Low energy signatures of nonlocal field theories
Belenchia, Alessio; Benincasa, Dionigi M. T.; Martín-Martínez, Eduardo; Saravani, Mehdi
2016-09-01
The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by nonanalytic functions of the d'Alembertian operator □ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy nonlocality scales. This allows us to suggest a nuclear physics experiment (˜MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity.
Low-Energy Signatures of Nonlocal Field Theories
Belenchia, Alessio; Martin-Martinez, Eduardo; Saravani, Mehdi
2016-01-01
The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by non-analytic functions of the d'Alembertian operator $\\Box$ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy non-locality scales. This allows us to suggest a nuclear physics experiment ($\\sim$ MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity.
Testing Hardy's nonlocality proof with genuine energy-time entanglement
Vallone, Giuseppe; Gianani, Ilaria; Inostroza, Enrique B.; Saavedra, Carlos; Lima, Gustavo; Cabello, Adán; Mataloni, Paolo
2011-04-01
We show two experimental realizations of Hardy’s ladder test of quantum nonlocality using energy-time correlated photons, following the scheme proposed by Cabello [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.102.040401 102, 040401 (2009)]. Unlike previous energy-time Bell experiments, these tests require precisely tailored nonmaximally entangled states. One of them is equivalent to the two-setting and two-outcome Bell test requiring a minimum detection efficiency. The reported experiments are still affected by the locality and detection loopholes, but are free of the post-selection loophole of previous energy-time and time-bin Bell tests.
Analysis of a micro piezoelectric vibration energy harvester by nonlocal elasticity theory
Directory of Open Access Journals (Sweden)
Hao Chen
2016-04-01
Full Text Available A theoretical model of a micro piezoelectric energy harvester is proposed based on the nonlocal elasticity theory, which is operated in the flexural mode for scavenging ambient vibration energy. A nonlocal scale is defined as the product of internal characteristic length and a constant related to the material. The dependences of performance of the harvester upon the nonlocal scale and the scale ratio of the nonlocal scale to the external characteristic parameter are investigated in detail. Numerical results show that output power of the harvester decreases, and resonance frequency reduces gradually at first then increases rapidly when nonlocal scale increases. The results of nonlocal elasticity theory are compared with that of classic beam theory. All the results are helpful for material and structure design of the micro piezoelectric energy harvester.
Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media
Wu, Zhen-Kun; Li, Peng; Gu, Yu-Zong
2017-10-01
We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.
Rigidity of critical points for a nonlocal Ohta-Kawasaki energy
Dipierro, Serena; Novaga, Matteo; Valdinoci, Enrico
2017-04-01
We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is sufficiently small with respect to its isodiametric ratio, thus extending a result previously known only for global minimizers. We also show that, at least in one-dimension, there exist critical points with arbitrarily small volume and large isodiametric ratio. This example shows that a constraint on the diameter is, in general, necessary to establish the radial symmetry of the critical points.
Non-local electron energy probability function in a plasma expanding along a magnetic nozzle.
Directory of Open Access Journals (Sweden)
Roderick William Boswell
2015-03-01
Full Text Available Electron energy probability functions (eepfs have been measured along the axis of low pressure plasma expanding in a magnetic nozzle. The eepf at the maximum magnetic field of the nozzle shows a depleted tail commencing at an energy corresponding to the measured potential drop in the magnetic nozzle. The eepfs measured along the axis demonstrate that the potential and kinetic energies of the electrons are conserved and confirm the non-local collisionless kinetics of the electron dynamics.
Local shell-to-shell energy transfer via nonlocal interactions in fluid turbulence
Indian Academy of Sciences (India)
Mahendra K Verma; Arvind Ayyer; Olivier Debliquy; Shishir Kumar; Amar V Chandra
2005-08-01
In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wave-number shells in incompressible fluid turbulence. The computation has been done using first-order perturbative field theory. In three dimensions, magnitude of triad interactions is large for nonlocal triads, and small for local triads. However, the shell-to-shell energy transfer rate is found to be local and forward. This result is due to the fact that the nonlocal triads occupy much less Fourier space volume than the local ones. The analytical results on three-dimensional shell-to-shell energy transfer match with their numerical counterparts. In two-dimensional turbulence, the energy transfer rates to the nearby shells are forward, but to the distant shells are backward; the cumulative effect is an inverse cascade of energy.
Nonlocality in the excitation energy transfer in the Fenna-Matthews-Olson complex
Bengtson, Charlotta; Sjöqvist, Erik
2015-01-01
Pigment protein complexes involved in photosynthesis are remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction centre where it is converted to and stored as chemical energy. Recent experimental and theoretical studies suggest that quantum coherence and correlations may play a role in explaining this efficiency. We examine whether bipartite nonlocality, a property that verifies a strong correlation between two quantum systems, exists between different pairs of chromophore states in the Fenna-Matthews-Olson (FMO) complex and how this is connected to the amount of bipartite entanglement. In particular, it is tested in what way these correlation properties are affected by different initial conditions (i.e., which chromophore is initially excited). When modeling the excitation energy transfer (EET) in the FMO complex with the hierarchically coupled equations of motions (HEOM), it is found that bipartite nonlocality indeed exists for some pairs of chromophore s...
Modification of a nonlocal electron energy distribution in a bounded plasma.
DeJoseph, C A; Demidov, V I; Kudryavtsev, A A
2005-09-01
It is demonstrated experimentally, in a pulsed discharge, that it is possible to modify the "tail" of a nonlocal electron energy distribution (EED) without significantly changing the electron density and temperature (mean energy). The EED tail is modified by changing the potential of a small portion of the plasma boundary and/or by changing the volume creation rate of electrons with energies in the range of the tail of the EED. The discussed effects are a direct result of the nonlocal nature of the EED and have applications to a number of basic research issues associated with discharges under nonequilibrium conditions. As an example, we discuss the possibility of utilizing these methods to measure electron impact excitation cross sections from the metastable states of atoms, which are difficult to measure by other means. The experiments have been conducted in an argon and argon-nitrogen pulsed rf inductively coupled plasma discharge.
Energy as a Detector of Nonlocality of Many-Body Spin Systems
Directory of Open Access Journals (Sweden)
J. Tura
2017-04-01
Full Text Available We present a method to show that low-energy states of quantum many-body interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its classical bound using dynamic programing. The Bell inequality is such that its quantum value for a given state, and for appropriate observables, corresponds to the energy of the state. Thus, the presence of nonlocal correlations can be certified for states of low enough energy. The method can also be used to optimize certain Bell inequalities: in the translationally invariant (TI case, we provide an exponentially faster computation of the classical bound and analytically closed expressions of the quantum value for appropriate observables and Hamiltonians. The power and generality of our method is illustrated through four representative examples: a tight TI inequality for eight parties, a quasi-TI uniparametric inequality for any even number of parties, ground states of spin-glass systems, and a nonintegrable interacting XXZ-like Hamiltonian. Our work opens the possibility for the use of low-energy states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality.
Energy Technology Data Exchange (ETDEWEB)
Del Sorbo, D.; Feugeas, J.-L.; Nicolaï, Ph.; Olazabal-Loumé, M.; Dubroca, B.; Guisset, S.; Touati, M.; Tikhonchuk, V. [Centre Lasers Intenses et Applications, Université de Bordeaux-CNRS-CEA, UMR 5107, F-33405 Talence (France)
2015-08-15
Hydrodynamic simulations of high-energy-density plasmas require a detailed description of energy fluxes. For low and intermediate atomic number materials, the leading mechanism is the electron transport, which may be a nonlocal phenomenon requiring a kinetic modeling. In this paper, we present and test the results of a nonlocal model based on the first angular moments of a simplified Fokker-Planck equation. This multidimensional model is closed thanks to an entropic relation (the Boltzman H-theorem). It provides a better description of the electron distribution function, thus enabling studies of small scale kinetic effects within the hydrodynamic framework. Examples of instabilities of electron plasma and ion-acoustic waves, driven by the heat flux, are presented and compared with the classical formula.
Del Sorbo, D.; Feugeas, J.-L.; Nicolaï, Ph.; Olazabal-Loumé, M.; Dubroca, B.; Guisset, S.; Touati, M.; Tikhonchuk, V.
2015-08-01
Hydrodynamic simulations of high-energy-density plasmas require a detailed description of energy fluxes. For low and intermediate atomic number materials, the leading mechanism is the electron transport, which may be a nonlocal phenomenon requiring a kinetic modeling. In this paper, we present and test the results of a nonlocal model based on the first angular moments of a simplified Fokker-Planck equation. This multidimensional model is closed thanks to an entropic relation (the Boltzman H-theorem). It provides a better description of the electron distribution function, thus enabling studies of small scale kinetic effects within the hydrodynamic framework. Examples of instabilities of electron plasma and ion-acoustic waves, driven by the heat flux, are presented and compared with the classical formula.
Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study
Rohringer, G.; Toschi, A.
2016-09-01
In this paper, we investigate how nonlocal correlations affect, selectively, the physics of correlated electrons over different energy scales, from the Fermi level to the band edges. This goal is achieved by applying a diagrammatic extension of dynamical mean field theory (DMFT), the dynamical vertex approximation (D Γ A ), to study several spectral and thermodynamic properties of the unfrustrated Hubbard model in two and three dimensions. Specifically, we focus first on the low-energy regime by computing the electronic scattering rate and the quasiparticle mass renormalization for decreasing temperatures at a fixed interaction strength. This way, we obtain a precise characterization of the several steps through which the Fermi-liquid physics is progressively destroyed by nonlocal correlations. Our study is then extended to a broader energy range, by analyzing the temperature behavior of the kinetic and potential energy, as well as of the corresponding energy distribution functions. Our findings allow us to identify a smooth but definite evolution of the nature of nonlocal correlations by increasing interaction: They either increase or decrease the kinetic energy w.r.t. DMFT depending on the interaction strength being weak or strong, respectively. This reflects the corresponding evolution of the ground state from a nesting-driven (Slater) to a superexchange-driven (Heisenberg) antiferromagnet (AF), whose fingerprints are, thus, recognizable in the spatial correlations of the paramagnetic phase. Finally, a critical analysis of our numerical results of the potential energy at the largest interaction allows us to identify possible procedures to improve the ladder-based algorithms adopted in the dynamical vertex approximation.
Energy Technology Data Exchange (ETDEWEB)
Zenkour, A. M.; Alnefaie, K. A.; Abu-Hamdeh, N. H.; Aljinaid, A. A.; Aifanti, E. C. [King Abdulaziz University, Jeddah (Saudi Arabia); Abouelregal, A. E. [Mansoura University, Mansoura (Egypt)
2015-07-15
In this article, an Euler-Bernoulli beam model based upon nonlocal thermoelasticity theory without energy dissipation is used to study the vibration of a nanobeam subjected to ramp-type heating. Classical continuum theory is inherently size independent, while nonlocal elasticity exhibits size dependence. Among other things, this leads to a new expression for the effective nonlocal bending moment as contrasted to its classical counterpart. The thermal problem is addressed in the context of the Green-Naghdi (GN) theory of heat transport without energy dissipation. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of modern control theory. Inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of nonlocality and ramping time parameters on the lateral vibration, temperature, displacement and bending moment are discussed.
Quantum Transfer Energy and Nonlocal Correlation in a Dimer with Time-Dependent Coupling Effect
El-Shishtawy, Reda M.; Berrada, K.; Haddon, Robert C.; Al-Hadeethi, Yas F.; Al-Heniti, Saleh H.; Raffah, Bahaaudin M.
2017-02-01
The presence of coherence phenomenon due to the interference of probability amplitude terms, is one of the most important features of quantum mechanics theory. Recent experiments show the presence of quantum processes whose coherence provided over suddenly large interval-time. In particular, photosynthetic mechanisms in light-harvesting complexes provide oscillatory behaviors in quantum mechanics due to quantum coherence. In this work, we investigate the coherent quantum transfer energy for a single-excitation and nonlocal correlation in a dimer system modelled by a two-level atom system with and without time-dependent coupling effect. We analyze and explore the required conditions that are feasible with real experimental realization for optimal transfer of quantum energy and generation of nonlocal quantum correlation. We show that the enhancement of the probability for a single-excitation transfer energy is greatly benefits from the combination of the energy detuning and time-dependent coupling effect. We investigate the presence of quantum correlations in the dimer using the entanglement of formation. We also find that the entanglement between the donor and acceptor is very sensitive to the physical parameters and it can be generated during the coherent energy transfer. On the other hand, we study the dynamical behavior of the quantum variance when performing a measurement on an observable of the density matrix operator. Finally, an interesting relationship between the transfer probability, entanglement and quantum variance is explored during the time evolution in terms of the physical parameters.
Energy conditions and DK stability criterion in the non-local gravity
Wu, Ya-Bo; Yang, Wei-Qiang; Zhang, Nan; Chen, Bo-Hai
2016-01-01
We study and derive the energy conditions and the Dolgov-Kawasaki (DK) stability criterion in non-local gravity, which is the modified theory of general relativity (GR) obtained by adding a term $m^2R\\Box^{-2}R$ to the Einstein-Hilbert action. Moreover, in order to get some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the parameter $\\alpha$ and redshift $z$. By analysis we give the constraint on the parameters $\\alpha$, namely, $|\\alpha|\\leq0.26$. Furthermore, by means of the Dolgov-Kawasaki stability criterion in the non-local gravity we find that the effective mass $m_\\text{eff}^2$ of the dynamical field $U$ is negative in any value ranges of parameter $\\alpha$, which is consistent with the result given in [JCAP 1607, 003 (2016)], i.e. the field $U$ is a ghost one. The result shows that the Dolgov-Kawasaki stability criterion cannot give any constraint on the parameter $\\alpha$.
Using nonlocal electrostatics for solvation free energy computations ions and small molecules
Hildebrandt, A; Blossey, R; Lenhof, H P
2002-01-01
Solvation free energy is an important quantity in Computational Chemistry with a variety of applications, especially in drug discovery and design. The accurate prediction of solvation free energies of small molecules in water is still a largely unsolved problem, which is mainly due to the complex nature of the water-solute interactions. In this letter we develop a scheme for the determination of the electrostatic contribution to the solvation free energy of charged molecules based on nonlocal electrostatics involving a minimal parameter set which in particular allows to introduce atomic radii in a consistent way. We test our approach on simple ions and small molecules for which both experimental results and other theoretical descriptions are available for quantitative comparison. We conclude that our approach is both physically transparent and quantitatively reliable.
Energy method for multi-dimensional balance laws with non-local dissipation
Duan, Renjun
2010-06-01
In this paper, we are concerned with a class of multi-dimensional balance laws with a non-local dissipative source which arise as simplified models for the hydrodynamics of radiating gases. At first we introduce the energy method in the setting of smooth perturbations and study the stability of constants states. Precisely, we use Fourier space analysis to quantify the energy dissipation rate and recover the optimal time-decay estimates for perturbed solutions via an interpolation inequality in Fourier space. As application, the developed energy method is used to prove stability of smooth planar waves in all dimensions n2, and also to show existence and stability of time-periodic solutions in the presence of the time-periodic source. Optimal rates of convergence of solutions towards the planar waves or time-periodic states are also shown provided initially L1-perturbations. © 2009 Elsevier Masson SAS.
Electromagnetic reflection, transmission, and energy density at boundaries of nonlocal media
Churchill, R. J.; Philbin, T. G.
2016-12-01
We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material that propagate to the surface. Specific values of these coefficients correspond to various additional boundary conditions (ABCs) for Maxwell's equations. We derive the electromagnetic reflection and transmission coefficients at the boundary and investigate their dependence on material parameters and ABCs. We also investigate the electromagnetic zero-point and thermal spectral energy density outside the dielectric. The nonlocal response removes the boundary divergence of the spectral energy density that is present in a local model. The spectral energy density shows a large dependence on the difference between the transverse and longitudinal susceptibilities, even at distances up to 10 nm from the boundary.
Electromagnetic reflection, transmission and energy density at boundaries of nonlocal media
Churchill, R J
2016-01-01
We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material that propagate to the surface. Specific values of these coefficients correspond to various additional boundary conditions (ABC) for Maxwell's equations. We derive the electromagnetic reflection and transmission coefficients at the boundary and investigate their dependence on material parameters and ABC. We also investigate the electromagnetic zero-point and thermal spectral energy density outside the dielectric. The nonlocal response removes the boundary divergence of the spectral energy density that is present in a local model. The spectral energy density shows a large dependence on the difference between the transverse and longitudinal susceptibilities, even at distances up to 10nm from the boundary.
Interaction of Kelvin waves and non-locality of the energy transfer in superfluids
Laurie, Jason; Nazarenko, Sergey; Rudenko, Oleksii
2009-01-01
We argue that the physics of interacting Kelvin Waves (KWs) is highly non-trivial and cannot be understood on the basis of pure dimensional reasoning only. A consistent theory of KWs turbulence in superfluids should be based on explicit knowledge of the details of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KWs, thereby fixing previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we show that the previously suggested Kozik-Svistunov energy spectrum of KWs, which has been often used for analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based on an erroneous assumption of the locality of the energy transfer through scales. We also demonstrate weak non-locality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.
Suarez, Antoine
2012-01-01
In the Solvay conference (1927) Einstein argued against the quantum nonlocal decision at detection on the basis of a simple single-particle experiment, but thereafter he withdrew towards the more complicated 2-particle EPR argument. It has been claimed that Einstein was seeking for an "epistemic interpretation". In the light of a recent experiment I argue that Einstein missed an important point: One cannot have conservation of energy without nonlocality at detection. This experiment refutes also straightforwardly "epistemic" and "ontic" alternatives to quantum theory, and shows that Einstein's "epistemicism" entails "superdeterminism".
