, Tobias; Kinaret, Jari; Fogelström, Mikael
2018-02-01
This work analyzes how impurities and vacancies on the surface of a graphene sample affect its optical conductivity and plasmon excitations. The disorder is analyzed in the self-consistent Green's function formulation and nonlocal effects are fully taken into account. It is shown that impurities modify the linear spectrum and give rise to an impurity band whose position and width depend on the two parameters of our model, the density and the strength of impurities. The presence of the impurity band strongly influences the electromagnetic response and the plasmon losses. Furthermore, we discuss how the impurity-band position can be obtained experimentally from the plasmon dispersion relation and discuss this in the context of sensing.
A nonlocal spatial model for Lyme disease
Yu, Xiao; Zhao, Xiao-Qiang
2016-07-01
This paper is devoted to the study of a nonlocal and time-delayed reaction-diffusion model for Lyme disease with a spatially heterogeneous structure. In the case of a bounded domain, we first prove the existence of the positive steady state and a threshold type result for the disease-free system, and then establish the global dynamics for the model system in terms of the basic reproduction number. In the case of an unbound domain, we obtain the existence of the disease spreading speed and its coincidence with the minimal wave speed. At last, we use numerical simulations to verify our analytic results and investigate the influence of model parameters and spatial heterogeneity on the disease infection risk.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.
2005-11-01
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
Directory of Open Access Journals (Sweden)
P.G.L. Leach
2005-11-01
Full Text Available We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R. The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Global solution branches for a nonlocal Allen-Cahn equation
Kuto, Kousuke; Mori, Tatsuki; Tsujikawa, Tohru; Yotsutani, Shoji
2018-05-01
We consider the Neumann problem of a 1D stationary Allen-Cahn equation with nonlocal term. Our previous paper [4] obtained a local branch of asymmetric solutions which bifurcates from a point on the branch of odd-symmetric solutions. This paper derives the global behavior of the branch of asymmetric solutions, and moreover, determines the set of all solutions to the nonlocal Allen-Cahn equation. Our proof is based on a level set analysis for an integral map associated with the nonlocal term.
Torsion of cracked nanorods using a nonlocal elasticity model
International Nuclear Information System (INIS)
Loya, J A; Aranda-Ruiz, J; Fernández-Sáez, J
2014-01-01
This paper presents a nonlocal cracked-rod model from which we have analysed the torsional vibrations of a carbon nanotube with a circumferential crack. Several types of boundary conditions, including the consideration of a buckyball at the end of the nanotube, have been studied. The nonlocal Eringen elasticity theory is used to formulate the problem. The cracked rod is modelled by dividing the cracked element into two segments connected by a torsional linear spring whose stiffness is related to the crack severity. The effect of the nonlocal small-scale parameter, crack severity, cracked section position, different boundary conditions and attached mass are examined in this work. (paper)
Nonlocal kinetic energy functionals by functional integration
Mi, Wenhui; Genova, Alessandro; Pavanello, Michele
2018-05-01
Since the seminal studies of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting kinetic energy, Ts[ρ], the subject of this work. The typical paradigm is to first approximate the energy functional and then take its functional derivative, δ/Ts[ρ ] δ ρ (r ) , yielding a potential that can be used in orbital-free DFT or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-functional derivative via functional integration. A new nonlocal functional for Ts[ρ] is prescribed [which we dub Mi-Genova-Pavanello (MGP)] having a density independent kernel. MGP is constructed to satisfy three exact conditions: (1) a nonzero "Kinetic electron" arising from a nonzero exchange hole; (2) the second functional derivative must reduce to the inverse Lindhard function in the limit of homogenous densities; (3) the potential is derived from functional integration of the second functional derivative. Pilot calculations show that MGP is capable of reproducing accurate equilibrium volumes, bulk moduli, total energy, and electron densities for metallic (body-centered cubic, face-centered cubic) and semiconducting (crystal diamond) phases of silicon as well as of III-V semiconductors. The MGP functional is found to be numerically stable typically reaching self-consistency within 12 iterations of a truncated Newton minimization algorithm. MGP's computational cost and memory requirements are low and comparable to the Wang-Teter nonlocal functional or any generalized gradient approximation functional.
Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space
Volkoff, T. J.; Whaley, K. B.
2014-12-01
We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch-distinguishability measure is obtained and applied to superposition states of N quantum harmonic oscillators composed of Gaussian branches. Considering optimal distinguishability of pure states on a time-evolution path leads naturally to a notion of distinguishability time that generalizes the well-known orthogonalization times of Mandelstam and Tamm and Margolus and Levitin. We further show that the distinguishability time provides a compact operational expression for the superposition size measure based on the relative quantum Fisher information. By restricting the maximization procedure in the definition of this measure to an appropriate algebra of observables, we show that the superposition size of, e.g., NOON states and hierarchical cat states, can scale linearly with the number of elementary particles comprising the superposition state, implying precision scaling inversely with the total number of photons when these states are employed as probes in quantum parameter estimation of a 1-local Hamiltonian in this algebra.
Unambiguous discrimination among oracle operators
International Nuclear Information System (INIS)
Chefles, Anthony; Kitagawa, Akira; Takeoka, Masahiro; Sasaki, Masahide; Twamley, Jason
2007-01-01
We address the problem of unambiguous discrimination among oracle operators. The general theory of unambiguous discrimination among unitary operators is extended with this application in mind. We prove that entanglement with an ancilla cannot assist any discrimination strategy for commuting unitary operators. We also obtain a simple, practical test for the unambiguous distinguishability of an arbitrary set of unitary operators on a given system. Using this result, we prove that the unambiguous distinguishability criterion is the same for both standard and minimal oracle operators. We then show that, except in certain trivial cases, unambiguous discrimination among all standard oracle operators corresponding to integer functions with fixed domain and range is impossible. However, we find that it is possible to unambiguously discriminate among the Grover oracle operators corresponding to an arbitrarily large unsorted database. The unambiguous distinguishability of standard oracle operators corresponding to totally indistinguishable functions, which possess a strong form of classical indistinguishability, is analysed. We prove that these operators are not unambiguously distinguishable for any finite set of totally indistinguishable functions on a Boolean domain and with arbitrary fixed range. Sets of such functions on a larger domain can have unambiguously distinguishable standard oracle operators, and we provide a complete analysis of the simplest case, that of four functions. We also examine the possibility of unambiguous oracle operator discrimination with multiple parallel calls and investigate an intriguing unitary superoperator transformation between standard and entanglement-assisted minimal oracle operators
Wang, Zi-Hang; Yu, Wen-Xuan; Wu, Xiao-Yuan; Gao, Cheng-Yan; Alzahrani, Faris; Hobiny, Aatef; Deng, Fu-Guo
2018-03-01
We present two different hyperentanglement concentration protocols (hyper-ECPs) for two-photon systems in nonlocal polarization-time-bin hyperentangled states with known parameters, including Bell-like and cluster-like states, resorting to the parameter splitting method. They require only one of two parties in quantum communication to operate her photon in the process of entanglement concentration, not two, and they have the maximal success probability. They work with linear optical elements and have good feasibility in experiment, especially in the case that there are a big number of quantum data exchanged as the parties can obtain the information about the parameters of the nonlocal hyperentangled states by sampling a subset of nonlocal hyperentangled two-photon systems and measuring them. As the quantum state of photons in the time-bin degree of freedom suffers from less noise in an optical-fiber channel, these hyper-ECPs may have good applications in practical long-distance quantum communication in the future.
Non-local electrical spin injection and detection in germanium at room temperature
Rortais, F.; Vergnaud, C.; Marty, A.; Vila, L.; Attané, J.-P.; Widiez, J.; Zucchetti, C.; Bottegoni, F.; Jaffrès, H.; George, J.-M.; Jamet, M.
2017-10-01
Non-local carrier injection/detection schemes lie at the very foundation of information manipulation in integrated systems. This paradigm consists in controlling with an external signal the channel where charge carriers flow between a "source" and a well separated "drain." The next generation electronics may operate on the spin of carriers in addition to their charge and germanium appears as the best hosting material to develop such a platform for its compatibility with mainstream silicon technology and the predicted long electron spin lifetime at room temperature. In this letter, we demonstrate injection of pure spin currents (i.e., with no associated transport of electric charges) in germanium, combined with non-local spin detection at 10 K and room temperature. For this purpose, we used a lateral spin valve with epitaxially grown magnetic tunnel junctions as spin injector and spin detector. The non-local magnetoresistance signal is clearly visible and reaches ≈15 mΩ at room temperature. The electron spin lifetime and diffusion length are 500 ps and 1 μm, respectively, the spin injection efficiency being as high as 27%. This result paves the way for the realization of full germanium spintronic devices at room temperature.
Nonlocal microscopic theory of quantum friction between parallel metallic slabs
International Nuclear Information System (INIS)
Despoja, Vito; Echenique, Pedro M.; Sunjic, Marijan
2011-01-01
We present a new derivation of the friction force between two metallic slabs moving with constant relative parallel velocity, based on T=0 quantum-field theory formalism. By including a fully nonlocal description of dynamically screened electron fluctuations in the slab, and avoiding the usual matching-condition procedure, we generalize previous expressions for the friction force, to which our results reduce in the local limit. Analyzing the friction force calculated in the two local models and in the nonlocal theory, we show that for physically relevant velocities local theories using the plasmon and Drude models of dielectric response are inappropriate to describe friction, which is due to excitation of low-energy electron-hole pairs, which are properly included in nonlocal theory. We also show that inclusion of dissipation in the nonlocal electronic response has negligible influence on friction.
Size-dependent nonlocal effects in plasmonic semiconductor particles
DEFF Research Database (Denmark)
Maack, Johan Rosenkrantz; Mortensen, N. Asger; Wubs, Martijn
2017-01-01
Localized surface plasmons (LSP) in semiconductor particles are expected to exhibit spatial nonlocal response effects as the geometry enters the nanometer scale. To investigate these nonlocal effects, we apply the hydrodynamic model to nanospheres of two different semiconductor materials: intrinsic...... InSb and n-doped GaAs. Our results show that the semiconductors indeed display nonlocal effects, and that these effects are even more pronounced than in metals. In a 150 nm InSb particle at 300 K, the LSP frequency is blueshifted 35%, which is orders of magnitude larger than the blueshift in a metal...... particle of the same size. This property, together with their tunability, makes semiconductors a promising platform for experiments in nonlocal effects. Copyright (C)EPLA, 2017...
Entanglement and nonlocality in multi-particle systems
Reid, Margaret D.; He, Qiong-Yi; Drummond, Peter D.