Zhang, Houjin; Zeng, Dong; Lin, Jiahui; Zhang, Hao; Bian, Zhaoying; Huang, Jing; Gao, Yuanyuan; Zhang, Shanli; Zhang, Hua; Feng, Qianjin; Liang, Zhengrong; Chen, Wufan; Ma, Jianhua
2017-07-01
Reducing radiation dose in dual energy computed tomography (DECT) is highly desirable but it may lead to excessive noise in the filtered backprojection (FBP) reconstructed DECT images, which can inevitably increase the diagnostic uncertainty. To obtain clinically acceptable DECT images from low-mAs acquisitions, in this work we develop a novel scheme based on measurement of DECT data. In this scheme, inspired by the success of edge-preserving non-local means (NLM) filtering in CT imaging and the intrinsic characteristics underlying DECT images, i.e. global correlation and non-local similarity, an averaged image induced NLM-based (aviNLM) regularization is incorporated into the penalized weighted least-squares (PWLS) framework. Specifically, the presented NLM-based regularization is designed by averaging the acquired DECT images, which takes the image similarity within the two energies into consideration. In addition, the weighted least-squares term takes into account DECT data-dependent variance. For simplicity, the presented scheme was termed as ‘PWLS-aviNLM’. The performance of the presented PWLS-aviNLM algorithm was validated and evaluated on digital phantom, physical phantom and patient data. The extensive experiments validated that the presented PWLS-aviNLM algorithm outperforms the FBP, PWLS-TV and PWLS-NLM algorithms quantitatively. More importantly, it delivers the best qualitative results with the finest details and the fewest noise-induced artifacts, due to the aviNLM regularization learned from DECT images. This study demonstrated the feasibility and efficacy of the presented PWLS-aviNLM algorithm to improve the DECT reconstruction and resulting material decomposition.
Imprint of primordial inflation on the dark energy equation of state in non-local gravity
Cusin, Giulia; Maggiore, Michele; Mancarella, Michele
2016-01-01
In cosmological models where dark energy has a dynamical origin one would expect that a primordial inflationary epoch leaves no imprint on the behavior of dark energy near the present epoch. We show that a notable exception to this behavior is provided by a nonlocal infrared modification of General Relativity, the so-called RT model. It has been previously shown that this model fits the cosmological data with an accuracy comparable to $\\Lambda$CDM, with the same number of free parameters. Here we show that in this model the dark energy equation of state (EOS) near the present epoch is significantly affected by the existence of an epoch of primordial inflation. A smoking-gun signature of the model is a well-defined prediction for the dark energy EOS, $w_{\\rm DE}(z)$, evolving with redshift from a non-phantom to a phantom behavior, with deviations from $-1$ already very close to the limits excluded by the Planck 2015 data. Future missions such as Euclid should be able to clearly confirm or disprove this predict...
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...
Interaction of Kelvin waves and nonlocality of energy transfer in superfluids
Laurie, Jason; L'Vov, Victor S.; Nazarenko, Sergey; Rudenko, Oleksii
2010-03-01
We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.
Katriel, Jacob; Bauer, Michael; Springborg, Michael; McCarthy, Shane P; Thakkar, Ajit J
2007-07-14
Reparametrization of Wigner's correlation energy density functional yields a very close fit to the correlation energies of the helium isoelectronic sequence. However, a quite different reparametrization is required to obtain an equally close fit to the isoelectronic sequence of Hooke's atom. In an attempt to avoid having to reparametrize the functional for different choices of the one-body potential, we propose a parametrization that depends on global characteristics of the ground-state electron density as quantified by scale-invariant combinations of expectation values of local one-body operators. This should be viewed as an alternative to the density-gradient paradigm, allowing one to introduce the nonlocal dependence of the density functional on the density in a possibly more effective way. Encouraging results are obtained for two-electron systems with one-body potentials of the form r(zeta) with zeta=-12,+12,1, which span the range between the Coulomb potential (zeta=-1) and the Hooke potential (zeta=2).
Lee, Myeong H.; Troisi, Alessandro
2017-02-01
It has been reported in recent years that vibronic resonance between vibrational energy of the intramolecular nuclear mode and excitation-energy difference is crucial to enhance excitation energy transport in light harvesting proteins. Here we investigate how vibronic enhancement induced by vibronic resonance is influenced by the details of local and non-local exciton-phonon interactions. We study a heterodimer model with parameters relevant to the light-harvesting proteins with the surrogate Hamiltonian quantum dynamics method in a vibronic basis. In addition, the impact of field-driven excitation on the efficiency of population transfer is compared with the instantaneous excitation, and the effect of multi-mode vibronic coupling is presented in comparison with the coupling to a single effective vibrational mode. We find that vibronic enhancement of site population transfer is strongly suppressed with the increase of non-local exciton-phonon interaction and increasing the number of strongly coupled high-frequency vibrational modes leads to a further decrease in vibronic enhancement. Our results indicate that vibronic enhancement is present but may be much smaller than previously thought and therefore care needs to be taken when interpreting its role in excitation energy transport. Our results also suggest that non-local exciton-phonon coupling, which is related to the fluctuation of the excitonic coupling, may be as important as local exciton-phonon coupling and should be included in any quantum dynamics model.
Weak-coupling approach to the semi-infinite Hubbard model: Non-locality of the self-energy
Potthoff, M.; Nolting, W.
1997-01-01
The Hubbard model on a semi-infinite three-dimensional lattice is considered to investigate electron-correlation effects at single-crystal surfaces. The standard second-order perturbation theory in the interaction U is used to calculate the electronic self-energy and the quasi-particle density of states (QDOS) in the bulk as well as in the vicinity of the surface. Within a real-space representation we fully account for the non-locality of the self-energy and examine the quality of the local a...
Exact Solutions in Nonlocal Linear Models
Vernov, S. Yu.
2008-01-01
A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing Universe with the phantom dark energy.
Serendipitous discoveries in nonlocal ghost-free gravity theory: dark energy and dark matter
Barvinsky, Andrei O
2011-01-01
We present a class of generally covariant nonlocal gravity models briefly reported in arXiv:1107.1463, which have a flat-space general relativistic (GR) limit and also possess a stable de Sitter (dS) or Anti-de Sitter (AdS) background with an arbitrary value of its cosmological constant. The nonlocal action of the theory is formulated in the Euclidean signature spacetime and is understood as an approximation to the quantum effective action (generating functional of one-particle irreducible diagrams) originating from fundamental quantum gravity theory. Using the known relation between the Schwinger-Keldysh technique for quantum expectation values and the Euclidean quantum field theory we derive from this action the {\\em causal} effective equations of motion for mean value of the metric field in the physical Lorentzian-signature spacetime. Thus we show that the (A)dS background of the theory carries as free propagating modes massless gravitons having two polarizations identical to those of the Einstein theory w...
Hobson, Art
2012-01-01
Nonlocality arises from the unified "all or nothing" interactions of a spatially extended field quantum such as a photon or an electron. In the double-slit experiment with light, for example, each photon comes through both slits and arrives at the viewing screen as an extended but unified energy bundle or "field quantum." When the photon interacts…
Hobson, Art
2012-01-01
Nonlocality arises from the unified "all or nothing" interactions of a spatially extended field quantum such as a photon or an electron. In the double-slit experiment with light, for example, each photon comes through both slits and arrives at the viewing screen as an extended but unified energy bundle or "field quantum." When the photon interacts…
Barnaby, Neil
2008-01-01
We consider the possibility of realizing inflation in nonlocal field theories containing infinitely many derivatives. Such constructions arise naturally in string field theory and also in a number of toy models, such as the p-adic string. After reviewing the complications (ghosts and instabilities) that arise when working with high derivative theories we discuss the initial value problem and perturbative stability of theories with infinitely many derivatives. Next, we examine the inflationary dynamics and phenomenology of such theories. Nonlocal inflation can proceed even when the potential is naively too steep and generically predicts large nongaussianity in the Cosmic Microwave Background.
Giddings, Steven B
2012-01-01
If quantum mechanics governs nature, black holes must evolve unitarily, providing a powerful constraint on the dynamics of quantum gravity. Such evolution apparently must in particular be nonlocal, when described from the usual semiclassical geometric picture, in order to transfer quantum information into the outgoing state. While such transfer from a disintegrating black hole has the dangerous potential to be violent to generic infalling observers, this paper proposes the existence of a more innocuous form of information transfer, to relatively soft modes in the black hole atmosphere. Simplified models for such nonlocal transfer are described and parameterized, within a possibly more basic framework of a Hilbert tensor network. Sufficiently sensitive measurements by infalling observers may detect departures from Hawking's predictions, and in generic models black holes decay more rapidly. Constraints of consistency -- internally and with known and expected features of physics -- restrict the form of informati...
Nonlocal modulation of the energy cascade in broadband-forced turbulence
Kuczaj, Arkadiusz K.; Geurts, Bernardus J.; McComb, W. David
2006-01-01
Classically, large-scale forced turbulence is characterized by a transfer of energy from large to small scales via nonlinear interactions. We have investigated the changes in this energy transfer process in broadband forced turbulence where an additional perturbation of flow at smaller scales is int
Nonlocal response in thin-film waveguides: loss versus nonlocality and breaking of complementarity
Raza, Søren; Wubs, Martijn; Bozhevolnyi, Sergey I; Mortensen, N Asger
2013-01-01
We investigate the effects of nonlocal response on the surface-plasmon polariton guiding properties of the metal-insulator (MI), metal-insulator-metal (MIM), and insulator-metal-insulator (IMI) waveguides. The nonlocal effects are described by a linearized hydrodynamic model, which includes 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 in the metal. We also show that nonlocality breaks the complementarity of the MIM and IMI waveguides found in the non-retarded limit.
Local and Nonlocal Regularization to Image Interpolation
Directory of Open Access Journals (Sweden)
Yi Zhan
2014-01-01
Full Text Available This paper presents an image interpolation model with local and nonlocal regularization. A nonlocal bounded variation (BV regularizer is formulated by an exponential function including gradient. It acts as the Perona-Malik equation. Thus our nonlocal BV regularizer possesses the properties of the anisotropic diffusion equation and nonlocal functional. The local total variation (TV regularizer dissipates image energy along the orthogonal direction to the gradient to avoid blurring image edges. The derived model efficiently reconstructs the real image, leading to a natural interpolation which reduces blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.
Demidov, V. I.; Adams, S. F.; Miles, J. A.; Koepke, M. E.; Kurlyandskaya, I. P.
2016-10-01
Details of ground-state and excited-state neutral atoms and molecules in an atmospheric-pressure micro-discharge plasma may be obtained by plasma electron spectroscopy (PLES), based on a wall probe. The presence and transport of energetic (suprathermal) electrons, having a nonlocal origin, are responsible for electrostatic charging of the plasma boundary surfaces to potentials many times that associated with the ambient electron kinetic energy. The energy-flux distribution function is shown to be controllable for applications involving analysis of composition and processes taking place in a multiphase (plasma-gas-solid), chemically reactive, interaction region.
Nonlocal energy density functionals for pairing and beyond-mean-field calculations
Bennaceur, K; Dobaczewski, J; Dobaczewski, P; Kortelainen, M; Raimondi, F
2016-01-01
We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy density functional (EDF) in both particle-hole and particle-particle channels, which makes it free from self-interaction and self-pairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order (NLO) and next-to-next-to-leading order (N2LO), which fairly well describe infinite-nuclear-matter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large effective mass, the obtained solutions constitute a preliminary step towards future implementations, which will include, e.g., EDF terms generated by three-body pseudopotentials.
On instabilities in tensorial nonlocal gravity
Nersisyan, Henrik; Amendola, Luca; Koivisto, Tomi S; Rubio, Javier; Solomon, Adam R
2016-01-01
We discuss the cosmological implications of nonlocal modifications of general relativity containing tensorial structures. Assuming the presence of standard radiation- and matter-dominated eras, we show that, except in very particular cases, the nonlocal terms contribute a rapidly-growing energy density. These models therefore generically do not have a stable cosmological evolution.
Multipole vector solitons in nonlocal nonlinear media.
Kartashov, Yaroslav V; Torner, Lluis; Vysloukh, Victor A; Mihalache, Dumitru
2006-05-15
We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.
Filk, Thomas
2013-04-01
In this article I investigate several possibilities to define the concept of "temporal non-locality" within the standard framework of quantum theory. In particular, I analyze the notions of "temporally non-local states", "temporally non-local events" and "temporally non-local observables". The idea of temporally non-local events is already inherent in the standard formalism of quantum mechanics, and Basil Hiley recently defined an operator in order to measure the degree of such a temporal non-locality. The concept of temporally non-local states enters as soon as "clock-representing states" are introduced in the context of special and general relativity. It is discussed in which way temporally non-local measurements may find an interesting application for experiments which test temporal versions of Bell inequalities.
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Wyller, John
2004-01-01
We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons.......We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons....
NONLOCAL SYMMETRIES AND NONLOCAL RECURSION OPERATORS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
An expose about covering method on differential equations was given. The general formulae to determine nonlocal symmetries were derived which are analogous to the prolongation formulae of generalized symmetries. In addition, a new definition of nonlocal recursion operators was proposed, which gave a satisfactory explalnation in covering theory for the integro-differcntial recursion operators.
Nonlocal Galileons and self-acceleration
Gabadadze, Gregory; Yu, Siqing
2017-05-01
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.
Nonlocal Galileons and self-acceleration
Directory of Open Access Journals (Sweden)
Gregory Gabadadze
2017-05-01
Full Text Available 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.
Nonlocal thermal transport in solar flares
Karpen, Judith T.; Devore, C. Richard
1987-01-01
A flaring solar atmosphere is modeled assuming classical thermal transport, locally limited thermal transport, and nonlocal thermal transport. The classical, local, and nonlocal expressions for the heat flux yield significantly different temperature, density, and velocity profiles throughout the rise phase of the flare. Evaporation of chromospheric material begins earlier in the nonlocal case than in the classical or local calculations, but reaches much lower upward velocities. Much higher coronal temperatures are achieved in the nonlocal calculations owing to the combined effects of delocalization and flux limiting. The peak velocity and momentum are roughly the same in all three cases. A more impulsive energy release influences the evolution of the nonlocal model more than the classical and locally limited cases.
Nonlocal study of ultimate plasmon hybridization.
Raza, Søren; Wubs, Martijn; Bozhevolnyi, Sergey I; Mortensen, N Asger
2015-03-01
Within our recently proposed generalized nonlocal optical response (GNOR) model, where nonlocal response is included by taking into account both convective and diffusive currents of the conduction electrons, we revisit the fundamental problem of an optically excited plasmonic dimer. We consider 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 for the resonance energies.
The neglected nonlocal effects of deforestation
Winckler, Johannes; Reick, Christian; Pongratz, Julia
2017-04-01
Deforestation changes surface temperature locally via biogeophysical effects by changing the water, energy and momentum balance. Adding to these locally induced changes (local effects), deforestation at a given location can cause changes in temperature elsewhere (nonlocal effects). Most previous studies have not considered local and nonlocal effects separately, but investigated the total (local plus nonlocal) effects, for which global deforestation was found to cause a global mean cooling. Recent modeling and observational studies focused on the isolated local effects: The local effects are relevant for local living conditions, and they can be obtained from in-situ and satellite observations. Observational studies suggest that the local effects of potential deforestation cause a warming when averaged globally. This contrast between local warming and total cooling indicates that the nonlocal effects of deforestation are causing a cooling and thus counteract the local effects. It is still unclear how the nonlocal effects depend on the spatial scale of deforestation, and whether they still compensate the local warming in a more realistic spatial distribution of deforestation. To investigate this, we use a fully coupled climate model and separate local and nonlocal effects of deforestation in three steps: Starting from a forest world, we simulate deforestation in one out of four grid boxes using a regular spatial pattern and increase the number of deforestation grid boxes step-wise up to three out of four boxes in subsequent simulations. To compare these idealized spatial distributions of deforestation to a more realistic case, we separate local and nonlocal effects in a simulation where deforestation is applied in regions where it occurred historically. We find that the nonlocal effects scale nearly linearly with the number of deforested grid boxes, and the spatial distribution of the nonlocal effects is similar for the regular spatial distribution of deforestation
Fully nonlocal quantum correlations
Aolita, Leandro; Acín, Antonio; Chiuri, Andrea; Vallone, Giuseppe; Mataloni, Paolo; Cabello, Adán
2011-01-01
Quantum mechanics is a nonlocal theory, but not as nonlocal as the no-signalling principle allows. However, there exist quantum correlations that exhibit maximal nonlocality: they are as nonlocal as any non-signalling correlations and thus have a local content, quantified by the fraction $p_L$ of events admitting a local description, equal to zero. Previous examples of maximal quantum nonlocality between two parties require an infinite number of measurements, and the corresponding Bell violation is not robust against noise. We show how every proof of the Kochen-Specker theorem gives rise to maximally nonlocal quantum correlations that involve a finite number of measurements and are robust against noise. We perform the experimental demonstration of a Bell test originating from the Peres-Mermin Kochen-Specker proof, providing an upper bound on the local content $p_L\\lesssim 0.22$.
Mashhoon, B
2014-01-01
A brief account of the present status of the recent nonlocal generalization of Einstein's theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenb\\"ock's torsion, and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline-Kuhn approach to modified gravity. To account for the observational data regarding dark matter, nonlocality is associated with a characteristic length scale of order 1 kpc. The confrontation of nonlocal gravity with observation is briefly discussed.
Zhao, Wei; Xing, Lei; Xie, Yaoqin; Xiong, Guanglei; Elmore, Kimberly; Zhu, Jun; Wang, Luyao; Min, James K
2016-01-01
Increased noise is a general concern for dual-energy material decomposition. Here, we develop an image-domain material decomposition algorithm for dual-energy CT (DECT) by incorporating an edge-preserving filter into the Local HighlY constrained backPRojection Reconstruction (HYPR-LR) framework. With effective use of the non-local mean, the proposed algorithm, which is referred to as HYPR-NLM, reduces the noise in dual energy decomposition while preserving the accuracy of quantitative measurement and spatial resolution of the material-specific dual energy images. We demonstrate the noise reduction and resolution preservation of the algorithm with iodine concentrate numerical phantom by comparing the HYPR-NLM algorithm to the direct matrix inversion, HYPR-LR and iterative image-domain material decomposition (Iter-DECT). We also show the superior performance of the HYPR-NLM over the existing methods by using two sets of cardiac perfusing imaging data. The reference drawn from the comparison study includes: (1) ...
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
Nonlocality from Local Contextuality
Liu, Bi-Heng; Hu, Xiao-Min; Chen, Jiang-Shan; Huang, Yun-Feng; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can; Cabello, Adán
2016-11-01
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.
Nonlocality from Local Contextuality.
Liu, Bi-Heng; Hu, Xiao-Min; Chen, Jiang-Shan; Huang, Yun-Feng; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can; Cabello, Adán
2016-11-25
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.
Modesto, Leonardo
2013-01-01
We present a general covariant action for massive gravity merging together a class of "non-polynomial" and super-renormalizable or finite theories of gravity with the non-local theory of gravity recently proposed by Jaccard, Maggiore and Mitsou (arXiv:1305.3034 [hep-th]). Our diffeomorphism invariant action gives rise to the equations of motion appearing in non-local massive massive gravity plus quadratic curvature terms. Not only the massive graviton propagator reduces smoothly to the massless one without a vDVZ discontinuity, but also our finite theory of gravity is unitary at tree level around the Minkowski background. We also show that, as long as the graviton mass $m$ is much smaller the today's Hubble parameter $H_0$, a late-time cosmic acceleration can be realized without a dark energy component due to the growth of a scalar degree of freedom. In the presence of the cosmological constant $\\Lambda$, the dominance of the non-local mass term leads to a kind of "degravitation" for $\\Lambda$ at the late cos...
Millen, James
2016-04-01
George Musser's book Spooky Action at a Distance focuses on one of quantum physics' more challenging concepts, nonlocality, and its multitude of implications, particularly its assault on space itself.
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...
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.
Disentangling Nonlocality and Teleportation
Hardy, L
1999-01-01
Quantum entanglement can be used to demonstrate nonlocality and to teleport a quantum state from one place to another. The fact that entanglement can be used to do both these things has led people to believe that teleportation is a nonlocal effect. In this paper it is shown that teleportation is conceptually independent of nonlocality. This is done by constructing a toy local theory in which cloning is not possible (without a no-cloning theory teleportation makes limited sense) but teleportation is. Teleportation in this local theory is achieved in an analogous way to the way it is done with quantum theory. This work provides some insight into what type of process teleportation is.
Kimura, Tetsuji; Noumi, Toshifumi; Yamaguchi, Masahide
2016-01-01
We construct $\\mathcal{N}=1$ supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of K\\"ahler 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.
Incompressible turbulence as non-local field theory
Indian Academy of Sciences (India)
Mahendra K Verma
2005-03-01
It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.
Indian Academy of Sciences (India)
Aurelien Drezet
2007-03-01
In a paper by Home and Agarwal [1], it is claimed that quantum nonlocality can be revealed in a simple interferometry experiment using only single particles. A critical analysis of the concept of hidden variable used by the authors of [1] shows that the reasoning is not correct.
Nonlocal Classical Matter in Self-contained Machian Relativism
Bulyzhenkov-Widicker, I E
2007-01-01
The continuous elementary source in Einstein's gravitational theory is the r^{-4} radial distribution of the energy-momentum tensor density. The space energy integral of such an infinite (astro)source-particle is finite and determines its nonlocal gravitational charge for the energy-to-energy attraction of other (astro)particles. Non-empty flat space of the undivided material Universe is charged continuously by the world energy density of the global ensemble of overlapping radial particles. Nonlocal gravitational/inertial energy-charges incorporate Machian relativism quantitatively into Einstein's gravitation for self-contained GR-SR relations without references to Newton's mass-to-mass attraction.
Nonlocal transformation optics
Castaldi, Giuseppe; Alu', Andrea; Engheta, Nader
2011-01-01
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 equi-frequency 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.
Nonlocality of quantum correlations
Streltsov, A; Roga, W; Bruß, D; Illuminati, F
2012-01-01
We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. This type of nonlocality occurs also for states that do not violate a Bell inequality, such as, for instance, Werner states with a low degree of entanglement. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord, thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish rigorously that Werner states are the maximally quantum correlated two-qubit states, and thus are the ones that maximize this novel type of nonlocality.
Entanglement without hidden nonlocality
Hirsch, Flavien; Túlio Quintino, Marco; Bowles, Joseph; Vértesi, Tamás; Brunner, Nicolas
2016-11-01
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.
Acausality in Nonlocal Gravity Theory
Zhang, Ying-li; Sasaki, Misao; Zhao, Gong-Bo
2016-01-01
We investigate the nonlocal gravity theory by deriving nonlocal equations of motion using the traditional variation principle in a homogeneous background. We focus on a class of models with a linear nonlocal modification term in the action. It is found that the resulting equations of motion contain the advanced Green's function, implying that there is an acausality problem. As a consequence, a divergence arises in the solutions due to contributions from the future infinity unless the Universe will go back to the radiation dominated era or become the Minkowski spacetime in the future. We also discuss the relation between the original nonlocal equations and its biscalar-tensor representation and identify the auxiliary fields with the corresponding original nonlocal terms. Finally, we show that the acusality problem cannot be avoided by any function of nonlocal terms in the action.
Lim, C. W.; Zhang, G.; Reddy, J. N.
2015-05-01
In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory. In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed. It is based on the nonlocal effects of the strain field and first gradient strain field. This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational
Noether's theorem in non-local field theories
Krivoruchenko, M I
2016-01-01
Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\\'e group in field theories with higher-order derivatives and in non-local field theories. An example of non-local charged scalar field equations with broken C and CPT symmetries is considered. For this case, we find simple analytical expressions for the conserved currents.
Causality, Nonlocality, and Negative Refraction.
Forcella, Davide; Prada, Claire; Carminati, Rémi
2017-03-31
The importance of spatial nonlocality in the description of negative refraction in electromagnetic materials has been put forward recently. We develop a theory of negative refraction in homogeneous and isotropic media, based on first principles, and that includes nonlocality in its full generality. The theory shows that both dissipation and spatial nonlocality are necessary conditions for the existence of negative refraction. It also provides a sufficient condition in materials with weak spatial nonlocality. These fundamental results should have broad implications in the theoretical and practical analyses of negative refraction of electromagnetic and other kinds of waves.
Nonlocal gravity: Conformally flat spacetimes
Bini, Donato
2016-01-01
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity in two-dimensional spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein's field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of nonlocal gravity.
Analytical theory of dark nonlocal solitons
DEFF Research Database (Denmark)
Kong, Qian; Wang, Qi; Bang, Ole;
2010-01-01
We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality.......We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality....
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.......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....
Senno, Gabriel; Bendersky, Ariel; Figueira, Santiago
2016-07-01
The concepts of randomness and non-locality are intimately intertwined outcomes of randomly chosen measurements over entangled systems exhibiting non-local correlations are, if we preclude instantaneous influence between distant measurement choices and outcomes, random. In this paper, we survey some recent advances in the knowledge of the interplay between these two important notions from a quantum information science perspective.
Observers in Spacetime and Nonlocality
Mashhoon, B
2012-01-01
Characteristics of observers in relativity theory are critically examined. For field measurements in Minkowski spacetime, the Bohr-Rosenfeld principle implies that the connection between actual (i.e., noninertial) and inertial observers must be nonlocal. Nonlocal electrodynamics of non-uniformly rotating observers is discussed and the consequences of this theory for the phenomenon of spin-rotation coupling are briefly explored.
Quadratic solitons as nonlocal solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole
2003-01-01
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...
An operational framework for nonlocality
Gallego, Rodrigo; Acín, Antonio; Navascués, Miguel
2011-01-01
Due to the importance of entanglement for quantum information purposes, a framework has been developed for its characterization and quantification as a resource based on the following operational principle: entanglement among $N$ parties cannot be created by local operations and classical communication, even when $N-1$ parties collaborate. More recently, nonlocality has been identified as another resource, alternative to entanglement and necessary for device-independent quantum information protocols. We introduce an operational framework for nonlocality based on a similar principle: nonlocality among $N$ parties cannot be created by local operations and allowed classical communication even when $N-1$ parties collaborate. We then show that the standard definition of multipartite nonlocality, due to Svetlichny, is inconsistent with this operational approach: according to it, genuine tripartite nonlocality could be created by two collaborating parties. We finally discuss alternative definitions for which consist...
Nonlocal and quasilocal field theories
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
Thompson, Ian
2010-11-01
In all direct reactions to probe the structure of exotic nuclei at FRIB, optical potentials will be needed in the entrance and exit channels. At high energies Glauber approximations may be useful, but a low energies (5 to 20 MeV/nucleon) other approaches are required. Recent work of the UNEDF project [1] has shown that reaction cross sections at these energies can be accounted for by calculating all inelastic and transfer channels reachable by one particle-hole transitions from the elastic channel. In this model space, we may also calculate the two-step dynamic polarization potential (DPP) that adds to the bare folded potential to form the complex optical potential. Our calculations of the DPP, however, show that its non-localities are very significant, as well as the partial-wave dependence of both its real and imaginary components. The Perey factors (the wave function ratio to that from an equivalent local potential) are more than 20% different from unity, especially for partial waves inside grazing. These factors combine to suggest a reexamination of the validity of local and L-independent fitted optical potentials, especially for capture reactions that are dominated by low partial waves. Prepared by LLNL under Contract DE-AC52-07NA27344. [1] G.P.A. Nobre, F.S. Dietrich, J.E. Escher, I.J. Thompson, M. Dupuis, J. Terasaki and J. Engel, submitted to Phys. Rev. Letts., 2010.
Institute of Scientific and Technical Information of China (English)
Ouyang Shi-Gen; Guo Qi; Lan Sheng; Wu Li-Jun
2007-01-01
The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schr(o)dinger equation for several types of nonlocal responses are calculated by Ritz's variational method.For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but difierent degrees of nonlocality are identical except for an amplitude factor.For a nonlocal case where the nonlocal response function decays in direct proportion to the ruth power of the distance near the source point,the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the(m+2)th power of its beam width.
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.
Koutsoumaris, C. Chr.; Eptaimeros, K. G.; Zisis, T.; Tsamasphyros, G. J.
2016-12-01
The nonlocal theory of elasticity is widely employed to the study of nanoscale problems. The differential approach of Eringen's nonlocal beam theory has been widely used to solve problems whose size effect is substantial in structures. However, in the case of Euler-Bernoulli beam theory (EBBT), this approach reveals inconsistencies that do not allow for the energy functional formulation. To avoid these inconsistencies, an alternative route is to use the integral form of nonlocal elasticity. This study revolves around the nonlocal integral beam model for various attenuation functions with the intention to explore the static response of a beam (or a nanobeam) for different types of loadings and boundary conditions (BC).
Optimal measurements for nonlocal correlations
Schwarz, Sacha; Stefanov, André; Wolf, Stefan; Montina, Alberto
2016-08-01
A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. There are however some complications with Bell inequalities. First and foremost it is unfeasible to determine the whole set of Bell inequalities already for a few measurements and thus unfeasible to find the experimental setup maximizing their violation. Second, the Bell violation suffers from an ambiguity stemming from the choice of the normalization of the Bell coefficients. An alternative measure of nonlocality with a direct information-theoretic interpretation is the minimal amount of classical communication required for simulating nonlocal correlations. In the case of many instances simulated in parallel, the minimal communication cost per instance is called nonlocal capacity, and its computation can be reduced to a convex-optimization problem. This quantity can be computed for a higher number of measurements and turns out to be useful for finding the optimal experimental setup. Focusing on the bipartite case, we present a simple method for maximizing the nonlocal capacity over a given configuration space and, in particular, over a set of possible measurements, yielding the corresponding optimal setup. Furthermore, we show that there is a functional relationship between Bell violation and nonlocal capacity. The method is illustrated with numerical tests and compared with the maximization of the violation of CGLMP-type Bell inequalities on the basis of entangled two-qubit as well as two-qutrit states. Remarkably, the anomaly of nonlocality displayed by qutrits turns out to be even stronger if the nonlocal capacity is employed as a measure of nonlocality.
Towards LHC physics with nonlocal Standard Model
Tirthabir Biswas; Nobuchika Okada
2015-01-01
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 Stan...
Solutions of Nonlocal -Laplacian Equations
Directory of Open Access Journals (Sweden)
Mustafa Avci
2013-01-01
Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.
Spontaneous Emission in Nonlocal Materials
Ginzburg, Pavel; Nasir, Mazhar E; Olvera, Paulina Segovia; Krasavin, Alexey V; Levitt, James; Hirvonen, Liisa M; Wells, Brian; Suhling, Klaus; Richards, David; Podolskiy, Viktor A; Zayats, Anatoly V
2016-01-01
Light-matter interactions can be dramatically modified by the surrounding environment. Here we report on the first experimental observation of molecular spontaneous emission inside a highly nonlocal metamaterial based on a plasmonic nanorod assembly. We show that the emission process is dominated not only by the topology of its local effective medium dispersion, but also by the nonlocal response of the composite, so that metamaterials with different geometric parameters but the same local effective medium properties exhibit different Purcell factors. A record-high enhancement of a decay rate is observed, in agreement with the developed quantitative description of the Purcell effect in a nonlocal medium. An engineered material nonlocality introduces an additional degree of freedom into quantum electrodynamics, enabling new applications in quantum information processing, photo-chemistry, imaging, and sensing.
Classical and Quantum Nonlocal Supergravity
Giaccari, Stefano
2016-01-01
We derive the N=1 supersymmetric extension for a class of weakly nonlocal four dimensional gravitational theories.The construction is explicitly done in the superspace and the tree-level perturbative unitarity is explicitly proved both in the superfield formalism and in field components. For the minimal nonlocal supergravity the spectrum is the same as in the local theory and in particular it is ghost-free. The supersymmetric extension of the super-renormalizable Starobinsky theory and of two alternative massive nonlocal supergravities are found as straightforward applications of the formalism. Power-counting arguments ensure super-renormalizability with milder requirement for the asymptotic behavior of form factors than in ordinary nonlocal gravity. The most noteworthy result, common to ordinary supergravity, is the absence of quantum corrections to the cosmological constant in any regularization procedure. We cannot exclude the usual one-loop quadratic divergences. However, local vertices in the superfields...
Dynamical nonlocal coherent-potential approximation for itinerant electron magnetism.
Rowlands, D A; Zhang, Yu-Zhong
2014-11-26
A dynamical generalisation of the nonlocal coherent-potential approximation is derived based upon the functional integral approach to the interacting electron problem. The free energy is proven to be variational with respect to the self-energy provided a self-consistency condition on a cluster of sites is satisfied. In the present work, calculations are performed within the static approximation and the effect of the nonlocal physics on the formation of the local moment state in a simple model is investigated. The results reveal the importance of the dynamical correlations.
Study of Nonlocal Optical Potential
Institute of Scientific and Technical Information of China (English)
TIAN; Yuan
2013-01-01
It is generally known that nuclear optical potentials are theoretically expected to be non-local.The non-locality arises from the exchange of particles between the projectile and target and from coupling tonon-elastic channels.This non-locality was first introduced by Frahn and Lemmer,and developed further by Perey and Buck(PB).The kernel is of the form
Nonlocal optical response in metallic nanostructures.
Raza, Søren; Bozhevolnyi, Sergey I; Wubs, Martijn; Asger Mortensen, N
2015-05-13
This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response.
Nonlocal optical response in metallic nanostructures
DEFF Research Database (Denmark)
Raza, Søren; Bozhevolnyi, Sergey I.; Wubs, Martijn
2015-01-01
This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response...... on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response....
Nonlocal Anomalous Hall Effect
Zhang, Steven S.-L.; Vignale, Giovanni
2016-04-01
The anomalous Hall (AH) effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator [yttrium iron garnet (YIG)], even when precautions are taken to ensure that there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin-Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect—the only difference being the spatial separation of the spin-orbit interaction and the magnetization. For this reason we name this effect the nonlocal anomalous Hall effect and predict that its sign will be determined by the sign of the spin-Hall angle in the metal. The AH conductivity that we calculate from our theory is in order of magnitude agreement with the measured values in Pt /YIG structures.
Nonlocal Anomalous Hall Effect.
Zhang, Steven S-L; Vignale, Giovanni
2016-04-01
The anomalous Hall (AH) effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator [yttrium iron garnet (YIG)], even when precautions are taken to ensure that there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin-Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect-the only difference being the spatial separation of the spin-orbit interaction and the magnetization. For this reason we name this effect the nonlocal anomalous Hall effect and predict that its sign will be determined by the sign of the spin-Hall angle in the metal. The AH conductivity that we calculate from our theory is in order of magnitude agreement with the measured values in Pt/YIG structures.
Nonlocal Measurements via Quantum Erasure.
Brodutch, Aharon; Cohen, Eliahu
2016-02-19
Nonlocal observables play an important role in quantum theory, from Bell inequalities and various postselection paradoxes to quantum error correction codes. Instantaneous measurement of these observables is known to be a difficult problem, especially when the measurements are projective. The standard von Neumann Hamiltonian used to model projective measurements cannot be implemented directly in a nonlocal scenario and can, in some cases, violate causality. We present a scheme for effectively generating the von Neumann Hamiltonian for nonlocal observables without the need to communicate and adapt. The protocol can be used to perform weak and strong (projective) measurements, as well as measurements at any intermediate strength. It can also be used in practical situations beyond nonlocal measurements. We show how the protocol can be used to probe a version of Hardy's paradox with both weak and strong measurements. The outcomes of these measurements provide a nonintuitive picture of the pre- and postselected system. Our results shed new light on the interplay between quantum measurements, uncertainty, nonlocality, causality, and determinism.
A Nonlocal Poisson-Fermi Model for Ionic Solvent
Xie, Dexuan; Eisenberg, Bob; Scott, L Ridgway
2016-01-01
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-type kernel function. Moreover, the Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Finally, numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.