2012-02-01
Entanglement, the Einstein-Podolsky-Rosen (EPR) paradox and Bell's failure of local-hiddenvariable (LHV) theories are three historically famous forms of "quantum nonlocality". We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequalities that address the degree of reduction in the variance of collective spins. The latter have been particularly useful as a tool for investigating entanglement in Bose-Einstein condensates (BEC). We present solutions for two topical quantum states: multi-qubit Greenberger-Horne-Zeilinger (GHZ) states, and the ground state of a two-well BEC.
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems
Energy Technology Data Exchange (ETDEWEB)
D’Elia, M., E-mail: mdelia@fsu.edu, E-mail: mdelia@sandia.gov [Sandia National Laboratories (United States); Gunzburger, M. [Florida State University (United States)
2016-04-15
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the control and the parameter function as the control variable. The analysis makes use of a nonlocal vector calculus that allows one to define a variational formulation of the nonlocal problem. In a manner analogous to the local partial differential equations counterpart, we demonstrate, for certain kernel functions, the existence of at least one optimal solution in the space of admissible parameters. We introduce a Galerkin finite element discretization of the optimal control problem and derive a priori error estimates for the approximate state and control variables. Using one-dimensional numerical experiments, we illustrate the theoretical results and show that by using nonlocal models it is possible to estimate non-smooth and discontinuous diffusion parameters.
Non-local means filter for trim statics
Huang, Yunsong; Wang, Xin; Schuster, Gerard T.
2014-01-01
this problem, we propose a trim statics inspired by the non-local means algorithm originally developed for image denoising. This method differs from the conventional one in two fundamental respects. First, the trim statics are computed by comparing image
A single variable shear deformable nonlocal theory for transversely ...
Indian Academy of Sciences (India)
Rameshchandra P Shimpi
2018-05-11
May 11, 2018 ... Abstract. In this paper, a simple single variable shear deformable nonlocal theory for bending of micro- and ... the models based upon continuum mechanics are widely .... of the body. ...... Elsevier Science Ltd, Oxford, UK. pp.
Nonlocality versus complementarity: a conservative approach to the information problem
International Nuclear Information System (INIS)
Giddings, Steven B
2011-01-01
A proposal for resolution of the information paradox is that 'nice slice' states, which have been viewed as providing a sharp argument for information loss, do not in fact do so as they do not give a fully accurate description of the quantum state of a black hole. This however leaves an information problem, which is to provide a consistent description of how information escapes when a black hole evaporates. While a rather extreme form of nonlocality has been advocated in the form of complementarity, this paper argues that is not necessary, and more modest nonlocality could solve the information problem. One possible distinguishing characteristic of scenarios is the information retention time. The question of whether such nonlocality implies acausality, and particularly inconsistency, is briefly addressed. The need for such nonlocality, and its apparent tension with our empirical observations of local quantum field theory, may be a critical missing piece in understanding the principles of quantum gravity.
Analytical and unitary approach in mesons electromagnetic form factor applications
International Nuclear Information System (INIS)
Liptaj, A.
2010-07-01
In the dissertation thesis we address several topics related to the domain of particle physics. All of them represent interesting open problems that can be connected to the elastic or transition electromagnetic form factors of mesons, the form factors being the main objects of our interest. Our ambition is to contribute to the solution of these problems and use for that purpose known analytic properties of the form factors and the unitarity condition. These two tools are very powerful in the low energy domain (such as bound states of partons), where the perturbative QCD looses its validity. This is the motivation for construction of the unitary and analytic (U and A) models of studied form factors, that enable us to get the majority of our results. We use the U and A model to evaluate the contribution of the processes e"+e"- → Pγ, P = π"0, η, η to the muon magnetic anomaly a_μ in the lowest order of the hadronic vacuum polarization. For the contribution a_μ"h"a"d","L"O (π"+π"-) we demonstrate, that the use of the model leads to a dramatic error reduction with respect to the results of other authors. We also get a shift in the central value in the 'correct' direction, that brings the theoretical value closer to the experimental one. This results encourages us to use the model also for the evaluation of a_μ"h"a"d","L"O (P_γ). These contributions are smaller, however the precision of the experiment makes their evaluation necessary. We further use the U and A model of the transition form factors of π"0, η and η"' mesons to predict the partial decay widths of these particles Γ_π_"0_→_γ_γ and Γ_η_→_γ_γ and Γ_η_"'_→_γ_γ. In this way we make an independent cross check of the PDG table values. We find an agreement in the case of Γ_η_→_γ_γ and Γ_η_"'_→_γ_γ, even a smaller uncertainty for Γ_η_"'_→_γ_γ. In the case of Γ_π_"0_→_γ_γ we find a disagreement that points to an interesting problem. We wonder whether it could be
Self-organization analysis for a nonlocal convective Fisher equation
Energy Technology Data Exchange (ETDEWEB)
Cunha, J.A.R. da [Instituto de Fisica, Universidade de Brasilia, 70919-970 Brasilia DF (Brazil); International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil); Penna, A.L.A. [Instituto de Fisica, Universidade de Brasilia, 70919-970 Brasilia DF (Brazil); International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil)], E-mail: penna.andre@gmail.com; Vainstein, M.H. [Instituto de Fisica, Universidade de Brasilia, 70919-970 Brasilia DF (Brazil); International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil); Morgado, R. [International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil); Departamento de Matematica, Universidade de Brasilia, 70910-900 Brasilia DF (Brazil); Oliveira, F.A. [Instituto de Fisica, Universidade de Brasilia, 70919-970 Brasilia DF (Brazil); International Center for Condensed Matter Physics, CP 04513, 70919-970 Brasilia DF (Brazil)
2009-02-02
Using both an analytical method and a numerical approach we have investigated pattern formation for a nonlocal convective Fisher equation with constant and spatial velocity fields. We analyze the limits of the influence function due to nonlocal interaction and we obtain the phase diagram of critical velocities v{sub c} as function of the width {mu} of the influence function, which characterize the self-organization of a finite system.
A Systems-Theoretical Generalization of Non-Local Correlations
von Stillfried, Nikolaus
Non-local correlations between quantum events are not due to a causal interaction in the sense of one being the cause for the other. In principle, the correlated events can thus occur simultaneously. Generalized Quantum Theory (GQT) formalizes the idea that non-local phenomena are not exclusive to quantum mechanics, e.g. due to some specific properties of (sub)atomic particles, but that they instead arise as a consequence of the way such particles are arranged into systems. Non-local phenomena should hence occur in any system which fulfils the necessary systems-theoretical parameters. The two most important parameters with respect to non-local correlations seem to be a conserved global property of the system as a whole and sufficient degrees of freedom of the corresponding property of its subsystems. Both factors place severe limitations on experimental observability of the phenomena, especially in terms of replicability. It has been suggested that reported phenomena of a so-called synchronistic, parapsychological or paranormal kind could be understood as instances of systems-inherent non-local correlations. From a systems-theoretical perspective, their phenomenology (including the favorable conditions for their occurrence and their lack of replicability) displays substantial similarities to non-local correlations in quantum systems and matches well with systems-theoretical parameters, thus providing circumstantial evidence for this hypothesis.
Coupling of nonlocal and local continuum models by the Arlequinapproach
Han, Fei
2011-08-09
The objective of this work is to develop and apply the Arlequin framework to couple nonlocal and local continuum mechanical models. A mechanically-based model of nonlocal elasticity, which involves both contact and long-range forces, is used for the \\'fine scale\\' description in which nonlocal interactions are considered to have non-negligible effects. Classical continuum mechanics only involving local contact forces is introduced for the rest of the structure where these nonlocal effects can be neglected. Both models overlap in a coupling subdomain called the \\'gluing area\\' in which the total energy is separated into nonlocal and local contributions by complementary weight functions. A weak compatibility is ensured between kinematics of both models using Lagrange multipliers over the gluing area. The discrete formulation of this specific Arlequin coupling framework is derived and fully described. The validity and limits of the technique are demonstrated through two-dimensional numerical applications and results are compared against those of the fully nonlocal elasticity method. © 2011 John Wiley & Sons, Ltd.
Probing non-unitary CP violation effects in neutrino oscillation experiments
Verma, Surender; Bhardwaj, Shankita
2018-05-01
In the present work, we have considered minimal unitarity violation scheme to obtain the general expression for ν _{μ }→ ν _{τ } oscillation probability in vacuum and matter. For this channel, we have investigated the sensitivities of short baseline experiments to non-unitary parameters |ρ _{μ τ }| and ω _{μ τ } for normal as well as inverted hierarchical neutrino masses and θ _{23} being above or below maximality. We find that for normal hierarchy, the 3σ sensitivity of |ρ _{μ τ }| is maximum for non-unitary phase ω _{μ τ }=0 whereas it is minimum for ω _{μ τ }=± π . For inverted hierarchy, the sensitivity is minimum at ω _{μ τ }=0 and maximum for ω _{μ τ }=± π . We observe that the sensitivity to measure non-unitarity remains unaffected for unitary CP phase δ =0 or δ =π /2 . We have, also, explored wide spectrum of L/E ratio to investigate the possibilities to observe CP-violation due to unitary (δ ) and non-unitary (ω _{μ τ } ) phases. We find that the both phases can be disentangled, in principle, from each other for L/E<200 km/GeV.
QCD topological susceptibility from the nonlocal chiral quark model
Nam, Seung-Il; Kao, Chung-Wen
2017-06-01
We investigate the quantum chromodynamics (QCD) topological susceptibility χ by using the semi-bosonized nonlocal chiral-quark model (SB-NLχQM) for the leading large- N c contributions. This model is based on the liquid-instanton QCD-vacuum configuration, in which SU(3) flavor symmetry is explicitly broken by the finite current-quark mass ( m u,d, m s) ≈ (5, 135) MeV. To compute χ, we derive the local topological charge-density operator Q t( x) from the effective action of SB-NLχQM. We verify that the derived expression for χ in our model satisfies the Witten- Veneziano (WV) and the Leutwyler-Smilga (LS) formulae, and the Crewther theorem in the chiral limit by construction. Once the average instanton size and the inter-instanton distance are fixed with ρ¯ = 1/3 fm and R¯ = 1 fm, respectively, all the other parameters are determined self-consistently within the model. We obtain χ = (167.67MeV)4, which is comparable with the empirical value χ = (175±5MeV)4 whereas it turns out that χ QL = (194.30MeV)4 in the quenched limit. Thus, we conclude that the value of χ will be reduced around 10 20% by the dynamical-quark contribution.