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 theory of longitudinal waves in thermoelastic bars
Directory of Open Access Journals (Sweden)
Esin Inan
1991-05-01
Full Text Available The longitudinal waves in thermoelastic bars are investigated in the context of nonlocal theory. Using integral forms of constitutive equations, balance of momenta and energy, field equations are obtained. Then the frequency equation is found in generalized form. To obtain tangible results, an approximate procedure is applied and numerical results are given for short waves.
Nonlocal dispersive optical model ingredients for ${}^{40}$Ca
Mahzoon, M H; Dickhoff, W H; Dussan, H; Waldecker, S J
2013-01-01
A comprehensive description of all single-particle properties associated with the nucleus ${}^{40}$Ca has been generated by employing a nonlocal dispersive optical potential capable of simultaneously reproducing all relevant data above and below the Fermi energy. We gather all relevant functional forms and the numerical values of the parameters in this contribution.
Bardhan, Jaydeep P
2011-09-14
We study the energetics of burying charges, ion pairs, and ionizable groups in a simple protein model using nonlocal continuum electrostatics. Our primary finding is that the nonlocal response leads to markedly reduced solvent screening, comparable to the use of application-specific protein dielectric constants. Employing the same parameters as used in other nonlocal studies, we find that for a sphere of radius 13.4 Å containing a single +1e charge, the nonlocal solvation free energy varies less than 18 kcal/mol as the charge moves from the surface to the center, whereas the difference in the local Poisson model is ∼35 kcal/mol. Because an ion pair (salt bridge) generates a comparatively more rapidly varying Coulomb potential, energetics for salt bridges are even more significantly reduced in the nonlocal model. By varying the central parameter in nonlocal theory, which is an effective length scale associated with correlations between solvent molecules, nonlocal-model energetics can be varied from the standard local results to essentially zero; however, the existence of the reduction in charge-burial penalties is quite robust to variations in the protein dielectric constant and the correlation length. Finally, as a simple exploratory test of the implications of nonlocal response, we calculate glutamate pK(a) shifts and find that using standard protein parameters (ε(protein) = 2-4), nonlocal results match local-model predictions with much higher dielectric constants. Nonlocality may, therefore, be one factor in resolving discrepancies between measured protein dielectric constants and the model parameters often used to match titration experiments. Nonlocal models may hold significant promise to deepen our understanding of macromolecular electrostatics without substantially increasing computational complexity.
Nonlocal optical response in metallic nanostructures
Raza, Søren; Bozhevolnyi, Sergey I.; Wubs, Martijn; Mortensen, N. Asger
2014-01-01
This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future w...
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.
Totality of Subquantum Nonlocal Correlations
Khrennikov, Andrei
2011-01-01
In a series of previous papers we developed a purely field model of microphenomena, so called prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of QM including correlations for entangled systems, but it also gives a possibility to go beyond quantum mechanics (QM), i.e., to make predictions of phenomena which could be observed at the subquantum level. In this paper we discuss one of such predictions - existence of nonlocal correlations between prequantum random fields corresponding to {\\it 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 one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random back...
Aspects of nonlocality in quantum field theory, quantum gravity and cosmology
Barvinsky, A. O.
2015-02-01
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter (dS) cosmological evolution at an arbitrary value of Λ — a model of dark energy with the dynamical scale selected by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of a scalar mediated gravity and the short distance general relativistic limit in a special metric frame related by a nonlocal conformal transformation to the original metric.
A morphing strategy to couple non-local to local continuum mechanics
Lubineau, Gilles
2012-06-01
A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. © 2012 Elsevier Ltd.
Anderson Localization in Nonlocal Nonlinear Media
Folli, Viola; 10.1364/OL.37.000332
2012-01-01
The effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation in the presence of a random potential, showing that nonlocality stabilizes Anderson states.
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...
Nonlocally Centralized Simultaneous Sparse Coding
Institute of Scientific and Technical Information of China (English)
雷阳; 宋占杰
2016-01-01
The concept of structured sparse coding noise is introduced to exploit the spatial correlations and nonlo-cal constraint of the local structure. Then the model of nonlocally centralized simultaneous sparse coding(NC-SSC)is proposed for reconstructing the original image, and an algorithm is proposed to transform the simultaneous sparse coding into reweighted low-rank approximation. Experimental results on image denoisng, deblurring and super-resolution demonstrate the advantage of the proposed NC-SSC method over the state-of-the-art image resto-ration methods.
Energy Technology Data Exchange (ETDEWEB)
Maccari, A. [Istituto Tecnico `G. Cardano`, Monterotondo, Rome (Italy)
1996-08-01
The most important characteristics of the non-local oscillator, an oscillator subjected to an additional non-local force, are extensively studied by means of a new asymptotic perturbation method that is able to furnish an approximate solution of weakly non-linear differential equations. The resulting motion is doubly periodic, because a second little frequency appears, in addition to the fundamental harmonic frequency. Comparison with the numerical solution obtained by the Runge-Kitta method confirms the validity of the asymptotic perturbation method and its importance for the study of non-linear dynamical systems.
Nonlocal nuclear interactions and anomalous off-shell behavior of the two-nucleon amplitudes
Gajnutdinov, R K
2002-01-01
The problem of the ultraviolet divergences that arise in describing the nucleon dynamics at low energies is considered. By using the example of an exactly-solvable model it is shown that after renormalization the interaction generating nucleon dynamics is nonlocal in time. Effects of such nonlocality on low-energy nucleon dynamics are investigated. It is shown that nonlocality in time of nucleon-nucleon interactions gives rise to an anomalous off-shell behavior of the two-nucleon amplitudes that have significant effects on the dynamics of many-nucleon systems
Non-local models for ductile failure
César de Sá, José; Azinpour, Erfan; Santos, Abel
2016-08-01
Ductile damage can be dealt with continuous descriptions of material, resorting, for example, to continuous damage mechanic descriptions or micromechanical constitutive models. When it comes to describe material behaviour near and beyond fracture these approaches are no longer sufficient or valid and continuous/discontinuous approaches can be adopted to track fracture initiation and propagation. Apart from more pragmatic solutions like element erosion or remeshing techniques more advanced approaches based on the X-FEM concept, in particular associated with non-local formulations, may be adopted to numerically model these problems. Nevertheless, very often, for practical reasons, some important aspects are somewhat left behind, specially energetic requirements to promote the necessary transition of energy release associated with material damage and fracture energy associated to a crack creation and evolution. Phase-field methods may combine advantages of regularised continuous models by providing a similar description to non-local thermodynamical continuous damage mechanics, as well as, a "continuous" approach to numerically follow crack evolution and branching
Nonlocal modeling and buckling features of cracked nanobeams with von Karman nonlinearity
Akbarzadeh Khorshidi, Majid; Shaat, Mohamed; Abdelkefi, Abdessattar; Shariati, Mahmoud
2017-01-01
Buckling and postbuckling behaviors of cracked nanobeams made of single-crystalline nanomaterials are investigated. The nonlocal elasticity theory is used to model the nonlocal interatomic effects on the beam's performance accounting for the beam's axial stretching via von Karman nonlinear theory. The crack is then represented as torsional spring where the crack severity factor is derived accounting for the nonlocal features of the beam. By converting the beam into an equivalent infinite long plate with an edge crack subjected to a tensile stress at the far field, the crack energy release rate, intensity factor, and severity factor are derived according to the nonlocal elasticity theory. An analytical solution for the buckling and the postbuckling responses of cracked nonlocal nanobeams accounting for the beam axial stretching according to von Karman nonlinear theory of kinematics is derived. The impacts of the nonlocal parameter on the critical buckling loads and the static nonlinear postbuckling responses of cracked nonlocal nanobeams are studied. The results indicate that the buckling and postbuckling behaviors of cracked nanobeams are strongly affected by the crack location, crack depth, nonlocal parameter, and length-to-thickness ratio.
A simple nonlocal model for exchange.
Janesko, Benjamin G
2009-12-21
This work presents a new nonlocal model for the exchange energy density. The model is obtained from the product of the Kohn-Sham one-particle density matrix used to construct exact [Hartree-Fock-like (HF)] exchange, and an approximate density matrix used to construct local spin-density approximation (LSDA) exchange. The proposed exchange energy density has useful formal properties, including correct spin and coordinate scaling and the correct uniform limit. It can readily be evaluated in finite basis sets, with a computational scaling intermediate between HF exchange and semilocal quantities such as the noninteracting kinetic energy density. Applications to representative systems indicate that its properties are typically intermediate between HF and LSDA exchange, and often similar to global hybrids of HF and LSDA exchange. The model is proposed as a novel "Rung 3.5" ingredient for constructing approximate exchange-correlation functionals.
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.
A nonlocal discretization of fields
Campos, R G; Pimentel, L O; Campos, Rafael G.; Tututi, Eduardo S.
2001-01-01
A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion doubling or the breaking of chiral symmetry for the massless case, are absent in this method.
Learning Non-Local Dependencies
Kuhn, Gustav; Dienes, Zoltan
2008-01-01
This paper addresses the nature of the temporary storage buffer used in implicit or statistical learning. Kuhn and Dienes [Kuhn, G., & Dienes, Z. (2005). Implicit learning of nonlocal musical rules: implicitly learning more than chunks. "Journal of Experimental Psychology-Learning Memory and Cognition," 31(6) 1417-1432] showed that people could…
Learning Non-Local Dependencies
Kuhn, Gustav; Dienes, Zoltan
2008-01-01
This paper addresses the nature of the temporary storage buffer used in implicit or statistical learning. Kuhn and Dienes [Kuhn, G., & Dienes, Z. (2005). Implicit learning of nonlocal musical rules: implicitly learning more than chunks. "Journal of Experimental Psychology-Learning Memory and Cognition," 31(6) 1417-1432] showed that people could…
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.
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonloc......We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...
Nonlocal effect in surface plasmon polariton of ultrathin metal films
Energy Technology Data Exchange (ETDEWEB)
Xue, Hong-jie; Yu, Yabin, E-mail: apybyu@hnu.edu.cn; Wu, Reng-lai; Yu, Yan-qin; Wang, Ya-xin
2015-09-01
Using the nonlocal conductivity based on quantum response theory, we study the optical properties of p-polarized wave in quartz–metal–film–air structures, especially the influence of nonlocal effect on the surface plasmon polaritons (SPPs) resonance. In absorption spectrum, the resonant peak of SPP is found, and the dependence of the resonant peak on film thickness shows that nonlocal effect in the SPP resonance is enhanced significantly with the decrease of film-thickness, especially in the less than 20 nm metal film. We calculate the surface charge density as a function of frequency, and find that the frequencies at the charge and absorption peaks are the same. This clearly confirms that the absorption peak stems from SPP resonance excitation, and SPPs absorb the energy of the electromagnetic wave via charge oscillations. In the case of SPP resonance, the charge and electric field on the down-surface of thin film are always greater than that on the up-surface; however, the situation is just opposite in the case of no SPP resonance. This implies that the SPP resonance occurs near the down-surface of the film. Moreover, due to the nonlocal response of electric current to the electric field, the energy flow and electric current show anomalous oscillations, and with the increase of film thickness the anomalous oscillations exhibit obvious attenuation.
Structure of nonlocality of plasma turbulence
Gürcan, Ö. D.; Vermare, L.; Hennequin, P.; Berionni, V.; Diamond, P. H.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, P.; Grandgirard, V.; McDevitt, C. J.; Morel, P.; Sarazin, Y.; Storelli, A.; Bourdelle, C.; the Tore Supra Team
2013-07-01
Various indications on the weakly nonlocal character of turbulent plasma transport both from experimental fluctuation measurements from Tore Supra and observations from the full-f, flux-driven gyrokinetic code GYSELA are reported. A simple Fisher equation model of this weakly nonlocal dynamics can be formulated in terms of an evolution equation for the turbulent entropy density, which contains the basic phenomenon of radial turbulence spreading in addition to avalanche-like dynamics via coupling to profile modulations. A derivation of this model, which contains the so-called beach effect, a diffusive and convective flux components for the flux of turbulence intensity, in addition to linear group propagation is given, starting from the drift-kinetic equation. The proposed model has the form of a transport equation for turbulence intensity, and may be considered as an addition to transport modelling. The kinetic fluxes given, can be computed using model closures, or local gyrokinetics. The model is also used in a particular setup that represents the near edge region as a relatively stable zone between the core and edge region where the energy injection is locally more substantial. It is observed that with constant, physical coefficients, the model gives a convincing qualitative profile of fluctuation intensity when the turbulence is coming from the core region with either a group velocity or a convective flux.
Nonlocal bottleneck effect in two-dimensional turbulence
Biskamp, D; Schwarz, E
1998-01-01
The bottleneck pileup in the energy spectrum is investigated for several two-dimensional (2D) turbulence systems by numerical simulation using high-order diffusion terms to amplify the effect, which is weak for normal diffusion. For 2D magnetohydrodynamic (MHD) turbulence, 2D electron MHD (EMHD) turbulence and 2D thermal convection, which all exhibit direct energy cascades, a nonlocal behavior is found resulting in a logarithmic enhancement of the spectrum.
Lan, Tran Nguyen; Zgid, Dominika
2016-01-01
We present a detailed discussion of self-energy embedding theory (SEET) which is a quantum embedding scheme allowing us to describe a chosen subsystem very accurately while keeping the description of the environment at a lower cost. We apply SEET to molecular examples where commonly our chosen subsystem is made out of a set of strongly correlated orbitals while the weakly correlated orbitals constitute an environment. Such a self-energy separation is very general and to make this procedure applicable to multiple systems a detailed and practical procedure for the evaluation of the system and environment self-energy is necessary. We list all the intricacies for one of the possible procedures while focusing our discussion on many practical implementation aspects such as the choice of best orbital basis, impurity solver, and many steps necessary to reach chemical accuracy. Finally, on a set of carefully chosen molecular examples, we demonstrate that SEET which is a controlled, systematically improvable Green's fu...
Investigation of local and nonlocal nonlinear optical refraction effect in IZO thin films
Htwe, Zin Maung; Zhang, Yun-Dong; Yao, Cheng-Bao; Li, Hui; Yuan, Ping
2016-10-01
We report the local and nonlocal nonlinear optical refraction properties of indium doped zinc oxide (IZO) thin films using closed aperture Z-scan technique. The Z-scan results show the films have positive nonlinear optical refraction properties. The nonlocal parameter m of samples is increased with indium. In both of local and nonlocal studies, the nonlinear optical refractions of thin films were increased with In contents and laser energy. This relation reveals the role of In composition in IZO affects on the nonlinear optical responses of the films. These results make the IZO thin films as the promising application in optoelectronics devices.
Nonlocal electron-phonon coupling: Consequences for the nature of polaron states
Stojanović, Vladimir M.; Bobbert, P. A.; Michels, M. A.
2004-04-01
We develop a variational approach to an extended Holstein model, comprising both local and nonlocal electron-phonon coupling. The approach is based on the minimization of a Bogoliubov bound to the Helmholtz free energy. The ambivalent character of nonlocal coupling, which both promotes and hinders transport, is clearly observed. Furthermore, a salient feature of our results is that the local and nonlocal couplings can compensate each other, leading to a reduction of polaronic effects and a quasi-free character of the excitation. Our findings have implications for organic crystals of π-conjugated molecules, where this electron-phonon coupling mechanism plays an important role.
Nonlocal electron-phonon coupling: influence on the nature of polarons
Stojanovi, V. M.; Bobbert, P. A.; Michels, M. A. J.
2004-01-01
We present a variational approach to an extended Holstein model, comprising both local and nonlocal electron-phonon coupling. The approach is based on the minimization of a Bogoliubov bound to the free energy of the coupled electron-phonon system, and is implemented for a one-dimensional nearest-neighbor model, with Einstein phonons. The ambivalent character of nonlocal coupling, which both promotes and hinders transport, is clearly observed. A salient feature of our results is that the local and nonlocal couplings can compensate each other, leading to a supression of polaronic effects.
Ho, Gregory S.; Lignères, Vincent L.; Carter, Emily A.
2008-07-01
We derive an analytic form of the Wang-Govind-Carter (WGC) [Wang , Phys. Rev. B 60, 16350 (1999)] kinetic energy density functional (KEDF) with the density-dependent response kernel. A real-space aperiodic implementation of the WGC KEDF is then described and used in linear scaling orbital-free density functional theory (OF-DFT) calculations.
Nonlocal elasticity tensors in dislocation and disclination cores
Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.
2017-03-01
Nonlocal elastic constitutive laws are introduced for crystals containing defects such as dislocations and disclinations. In addition to pointwise elastic moduli tensors adequately reflecting 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. 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.
Chaudhury, Kunal N; Singer, Amit
2012-11-01
In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.
Extreme nonlocality with one photon
Heaney, Libby; Santos, Marcelo F; Vedral, Vlatko
2009-01-01
The bizarre concept of nonlocality appears in quantum mechanics because the properties of two or more particles may be assigned globally and are not always pinned to each particle individually. Experiments using two, three, or more of these entangled particles have strongly rejected a local realist interpretation of nature. Nonlocality is also argued to be an intrinsic property of a quantum field, implying that just one excitation, a photon for instance, could also by itself violate local realism. Here we show that one photon superposed symmetrically over many distant sites (which in quantum information terms is a W-state) can give a stunning all-versus-nothing demolition of local realism in an identical manner to the GHZ class of states. The elegance of this result is that it is due solely to the wave-particle duality of light and matter. We present experimental implementations capable of testing our predictions.
Percolation transitions with nonlocal constraint.
Shim, Pyoung-Seop; Lee, Hyun Keun; Noh, Jae Dong
2012-09-01
We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose r-neighbors share any exclusive pair. The r-neighbor of a node x is defined as a set of at most N(r) neighbors of x, where N is the total number of nodes. The parameter r controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean-field universality class for r1/2, the system undergoes a peculiar phase transition from a nonpercolating phase to a quasicritical phase where the largest cluster size G scales as G~N(α) with α=0.74(1). In the marginal case with r=1/2, the model displays a percolation transition that does not belong to the mean-field universality class.