Cohering power of quantum operations
Energy Technology Data Exchange (ETDEWEB)
Bu, Kaifeng, E-mail: bkf@zju.edu.cn [School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China); Kumar, Asutosh, E-mail: asukumar@hri.res.in [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019 (India); Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094 (India); Zhang, Lin, E-mail: linyz@zju.edu.cn [Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018 (China); Wu, Junde, E-mail: wjd@zju.edu.cn [School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China)
2017-05-18
Highlights: • Quantum coherence. • Cohering power: production of quantum coherence by quantum operations. • Study of cohering power and generalized cohering power, and their comparison for differentmeasures of quantum coherence. • Operational interpretation of cohering power. • Bound on cohering power of a generic quantum operation. - Abstract: Quantum coherence and entanglement, which play a crucial role in quantum information processing tasks, are usually fragile under decoherence. Therefore, the production of quantum coherence by quantum operations is important to preserve quantum correlations including entanglement. In this paper, we study cohering power–the ability of quantum operations to produce coherence. First, we provide an operational interpretation of cohering power. Then, we decompose a generic quantum operation into three basic operations, namely, unitary, appending and dismissal operations, and show that the cohering power of any quantum operation is upper bounded by the corresponding unitary operation. Furthermore, we compare cohering power and generalized cohering power of quantum operations for different measures of coherence.
Energy Technology Data Exchange (ETDEWEB)
Lamy-Poirier, Joel, E-mail: jlamypoirier@perimeterinstitute.c [Departement de Physique, de Genie Physique et d' Optique, Universite Laval, Quebec, Canada, G1V 0A6 (Canada); Mathieu, Pierre, E-mail: pmathieu@phy.ulaval.c [Departement de Physique, de Genie Physique et d' Optique, Universite Laval, Quebec, Canada, G1V 0A6 (Canada)
2011-06-01
This is the second of two articles (independent of each other) devoted to the analysis of the path description of the states in su-hat (2){sub k} WZW models. Here we present a constructive derivation of the fermionic character at level k based on these paths. The starting point is the expression of a path in terms of a sequence of nonlocal (formal) operators acting on the vacuum ground-state path. Within this framework, the key step is the construction of the level-k operator sequences out of those at level-1 by the action of a new type of operators. These actions of operators on operators turn out to have a path interpretation: these paths are precisely the finitized RSOS paths related to the unitary minimal models M(k+1,k+2). We thus unravel - at the level of the path representation of the states - a direct factorization into a k=1 spinon part times a RSOS factor. It is also pointed out that since there are two fermionic forms describing these finite RSOS paths, the resulting fermionic su-hat (2){sub k} characters arise in two versions. Finally, the relation between the present construction and the Nagoya spectral decomposition of the path space is sketched.
Treating experimental data of inverse kinetic method by unitary linear regression analysis
International Nuclear Information System (INIS)
Zhao Yusen; Chen Xiaoliang
2009-01-01
The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)
Unitary relation for the time-dependent SU(1,1) systems
International Nuclear Information System (INIS)
Song, Dae-Yup
2003-01-01
The system whose Hamiltonian is a linear combination of the generators of SU(1,1) group with time-dependent coefficients is studied. It is shown that there is a unitary relation between the system and a system whose Hamiltonian is simply proportional to the generator of the compact subgroup of SU(1,1). The unitary relation is described by the classical solutions of a time-dependent (harmonic) oscillator. Making use of the relation, the wave functions satisfying the Schroedinger equation are given, for a general unitary representation, in terms of the matrix elements of a finite group transformation (Bargmann function). The wave functions of the harmonic oscillator with an inverse-square potential is studied in detail, and it is shown that through an integral, the model provides a way of deriving the Bargmann function for the representation of positive discrete series of SU(1,1)
Glueball phenomenology within a nonlocal approach
International Nuclear Information System (INIS)
Giacosa, F.
2005-01-01
In this thesis we describe the properties of glueball phenomenology within a nonlocal covariant constituent approach. The search for glueballs, their theoretical description and the mixing with quarkonia mesons is an active and unsolved issue of hadronic QCD. Different models and assignments have been proposed, but up to now no certain statement about their existence can be done. After introducing the theoretical framework in which we will work in, the attention will be focused on the problem of the scalar glueball, which lattice QCD predicts to be the lightest gluonic state with a mass between 1.4-1.8 GeV. In the same mass region one encounters many scalar resonances; mixing between the bare glueball and quarkonia states is therefore likely. In a covariant constituent approach one cannot define rigorously a mixing matrix connecting the bare to physical fields. However, we propose a definition which satisfies the correct requirements and which can be compared to other phenomenological studies. The two-photon decay of isoscalar-scalar states is believed to be crucial to pin down the flavor content of the resonances between 1 and 2 GeV. We discuss and calculate the two-photon decay rates of the mixed states glueball-quarkonia, getting results which are consistent with the current experimental upper limits
Causality and local determinism versus quantum nonlocality
International Nuclear Information System (INIS)
Kupczynski, M
2014-01-01
The entanglement and the violation of Bell and CHSH inequalities in spin polarization correlation experiments (SPCE) is considered to be one of the biggest mysteries of Nature and is called quantum nonlocality. In this paper we show once again that this conclusion is based on imprecise terminology and on the lack of understanding of probabilistic models used in various proofs of Bell and CHSH theorems. These models are inconsistent with experimental protocols used in SPCE. This is the only reason why Bell and CHSH inequalities are violated. A probabilistic non-signalling description of SPCE, consistent with quantum predictions, is possible and it depends explicitly on the context of each experiment. It is also deterministic in the sense that the outcome is determined by supplementary local parameters describing both physical signals and measuring instruments. The existence of such description gives additional arguments that quantum theory is emergent from some more detailed theory respecting causality and local determinism. If quantum theory is emergent then there exist perhaps some fine structures in time-series of experimental data which were not predicted by quantum theory. In this paper we explain how a systematic search for such fine structures can be done. If such reproducible fine structures were found it would show that quantum theory is not predictably complete, which would be a major discovery.
Exploring nonlocal observables in shock wave collisions
Energy Technology Data Exchange (ETDEWEB)
Ecker, Christian; Grumiller, Daniel; Stanzer, Philipp; Stricker, Stefan A. [Institut für Theoretische Physik, Technische Universität Wien,Wiedner Hauptstrasse 8-10, A-1040 Vienna (Austria); Schee, Wilke van der [Center for Theoretical Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, MA 02139 (United States)
2016-11-09
We study the time evolution of 2-point functions and entanglement entropy in strongly anisotropic, inhomogeneous and time-dependent N=4 super Yang-Mills theory in the large N and large ’t Hooft coupling limit using AdS/CFT. On the gravity side this amounts to calculating the length of geodesics and area of extremal surfaces in the dynamical background of two colliding gravitational shockwaves, which we do numerically. We discriminate between three classes of initial conditions corresponding to wide, intermediate and narrow shocks, and show that they exhibit different phenomenology with respect to the nonlocal observables that we determine. Our results permit to use (holographic) entanglement entropy as an order parameter to distinguish between the two phases of the cross-over from the transparency to the full-stopping scenario in dynamical Yang-Mills plasma formation, which is frequently used as a toy model for heavy ion collisions. The time evolution of entanglement entropy allows to discern four regimes: highly efficient initial growth of entanglement, linear growth, (post) collisional drama and late time (polynomial) fall off. Surprisingly, we found that 2-point functions can be sensitive to the geometry inside the black hole apparent horizon, while we did not find such cases for the entanglement entropy.
PET reconstruction via nonlocal means induced prior.
Hou, Qingfeng; Huang, Jing; Bian, Zhaoying; Chen, Wufan; Ma, Jianhua
2015-01-01
The traditional Bayesian priors for maximum a posteriori (MAP) reconstruction methods usually incorporate local neighborhood interactions that penalize large deviations in parameter estimates for adjacent pixels; therefore, only local pixel differences are utilized. This limits their abilities of penalizing the image roughness. To achieve high-quality PET image reconstruction, this study investigates a MAP reconstruction strategy by incorporating a nonlocal means induced (NLMi) prior (NLMi-MAP) which enables utilizing global similarity information of image. The present NLMi prior approximates the derivative of Gibbs energy function by an NLM filtering process. Specially, the NLMi prior is obtained by subtracting the current image estimation from its NLM filtered version and feeding the residual error back to the reconstruction filter to yield the new image estimation. We tested the present NLMi-MAP method with simulated and real PET datasets. Comparison studies with conventional filtered backprojection (FBP) and a few iterative reconstruction methods clearly demonstrate that the present NLMi-MAP method performs better in lowering noise, preserving image edge and in higher signal to noise ratio (SNR). Extensive experimental results show that the NLMi-MAP method outperforms the existing methods in terms of cross profile, noise reduction, SNR, root mean square error (RMSE) and correlation coefficient (CORR).
Experimental nonlocal steering of Bohmian trajectories.
Xiao, Ya; Kedem, Yaron; Xu, Jin-Shi; Li, Chuan-Feng; Guo, Guang-Can
2017-06-26
Interpretations of quantum mechanics (QM), or proposals for underlying theories, that attempt to present a definite realist picture, such as Bohmian mechanics, require strong non-local effects. Naively, these effects would violate causality and contradict special relativity. However if the theory agrees with QM the violation cannot be observed directly. Here, we demonstrate experimentally such an effect: we steer the velocity and trajectory of a Bohmian particle using a remote measurement. We use a pair of photons and entangle the spatial transverse position of one with the polarization of the other. The first photon is sent to a double-slit-like apparatus, where its trajectory is measured using the technique of Weak Measurements. The other photon is projected to a linear polarization state. The choice of polarization state, and the result, steer the first photon in the most intuitive sense of the word. The effect is indeed shown to be dramatic, while being easy to visualize. We discuss its strength and what are the conditions for it to occur.
Understanding quantum interference in general nonlocality
International Nuclear Information System (INIS)
Wang Haijun
2011-01-01
In this paper we attempt to give a new understanding of quantum double-slit interference of fermions in the framework of general nonlocality (GN) [J. Math. Phys. 49, 033513 (2008)] by studying the self-(inter)action of matter wave. From the metric of the GN, we derive a special formalism to interpret the interference contrast when the self-action is perturbative. According to the formalism, the characteristic of interference pattern is in agreement with experiment qualitatively. As examples, we apply the formalism to the cases governed by Schroedinger current and Dirac current, respectively, both of which are relevant to topology. The gap between these two cases corresponds to the fermion magnetic moment, which is possible to test in the near future. In addition, a general interference formalism for both perturbative and nonperturbative self-actions is presented. By analyzing the general formalism we predict that in the nonperturbative limit there is no interference at all. And by comparison with the special formalism of Schroedinger current, the coupling strength of self-action in the limit is found to be ∞. In the perturbative case, the interference from self-action turns out to be the same as that from the standard approach of quantum theory. Then comparing the corresponding coefficients quantitatively we conclude that the coupling strength of self-action in this case falls in the interval [0, 1].