Horikis, Theodoros P
2016-01-01
The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the contrary, a parameter regime is identified where the instability is suppressed but nevertheless the number and amplitude of the rogue events increase, as compared to the standard NLS (which is a limit of the nonlocal system). Furthermore, the nature of these waves is investigated; while no analytical solutions are known to model these events, numerically it is shown that they differ significantly from either the rational (Peregrine) or soliton solution of the limiting NLS equation. As such, these findings may also help in rogue wave realization experimentally in these media.
Nonlocal Quantum Effects in Cosmology
Dumin, Yurii V
2014-01-01
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 du...
Nonlocal reflection by photonic barriers
Vetter, R. -M.; A. Haibel; Nimtz, G.
2001-01-01
The time behaviour of microwaves undergoing partial reflection by photonic barriers was measured in the time and in the frequency domain. It was observed that unlike the duration of partial reflection by dielectric layers, the measured reflection duration of barriers is independent of their length. The experimental results point to a nonlocal behaviour of evanescent modes at least over a distance of some ten wavelengths. Evanescent modes correspond to photonic tunnelling in quantum mechanics.
Diaz, Pablo; Walton, Mark
2016-01-01
With the aim of investigating the relation between gravity and non-locality at the classical level, we study a bilocal scalar field model. Bilocality introduces new (internal) degrees of freedom that can potentially reproduce gravity. We show that the equations of motion of the massless branch of the free bilocal model match those of linearized gravity. We also discuss higher orders of perturbation theory, where there is self-interaction in both gravity and the bilocal field sectors.
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.
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 defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media...... for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose...
Towards LHC physics with nonlocal Standard Model
Directory of Open Access Journals (Sweden)
Tirthabir Biswas
2015-09-01
Full Text Available 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.
Nonlocal transport in superconducting oxide nanostructures
Veazey, Joshua; Cheng, Guanglei; Lu, Shicheng; Tomczyk, Michelle; Irvin, Patrick; Huang, Mengchen; Wung Bark, Chung; Ryu, Sangwoo; Eom, Chang-Beom; Levy, Jeremy
2013-03-01
We report nonlocal transport signatures in the superconducting state of nanostructures formed[2] at the LaAlO3/SrTiO3 interface using conductive AFM lithography. Nonlocal resistances (nonlocal voltage divided by current) are as large as 200 Ω when 2-10 μm separate the current-carrying segments from the voltage-sensing leads. The nonlocal resistance reverses sign at the local critical current of the superconducting state. Features observed in the nonlocal V-I curves evolve with back gate voltage and magnetic field, and are correlated with the local four-terminal V-I curves. We discuss how nonlocal and local transport effects in LaAlO3/SrTiO3 nanostructures may result from the electronic phase separation and superconducting inhomogeneity reported by others in planar structures[3]. This work is supported by AFOSR (FA9550-10-1-0524) and NSF DMR-0906443
Detrimental nonlocality in luminescence measurements
Pluska, Mariusz; Czerwinski, Andrzej
2017-08-01
Luminescence studies are used to investigate the local properties of various light-emitting materials. A critical issue of these studies is presented that the signals often lack all advantages of luminescence-studies of high locality, and may originate from an extended spatial region of even a few millimeters in size or the whole sample, i.e., places other than intended for investigation. This is a key problem for research and development in photonics. Due to this nonlocality, information indicating defects, irregularities, nonuniformities and inhomogeneities is lost. The issue refers to typical structures with a strong built-in electric field. Such fields exist intentionally in most photonic structures and occur unintentionally in many other materials investigated by applied physics. We reveal [using test samples prepared with focused ion beam (FIB) on an AlGaAs/GaAs laser heterostructure with an InGaAs quantum well (QW)] that nonlocality increases at low temperatures. This is contrary to the widely expected outcome, as low-temperature luminescence measurements are usually assumed to be free from disturbances. We explain many effects observed due to nonlocality in luminescence studies and prove that separation of the investigated area by focused ion beam milling is a practical solution enabling truly local luminescence measurements. All conclusions drawn using the example of cathodoluminescence are useful for other luminescence techniques.
Nonlocal response of hyperbolic metasurfaces.
Correas-Serrano, D; Gomez-Diaz, J S; Tymchenko, M; Alù, A
2015-11-16
We analyze and model the nonlocal response of ultrathin hyperbolic metasurfaces (HMTSs) by applying an effective medium approach. We show that the intrinsic spatial dispersion in the materials employed to realize the metasurfaces imposes a wavenumber cutoff on the hyperbolic isofrequency contour, inversely proportional to the Fermi velocity, and we compare it with the cutoff arising from the structure granularity. In the particular case of HTMSs implemented by an array of graphene nanostrips, we find that graphene nonlocality can become the dominant mechanism that closes the hyperbolic contour - imposing a wavenumber cutoff at around 300k(0) - in realistic configurations with periodicity Lnonlocal response is mainly relevant in hyperbolic metasurfaces and metamaterials with periodicity below a few nm, being very weak in practical scenarios. In addition, we investigate how spatial dispersion affects the spontaneous emission rate of emitters located close to HMTSs. Our results establish an upper bound set by nonlocality to the maximum field confinement and light-matter interactions achievable in practical HMTSs, and may find application in the practical development of hyperlenses, sensors and on-chip networks.
Making nonlocal reality compatible with relativity
Nikolic, H.
2010-01-01
It is often argued that hypothetic nonlocal reality responsible for nonlocal quantum correlations between entangled particles cannot be consistent with relativity. I review the most frequent arguments of that sort, explain how they can all be circumvented, and present an explicit Bohmian model of nonlocal reality (compatible with quantum phenomena) that fully obeys the principle of relativistic covariance and does not involve a preferred Lorentz frame.
Nonlocal Gravity in the Solar System
Chicone, C
2015-01-01
The implications of the recent classical nonlocal generalization of Einstein's theory of gravitation for gravitational physics in the Solar System are investigated. In this theory, the nonlocal character of gravity simulates dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a_0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a_0 is determined.
Nonlocal gravity in the solar system
Chicone, C.; Mashhoon, B.
2016-04-01
The implications of the recent classical nonlocal generalization of Einstein’s theory of gravitation for gravitational physics in the solar system are investigated. In this theory, the nonlocal character of gravity appears to simulate dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a 0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a 0 is determined.
Origin of Dynamical Quantum Non-locality
Pachon, Cesar E.; Pachon, Leonardo A.
2014-03-01
Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two ``flavours'': a kinematic non-locality- arising from the structure of the Hilbert space- and a dynamical non-locality- arising from the quantum equations of motion-. Kinematic non-locality is unable to induce any change in the probability distributions, so that the ``action-at-a-distance'' cannot manifest. Conversely, dynamical non-locality does create explicit changes in probability, though in a ``causality-preserving'' manner. The origin of non-locality of quantum measurements and its relations to the fundamental postulates of quantum mechanics, such as the uncertainty principle, have been only recently elucidated. Here we trace the origin of dynamical non-locality to the superposition principle. This relation allows us to establish and identify how the uncertainty and the superposition principles determine the non-local character of the outcome of a quantum measurement. Being based on group theoretical and path integral formulations, our formulation admits immediate generalizations and extensions to to, e.g., quantum field theory. This work was supported by the Departamento Administrativo de Ciencia, Tecnologia e Innovacion -COLCIENCIAS- of Colombia under the grant number 111556934912.
Perturbative loop corrections and nonlocal gravity
Maggiore, Michele
2016-01-01
Nonlocal gravity has been shown to provide a phenomenologically viable infrared modification of GR. A natural question is whether the required nonlocality can emerge from perturbative quantum loop corrections due to light particles. We show that this is not the case. For the value of the mass scale of the non-local models required by cosmology, the perturbative form factors obtained from the loop corrections, in the present cosmological epoch, are in the regime where they are local. The mechanism behind the generation of the required nonlocality must be more complex, possibly related to strong infrared effects and non-perturbative mass generation for the conformal mode.
Causality, Non-Locality and Negative Refraction
Forcella, Davide; Carminati, Rémi
2016-01-01
The importance of spatial non-locality in the description of negative refraction in electromagnetic materials has been put forward recently. We develop a theory of negative refraction in homogeneous and isotropic media, based on first principles, and that includes non-locality in its full generality. The theory shows that both dissipation and spatial non-locality are necessary conditions for the existence of negative refraction. It also provides a sufficient condition in materials with weak spatial non-locality. These fundamental results should have broad implications in the theoretical and practical analyses of negative refraction of electromagnetic and other kinds of waves.
Li, Zhixiu; Yang, Yuedong; Faraggi, Eshel; Zhan, Jian; Zhou, Yaoqi
2014-10-01
Locating sequences compatible with a protein structural fold is the well-known inverse protein-folding problem. While significant progress has been made, the success rate of protein design remains low. As a result, a library of designed sequences or profile of sequences is currently employed for guiding experimental screening or directed evolution. Sequence profiles can be computationally predicted by iterative mutations of a random sequence to produce energy-optimized sequences, or by combining sequences of structurally similar fragments in a template library. The latter approach is computationally more efficient but yields less accurate profiles than the former because of lacking tertiary structural information. Here we present a method called SPIN that predicts Sequence Profiles by Integrated Neural network based on fragment-derived sequence profiles and structure-derived energy profiles. SPIN improves over the fragment-derived profile by 6.7% (from 23.6 to 30.3%) in sequence identity between predicted and wild-type sequences. The method also reduces the number of residues in low complex regions by 15.7% and has a significantly better balance of hydrophilic and hydrophobic residues at protein surface. The accuracy of sequence profiles obtained is comparable to those generated from the protein design program RosettaDesign 3.5. This highly efficient method for predicting sequence profiles from structures will be useful as a single-body scoring term for improving scoring functions used in protein design and fold recognition. It also complements protein design programs in guiding experimental design of the sequence library for screening and directed evolution of designed sequences. The SPIN server is available at http://sparks-lab.org.
Non-local gravity with a Weyl-square term
Cusin, Giulia; Maggiore, Michele; Mancarella, Michele
2016-01-01
Recent work has shown that modifications of General Relativity based on the addition of a non-local term $R\\,\\Box^{-2}R$ produce a dynamical model of dark energy, which is cosmologically viable both at the background level and at the level of cosmological perturbations. We explore a more general class of models based on the addition of terms proportional to $R_{\\mu\
Structure formation in a nonlocally modified gravity model
Energy Technology Data Exchange (ETDEWEB)
Park, Sohyun; Dodelson, Scott
2013-01-01
We study a nonlocally modified gravity model proposed by Deser and Woodard which gives an explanation for current cosmic acceleration. By deriving and solving the equations governing the evolution of the structure in the Universe, we show that this model predicts a pattern of growth that differs from standard general relativity (+dark energy) at the 10-30% level. These differences will be easily probed by the next generation of galaxy surveys, so the model should be tested shortly.
Nonlocality of a single particle
Dunningham, Jacob; Vedral, Vlatko
2007-01-01
There has been a great deal of debate surrounding the issue of whether it is possible for a single photon to exhibit nonlocality. A number of schemes have been proposed that claim to demonstrate this effect, but each has been met with significant opposition. The objections hinge largely on the fact that these schemes use unobservable initial states and so, it is claimed, they do not represent experiments that could actually be performed. Here we show how it is possible to overcome these objec...
Directory of Open Access Journals (Sweden)
Antoni Buades
2011-09-01
Full Text Available We present in this paper a new denoising method called non-local means. The method is based on a simple principle: replacing the color of a pixel with an average of the colors of similar pixels. But the most similar pixels to a given pixel have no reason to be close at all. It is therefore licit to scan a vast portion of the image in search of all the pixels that really resemble the pixel one wants to denoise. The paper presents two implementations of the method and displays some results.
Monotone method for nonlinear nonlocal hyperbolic problems
Directory of Open Access Journals (Sweden)
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
Nonlocality as Evidence for a Multiverse Cosmology
Tipler, Frank J
2010-01-01
I show that observations of quantum nonlocality can be interpreted as purely local phenomena, provided one assumes that the cosmos is a multiverse. Conversely, the observation of quantum nonlocality can be interpreted as observation evidence for a multiverse cosmology, just as observation of the setting of the Sun can be interpreted as evidence for the Earth's rotation.
Nonlocal study of ultimate plasmon hybridization
DEFF Research Database (Denmark)
Raza, Søren; Wubs, Martijn; Bozhevolnyi, Sergey I.
2015-01-01
Within our recently proposed generalized nonlocal optical response (GNOR) model, where nonlocal response is included by taking into account both convective and diffusive currents of the conduction electrons, we revisit the fundamental problem of an optically excited plasmonic dimer. We consider...
A New Model of Nonlocal Modified Gravity
Dimitrijevic, Ivan; Grujic, Jelena; Rakic, Zoran
2014-01-01
We consider a new modified gravity model with nonlocal term of the form $R^{-1} \\mathcal{F}(\\Box) R. $ This kind of nonlocality is motivated by investigation of applicability of a few unusual ans\\"atze to obtain some exact cosmological solutions. In particular, we find attractive and useful quadratic ansatz $\\Box R = q R^{2}.$
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...... of dark solitons. (C) 2004 Optical Society of America...
Creation of Entanglement with Nonlocal Operations
Institute of Scientific and Technical Information of China (English)
ZHANG Yong; CAO Wan-Cang; LONG Gui-Lu
2005-01-01
We discuss how to create more entanglement with nonlocal operations acting on two-particle states. For a given nonlocal operation, we find that some input states cannot produce entanglement and some produce the maximal entanglement, and find that any initial entangled states can produce more entanglement than initial product states.
Spectral Dimension from Causal Set Nonlocal Dynamics
Belenchia, Alessio; Marciano, Antonino; Modesto, Leonardo
2015-01-01
We investigate the spectral dimension obtained from non-local continuum d'Alembertians derived from causal sets. We find a universal dimensional reduction to 2 dimensions, in all dimensions. We conclude by discussing the validity and relevance of our results within the broader context of quantum field theories based on these nonlocal dynamics.
Katanin, A. A.; Belozerov, A. S.; Anisimov, V. I.
2016-01-01
We consider nonlocal correlations in iron in the vicinity of the $\\alpha$-$\\gamma$ phase transition within the spin-rotationally-invariant dynamical mean-field theory (DMFT) approach, combined with the recently proposed spin-fermion model of iron. The obtained nonlocal corrections to DMFT yield a decrease of the Curie temperature of the $\\alpha$ phase, leading to an agreement with its experimental value. We show that the corresponding nonlocal corrections to the energy of the $\\alpha$ phase a...
Nonlocal and quasi-local field theories
Tomboulis, E T
2015-01-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasi-local (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasi-local kernels all acausal effects are confined within the compact support regi...
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
DEFF Research Database (Denmark)
Yan, Wei; Mortensen, N. Asger; Wubs, Martijn
2013-01-01
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......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...
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 parallel transport in BOUT++
Omotani, J T; Havlickova, E; Umansky, M
2015-01-01
Non-local closures allow kinetic effects on parallel transport to be included in fluid simulations. This is especially important in the scrape-off layer, but to be useful there the non-local model requires consistent kinetic boundary conditions at the sheath. A non-local closure scheme based on solution of a kinetic equation using a diagonalized moment expansion has been previously reported. We derive a method for imposing kinetic boundary conditions in this scheme and discuss their implementation in BOUT++. To make it feasible to implement the boundary conditions in the code, we are lead to transform the non-local model to a different moment basis, better adapted to describe parallel dynamics. The new basis has the additional benefit of enabling substantial optimization of the closure calculation, resulting in an O(10) speedup of the non-local code.
Virial Theorem in Nonlocal Newtonian Gravity
Mashhoon, B
2015-01-01
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---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 times a universal length that is the basic nonlocality length scale of about 3 kpc.
Virial Theorem in Nonlocal Newtonian Gravity
Mashhoon, Bahram
2016-05-01
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---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 times a universal length that is the basic nonlocality length scale of about 3 kpc.
Dissociative electron attachment to halogen molecules: Angular distributions and nonlocal effects
Fabrikant, I. I.
2016-11-01
We study dissociative electron attachment (DEA) to the ClF and F2 molecules. We formulate a method for calculation of partial resonance widths and calculate the angular distributions of the products in the ClF case using the local and nonlocal versions of the complex potential theory of DEA. They show the dominance of the p wave except in a narrow energy region close to zero energy. Comparison of the local and nonlocal DEA cross sections show that the former are smaller than the latter by a factor of 2 in the energy region important for calculation of thermal rate coefficients. This result is confirmed by comparison of the local and nonlocal calculations for F2. Only at low energies below 30 meV the local cross sections exceed nonlocal due to the 1 /E divergence of the local results. On the other hand, the thermal rate coefficients generated from the local cross sections agree better with experiment than those calculated from the nonlocal cross sections. The most likely reason for this disagreement is the overestimated resonance width in the region of internuclear distances close to the point of crossing between the neutral and anion potential-energy curves.
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.
Retarded versus time-nonlocal quantum kinetic equations
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Spicka, V.; Lipavsky, P. [Institute of Physics, Academy of Sciences, Praha (Czech Republic)
2000-07-01
The finite duration of the collisions in Fermionic systems as expressed by the retardation time in the non-Markovian Levinson equation is discussed in the quasiclassical limit. The separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates and (iii) of the single-particle energy, (iv) collision delay and (v) related non-local corrections to the scattering integral. In this way we transform the Levison equation into the Landau-Silin equation extended by the non-local corrections known from the theory of dense gases. The derived kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other. (authors)
Structure-Aware Nonlocal Optimization Framework for Image Colorization
Institute of Scientific and Technical Information of China (English)
Han-Li Zhao; Gui-Zhi Nie; Xu-Jie Li; CCF Xiao-Gang Jin; Zhi-Geng Pan
2015-01-01
This paper proposes a structure-aware nonlocal energy optimization framework for interactive image colo-rization with sparse scribbles. Our colorization technique propagates colors to both local intensity-continuous regions and remote texture-similar regions without explicit image segmentation. We implement the nonlocal principle by computing k nearest neighbors in the high-dimensional feature space. The feature space contains not only image coordinates and intensities but also statistical texture features obtained with the direction-aligned Gabor wavelet filter. Structure maps are utilized to scale texture features to avoid artifacts along high-contrast boundaries. We show various experimental results and comparisons on image colorization, selective recoloring and decoloring, and progressive color editing to demonstrate the effectiveness of the proposed approach.