A unified approach to the minimal unitary realizations of noncompact groups and supergroups
International Nuclear Information System (INIS)
Guenaydin, Murat; Pavlyk, Oleksandr
2006-01-01
We study the minimal unitary representations of non-compact groups and supergroups obtained by quantization of their geometric realizations as quasi-conformal groups and supergroups. The quasi-conformal groups G leave generalized light-cones defined by a quartic norm invariant and have maximal rank subgroups of the form H x SL(2, R) such that G/H x SL(2, R) are para-quaternionic symmetric spaces. We give a unified formulation of the minimal unitary representations of simple non-compact groups of type A 2 , G 2 , D 4 , F 4 , E 6 , E 7 , E 8 and Sp(2n, R). The minimal unitary representations of Sp(2n, R) are simply the singleton representations and correspond to a degenerate limit of the unified construction. The minimal unitary representations of the other noncompact groups SU(m, n), SO(m, n), SO*(2n) and SL(m, R) are also given explicitly. We extend our formalism to define and construct the corresponding minimal representations of non-compact supergroups G whose even subgroups are of the form H x SL(2, R). If H is noncompact then the supergroup G does not admit any unitary representations, in general. The unified construction with H simple or Abelian leads to the minimal representations of G(3), F(4) and O Sp(n|2, R) (in the degenerate limit). The minimal unitary representations of O Sp(n|2, R) with even subgroups SO(n) x SL(2, R) are the singleton representations. We also give the minimal realization of the one parameter family of Lie superalgebras D(2, 1; σ)
International Nuclear Information System (INIS)
Qin Fang; Chen Jisheng
2010-01-01
We utilize the fractional exclusion statistics of the Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function of the energy per particle and energy per particle versus rescaled temperature are numerically compared with the experimental data. The study shows that, except the chemical potential behaviour, there exists a reasonable consistency between the experimental measurement and theoretical attempt for the entropy and energy per particle. In the fractional exclusion statistics formalism, the behaviour of the isochore heat capacity for a trapped unitary Fermi gas is also analysed.
Comparison of the unitary pole and Adhikari-Sloan expansions in the three nucleon system
International Nuclear Information System (INIS)
Afnan, I.R.; Birrell, N.D.
1977-01-01
The binding energy of 3 H, percentage S-, S'- and D-state probability, and charge form factor of 3 He are calculated using the unitary pole and Adhikari-Sloan separable expansions to the Reid soft core potential. Comparison of the results for the two separable expansions show that the expansion of Adhikari and Sloan has the better convergence property, and the lowest rank expansion considered (equivalent to the unitary pole approximation) gives a good approximation to the binding energy of 3 H and the charge form factor of 3 He, even at large momentum transfer (K 2 -2 ). (Author)
Mohamed, Abdel-Baset A.
2018-04-01
In this paper, some non-classical correlations are investigated for bipartite partitions of two qubits trapped in two spatially separated cavities connected by an optical fiber. The results show that the trace distance discord and Bell's non-locality introduce other quantum correlations beyond the entanglement. Moreover, the correlation functions of the trace distance discord and the Bell's non-locality are very sensitive to the initial correlations, the coupling strengths, and the dissipation rates of the cavities. The fluctuations of the correlation functions between their initial values and gained (loss) values appear due to the unitary evolution of the system. These fluctuations depend on the chosen initial correlations between the two subsystems. The maximal violations of Bell's inequality occur when the logarithmic negativity and the trace distance discord reach certain values. It is shown that the robustness of the non-classical correlations, against the dissipation rates of the cavities, depends on the bipartite partitions reduced density matrices of the system, and is also greatly enhanced by choosing appropriate coupling strengths.
Technical skills assessment toolbox: a review using the unitary framework of validity.
Ghaderi, Iman; Manji, Farouq; Park, Yoon Soo; Juul, Dorthea; Ott, Michael; Harris, Ilene; Farrell, Timothy M
2015-02-01
The purpose of this study was to create a technical skills assessment toolbox for 35 basic and advanced skills/procedures that comprise the American College of Surgeons (ACS)/Association of Program Directors in Surgery (APDS) surgical skills curriculum and to provide a critical appraisal of the included tools, using contemporary framework of validity. Competency-based training has become the predominant model in surgical education and assessment of performance is an essential component. Assessment methods must produce valid results to accurately determine the level of competency. A search was performed, using PubMed and Google Scholar, to identify tools that have been developed for assessment of the targeted technical skills. A total of 23 assessment tools for the 35 ACS/APDS skills modules were identified. Some tools, such as Operative Performance Rating System (OSATS) and Objective Structured Assessment of Technical Skill (OPRS), have been tested for more than 1 procedure. Therefore, 30 modules had at least 1 assessment tool, with some common surgical procedures being addressed by several tools. Five modules had none. Only 3 studies used Messick's framework to design their validity studies. The remaining studies used an outdated framework on the basis of "types of validity." When analyzed using the contemporary framework, few of these studies demonstrated validity for content, internal structure, and relationship to other variables. This study provides an assessment toolbox for common surgical skills/procedures. Our review shows that few authors have used the contemporary unitary concept of validity for development of their assessment tools. As we progress toward competency-based training, future studies should provide evidence for various sources of validity using the contemporary framework.
Evidence of Non-local Chemical, Thermal and Gravitational Effects
Directory of Open Access Journals (Sweden)
Hu H.
2007-04-01
Full Text Available Quantum entanglement is ubiquitous in the microscopic world and manifests itself macroscopically under some circumstances. But common belief is that it alone cannot be used to transmit information nor could it be used to produce macroscopic non- local effects. Yet we have recently found evidence of non-local effects of chemical substances on the brain produced through it. While our reported results are under independent verifications by other groups, we report here our experimental findings of non-local chemical, thermal and gravitational effects in simple physical systems such as reservoirs of water quantum-entangled with water being manipulated in a remote reservoir. With the aids of high-precision instruments, we have found that the pH value, temperature and gravity of water in the detecting reservoirs can be non-locally affected through manipulating water in the remote reservoir. In particular, the pH value changes in the same direction as that being manipulated; the temperature can change against that of local environment; and the gravity apparently can also change against local gravity. These non-local effects are all reproducible and can be used for non-local signalling and many other purposes. We suggest that they are mediated by quantum entanglement between nuclear and/or electron spins in treated water and discuss the implications of these results.
On a non-local gas dynamics like integrable hierarchy
International Nuclear Information System (INIS)
Brunelli, Jose Carlos; Das, Ashok
2004-01-01
We study a new hierarchy of equations derived from the system of isentropic gas dynamics equations where the pressure is a non-local function of the density. We show that the hierarchy of equations is integrable. We construct the two compatible Hamiltonian structures and show that the first structure has three distinct Casimirs while the second has one. The existence of Casimirs allows us to extend the flows to local ones. We construct an infinite series of commuting local Hamiltonians as well as three infinite series (related to the three Casimirs) of non-local charges. We discuss the zero curvature formulation of the system where we obtain a simple expression for the non-local conserved charges, which also clarifies the existence of the three series from a Lie algebraic point of view. We point out that the non-local hierarchy of Hunter-Zheng equations can be obtained from our non-local flows when the dynamical variables are properly constrained. (author)
Localized solutions for a nonlocal discrete NLS equation
Energy Technology Data Exchange (ETDEWEB)
Ben, Roberto I. [Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, 1613 Los Polvorines (Argentina); Cisneros Ake, Luís [Department of Mathematics, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 México D.F. (Mexico); Minzoni, A.A. [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico); Panayotaros, Panayotis, E-mail: panos@mym.iimas.unam.mx [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico)
2015-09-04
We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces.
Multiclustered chimeras in large semiconductor laser arrays with nonlocal interactions
Shena, J.; Hizanidis, J.; Hövel, P.; Tsironis, G. P.
2017-09-01
The dynamics of a large array of coupled semiconductor lasers is studied numerically for a nonlocal coupling scheme. Our focus is on chimera states, a self-organized spatiotemporal pattern of coexisting coherence and incoherence. In laser systems, such states have been previously found for global and nearest-neighbor coupling, mainly in small networks. The technological advantage of large arrays has motivated us to study a system of 200 nonlocally coupled lasers with respect to the emerging collective dynamics. Moreover, the nonlocal nature of the coupling allows us to obtain robust chimera states with multiple (in)coherent domains. The crucial parameters are the coupling strength, the coupling phase and the range of the nonlocal interaction. We find that multiclustered chimera states exist in a wide region of the parameter space and we provide quantitative characterization for the obtained spatiotemporal patterns. By proposing two different experimental setups for the realization of the nonlocal coupling scheme, we are confident that our results can be confirmed in the laboratory.
Localized solutions for a nonlocal discrete NLS equation
International Nuclear Information System (INIS)
Ben, Roberto I.; Cisneros Ake, Luís; Minzoni, A.A.; Panayotaros, Panayotis
2015-01-01
We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces
Non-local magnetoresistance in YIG/Pt nanostructures
Energy Technology Data Exchange (ETDEWEB)
Goennenwein, Sebastian T. B., E-mail: goennenwein@wmi.badw.de; Pernpeintner, Matthias; Gross, Rudolf; Huebl, Hans [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Walther-Meißner-Str. 8, 85748 Garching (Germany); Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München (Germany); Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching (Germany); Schlitz, Richard; Ganzhorn, Kathrin [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Walther-Meißner-Str. 8, 85748 Garching (Germany); Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching (Germany); Althammer, Matthias [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Walther-Meißner-Str. 8, 85748 Garching (Germany)
2015-10-26
We study the local and non-local magnetoresistance of thin Pt strips deposited onto yttrium iron garnet. The local magnetoresistive response, inferred from the voltage drop measured along one given Pt strip upon current-biasing it, shows the characteristic magnetization orientation dependence of the spin Hall magnetoresistance. We simultaneously also record the non-local voltage appearing along a second, electrically isolated, Pt strip, separated from the current carrying one by a gap of a few 100 nm. The corresponding non-local magnetoresistance exhibits the symmetry expected for a magnon spin accumulation-driven process, confirming the results recently put forward by Cornelissen et al. [“Long-distance transport of magnon spin information in a magnetic insulator at room temperature,” Nat. Phys. (published online 14 September 2015)]. Our magnetotransport data, taken at a series of different temperatures as a function of magnetic field orientation, rotating the externally applied field in three mutually orthogonal planes, show that the mechanisms behind the spin Hall and the non-local magnetoresistance are qualitatively different. In particular, the non-local magnetoresistance vanishes at liquid Helium temperatures, while the spin Hall magnetoresistance prevails.