Can EPR non-locality be geometrical?
Energy Technology Data Exchange (ETDEWEB)
Ne`eman, Y. [Tel-Aviv Univ. (Israel). Raymond and Beverly Sackler Faculty of Exact Sciences]|[Univ. of Texas, Austin, TX (United States). Center for Particle Physics; Botero, A. [Texas Univ., Austin, TX (United States)
1995-10-01
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.
Nonlinear and Nonlocal Feedbacks in an Aquaplanet
Feldl, N.; Roe, G.
2012-12-01
The power of the feedback framework lies in its ability to reveal the energy pathways by which the climate system adjusts to an imposed forcing. By understanding the closure of the energy budget in as much detail and precision as possible, and within as clean an experimental set-up as possible, we are also able to isolate nonlinear interactions between feedbacks. For an aquaplanet simulation under perpetual equinox conditions, we account for rapid tropospheric adjustments to CO2 and diagnose radiative kernels for this precise model set-up. We characterize the contributions of feedbacks, heat transport, and nonlinearities in controlling the meridional structure of the climate response. The presence of strongly positive subtropical feedbacks, combined with polar amplification, implies a critical role for transport and nonlinear effects, with the latter acting to substantially reduce global climate sensitivity. At the hemispheric scale, a rich picture emerges: net heat divergence away from strong positive feedbacks in the tropics; nonlinearities induced by circulation changes that cool the tropics and warm the high-latitudes; and strong ice-line feedbacks that drive further amplification of polar warming. Overall, these results highlight how spatial patterns in feedbacks affect both the local and nonlocal climate response, with implications for regional predictability.
Local, nonlocal quantumness and information theoretic measures
Agrawal, Pankaj; Sazim, Sk; Chakrabarty, Indranil; Pati, Arun K.
2016-08-01
It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by information theoretic quantities such as quantum discord, but not by the conventional measures of entanglement. We argue that a state displays quantumness, that can be of local and nonlocal origin. Information theoretic measures not only characterize the nonlocal quantumness, but also the local quantumness, such as the “local superposition”. This can be a reason, why such measures are nonzero, when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of local quantumness, nonlocal quantumness and classical mixedness of a state.
Nonlocal-response diffusion model of holographic recording in photopolymer
Sheridan, John T.; Lawrence, Justin R.
2000-01-01
The standard one-dimensional diffusion equation is extended to include nonlocal temporal and spatial medium responses. How such nonlocal effects arise in a photopolymer is discussed. It is argued that assuming rapid polymer chain growth, any nonlocal temporal response can be dealt with so that the response can be completely understood in terms of a steady-state nonlocal spatial response. The resulting nonlocal diffusion equation is then solved numerically, in low-harmonic approximation, to de...
Film edge nonlocal spin valves.
McCallum, Andrew T; Johnson, Mark
2009-06-01
Spintronics is a new paradigm for integrated digital electronics. Recently established as a niche for nonvolatile magnetic random access memory (MRAM), it offers new functionality while demonstrating low-power and high-speed performance. However, to reach high density spintronic technology must make a transition to the nanometer scale. Prototype devices are presently made using a planar geometry and have an area determined by the lithographic feature size, currently about 100 nm. Here we present a new nonplanar geometry in which one lateral dimension is given by a film thickness, on the order of 10 nm. With this new approach, cell sizes can shrink by an order of magnitude. The geometry is demonstrated with a nonlocal spin valve, where we study devices with an injector/detector separation much less than the spin diffusion length.
Nonlocality in uniaxially polarizable media
Gorlach, Maxim A
2015-01-01
We reveal extraordinary electromagnetic properties for a general class of uniaxially polarizable media. Depending on parameters, such metamaterials may have wide range of nontrivial shapes of isofrequency contours including lemniscate, diamond and multiply connected curves with connectivity number reaching five. The possibility of the dispersion engineering paves a way to more flexible manipulation of electromagnetic waves. Employing first-principle considerations we prove that uniaxially polarizable media should be described in terms of the nonlocal permittivity tensor which by no means can be reduced to local permittivity and permeability even in the long-wavelength limit. We introduce an alternative set of local material parameters including quadrupole susceptibility capable to capture all of the second-order spatial dispersion effects.
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.
Experimental test of nonlocal causality.
Ringbauer, Martin; Giarmatzi, Christina; Chaves, Rafael; Costa, Fabio; White, Andrew G; Fedrizzi, Alessandro
2016-08-01
Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell's local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect.
Experimental test of nonlocal causality
Ringbauer, Martin; Giarmatzi, Christina; Chaves, Rafael; Costa, Fabio; White, Andrew G.; Fedrizzi, Alessandro
2016-01-01
Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell’s local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect. PMID:27532045
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
We investigate the effects of nonlocal response on the surface-plasmon polariton guiding properties of the metal-insulator (MI), metal-insulator-metal (MIM), and insulator-metal-insulator (IMI) waveguides. The nonlocal effects are described by a linearized hydrodynamic model, which includes...... in the metal. We also show that nonlocality breaks the complementarity of the MIM and IMI waveguides found in the nonretarded limit....
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...
A mixed SOC-turbulence model for nonlocal transport and space-fractional Fokker-Planck equation
Milovanov, Alexander V
2013-01-01
The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid turbulence, and the ideas of avalanching behavior, associable with self-organized critical (SOC) behavior. Using statistical arguments, it is shown that an amplification mechanism is needed to introduce nonlocality into dynamics. We obtain a consistent derivation of nonlocal Fokker-Planck equation with space-fractional derivatives from a stochastic Markovian process with the transition probabilities defined in reciprocal space.
A mixed SOC-turbulence model for nonlocal transport and Lévy-fractional Fokker–Planck equation
Energy Technology Data Exchange (ETDEWEB)
Milovanov, Alexander V. [ENEA National Laboratory, Centro Ricerche Frascati, I-00044 Frascati, Rome (Italy); Department of Space Plasma Physics, Space Research Institute, Russian Academy of Sciences, 117997 Moscow (Russian Federation); Juul Rasmussen, Jens [Physics Department, Technical University of Denmark, DK-2800 Kgs. Lyngby (Denmark)
2014-04-01
The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid turbulence, and the ideas of avalanching behavior, associable with self-organized critical (SOC) behavior. Using statistical arguments, it is shown that an amplification mechanism is needed to introduce nonlocality into dynamics. We obtain a consistent derivation of nonlocal Fokker–Planck equation with space-fractional derivatives from a stochastic Markov process with the transition probabilities defined in reciprocal space. The hybrid model observes the Sparre Andersen universality and defines a new universality class of SOC.
Lin, D H
2003-01-01
Partial wave theory of a three dmensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard shere'' like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermion and boson model in the fractional quantum Hall effect. Since the nonlocal quantum interference of magnetic flux on the charged particles is universal, the nonlocal effect is expected to appear in quite general potential system and will be useful in understanding some other phenomena in mesoscopic phyiscs.
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.
Dispersive shock waves with nonlocal nonlinearity
Barsi, Christopher; Sun, Can; Fleischer, Jason W
2007-01-01
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Family of nonlocal bound entangled states
Yu, Sixia; Oh, C. H.
2017-03-01
Bound entanglement, being entangled yet not distillable, is essential to our understanding of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we construct this kind of nonlocal bound entangled state for all finite dimensions larger than two, making possible their experimental demonstration in most general systems. We propose a Bell inequality, based on a Hardy-type argument for nonlocality, and a steering inequality to identify their nonlocality. We also provide a family of entanglement witnesses to detect their entanglement beyond the Bell inequality and the steering inequality.
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...
Symmetric states: Their nonlocality and entanglement
Energy Technology Data Exchange (ETDEWEB)
Wang, Zizhu; Markham, Damian [CNRS LTCI, Département Informatique et Réseaux, Telecom ParisTech, 23 avenue d' Italie, CS 51327, 75214 Paris CEDEX 13 (France)
2014-12-04
The nonlocality of permutation symmetric states of qubits is shown via an extension of the Hardy paradox and the extension of the associated inequality. This is achieved by using the Majorana representation, which is also a powerful tool in the study of entanglement properties of symmetric states. Through the Majorana representation, different nonlocal properties can be linked to different entanglement properties of a state, which is useful in determining the usefulness of different states in different quantum information processing tasks.
On a Nonlocal Damping Model in Ferromagnetism
Directory of Open Access Journals (Sweden)
M. Moumni
2015-01-01
Full Text Available We consider a mathematical model describing nonlocal damping in magnetization dynamics. The model consists of a modified form of the Landau-Lifshitz-Gilbert (LLG equation for the evolution of the magnetization vector in a rigid ferromagnet. We give a global existence result and characterize the long time behaviour of the obtained solutions. The sensitivity of the model with respect to large and small nonlocal damping parameters is also discussed.
Quantum theory of nonlocal nonlinear Schrodinger equation
Vyas, Vivek M
2015-01-01
Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.
Experimental falsification of Leggett's nonlocal variable model.
Branciard, Cyril; Ling, Alexander; Gisin, Nicolas; Kurtsiefer, Christian; Lamas-Linares, Antia; Scarani, Valerio
2007-11-23
Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also, some models based on nonlocal variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In this Letter, we introduce a family of inequalities, which use a finite number of measurement settings, and which therefore allow testing Leggett's nonlocal model versus quantum physics. Our experimental data falsify Leggett's model and are in agreement with quantum predictions.
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.
Nonlocal Infrared Modifications of Gravity. A Review
Maggiore, Michele
2016-01-01
We review an approach developed in the last few years by our group in which GR is modified in the infrared, at an effective level, by nonlocal terms associated to a mass scale. We begin by recalling the notion of quantum effective action and its associated nonlocalities, illustrating some of their features with the anomaly-induced effective actions in $D=2$ and $D=4$. We examine conceptual issues of nonlocal theories such as causality, degrees of freedoms and ghosts, stressing the importance of the fact that these nonlocalities only emerge at the effective level. We discuss a particular class of nonlocal theories where the nonlocal operator is associated to a mass scale, and we show that they perform very well in the comparison with cosmological observations, to the extent that they fit CMB, supernovae, BAO and structure formation data at a level fully competitive with $\\Lambda$CDM, with the same number of free parameters. We explore some extensions of these `minimal' models, and we finally discuss some direc...
Effects of Nonlocality on Transfer Reactions
Titus, Luke J
2016-01-01
We solved the nonlocal scattering and bound state equations using the Perey-Buck type interaction, and compared to local equivalent calculations. Using the distorted wave Born approximation we construct the T-matrix for (p,d) transfer on 17O, 41Ca, 49Ca, 127Sn, 133Sn, and 209Pb at 20 and 50 MeV. Additionally we studied (p,d) reactions on 40Ca using the the nonlocal dispersive optical model. We have also included nonlocality consistently into the adiabatic distorted wave approximation and have investigated the effects of nonlocality on on (d,p) transfer reactions for deuterons impinged on 16O, 40Ca, 48Ca, 126Sn, 132Sn, 208Pb at 10, 20, and 50 MeV. We found that for bound states the Perry corrected wave functions resulting from the local equation agreed well with that from the nonlocal equation in the interior region, but discrepancies were found in the surface and peripheral regions. Overall, the Perey correction factor was adequate for scattering states, with the exception for a few partial waves. Nonlocality...
Let's call it Nonlocal Quantum Physics
Requardt, M
2000-01-01
In the following we undertake to derive quantum theory as a stochastic low-energy and coarse-grained theory from a more primordial discrete and basically geometric theory living on the Planck scale and which (as we argue) possibly underlies also \\tit{string theory}. We isolate the so-called \\tit{ideal elements} which represent at the same time the cornerstones of the framework of ordinary quantum theory and show how and why they encode the \\tit{non-local} aspects, being ubiquituous in the quantum realm, in a, on the surface, local way. We show that the quantum non-locality emerges in our approach as a natural consequence of the underlying \\tit{two-storey} nature of space-time or the physical vacuum, that is, quantum theory turns out to be a residual effect of the geometric depth structure of space-time on the Planck scale. We indicate how the \\tit{measurement problem} and the emergence of the \\tit{macroscopic sub-regime} can be understood in this framework.
On the one-loop effective potential in nonlocal supersymmetric theories
de Mello, E R Bezerra; Nascimento, J R; Petrov, A Yu
2016-01-01
Within the superfield approach, we consider the nonlocal generalization of the Wess-Zumino model and calculate the one-loop low-energy contributions to the effective action. Four different nonlocal models are considered, among which only the first model does not reduce to the standard Wess-Zumino model when we take the parameter of nonlocality of the model, $\\Lambda$, much greater than any energy scale; in addition, this model also depends on an extra parameter, $\\xi$. As to the other three models, the result looks like the renormalized effective potential for the usual Wess-Zumino model, where the normalization scale $\\mu$ is replaced by the $\\Lambda$. Moreover, the fourth model displays a divergence which can be eliminated through the appropriate wave function renormalization.
Kunkri, Samir; Choudhary, Sujit K.; Ahanj, Ali; Joag, Pramod
2006-02-01
Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardy’s nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardy’s argument.
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.......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...
Soft Matrix Elements in Non-local Chiral Quark Model
Kotko, Piotr
2009-01-01
Using non-local chiral quark model and currents satisfying Ward-Takahashi identities we analyze Distribution Amplitudes (DA) of photon and pion-to-photon Transition Distribution Amplitudes (TDA) in the low energy regime. Photon DA's are calculated analytically up to twist-4 and reveal several interesting features of photon structure. TDA's calculated in the present model satisfy polynomiality condition. Normalization of vector TDA is fixed by the axial anomaly. We also compute relevant form factors and compare them with existing data. Axial form factor turns out to be much lower then the vector one, what indeed is seen in the experimental data.
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...
Slater's nonlocal exchange potential and beyond
Howard, I. A.; March, N. H.
The local density approximation (LDA) to the exchange potential Vx(r), namely the ρ1/3 electron gas form, was already transcended in Slater's 1951 paper. Here, using Dirac's 1930 form for the exchange energy density γx(r), the Slater (Sl) nonlocal exchange potential V Slx(r) is defined by 2γx(r)/ρ(r). In spherical atomic ions, say the Be or Ne-like series, this form V Slx(r) already has the correct behavior in both r → 0 and r → ∞ limits when known properties of the exchange energy density γx(r) and the ground-state electron density ρ(r) are invoked. As examples, some emphasis will first be given to the use of the so-called 1/Z expansion in such spherical atomic ions, for which analytic results can be obtained for both γx(r) and ρ(r) as the atomic number Z becomes large. The usefulness of the 1/Z expansion is directly demonstrated for the U atomic ion with 18 electrons by comparison with the optimized effective potential prediction. A rather general integral equation for the exchange potential is then proposed. Finally, without appeal to large Z, two-level systems are considered, with specific reference to the Be atom and to the LiH molecule. In all cases treated, the Slater potential V Slx(r) is a valuable starting point, even though it needs appreciable quantitative corrections reflecting directly atomic shell structure.
Tensor decomposition and nonlocal means based spectral CT reconstruction
Zhang, Yanbo; Yu, Hengyong
2016-10-01
As one of the state-of-the-art detectors, photon counting detector is used in spectral CT to classify the received photons into several energy channels and generate multichannel projection simultaneously. However, the projection always contains severe noise due to the low counts in each energy channel. How to reconstruct high-quality images from photon counting detector based spectral CT is a challenging problem. It is widely accepted that there exists self-similarity over the spatial domain in a CT image. Moreover, because a multichannel CT image is obtained from the same object at different energy, images among channels are highly correlated. Motivated by these two characteristics of the spectral CT, we employ tensor decomposition and nonlocal means methods for spectral CT iterative reconstruction. Our method includes three basic steps. First, each channel image is updated by using the OS-SART. Second, small 3D volumetric patches (tensor) are extracted from the multichannel image, and higher-order singular value decomposition (HOSVD) is performed on each tensor, which can help to enhance the spatial sparsity and spectral correlation. Third, in order to employ the self-similarity in CT images, similar patches are grouped to reduce noise using the nonlocal means method. These three steps are repeated alternatively till the stopping criteria are met. The effectiveness of the developed algorithm is validated on both numerically simulated and realistic preclinical datasets. Our results show that the proposed method achieves promising performance in terms of noise reduction and fine structures preservation.
Existence of solutions for a third order non-local equation appearing in crack dynamics
Imbert, Cyril
2010-01-01
In this paper, we prove the existence of non-negative solutions for a non-local third order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann type operator (which can be defined using the periodic Hilbert transform). The main difficulties are due to the fact that this equation is non-local, and that the natural energy estimates are not as good as in the case of the thin film equation.
Cosmological perturbations in SFT inspired non-local scalar field models
Energy Technology Data Exchange (ETDEWEB)
Koshelev, Alexey S. [Vrije Universiteit Brussel and The International Solvay Institutes, Theoretische Natuurkunde, Brussels (Belgium); Vernov, Sergey Yu. [Instituto de Ciencias del Espacio (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Bellaterra, Barcelona (Spain); Lomonosov Moscow State University, Theoretical High Energy Physics Division, Skobeltsyn Institute of Nuclear Physics, Moscow (Russian Federation)
2012-10-15
We study cosmological perturbations in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field and explicitly prove that for the free field it is identical to a system of local cosmological perturbation equations in a particular model with multiple (maybe infinitely many) local free scalar fields. We also show that vector and tensor perturbations are absent in this set-up. (orig.)