Nonlocal non-Markovian effects in dephasing environments
International Nuclear Information System (INIS)
Xie Dong; Wang An-Min
2014-01-01
We study the nonlocal non-Markovian effects through local interactions between two subsystems and the corresponding two environments. It has been found that the initial correlations between two environments can turn a Markovian to a non-Markovian regime with extra control on the local interaction time. We further research the nonlocal non-Markovian effects from two situations: without extra control, the nonlocal non-Markovian effects only appear under the condition that two local dynamics are non-Markovian–non-Markovian (both of the two local dynamics are non-Markovian) or Markovian–non-Markovian, but not under the condition of Markovian–Markovian; with extra control, the nonlocal non-Markovian effects can occur under the condition of Markovian–Markovian. It shows that the function of correlations between two environments has an upper bound, which makes a flow of information from the environment back to the global system beginning finitely earlier than that back to one of the two local systems, not infinitely. Then, we proposed two special ways to distribute classical correlations between two environments without initial correlations. Finally, from numerical solutions in the spin star configuration, we found that the self-correlation (internal correlation) of each environment promotes the nonlocal non-Markovian effects. (general)
Nonlocal conductivity in type-II superconductors
International Nuclear Information System (INIS)
Mou, C.; Wortis, R.; Dorsey, A.T.; Huse, D.A.
1995-01-01
Multiterminal transport measurements on YBa 2 Cu 2 O 7 crystals in the vortex liquid regime have shown nonlocal conductivity on length scales up to 50 microns. Motivated by these results we explore the wave vector (k) dependence of the dc conductivity tensor, σ μν (k), in the Meissner, vortex lattice, and disordered phases of a type-II superconductor. Our results are based on time-dependent Ginzburg-Landau (TDGL) theory and on phenomenological arguments. We find four qualitatively different types of behavior. First, in the Meissner phase, the conductivity is infinite at k=0 and is a continuous function of k, monotonically decreasing with increasing k. Second, in the vortex-lattice phase, in the absence of pinning, the conductivity is finite (due to flux flow) at k=0; it is discontinuous there and remains qualitatively like the Meissner phase for k>0. Third, in the vortex liquid regime in a magnetic field and at low temperature, the conductivity is finite, smooth and nonmonotonic, first increasing with k at small k and then decreasing at larger k. This third behavior is expected to apply at temperatures just above the melting transition of the vortex lattice, where the vortex liquid shows strong short-range order and a large viscosity. Finally, at higher temperatures in the disordered phase, the conductivity is finite, smooth and again monotonically decreasing with k. This last, monotonic behavior applies in zero magnetic field for the entire disordered phase, i.e., at all temperatures above T c , while in a field the nonmonotonic behavior may occur in a low-temperature portion of the disordered phase
Random access codes and nonlocal resources
Chaturvedi, Anubhav; Pawlowski, Marcin; Horodecki, Karol
2017-08-01
This work explores the notion of inter-convertibility between a cryptographic primitive: the random access code (RAC) and bipartite no-signaling nonlocal resources. To this end we introduce two generalizations of the Popescu-Rohrlich box (PR) and investigate their relation with the corresponding RACs. The first generalization is based on the number of Alice's input bits; we refer to it as the Bn-box. We show that the no-signaling condition imposes an equivalence between the Bn-box and the (n →1 ) RAC (encoding of n input bits to 1 bit of message). As an application we show that (n -1 ) PRs supplemented with one bit communication are necessary and sufficient to win a (n →1 ) RAC with certainty. Furthermore, we present a signaling instant of a perfectly working (n →1 ) RAC which cannot simulate the Bn-box, thus showing that it is weaker than its no-signaling counterpart. For the second generalization we replace Alice's input bits with d its (d -leveled classical systems); we call this the Bnd-box. In this case the no-signaling condition is not enough to enforce an equivalence between the Bnd-box and (n →1 ,d ) RAC (encoding of n input d its to 1 d it of message); i.e., while the Bnd-box can win a (n →1 ,d ) RAC with certainty, not all no-signaling instances of a (n →1 ,d ) RAC can simulate the Bnd-box. We use resource inequalities to quantitatively capture these results.
Experimental implementation of optimal linear-optical controlled-unitary gates
Czech Academy of Sciences Publication Activity Database
Lemr, K.; Bartkiewicz, K.; Černoch, Antonín; Dušek, M.; Soubusta, Jan
2015-01-01
Roč. 114, č. 15 (2015), "153602-1"-"153602-5" ISSN 0031-9007 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : two-qubit gates * optimal linear-optical controlled-unitary gates * quantum computing Subject RIV: BH - Optics, Masers, Lasers Impact factor: 7.645, year: 2015
The flexible focus: whether spatial attention is unitary or divided depends on observer goals.
Jefferies, Lisa N; Enns, James T; Di Lollo, Vincent
2014-04-01
The distribution of visual attention has been the topic of much investigation, and various theories have posited that attention is allocated either as a single unitary focus or as multiple independent foci. In the present experiment, we demonstrate that attention can be flexibly deployed as either a unitary or a divided focus in the same experimental task, depending on the observer's goals. To assess the distribution of attention, we used a dual-stream Attentional Blink (AB) paradigm and 2 target pairs. One component of the AB, Lag-1 sparing, occurs only if the second target pair appears within the focus of attention. By varying whether the first-target-pair could be expected in a predictable location (always in-stream) or not (unpredictably in-stream or between-streams), observers were encouraged to deploy a divided or a unitary focus, respectively. When the second-target-pair appeared between the streams, Lag-1 sparing occurred for the Unpredictable group (consistent with a unitary focus) but not for the Predictable group (consistent with a divided focus). Thus, diametrically different outcomes occurred for physically identical displays, depending on the expectations of the observer about where spatial attention would be required.
Gaussian elimination in split unitary groups with an application to public-key cryptography
Directory of Open Access Journals (Sweden)
Ayan Mahalanobis
2017-07-01
Full Text Available Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to split unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate that.
Unitary eikonal formalism for multiproduction of isovector mesons at high energy
Redei, L B
1973-01-01
Unitary eikonal models for multiproduction of isovector mesons are discussed in general terms. A closed analytic expression is derived for the partial production cross sections and for the meson multiplicity moments. A simple class of models is discussed in more detail. (11 refs).
Point transformations and renormalization in the unitary gauge. III. Renormalization effects
International Nuclear Information System (INIS)
Sherry, T.N.
1976-06-01
An analysis of two simple gauge theory models is continued using point transformations rather than gauge transformations. The renormalization constants are examined directly in two gauges, the renormalization (Landau) and unitary gauges. The result is that the individual coupling constant renormalizations are identical when calculated in each of the above two gauges, although the wave-function and proper vertex renormalizations differ
Topology of unitary groups and the prime orders of binomial coefficients
Duan, HaiBao; Lin, XianZu
2017-09-01
Let $c:SU(n)\\rightarrow PSU(n)=SU(n)/\\mathbb{Z}_{n}$ be the quotient map of the special unitary group $SU(n)$ by its center subgroup $\\mathbb{Z}_{n}$. We determine the induced homomorphism $c^{\\ast}:$ $H^{\\ast}(PSU(n))\\rightarrow H^{\\ast}(SU(n))$ on cohomologies by computing with the prime orders of binomial coefficients
An Integral Representation of Standard Automorphic L Functions for Unitary Groups
Directory of Open Access Journals (Sweden)
Yujun Qin
2007-01-01
Full Text Available Let F be a number field, G a quasi-split unitary group of rank n. We show that given an irreducible cuspidal automorphic representation π of G(A, its (partial L function LS(s,π,σ can be represented by a Rankin-Selberg-type integral involving cusp forms of π, Eisenstein series, and theta series.
Beyond the Tipping Point: Issues of Racial Diversity in Magnet Schools Following Unitary Status
Smrekar, Claire
2009-01-01
This article uses qualitative case study methodology to examine why the racial composition of magnet schools in Nashville, Tennessee, has shifted to predominantly African American in the aftermath of unitary status. The article compares the policy contexts and parents' reasons for choosing magnet schools at two points in time--under court order…
J(l)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting
Alpay, D.; Dijksma, A.; Langer, H.
2006-01-01
We introduce a Schur transformation for generalized Nevanlinna functions and show that it can be used in obtaining the unique minimal factorization of a class of rational J(l)-unitary 2 x 2 matrix functions into elementary factors from the same class. (c) 2006 Elsevier Inc. All rights reserved.
Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model
Ni, Wenjie; Shi, Junping; Wang, Mingxin
2018-06-01
A diffusive Lotka-Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka-Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper-lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients.
Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axial load
International Nuclear Information System (INIS)
Li, C; Yu, J L; Lim, C W
2011-01-01
This paper investigates the natural frequency, steady-state resonance and stability for the transverse vibrations of a nanobeam subjected to a variable initial axial force, including axial tension and axial compression, based on nonlocal elasticity theory. It is reported that the nonlocal nanoscale has significant effects on vibration behavior, which results in a new effective nonlocal bending moment different to but dependent on the corresponding nonlocal bending moment. The effects of nonlocal nanoscale and the variation of initial axial force on the natural frequency as well as the instability regions are analyzed by the perturbation method. It concludes that both the nonlocal nanoscale and the initial tension, including static and dynamic tensions, cause an increase in natural frequency, while an initial compression causes the natural frequency to decrease. Instability regions are also greatly influenced by the nonlocal nanoscale and initial tension and they become smaller with stronger nonlocal effects or larger initial tension
Park, Sohyun
2018-02-01
We examine the origin of two opposite results for the growth of perturbations in the Deser-Woodard (DW) nonlocal gravity model. One group previously analyzed the model in its original nonlocal form and showed that the growth of structure in the DW model is enhanced compared to general relativity (GR) and thus concluded that the model was ruled out. Recently, however, another group has reanalyzed it by localizing the model and found that the growth in their localized version is suppressed even compared to the one in GR. The question was whether the discrepancy originates from an intrinsic difference between the nonlocal and localized formulations or is due to their different implementations of the subhorizon limit. We show that the nonlocal and local formulations give the same solutions for the linear perturbations as long as the initial conditions are set the same. The different implementations of the subhorizon limit lead to different transient behaviors of some perturbation variables; however, they do not affect the growth of matter perturbations at the sub-horizon scale much. In the meantime, we also report an error in the numerical calculation code of the former group and verify that after fixing the error the nonlocal version also gives the suppressed growth. Finally, we discuss two alternative definitions of the effective gravitational constant taken by the two groups and some open problems.
Schweigert, Igor V; Bartlett, Rodney J
2008-09-28
Adding a fraction of the nonlocal exchange operator to the local orbital-dependent exchange potential improves the many-body perturbation expansion based on the Kohn-Sham determinant. The effect of such a hybrid scheme on the performance of the orbital-dependent correlation functional from the second-order perturbation theory (PT2H) is investigated numerically. A small fraction of the nonlocal exchange is often sufficient to ensure the existence of the self-consistent solution for the PT2H potential. In the He and Be atoms, including 37% of the nonlocal exchange leads to the correlation energies and electronic densities that are very close to the exact ones. In molecules, varying the fraction of the nonlocal exchange may result in the PT2H energy closely reproducing the CCSD(T) value; however such a fraction depends on the system and does not always result in an accurate electronic density. We also numerically verify that the "semicanonical" perturbation series includes most of the beneficial effects of the nonlocal exchange without sacrificing the locality of the exchange potential.
Nonlocal Free Energy of a Spatially Inhomogeneous Superconductor
International Nuclear Information System (INIS)
Grigorishin, K.V.; Lev, B.I.
2012-01-01
The microscopic approach is developed for obtaining of the free energy of a superconductor based on direct calculation of the vacuum amplitude. The free energy functional of the spatially inhomogeneous superconductor in a magnetic field is obtained with help of the developed approach. The obtained functional is generalization of Ginzburg-Landau functionals for any temperature, for arbitrary spatial variations of the order parameter and for the nonlocality of a magnetic response and the order parameter. Moreover, the nonlocality of the magnetic response is the consequence of order parameter's nonlocality. The extremals of this functional are considered in the explicit form in the low- and high-temperature limit at the condition of slowness of spatial variations of the order parameter. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Nonlocal superconducting correlations in graphene in the quantum Hall regime
Beconcini, Michael; Polini, Marco; Taddei, Fabio
2018-05-01
We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nat. Phys. 13, 693 (2017), 10.1038/nphys4084]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-Büttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair edge and with a wide superconducting region (as compared to the superconducting coherence length), CAR exhibits large oscillations as a function of the magnetic field due to interference effects. This results in sign changes of the nonlocal resistance.
Nonlocal surface plasmons by Poisson Green's function matching
International Nuclear Information System (INIS)
Morgenstern Horing, Norman J
2006-01-01
The Poisson Green's function for all space is derived for the case in which an interface divides space into two separate semi-infinite media, using the Green's function matching method. Each of the separate semi-infinite constituent parts has its own dynamic, nonlocal polarizability, which is taken to be unaffected by the presence of the interface and is represented by the corresponding bulk response property. While this eliminates Friedel oscillatory phenomenology near the interface with p ∼ 2p F , it is nevertheless quite reasonable and useful for a broad range of lower (nonvanishing) wavenumbers, p F . The resulting full-space Poisson Green's function is dynamic, nonlocal and spatially inhomogeneous, and its frequency pole yields the surface plasmon dispersion relation, replete with dynamic and nonlocal features. It also accommodates an ambient magnetic field
Non-local charges in local quantum field theory
International Nuclear Information System (INIS)
Buchholz, D.; Lopuszanski, J.T.; Rabsztyn, S.
1985-05-01
Non-local charges are studied in the general setting of local quantum field theory. It is shown, that these charges can be represented as polynomials in the incoming respectively outgoing fields with coefficients (kernels) which are subject to specific constraints. For the restricted class of models of a scalar, massive, self interacting particle in four dimensions, a more detailed analysis shows that all non-local charges of the generic type (genus 2) are products of generators of the Poincare group. This analysis, which is based on the macroscopic causality properties of the S-matrix, seems to indicate that less trivial examples of non-local charges can only exist in two dimensions. (orig.)
Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams
Ebrahimi, Farzad; Reza Barati, Mohammad
2016-09-01
In this work, a size-dependent curved beam model is developed to take into account the effects of nonlocal stresses on the buckling behavior of curved magneto-electro-elastic FG nanobeams for the first time. The governing differential equations are derived based on the principle of virtual work and Euler-Bernoulli beam theory. The power-law function is employed to describe the spatially graded magneto-electro-elastic properties. By extending the radius of the curved nanobeam to infinity, the results of straight nonlocal FG beams can be rendered. The effects of magnetic potential, electric voltage, opening angle, nonlocal parameter, power-law index and slenderness ratio on buckling loads of curved MEE-FG nanobeams are studied.
A non-local variable for general relativity
International Nuclear Information System (INIS)
Kozameh, C.N.; Newman, E.T.
1983-01-01
The usual description of differential geometry and general relativity is in terms of local fields, e.g. the metric, the curvature tensor, etc, which satisfy local differential equations. The authors introduce a new non-local field (Z) from which the local fields can be derived. Basically Z, though it is non-local, should be thought of as a function on the bundle of null directions on a space-time. The program can be divided into two parts; first the authors want to show the geometric meaning of and the relationship between Z and the local field. Then they want to provide field equations (non-local) for Z which will be equivalent to the vacuum Einstein equations for the local field. (Auth.)
Non-local quantal Noether identities and their applications
International Nuclear Information System (INIS)
Li Ziping
2002-01-01
Based on the phase-space generating functional for a system with a singular high-order Lagrangian, the quantal canonical Noether identities under the local and non-local transformation in phase space for such system have been derived. For a gauge-invariant system with a higher-order Lagrangian, the quantal Noether identities under the local and non-local transformation in configuration space have also been derived. it has been pointed out that in certain cases the quantal Noether identities may be converted to the conservation laws at the quantum level. This algorithm to derive the quantal conservation laws is significantly different from the first quantal Noether theorem. The applications to the non-Abelian CS theories with higher-order derivatives are given. The conserved quantities at the quantum level for some local and non-local transformation are found respectively
Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions
Directory of Open Access Journals (Sweden)
Liu Jinn-Liang
2017-10-01
Full Text Available We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation efects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell’s displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+.
Shape Changing Nonlocal Molecular Deformations in a Nematic Liquid Crystal
International Nuclear Information System (INIS)
Kavitha, L.; Venkatesh, M.; Gopi, D.
2010-07-01
The nature of nonlinear molecular deformations in a homeotropically aligned nematic liquid crystal (NLC) is presented. We start from the basic dynamical equation for the director axis of a NLC with elastic deformation mapped onto an integro-differential perturbed Nonlinear Schroedinger equation which includes the nonlocal term. By invoking the modified extended tangent hyperbolic function method aided with symbolic computation, we obtain a series of solitary wave solutions. Under the influence of the nonlocality induced by the reorientation nonlinearity due to fluctuations in the molecular orientation, the solitary wave exhibits shape changing property for different choices of parameters. This intriguing property, as a result of the relation between the coherence of the solitary deformation and the nonlocality, reveals a strong need for deeper understanding in the theory of self-localization in NLC systems. (author)
Non-binary unitary error bases and quantum codes
Energy Technology Data Exchange (ETDEWEB)
Knill, E.
1996-06-01
Error operator bases for systems of any dimension are defined and natural generalizations of the bit-flip/ sign-change error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of Abelian groups. As a consequence, quantum codes can be constructed form linear codes over {ital Z}{sub {ital n}} for any {ital n}. The generalization of the punctured code construction leads to many codes which permit transversal (i.e. fault tolerant) implementations of certain operations compatible with the error basis.
A strange recursion operator demystified
International Nuclear Information System (INIS)
Sergyeyev, A
2005-01-01
We show that a new integrable two-component system of KdV type studied by Karasu (Kalkanli) et al (2004 Acta Appl. Math. 83 85-94) is bi-Hamiltonian, and its recursion operator, which has a highly unusual structure of nonlocal terms, can be written as a ratio of two compatible Hamiltonian operators found by us. Using this we prove that the system in question possesses an infinite hierarchy of local commuting generalized symmetries and conserved quantities in involution, and the evolution systems corresponding to these symmetries are bi-Hamiltonian as well. We also show that upon introduction of suitable nonlocal variables the nonlocal terms of the recursion operator under study can be written in the usual form, with the integration operator D -1 x appearing in each term at most once. (letter to the editor)
International Nuclear Information System (INIS)
Zunger, A.; Cohen, M.L.
1978-01-01
We present a method for obtaining first-principles nonlocal atomic pseudopotentials in the density-functional formalism by direct inversion of the pseudopotential eigenvalue problem, where the pseudo-wave-functions are represented as a unitary rotation of the exact all-electron wave functions. The usual pseudopotential nonuniqueness of the orbitals is fixed by imposing the physically appealing constraints of maximum similarity to the all-electron wave functions and minimum radial kinetic energy. These potentials are shown to yield very accurate energy eigenvalues, total energy differences, and wave-function moments over a wide range of excited atomic configurations. We have calculated the potentials for 68 transition and nontransition elements of rows 1--5 in the Periodic Table. Their characteristic features, such as classical turning points and minimum potential radii, faithfully reflect the chemical regularities of the Periodic Table. The nonempirical nature of these potentials permits both an analysis of their dominant features in terms of the underlying interelectronic potentials and the systematic improvement of their predictions through inclusion of appropriate correlation terms. As these potentials accurately reproduce both energy eigenvalues and wave functions and can be readily fit to analytic forms with known asymptotic behavior, they can be used directly for studies of many structural and electronic properties of solids
Strong Local-Nonlocal Coupling for Integrated Fracture Modeling
Energy Technology Data Exchange (ETDEWEB)
Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Silling, Stewart A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, John A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Seleson, Pablo D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parks, Michael L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Burnett, Damon J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ostien, Jakob [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Gunzburger, Max [Florida State Univ., Tallahassee, FL (United States)
2015-09-01
Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling," completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for
Nonlocal Poisson-Fermi model for ionic solvent.
Xie, Dexuan; Liu, Jinn-Liang; Eisenberg, Bob
2016-07-01
We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.
Nonlocal, yet translation invariant, constraints for rotationally invariant slave bosons
Ayral, Thomas; Kotliar, Gabriel
The rotationally-invariant slave boson (RISB) method is a lightweight framework allowing to study the low-energy properties of complex multiorbital problems currently out of the reach of more comprehensive, yet more computationally demanding methods such as dynamical mean field theory. In the original formulation of this formalism, the slave-boson constraints can be made nonlocal by enlarging the unit cell and viewing the quantum states enclosed in this new unit cell as molecular levels. In this work, we extend RISB to constraints which are nonlocal while preserving translation invariance. We apply this extension to the Hubbard model.
Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid.
Sahin, Buyukdagli; Ralf, Blossey
2014-07-16
We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.
Local models and hidden nonlocality in Quantum Theory
Guerini, Leonardo
2014-01-01
This Master's thesis has two central subjects: the simulation of correlations generated by local measurements on entangled quantum states by local hidden-variables models and the revelation of hidden nonlocality. We present and detail the Werner's local model and the hidden nonlocality of some Werner states of dimension $d\\geq5$, the Gisin-Degorre's local model for a Werner state of dimension $d=2$ and the local model of Hirsch et al. for mixtures of the singlet state and noise, all of them f...
Local and Nonlocal Parallel Heat Transport in General Magnetic Fields
International Nuclear Information System (INIS)
Castillo-Negrete, D. del; Chacon, L.