Xie, Dexuan; Jiang, Yi
2016-10-01
The nonlocal dielectric approach has been studied for more than forty years but only limited to water solvent until the recent work of Xie et al. (2013) [20]. As the development of this recent work, in this paper, a nonlocal modified Poisson-Boltzmann equation (NMPBE) is proposed to incorporate nonlocal dielectric effects into the classic Poisson-Boltzmann equation (PBE) for protein in ionic solvent. The focus of this paper is to present an efficient finite element algorithm and a related software package for solving NMPBE. Numerical results are reported to validate this new software package and demonstrate its high performance for protein molecules. They also show the potential of NMPBE as a better predictor of electrostatic solvation and binding free energies than PBE.
Wang, Qi; E, Weinan; Liu, Chun; Zhang, Pingwen
2002-05-01
The Doi kinetic theory for flows of homogeneous, rodlike liquid crystalline polymers (LCPs) is extended to model flows of nonhomogeneous, rodlike LCPs through a nonlocal (long-range) intermolecular potential. The theory features (i) a nonlocal, anisotropic, effective intermolecular potential in an integral form that is consistent with the chemical potential, (ii) short-range elasticity as well as long-range isotropic and anisotropic elasticity, (iii) a closed-form stress expression accounting for the nonlocal molecular interaction, and (iv) an extra elastic body force exclusively associated with the integral form of the intermolecular potential. With the effective intermolecular potential, the theory is proven to be well posed in that it warrants a positive entropy production and thereby the second law of thermodynamics. Approximate theories are obtained by gradient expansions of the number density function in the free energy density.
Nonlocal Response of Metallic Nanospheres Probed by Light, Electrons, and Atoms
DEFF Research Database (Denmark)
Christensen, Thomas; Yan, Wei; Raza, Søren
2014-01-01
Inspired by recent measurements on individual metallic nanospheres that cannot be explained with traditional classical electrodynamics, we theoretically investigate the effects of nonlocal response by metallic nanospheres in three distinct settings: atomic spontaneous emission, electron energy loss...... spectroscopy, and light scattering. These constitute two near-field and one far-field measurements, with zero-, one-, and two-dimensional excitation sources, respectively. We search for the clearest signatures of hydrodynamic pressure waves in nanospheres. We employ a linearized hydrodynamic model, and Mie......–Lorenz theory is applied for each case. Nonlocal response shows its mark in all three configurations, but for the two near-field measurements, we predict especially pronounced nonlocal effects that are not exhibited in far-field measurements. Associated with every multipole order is not only a single...
The charge-asymmetric nonlocally-determined local-electric (CANDLE) solvation model
Sundararaman, Ravishankar
2014-01-01
Many important applications of electronic structure methods involve molecules or solid surfaces in a solvent medium. Since explicit treatment of the solvent in such methods is usually not practical, calculations often employ continuum solvation models to approximate the effect of the solvent. Previous solvation models either involve a parametrization based on atomic radii, which limits the class of applicable solutes, or based on solute electron density, which is more general but less accurate, especially for charged systems. We develop an accurate and general solvation model that includes a cavity that is a nonlocal functional of both solute electron density and potential, local dielectric response on this nonlocally-determined cavity, and nonlocal approximations to the cavity-formation and dispersion energies. The dependence of the cavity on the solute potential enables an explicit treatment of the solvent charge asymmetry. With only three parameters per solvent, this `CANDLE' model simultaneously reproduce...
Dynamics in Nonlocal Cosmological Models Derived from String Field Theory
Joukovskaya, Liudmila
2007-01-01
A general class of nonlocal cosmological models is considered. A new method for solving nonlocal Friedmann equations is proposed, and solutions of the Friedmann equations with nonlocal operator are presented. The cosmological properties of these solutions are discussed. Especially indicated is $p$-adic cosmological model in which we have obtained nonsingular bouncing solution and string field theory tachyon model in which we have obtained full solution of nonlocal Friedmann equations with $w=...
Nonlocal Optics of Plasmonic Nanowire Metamaterials
Wells, Brian M; Podolskiy, Viktor A
2014-01-01
We present an analytical description of the nonlocal optical response of plasmonic nanowire metamaterials that enable negative refraction, subwavelength light manipulation, and emission lifetime engineering. We show that dispersion of optical waves propagating in nanowire media results from coupling of transverse and longitudinal electromagnetic modes supported by the composite and derive the nonlocal effective medium approximation for this dispersion. We derive the profiles of electric field across the unit cell, and use these expressions to solve the long-standing problem of additional boundary conditions in calculations of transmission and reflection of waves by nonlocal nanowire media. We verify our analytical results with numerical solutions of Maxwell's equations and discuss generalization of the developed formalism to other uniaxial metamaterials.
Transfer reaction code with nonlocal interactions
Titus, L J; Nunes, F M
2016-01-01
We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, $(d,N)$ or $(N,d)$, including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of $A(d,N)B$ or $B(N,d)A$. Details on the implementation of the T-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided. This code is suitable to be applied for deuteron induced reactions in the range of $E_d=10-70$ MeV, and provides cross sections with $4\\%$ accuracy.
Transfer reaction code with nonlocal interactions
Titus, L. J.; Ross, A.; Nunes, F. M.
2016-10-01
We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, (d , N) or (N , d) , including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of A(d , N) B or B(N , d) A. Details on the implementation of the T-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided. This code is suitable to be applied for deuteron induced reactions in the range of Ed =10-70 MeV, and provides cross sections with 4% accuracy.
Towards an emerging understanding of non-locality phenomena and non-local transport
Ida, K.; Shi, Z.; Sun, H. J.; Inagaki, S.; Kamiya, K.; Rice, J. E.; Tamura, N.; Diamond, P. H.; Dif-Pradalier, G.; Zou, X. L.; Itoh, K.; Sugita, S.; Gürcan, O. D.; Estrada, T.; Hidalgo, C.; Hahm, T. S.; Field, A.; Ding, X. T.; Sakamoto, Y.; Oldenbürger, S.; Yoshinuma, M.; Kobayashi, T.; Jiang, M.; Hahn, S. H.; Jeon, Y. M.; Hong, S. H.; Kosuga, Y.; Dong, J.; Itoh, S.-I.
2015-01-01
In this paper, recent progress on experimental analysis and theoretical models for non-local transport (non-Fickian fluxes in real space) is reviewed. The non-locality in the heat and momentum transport observed in the plasma, the departures from linear flux-gradient proportionality, and externally triggered non-local transport phenomena are described in both L-mode and improved-mode plasmas. Ongoing evaluation of ‘fast front’ and ‘intrinsically non-local’ models, and their success in comparisons with experimental data, are discussed
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...
Nonlocal regularization of abelian models with spontaneous symmetry breaking
Clayton, M. A.
2001-01-01
We demonstrate how nonlocal regularization is applied to gauge invariant models with spontaneous symmetry breaking. Motivated by the ability to find a nonlocal BRST invariance that leads to the decoupling of longitudinal gauge bosons from physical amplitudes, we show that the original formulation of the method leads to a nontrivial relationship between the nonlocal form factors that can appear in the model.
Nonlocality and entanglement as opposite properties
Vallone, G; Gómez, E S; Cañas, G; Larsson, J -A; Mataloni, P; Cabello, A
2011-01-01
We show that, for any chained Bell inequality with any number of settings, nonlocality and entanglement are not only essentially different properties but opposite ones. We first show that, in the absence of noise, the threshold detection efficiency for a loophole-free Bell test increases with the degree of entanglement, so that the closer the quantum states are to product states, the harder it is to reproduce the quantum predictions with local models. In the presence of white noise, we show that nonlocality and entanglement are simultaneously maximized only in the presence of extreme noise; in any other case, the lowest threshold detection efficiency is obtained by reducing the entanglement.
A Classical Framework for Nonlocality and Entanglement
Groessing, Gerhard; Pascasio, Johannes Mesa; Schwabl, Herbert
2012-01-01
Based on our model of quantum systems as emerging from the coupled dynamics between oscillating "bouncers" and the space-filling zero-point field, a sub-quantum account of nonlocal correlations is given. This is explicitly done for the example of the "double two-slit" variant of two-particle interferometry. However, it is also shown that the entanglement in two-particle interferometry is only a natural consequence of the fact that already a "single" two-slit experiment can be described on a sub-quantum level with the aid of "entangling currents" of a generally nonlocal nature.
Compressive Sensing via Nonlocal Smoothed Rank Function.
Fan, Ya-Ru; Huang, Ting-Zhu; Liu, Jun; Zhao, Xi-Le
2016-01-01
Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction.
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.
Breather solitons in highly nonlocal media
Alberucci, Alessandro; Assanto, Gaetano
2016-01-01
We investigate the breathing of optical spatial solitons in highly nonlocal media. Generalizing the Ehrenfest theorem, we demonstrate that oscillations in beam width obey a fourth-order ordinary differential equation. Moreover, in actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell [Science \\textbf{276}, 1538 (1997)] cannot accurately describe the dynamics of self-confined beams as the transverse size oscillations have a period which not only depends on power but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.
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 t...... 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....
Liang, Lin-mei; Li, Cheng-zu
2005-02-01
This Letter presents nonlocality without inequalities for two-qubit mixed states. This Letter was mainly sparked by Cabello's work [Phys. Rev. A 65 (2003) 032108] and is an extension of our recent work [Phys. Lett. A 318 (2003) 300].
Interaction of Nonlocal Incoherent White-Light Solitons
Institute of Scientific and Technical Information of China (English)
HUANG Chun-Fu; GUO Qi
2007-01-01
The propagation and interaction of nonlocal incoherent white-light solitons in strongly nonlocal kerr media is investigated. Numerical simulations show that the interaction properties of nonlocal incoherent white-light solitons are different from the case in local media. The interactions of nonlocal incoherent white-light solitons are always attractive independent of their relative phase, while the other parameters such as the extent of nonlocality and the input power have a great impact on the soliton interactions. Pertinent numerical examples are presented to show their propagation and interaction behaviour further.
Consequences and applications of the completeness of Hardy's nonlocality
Mansfield, Shane
2017-02-01
Logical nonlocality is completely characterized by Hardy's "paradox" in (2 ,2 ,l ) and (2 ,k ,2 ) scenarios. We consider a variety of consequences and applications of this fact. (i) Polynomial algorithms may be given for deciding logical nonlocality in these scenarios. (ii) Bell states are the only entangled two-qubit states which are not logically nonlocal under projective measurements. (iii) It is possible to witness Hardy nonlocality with certainty in a simple tripartite quantum system. (iv) Noncommutativity of observables is necessary and sufficient for enabling logical nonlocality.
Directory of Open Access Journals (Sweden)
M. Denche
1999-01-01
Full Text Available In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as regularity conditions, which guarantee the coerciveness for both the space variable and the spectral parameter, as well as guarantee the completeness of the system of root functions. The results obtained are then applied to the study of a nonlocal parabolic transmission problem.
Nonlocality as Evidence for a Multiverse Cosmology
Tipler, Frank J.
We show that observations of quantum nonlocaltiy can be interpreted as purely local phenomena, provided one assumes that the cosmos is a multiverse. Conversely, the observation of quantum nonlocality can be interpreted as observation evidence for a multiverse cosmology, just as observation of the setting of the Sun can be interpreted as evidence for the Earth's rotation.
Nonlocal dynamics of dissipative phononic fluids
Nemati, Navid; Lee, Yoonkyung E.; Lafarge, Denis; Duclos, Aroune; Fang, Nicholas
2017-06-01
We describe the nonlocal effective properties of a two-dimensional dissipative phononic crystal made by periodic arrays of rigid and motionless cylinders embedded in a viscothermal fluid such as air. The description is based on a nonlocal theory of sound propagation in stationary random fluid/rigid media that was proposed by Lafarge and Nemati [Wave Motion 50, 1016 (2013), 10.1016/j.wavemoti.2013.04.007]. This scheme arises from a deep analogy with electromagnetism and a set of physics-based postulates including, particularly, the action-response procedures, whereby the effective density and bulk modulus are determined. Here, we revisit this approach, and clarify further its founding physical principles through presenting it in a unified formulation together with the two-scale asymptotic homogenization theory that is interpreted as the local limit. Strong evidence is provided to show that the validity of the principles and postulates within the nonlocal theory extends to high-frequency bands, well beyond the long-wavelength regime. In particular, we demonstrate that up to the third Brillouin zone including the Bragg scattering, the complex and dispersive phase velocity of the least-attenuated wave in the phononic crystal which is generated by our nonlocal scheme agrees exactly with that reproduced by a direct approach based on the Bloch theorem and multiple scattering method. In high frequencies, the effective wave and its associated parameters are analyzed by treating the phononic crystal as a random medium.
Ring vortex solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Briedis, D.; Petersen, D.E.; Edmundson, D.;
2005-01-01
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....
Nonlocality and discrete cellular methods in optics
Wijers, C.M.J.; Boeij, de P.L.
2001-01-01
A subdivision of space into discrete cells underlies the traditional discrete dipole model. This model presumes that only nonlocal electric interactions between cells govern the electromagnetic response of a condensed matter system. Apart from the case of simple dielectrics, this is not realistic. C
Modeling elastic tensile fractures in snow using nonlocal damage mechanics
Borstad, C. P.; McClung, D. M.
2011-12-01
The initiation and propagation of tensile fractures in snow and ice are fundamental to numerous important physical processes in the cryosphere, from iceberg calving to ice shelf rift propagation to slab avalanche release. The heterogeneous nature of snow and ice, their proximity to the melting temperature, and the varied governing timescales typically lead to nonlinear fracture behavior which does not follow the predictions of Linear Elastic Fracture Mechanics (LEFM). Furthermore, traditional fracture mechanics is formally inapplicable for predicting crack initiation in the absence of a pre-existing flaw or stress concentration. An alternative to fracture mechanics is continuum damage mechanics, which accounts for the material degradation associated with cracking in a numerically efficient framework. However, damage models which are formulated locally (e.g. stress and strain are defined as point properties) suffer from mesh-sensitive crack trajectories, spurious localization of damage and improper fracture energy dissipation with mesh refinement. Nonlocal formulations of damage, which smear the effects of the material heterogeneity over an intrinsic length scale related to the material microstructure, overcome these difficulties and lead to numerically efficient and mesh-objective simulations of the tensile failure of heterogeneous materials. We present the results of numerical simulations of tensile fracture initiation and propagation in cohesive snow using a nonlocal damage model. Seventeen beam bending experiments, both notched and unnotched, were conducted using blocks of cohesive dry snow extracted from an alpine snowpack. Material properties and fracture parameters were calculated from the experimental data using beam theory and quasi-brittle fracture mechanics. Using these parameters, a nonlocal isotropic damage model was applied to two-dimensional finite element meshes of the same scale as the experiments. The model was capable of simulating the propagation
Circumferential nonlocal effect on the buckling and vibration of nanotubes
Energy Technology Data Exchange (ETDEWEB)
Wang, Cheng Yuan, E-mail: cywang@ujs.edu.cn; Li, Xiao Hu; Luo, Ying
2016-04-01
The nonlocal beam theories are widely used to study the mechanics of cylindrical nanotubes (NTs). The one-dimensional models however are unable to account for the nonlocal effect in the circumferential direction, which may substantially affect the applicability of the nonlocal beam models. To address the issue this letter examines the circumferential nonlocal effect (CNE) on the buckling and vibration of the NTs. Here the CNE is characterized by the difference between the nonlocal beam model considering the axial nonlocal effect only and the nonlocal shell model with both axial and circumferential nonlocal effects. The aspect ratio and radius-dependence of the CNE are calculated for the singlewall carbon NTs selected as a typical example. The results show that the CNE is substantial for the buckling and vibration of the NTs with small radius (e.g., <1 nm) and aspect ratio (e.g., <15). It however decreases with the rising radius and the aspect ratio, and turns out to be small for relatively wide and long NTs. The nonlocal beam theories thus may overestimate the buckling load and vibration frequency for the thin and short NTs. - Highlights: • First revealed the substantial circumferential nonlocal effect (CNE) on nanotube buckling. • Achieved radius/aspect ratio-dependence of CNE on nanotube buckling and vibration. • Located the range of applicability of the nonlocal beam theory without CNE.
Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling
Hackett-Jones, Emily J.
2012-04-17
Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations. © 2012 American Physical Society.
Entanglement-based quantum communication secured by nonlocal dispersion cancellation
Lee, Catherine; Zhang, Zheshen; Steinbrecher, Gregory R.; Zhou, Hongchao; Mower, Jacob; Zhong, Tian; Wang, Ligong; Hu, Xiaolong; Horansky, Robert D.; Verma, Varun B.; Lita, Adriana E.; Mirin, Richard P.; Marsili, Francesco; Shaw, Matthew D.; Nam, Sae Woo; Wornell, Gregory W.; Wong, Franco N. C.; Shapiro, Jeffrey H.; Englund, Dirk
2014-12-01
Quantum key distribution (QKD) enables participants to exchange secret information over long distances with unconditional security. However, the performance of today's QKD systems is subject to hardware limitations, such as those of available nonclassical-light sources and single-photon detectors. By encoding photons in high-dimensional states, the rate of generating secure information under these technical constraints can be maximized. Here, we demonstrate a complete time-energy entanglement-based QKD system with proven security against the broad class of arbitrary collective attacks. The security of the system is based on nonlocal dispersion cancellation between two time-energy entangled photons. This resource-efficient QKD system is implemented at telecommunications wavelength, is suitable for optical fiber and free-space links, and is compatible with wavelength-division multiplexing.