2011-01-01
A novel approach for the study of parallel transport in magnetized plasmas is presented. The method avoids numerical pollution issues of grid-based formulations and applies to integrable and chaotic magnetic fields with local or nonlocal parallel closures. In weakly chaotic fields, the method gives the fractal structure of the devil's staircase radial temperature profile. In fully chaotic fields, the temperature exhibits self-similar spatiotemporal evolution with a stretched-exponential scaling function for local closures and an algebraically decaying one for nonlocal closures. It is shown that, for both closures, the effective radial heat transport is incompatible with the quasilinear diffusion model.
Nonlocal thermoelectric symmetry relations in ferromagnet-superconductor proximity structures
Energy Technology Data Exchange (ETDEWEB)
Machon, Peter; Belzig, Wolfgang [Department of Physics, University of Konstanz, D-78457 Konstanz (Germany); Eschrig, Matthias [Department of Physics, University of Konstanz, D-78457 Konstanz (Germany); Department of Physics, Royal Holloway, University of London, Egham Hill, EGHAM, TW20 0EX (United Kingdom)
2012-07-01
The symmetries of thermal and electric transport coefficients in quantum coherent structures are related to fundamental thermodynamic principles by the Onsager reciprocity. We generalize Onsager's symmetry relation to nonlocal thermoelectric currents in a three terminal ferromagnet-superconductor heterostructure including spin-dependent crossed Andreev reflection and direct electron transfer processes. We proof this general symmetry by applying spin-dependent boundary conditions for quasi-classical Green's functions in both the clean and the dirty limit. We predict an anomalously large local thermopower and a nonlocal Seebeck effect, which can be explained by the spin-dependent spectral properties.
To the non-local theory of cold nuclear fusion.
Alexeev, Boris V
2014-10-01
In this paper, we revisit the cold fusion (CF) phenomenon using the generalized Bolzmann kinetics theory which can represent the non-local physics of this CF phenomenon. This approach can identify the conditions when the CF can take place as the soliton creation under the influence of the intensive sound waves. The vast mathematical modelling leads to affirmation that all parts of soliton move with the same velocity and with the small internal change of the pressure. The zone of the high density is shaped on the soliton's front. It means that the regime of the 'acoustic CF' could be realized from the position of the non-local hydrodynamics.
Faithful test of nonlocal realism with entangled coherent states
International Nuclear Information System (INIS)
Lee, Chang-Woo; Jeong, Hyunseok; Paternostro, Mauro
2011-01-01
We investigate the violation of Leggett's inequality for nonlocal realism using entangled coherent states and various types of local measurements. We prove mathematically the relation between the violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when tested by the same resources. For Leggett inequalities, we generalize the nonlocal realistic bound to systems in Hilbert spaces larger than bidimensional ones and introduce an optimization technique that allows one to achieve larger degrees of violation by adjusting the local measurement settings. Our work describes the steps that should be performed to produce a self-consistent generalization of Leggett's original arguments to continuous-variable states.
A nonlocal potential form for s-wave α-α scattering
International Nuclear Information System (INIS)
Amos, K.; Bennett, M.T.
1997-01-01
Low energy s-wave α-α phase shifts that agree well with the measured set, have been extracted using a nonlocal interaction formed by folding (local real) nucleon -α particle interactions with density matrix elements of the (projectile) α particle. The resultant nonlocal s-wave α-α interaction is energy dependent and has a nonlocality range of about 2 fm
Weyl calculus in QED I. The unitary group
Amour, L.; Lascar, R.; Nourrigat, J.
2017-01-01
In this work, we consider fixed 1/2 spin particles interacting with the quantized radiation field in the context of quantum electrodynamics. We investigate the time evolution operator in studying the reduced propagator (interaction picture). We first prove that this propagator belongs to the class of infinite dimensional Weyl pseudodifferential operators recently introduced in Amour et al. [J. Funct. Anal. 269(9), 2747-2812 (2015)] on Wiener spaces. We give a semiclassical expansion of the symbol of the reduced propagator up to any order with estimates on the remainder terms. Next, taking into account analyticity properties for the Weyl symbol of the reduced propagator, we derive estimates concerning transition probabilities between coherent states.
International Nuclear Information System (INIS)
Toi, Kazuo
2002-01-01
Experimental evidence and underlying physical processes of nonlocal characters and structural formation in magnetically confined toroidal plasmas are reviewed. Radial profiles of the plasmas exhibit characteristic structures, depending on the various confinement regimes. Profile stiffness subjected to some global constraint and rapid plasma responses to applied plasma perturbation result from nonlocal transport. Once the plasma is free from the constraint, the plasma state can be changed to a new state exhibiting various types of prominent structural formation such as an internal transport barrier. (author)
Generalized state spaces and nonlocality in fault-tolerant quantum-computing schemes
International Nuclear Information System (INIS)
Ratanje, N.; Virmani, S.
2011-01-01
We develop connections between generalized notions of entanglement and quantum computational devices where the measurements available are restricted, either because they are noisy and/or because by design they are only along Pauli directions. By considering restricted measurements one can (by considering the dual positive operators) construct single-particle-state spaces that are different to the usual quantum-state space. This leads to a modified notion of entanglement that can be very different to the quantum version (for example, Bell states can become separable). We use this approach to develop alternative methods of classical simulation that have strong connections to the study of nonlocal correlations: we construct noisy quantum computers that admit operations outside the Clifford set and can generate some forms of multiparty quantum entanglement, but are otherwise classical in that they can be efficiently simulated classically and cannot generate nonlocal statistics. Although the approach provides new regimes of noisy quantum evolution that can be efficiently simulated classically, it does not appear to lead to significant reductions of existing upper bounds to fault tolerance thresholds for common noise models.
Energy Technology Data Exchange (ETDEWEB)
Zhao, Jia-Qiang; Cao, Lian-Zhen; Wang, Xiao-Qin [Department of Physics and Electronic Science, Weifang University, Weifang, Shandong 261061 (China); Lu, Huai-Xin, E-mail: huaixinlu@yahoo.cn [Department of Physics and Electronic Science, Weifang University, Weifang, Shandong 261061 (China)
2012-07-16
We investigate theoretically and experimentally the tripartite entanglement defined by V. Coffman [Phys. Rev. A 61 (2000) 052306] and nonlocality expressed by the Mermin inequality [Phys. Rev. Lett. 65 (1990) 1838] in three-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) states. Using our GGHZ states with fidelity ∼0.84, we demonstrate experimentally the theoretical results of tripartite entanglement and the Mermin theorem successfully. It is shown that the experimental results are in good agreement with the theoretical predictions. -- Highlights: ► We theoretically calculated the tripartite entanglement and expressed the expectation value of Mermin operator in three-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) states. ► We demonstrate experimentally the theoretical results of tripartite entanglement and Mermin theorem successfully. ► The unique relationship between tripartite entanglement and tripartite nonlocality in GGHZ states have been shown.
International Nuclear Information System (INIS)
Zhao, Jia-Qiang; Cao, Lian-Zhen; Wang, Xiao-Qin; Lu, Huai-Xin
2012-01-01
We investigate theoretically and experimentally the tripartite entanglement defined by V. Coffman [Phys. Rev. A 61 (2000) 052306] and nonlocality expressed by the Mermin inequality [Phys. Rev. Lett. 65 (1990) 1838] in three-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) states. Using our GGHZ states with fidelity ∼0.84, we demonstrate experimentally the theoretical results of tripartite entanglement and the Mermin theorem successfully. It is shown that the experimental results are in good agreement with the theoretical predictions. -- Highlights: ► We theoretically calculated the tripartite entanglement and expressed the expectation value of Mermin operator in three-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) states. ► We demonstrate experimentally the theoretical results of tripartite entanglement and Mermin theorem successfully. ► The unique relationship between tripartite entanglement and tripartite nonlocality in GGHZ states have been shown.
Nonlocal elasticity tensors in dislocation and disclination cores
International Nuclear Information System (INIS)
Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.
2017-01-01
We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.
Tomograms and the quest for single particle nonlocality
International Nuclear Information System (INIS)
Anisimov, M A; Caponigro, M; Mancini, S; Man'ko, V I
2007-01-01
By using a tomographic approach to quantum states, we rise the problem of nonlocality within a single particle (single degree of freedom). We propose a possible way to look for such effects on a qubit. Although a conclusive answer is far from being reached, we provide some reflections on the foundational ground
Robustness of the Rabi Splitting under Nonlocal Corrections in Plexcitonics
DEFF Research Database (Denmark)
Tserkezis, Christos; Wubs, Martijn; Mortensen, N. Asger
2018-01-01
separations, either coated with or encapsulating an excitonic layer. Through detailed simulations based on the generalized nonlocal optical response theory, which simultaneously accounts both for modal shifts due to screening and for surface-enhanced Landau damping, we show that, contrary to expectations...... architectures with ultrafine geometrical details....
On nonlocal semi linear elliptic problem with an indefinite term
International Nuclear Information System (INIS)
Yechoui, Akila
2007-08-01
The aim of this paper is to investigate the existence of solutions of a nonlocal semi linear elliptic equation with an indefinite term. The monotone method, the method of upper and lower solutions and the classical maximum principle are used to obtain our results. (author)
Robustness of the Rabi Splitting under Nonlocal Corrections in Plexcitonics
DEFF Research Database (Denmark)
Tserkezis, Christos; Wubs, Martijn; Mortensen, N. Asger
2018-01-01
, the influence of nonlocality is rather limited, as in most occasions the width of the Rabi splitting remains largely unaffected and the two hybrid modes are well distinguishable. We discuss how this behavior can be understood in view of the popular coupled-harmonic-oscillator model, while we also provide...
Non-local model analysis of heat pulse propagation
International Nuclear Information System (INIS)
Iwasaki, Takuya; Itoh, Sanae-I.; Yagi, Masatoshi
1998-01-01
A new theoretical model equation which includes the non-local effect in the heat flux is proposed to study the transient transport phenomena. A non-local heat flux, which is expressed in terms of the integral equation, is superimposed on the conventional form of the heat flux. This model is applied to describe the experimental results from the power switching [Stroth U, et al 1996 Plasma Phys. Control. Fusion 38 1087] and the power modulation experiments [Giannone L, et al 1992 Nucl. Fusion 32 1985] in the W7-AS stellarator. A small fraction of non-local component in the heat flux is found to be very effective in modifying the response against an external modulation. The transient feature of the transport property, which are observed in the response of heat pulse propagation, are qualitatively reproduced by the transport simulations based on this model. A possibility is discussed to determine the correlation length of the non-local effect experimentally by use of the results of transport simulations. (author)
Effect of nonlocal dispersion on self-interacting excitations
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Rasmussen, Kim; Gaididei, Yu.B.
1996-01-01
The dynamics of self-interacting quasiparticles in 1Dsystems with long-range dispersive interactions isexpressed in terms of a nonlocal nonlinear Schrödingerequation. Two branches of stationary solutions are found.The new branch which contains a cusp soliton is shown to beunstable and blowup...
Nonlocal formalism for nanoplasmonics: Phenomenological and semi-classical considerations
DEFF Research Database (Denmark)
Mortensen, N. Asger
2013-01-01
. Without specifying further details of the underlying physical mechanism we show how this leads to a Laplacian correction term in the electromagnetic wave equation. Within the hydrodynamic model we demonstrate this explicitly and we identify the characteristic nonlocal range to be ξNL∼vF/ω where v...
A nonlocal phase-field system with inertial term
Czech Academy of Sciences Publication Activity Database
Grasselli, M.; Petzeltová, Hana; Schimperna, G.
2007-01-01
Roč. 65, č. 3 (2007), s. 451-469 ISSN 0033-569X R&D Projects: GA AV ČR(CZ) IAA100190606 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlocal phase-field system * Lojasiewicz inequality * convergence to equilibria Subject RIV: BA - General Mathematics Impact factor: 0.463, year: 2007
Sparse representation based image interpolation with nonlocal autoregressive modeling.
Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming
2013-04-01
Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.
Nonlocal ultrafast magnetization dynamics in the high fluence limit
Kuiper, K.C.; Malinowski, G.; Dalla Longa, F.; Koopmans, B.
2011-01-01
In order to explain a number of recent experimental observations of laser-induced femtosecond demagnetization in the large fluence limit, we discuss the consequences of a recently proposed nonlocal approach. A microscopic description of spin flip scattering is implemented in an effective three
Hard-type nonlocality proof for two maximally entangled particles
International Nuclear Information System (INIS)
Kalamidas, D.
2005-01-01
Full text: We present, for the first time, a Hardy-type proof of nonlocality for two maximally entangled particles in a four-dimensional total Hilbert space. Furthermore, the violation of local realistic predictions occurs for 25 % of trials, exceeding the 9 % maximum obtained by Hardy for nonmaximally entangled states. (author)
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Quantifying multipartite nonlocality via the size of the resource
Curchod, Florian John; Gisin, Nicolas; Liang, Yeong-Cherng
2015-01-01
The generation of (Bell-)nonlocal correlations, i.e., correlations leading to the violation of a Bell-like inequality, requires the usage of a nonlocal resource, such as an entangled state. When given a correlation (a collection of conditional probability distributions) from an experiment or from a theory, it is desirable to determine the extent to which the participating parties would need to collaborate nonlocally for its (re)production. Here, we propose to achieve this via the minimal group size (MGS) of the resource, i.e., the smallest number of parties that need to share a given type of nonlocal resource for the above-mentioned purpose. In addition, we provide a general recipe—based on the lifting of Bell-like inequalities—to construct MGS witnesses for nonsignaling resources starting from any given ones. En route to illustrating the applicability of this recipe, we also show that when restricted to the space of full-correlation functions, nonsignaling resources are as powerful as unconstrained signaling resources. Explicit examples of correlations where their MGS can be determined using this recipe and other numerical techniques are provided.
Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions
Directory of Open Access Journals (Sweden)
Hernán R. Henríquez
2014-01-01
Full Text Available In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness.
Nonlocal response in plasmonic waveguiding with extreme light confinement
DEFF Research Database (Denmark)
Toscano, Giuseppe; Raza, Søren; Yan, Wei
2013-01-01
We present a novel wave equation for linearized plasmonic response, obtained by combining the coupled real-space differential equations for the electric field and current density. Nonlocal dynamics are fully accounted for, and the formulation is very well suited for numerical implementation, allo...
Formulation analysis and computation of an optimization-based local-to-nonlocal coupling method.
Energy Technology Data Exchange (ETDEWEB)
D' Elia, Marta [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Bochev, Pavel Blagoveston [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
2017-01-01
In this paper, we present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the local and nonlocal problem domains, and the virtual controls are the nonlocal volume constraint and the local boundary condition. We present the method in the context of Local-to-Nonlocal di usion coupling. Numerical examples illustrate the theoretical properties of the approach.
International Nuclear Information System (INIS)
Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M
2011-01-01
In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)
Su, Zhaofeng; Li, Lvzhou; Ling, Jie
2018-04-01
Nonlocality is an important resource for quantum information processing. Genuine tripartite nonlocality, which is sufficiently confirmed by the violation of Svetlichny inequality, is a kind of more precious resource than the standard one. The genuine tripartite nonlocality is usually quantified by the amount of maximal violation of Svetlichny inequality. The problem of detecting and quantifying the genuine tripartite nonlocality of quantum states is of practical significance but still open for the case of general three-qubit quantum states. In this paper, we quantitatively investigate the genuine nonlocality of three-qubit states, which not only include pure states but also include mixed states. Firstly, we derive a simplified formula for the genuine nonlocality of a general three-qubit state, which is a function of the corresponding three correlation matrices. Secondly, we develop three properties of the genuine nonlocality which can help us to analyze the genuine nonlocality of complex states and understand the nature of quantum nonlocality. Further, we get analytical results of genuine nonlocality for two classes of three-qubit states which have special correlation matrices. In particular, the genuine nonlocality of generalized three-qubit GHZ states, which is derived by Ghose et al. (Phys. Rev. Lett. 102, 250404, 2009), and that of three-qubit GHZ-symmetric states, which is derived by Paul et al. (Phys. Rev. A 94, 032101, 2016), can be easily derived by applying the strategy and properties developed in this paper.
Rationale for switching to nonlocal functionals in density functional theory.
Lazić, P; Atodiresei, N; Caciuc, V; Brako, R; Gumhalter, B; Blügel, S
2012-10-24
Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.
Rationale for switching to nonlocal functionals in density functional theory
International Nuclear Information System (INIS)
Lazić, P; Atodiresei, N; Caciuc, V; Blügel, S; Brako, R; Gumhalter, B
2012-01-01
Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.
Controllable nonlocal behaviour by cascaded second-harmonic generation of fs pulses
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw
2008-01-01
Second-harmonic generation (SHG) of ultra-short pulses can act as a prototypical nonlocal nonlinear model, since the strength and nature of the temporal nonlocality can be controlled through the phase-mismatch parameter. The presence of a group-velocity mismatch namely implies that when the phase...... mismatch is small the nonlocal response function becomes oscillatory, while for large phase mismatch it becomes localized. In the transition between the two regimes the strength of the nonlocality diverges, and the system goes from a weakly nonlocal to a strongly nonlocal state. When simulating soliton...... compression to few-cycle pulses in the cascaded quadratic soliton compressor, the spectral content of the full coupled SHG model is predicted by the nonlocal model even when few-cycle pulses are interacting....
Dynamics of Three-Body Correlations in Quenched Unitary Bose Gases
Colussi, V. E.; Corson, J. P.; D'Incao, J. P.
2018-03-01
We investigate dynamical three-body correlations in the Bose gas during the earliest stages of evolution after a quench to the unitary regime. The development of few-body correlations is theoretically observed by determining the two- and three-body contacts. We find that the growth of three-body correlations is gradual compared to two-body correlations. The three-body contact oscillates coherently, and we identify this as a signature of Efimov trimers. We show that the growth of three-body correlations depends nontrivially on parameters derived from both the density and Efimov physics. These results demonstrate the violation of scaling invariance of unitary bosonic systems via the appearance of log-periodic modulation of three-body correlations.
Non-unitary neutrino mixing and CP violation in the minimal inverse seesaw model
International Nuclear Information System (INIS)
Malinsky, Michal; Ohlsson, Tommy; Xing, Zhi-zhong; Zhang He
2009-01-01
We propose a simplified version of the inverse seesaw model, in which only two pairs of the gauge-singlet neutrinos are introduced, to interpret the observed neutrino mass hierarchy and lepton flavor mixing at or below the TeV scale. This 'minimal' inverse seesaw scenario (MISS) is technically natural and experimentally testable. In particular, we show that the effective parameters describing the non-unitary neutrino mixing matrix are strongly correlated in the MISS, and thus, their upper bounds can be constrained by current experimental data in a more restrictive way. The Jarlskog invariants of non-unitary CP violation are calculated, and the discovery potential of such new CP-violating effects in the near detector of a neutrino factory is discussed.
Toward a self-consistent and unitary reaction network for big bang nucleosynthesis
Energy Technology Data Exchange (ETDEWEB)
Paris, Mark W.; Brown, Lowell S.; Hale, Gerald M.; Hayes-Sterbenz, Anna C.; Jungman, Gerard; Kawano, Toshihiko, E-mail: mparis@lanl.gov [Los Alamos National Laboratory, Los Alamos, New Mexico (United States); Fuller, George M.; Grohs, Evan B. [Department of Physics, University of California, San Diego, La Jolla, CA (United States); Kunieda, Satoshi [Nuclear Data Center, Japan Atomic Energy Agency, Tokai-mura Naka-gun, Ibaraki (Japan)
2014-07-01
Unitarity, the mathematical expression of the conservation of probability in multichannel reactions, is an essential ingredient in the development of accurate nuclear reaction networks appropriate for nucleosynthesis in a variety of environments. We describe our ongoing program to develop a 'unitary reaction network' for the big-bang nucleosynthesis environment and look at an example of the need and power of unitary parametrizations of nuclear scattering and reaction data. Recent attention has been focused on the possible role of the {sup 9}B compound nuclear system in the resonant destruction of {sup 7}Li during primordial nucleosynthesis. We have studied reactions in the {sup 9}B compound system with a multichannel, two-body unitary R-matrix code (EDA) using the known elastic and reaction data, in a four-channel treatment. The data include elastic {sup 6}Li({sup 3}He,{sup 3}He){sup 6}Li differential cross sections from 0.7 to 2.0 MeV, integrated reaction cross sections for energies from 0.7 to 5.0 MeV for {sup 6}Li({sup 3}He,p){sup 8}Be* and from 0.4 to 5.0 MeV for the {sup 6}Li({sup 3}He,γ){sup 7}Be reaction. Capture data have been added to the previous analysis with integrated cross section measurements from 0.7 to 0.825 MeV for {sup 6}Li({sup 3}He,γ){sup 9}B. The resulting resonance parameters are compared with tabulated values from TUNL Nuclear Data Group analyses. Previously unidentified resonances are noted and the relevance of this analysis and a unitary reaction network for big-bang nucleosynthesis are emphasized. (author)
International Nuclear Information System (INIS)
Namgung, W.
1991-01-01
The well known requirement that physical theories should be gauge independent is not so apparent in the actual calculation of gauge theories, especially in the perturbative approach. In this paper the authors show that the Weyl, Coulomb, and unitary gauges of the scalar QED are manifestly equivalent in the context of the functional Schrodinger picture. Further, the three gauge conditions are shown equivalent to the covariant gauge in the way that they correspond to some specific cases of the latter