Manifestation of nonlocal electron-electron interaction in graphene
Ulstrup, Søren; Schüler, Malte; Bianchi, Marco; Fromm, Felix; Raidel, Christian; Seyller, Thomas; Wehling, Tim; Hofmann, Philip
2016-08-01
Graphene is an ideal platform to study many-body effects due to its semimetallic character and the possibility to dope it over a wide range. Here we study the width of graphene's occupied π band as a function of doping using angle-resolved photoemission. Upon increasing electron doping, we observe the expected shift of the band to higher binding energies. However, this shift is not rigid and the bottom of the band moves less than the Dirac point. We show that the observed shift cannot be accounted for by single-particle effects and local self-energies alone, but that nonlocal many-body effects, in particular exchange interactions, must be taken into account.
Generalized Klein-Gordon and Dirac Equations from Nonlocal Kinetic Approach
El-Nabulsi, Rami Ahmad
2016-09-01
In this note, I generalized the Klein-Gordon and the Dirac equations by using Suykens's nonlocal-in-time kinetic energy approach, which is motivated from Feynman's kinetic energy functional formalism where the position differences are shifted with respect to one another. I proved that these generalized equations are similar to those obtained in literature in the presence of minimal length based on the Quesne-Tkachuk algebra.
Possible detection of causality violation in a non-local scalar model
Energy Technology Data Exchange (ETDEWEB)
Haque, Asrarul; Joglekar, Satish D [Department of Physics, IIT Kanpur, Kanpur 208016 (India)], E-mail: ahaque@iitk.ac.in, E-mail: sdj@iitk.ac.in
2009-02-13
We consider the possibility that there may be causality violation detectable at higher energies. We take a scalar non-local theory containing a mass scale {lambda} as a model example and make a preliminary study of how the causality violation can be observed. We show how to formulate an observable whose detection would signal causality violation. We study the range of energies (relative to {lambda}) and couplings to which the observable can be used.
Classification of scalar and dyadic nonlocal optical response models.
Wubs, M
2015-11-30
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, the transverse response, or both. In phenomenological scalar models the nonlocal response is described as a smearing out of the commonly assumed infinitely localized response, as characterized by a distribution with a finite width. Here we calculate explicitly whether and how tensorial models, such as the hydrodynamic Drude model and generalized nonlocal optical response theory, follow this phenomenological description. We find considerable differences, for example that nonlocal response functions, in contrast to simple distributions, assume negative and complex values. Moreover, nonlocal response regularizes some but not all diverging optical near fields. We identify the scalar model that comes closest to the hydrodynamic model. Interestingly, for the hydrodynamic Drude model we find that actually only one third (1/3) of the free-electron response is smeared out nonlocally. In that sense, nonlocal response is stronger for transverse and scalar nonlocal response models, where the smeared-out fractions are 2/3 and 3/3, respectively. The latter two models seem to predict novel plasmonic resonances also below the plasma frequency, in contrast to the hydrodynamic model that predicts standing pressure waves only above the plasma frequency.
Kelly, John V.; O'Brien, Jeff; O'Neill, Feidhlim T.; Gleeson, Michael R.; Sheridan, John T.
2004-10-01
Non-local and non-linear models of photopolymer materials, which include diffusion effects, have recently received much attention in the literature. The material response is non-local as it is assumed that monomers are polymerised to form polymer chains and that these chains grow away from a point of initiation. The non-locality is defined in terms of a spatial non-local material response function. The numerical method of solution typically involves retaining either two or four harmonics of the Fourier series of monomer concentration in the calculation. In this paper a general set of equations is derived which allows inclusion of higher number of harmonics for any response function. The numerical convergence for varying number of harmonics retained is investigated with special care being taken to note the effect of the; non-local material variance s, the power law degree k, and the rates of diffusion, D, and polymerisation F0. General non-linear material responses are also included.
Growth of perturbations in nonlocal gravity with non-$\\Lambda$CDM background
Park, Sohyun
2016-01-01
We re-analyze the nonlocal gravity model of Deser and Woodard which was proposed to account for the current phase of cosmic acceleration. We show that the growth of perturbations predicted by this nonlocal gravity model when its background evolution is fixed by some particular non-$\\Lambda$CDM models (models still consistent to the expansion history data) can be substantially lower than when its background is fixed by $\\Lambda$CDM. This can be seen when we consider the background expansion by a dark energy model with a slightly less negative equation of state with respect to cosmological constant. Our results hints towards a fact that the choice of the background expansion can play a crucial role how this nonlocal gravity model can fit the growth history data. While the growth data might show better consistency to GR models (among the background models we studied so far), it seems the nonlocal gravity model studied in this work is able to show comparable consistency to the growth data as well. Showing this co...
Mehralian, Fahimeh; Tadi Beni, Yaghoub; Karimi Zeverdejani, Mehran
2017-09-01
The present paper is concerned with the applicability of nonlocal strain gradient theory for axial buckling analysis of nanotubes. The first order shear deformation theory with the von Kármán geometrical nonlinearity is utilized to establish theoretical formulations. The governing equations and boundary conditions are derived using the minimum potential energy principle. As main purpose of this study, the small length scale parameters are calibrated for the axial buckling problem of carbon nanotubes (CNTs) using molecular dynamics (MDs) simulations. Further the influences of different geometrical and material parameters, such as length and thickness ratio as well as small length scale parameters on the buckling response of nanotubes are studied. It is indicated that the effect of small length scale parameters on the critical buckling load becomes more prominent by increasing thickness and decreasing length ratio. Moreover, the calibrated small length scale parameters presented herein would be useful for the purpose of applying the nonlocal strain gradient theory for the analysis of nanotubes. The calibrated nonlocal strain gradient theory presented herein should be useful for researchers who are using the nonlocal strain gradient shell theories for analysis of micro/nanotubes.
Non-local and nonlinear background suppression method controlled by multi-scale clutter metric
Gong, Jinnan; Hou, Qingyu; Zhang, Wei; Zhi, Xiyang
2015-07-01
To improve the detection performance for non-morphological multi-scale target in IR image containing complex cloud clutter, on basis of cloud scenario self-similarity feature, a non-local and nonlinear background suppression algorithm controlled by multi-scale clutter metric is presented. According to the classical achievements on cloud structure, self-similarity and relativity of cloud clutter on image for target detection is deeply analyzed by classical indicators firstly. Then we establish multi-scale clutter metric method based on LoG operator to describe scenes feature for controlled suppression method. After that, non-local means based on optimal strength similarity metric as non-local processing, and multi-scale median filter and on minimum gradient direction as local processing are set up. Finally linear fusing principle adopting clutter metric for local and non-local processing is put forward. Experimental results by two kinds of infrared imageries show that compared with classical and similar methods, the proposed method solves the existing problems of targets energy attenuation and suppression degradation in strongly evolving regions in previous methods. By evaluating indicators, the proposed method has a superior background suppression performance by increasing the BSF and ISCR 2 times at least.
Conroy, Aindriu; Mazumdar, Anupam; Teimouri, Ali
2014-01-01
Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows infinite inverse powers of the d'Alembertian operator, resulting in infrared non-local extensions of general relativity. The field equations are derived in full generality and their consistency is checked by verifying the Bianchi identities. The weak-field limit is computed and a straightforward algorithm is presented to infer the post-Newtonian corrections directly from the action. We then apply this to various infrared gravity models including non-local $Rf(R/ \\Box)$ cosmology and non-local dark energy and massive gravity models. Generically the Newtonian potentials are not identical and deviate from the $1/r$ behaviour at large distances. However, the former does not occur in a specific class of theories that does not introduce additional degrees of freedom in flat spacetime. A new nonlocal model within this class is proposed, defined by the exponential of the inverse d'Alembertian. This model ...
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.
Nonlocal diffusion second order partial differential equations
Benedetti, I.; Loi, N. V.; Malaguti, L.; Taddei, V.
2017-02-01
The paper deals with a second order integro-partial differential equation in Rn with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied. The dynamic is transformed into an abstract setting and the results come from an approximation solvability method. It combines a Schauder degree argument with an Hartman-type inequality and it involves a Scorza-Dragoni type result. The compact embedding of a suitable Sobolev space in the corresponding Lebesgue space is the unique amount of compactness which is needed in this discussion. The solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces.
Quantum Loops in Non-Local Gravity
Talaganis, Spyridon
2015-01-01
In this proceedings, I will consider quantum aspects of a non-local, infinite-derivative scalar field theory - a ${\\it toy \\, model}$ depiction of a covariant infinite-derivative, non-local extension of Einstein's general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it ${\\it asymptotically \\, free}$, thus providing strong prospects of resolving various classical and quantum divergences. In particular, I will find that at $1$-loop, the $2$-point function is still divergent, but once this amplitude is renormalized by adding appropriate counter terms, the ultraviolet (UV) behavior of all other $1$-loop diagrams as well as the $2$-loop, $2$-point function remains well under control. I will go on to discuss how one may be able to generalize our computations and arguments to arbitrary loops.
Nonlocal Condensate Model for QCD Sum Rules
Hsieh, Ron-Chou
2009-01-01
We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the K$\\ddot{\\mathrm{a}}$ll$\\acute{\\mathrm{e}}$n-Lehmann representation for a dressed fermion propagator, in which a negative spectral density function manifests their nonperturbative nature. Applying our formalism to the pion form factor as an example, QSR results are in good agreement with data for momentum transfer squared up to $Q^2 \\approx 10 $ GeV$^2$. It is observed that the nonlocal quark-condensate contribution descends like $1/Q^4$, different from the exponential decrease in $Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.
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...... averaging through both HDM and the recent Generalized Nonlocal Optical Response (GNOR) theory, which apart from the resonance frequency shifts accounts successfully for size-dependent damping as well. We examine NPs made of either ideal Drude-like metals [of plasmon frequency (wavelength) ωp (λp...
An Adaptive Iterated Nonlocal Interferometry Filtering Method
Directory of Open Access Journals (Sweden)
Lin Xue
2014-04-01
Full Text Available Interferometry filtering is one of the key steps in obtain high-precision Digital Elevation Model (DEM and Digital Orthophoto Map (DOM. In the case of low-correlation or complicated topography, traditional phase filtering methods fail in balancing noise elimination and phase preservation, which leads to inaccurate interferometric phase. This paper proposed an adaptive iterated nonlocal interferometry filtering method to deal with the problem. Based on the thought of nonlocal filtering, the proposed method filters the image with utilization of the image redundancy information. The smoothing parameter of the method is adaptive to the interferometry, and automatic iteration, in which the window size is adjusted, is applied to improve the filtering precision. Validity of the proposed method is verified by simulated and real data. Comparison with existed methods is given at the same time.
Nonlocal neurology: beyond localization to holonomy.
Globus, G G; O'Carroll, C P
2010-11-01
The concept of local pathology has long served neurology admirably. Relevant models include self-organizing nonlinear brain dynamics, global workspace and dynamic core theories. However such models are inconsistent with certain clinical phenomena found in Charles Bonnet syndrome, disjunctive agnosia and schizophrenia, where there is disunity of content within the unity of consciousness. This is contrasted with the split-brain case where there is disunity of content and disunity of consciousnesses. The development of quantum brain theory with it nonlocal mechanisms under the law of the whole ("holonomy") offers new possibilities for explaining disintegration within unity. Dissipative quantum brain dynamics and its approach to the binding problem, memory and consciousness are presented. A nonlocal neurology armed with a holonomic understanding might see more deeply into what clinical neurology has always aspired to: the patient as a whole.
Non-local geometry inside Lifshitz horizon
Hu, Qi; Lee, Sung-Sik
2017-07-01
Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U( N ) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.
Surface-enhanced Raman spectroscopy: nonlocal limitations
DEFF Research Database (Denmark)
Toscano, Giuseppe; Raza, S.; Xiao, Sanshui;
2012-01-01
Giant field enhancement and field singularities are a natural consequence of the commonly employed local-response framework. We show that a more general nonlocal treatment of the plasmonic response leads to new and possibly fundamental limitations on field enhancement with important consequences ...... by periodic arrays of half-cylinders (up to 120 nm in radius), we find no enhancement factors exceeding 10 orders of magnitude (10(10)). (C) 2012 Optical Society of America...
Structure of Nonlocal Vacuum Condensate of Quarks
Institute of Scientific and Technical Information of China (English)
周丽娟; 马维兴
2003-01-01
The Dyson-Schwinger formalism is used to derive a fully dressed quark propagator. By use of the derived form of the quark propagator, the structure of non-local quark vacuum condensate is studied, and the values of local quark vacuum condensate as well as quark gluon mixed condensate are calculated. The theoretical predictions are in good agreement with the empirical one used commonly in the literature.
Popper's experiment, Copenhagen Interpretation and Nonlocality
Qureshi, T
2003-01-01
A thought experiment, proposed by Karl Popper, which has been experimentally realized recently, is critically examined. A basic flaw in Popper's argument which has also been prevailing in subsequent debates, is pointed out. It is shown that Popper's experiment can be understood easily within the Copenhagen interpretation of quantum mechanics. An alternate experiment, based on discrete variables, is proposed, which constitutes Popper's test in a clearer way. It refutes the argument of absence of nonlocality in quantum mechanics.
Nonlocal Optical Response of Plasmonic Nanowire Metamaterials
2014-01-01
exceptional properties that are not readily found in nature. There are numerous applications in modern optics which can be realized through the study and...K., R. C. McPhedran, and Vladimir M. Shalaev. " Electrodynamics of metal-dielectric composites and electromagnetic crystals." Physical Review B 62.12...16.10 (2008): 7460-7470. [41] Pokrovsky, A. L., and A. L. Efros. "Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals." Physical
Dual-switching behavior of nonlocal interfaces
Sánchez-Curto, Julio; Chamorro-Posada, Pedro
2017-05-01
Nonlinear interfaces separating two diffusive Kerr-type media exhibit dual switching between total internal reflection and transmission. This property is found within a weakly nonlocal regime when both a nonparaxial treatment of the problem and a full two-dimensional model for carrier diffusion are assumed. The theoretical model is shown to predict an effective cubic-quintic nonlinearity with competing terms that produces such property. The validity of the analysis is contrasted with a full set of numerical simulations.
Fully nonlocal, monogamous and random genuinely multipartite quantum correlations
Aolita, Leandro; Cabello, Adán; Acín, Antonio
2011-01-01
Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and associated to fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality that appears in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy and full random outcomes are thus highly desired properties for multipartite correlations in intrinsically genuine-multipartite cryptographic scenarios. We prove that local measurements on Greenberger-Horne-Zeilinger states, for all local dimension and number of parts, can produce correlations that are fully genuine-multipartite nonlocal, monogamous and with fully random outcomes. A key ingredient in our proof is a multipartite chained Bell inequality detecting genuine-multipartite nonlocality, which we introduce. Finally, we discuss the applications of our results for intrinsically genuine-multipartite cryptographic pr...
FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2001-01-01
The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.
Maximum quantum nonlocality between systems that never interacted
Energy Technology Data Exchange (ETDEWEB)
Cabello, Adán, E-mail: adan@us.es [Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla (Spain)
2012-12-03
We show that there is a stronger form of bipartite quantum nonlocality in which systems that never interacted are as nonlocal as allowed by no-signaling. For this purpose, we first show that nonlocal boxes, theoretical objects that violate a bipartite Bell inequality as much as the no-signaling principle allows and which are physically impossible for most scenarios, are feasible if the two parties have 3 measurements with 4 outputs. Then we show that, in this case, entanglement swapping allows us to prepare mixtures of nonlocal boxes using systems that never interacted. -- Highlights: ► We show quantum correlations as nonlocal as allowed by no-signaling between systems that never interacted. ► We show that nonlocal boxes are feasible if 2 parties have 3 measurements with 4 outputs. ► Experimental implementations of 1 and 2 are proposed.
Nonlocal modeling of granular flows down inclines.
Kamrin, Ken; Henann, David L
2015-01-07
Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused on driven steady-flow problems. For layers thicker than the stopping height, the theoretical flow profiles display a thickness-dependent shape whose features are in agreement with previous discrete particle simulations. We also address the issue of the Froude number of the flows, which has been shown experimentally to collapse as a function of the ratio of layer thickness to stopping height. While the collapse is not obvious, two explanations emerge leading to a revisiting of the history of inertial rheology, which the nonlocal model references for its homogeneous flow response.
Relativistic three-partite non-locality
Montakhab, A
2015-01-01
Bell-like inequalities have been used in order to distinguish non-local quantum pure states by various authors. The behavior of such inequalities under Lorentz transformation has been a source of debate and controversies in the past. In this paper, we consider the two most commonly studied three-particle pure states, that of W and GHZ states which exhibit distinctly different type of entanglement. We discuss the various types of three-particle inequalities used in previous studies and point to their corresponding shortcomings and strengths. Our main result is that if one uses Svetlichny's inequality as the main measure of non-locality and uses the same angles in the rest frame ($S$) as well as the moving frame ($S^{\\prime}$), then maximally violated inequality in $S$ will decrease in the moving frame, and will eventually lead to lack of non-locality ( i.e. satisfaction of inequality) in the $v \\rightarrow c$ limit. This is shown for both GHZ and W states and in two different configurations which are commonly ...
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.
Commutative deformations of general relativity: nonlocality, causality, and dark matter
Energy Technology Data Exchange (ETDEWEB)
De Vegvar, P.G.N. [SWK Research, Bellingham, WA (United States)
2017-01-15
Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on commutative manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter fields are utilized to generate self-consistent Abelian Drinfeld twists in a background independent manner and their continuous and discrete symmetries are examined. There is negligible experimental effect on the standard model of particles. While baryonic twist producing matter would begin to behave acausally for rest masses above ∝1-10 TeV, other possibilities are viable dark matter candidates or a right-handed neutrino. First order deformed Maxwell equations are derived and yield immeasurably small cosmological dispersion and produce a propagation horizon only for photons at or above Planck energies. This model incorporates dark matter without any appeal to extra dimensions, supersymmetry, strings, grand unified theories, mirror worlds, or modifications of Newtonian dynamics. (orig.)
Commutative deformations of general relativity: nonlocality, causality, and dark matter
de Vegvar, P G N
2016-01-01
Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on \\emph{commutative} manifolds. A classical nonlocality length scale is produced above which standard light cone causality emerges. We introduce a sector of matter fields to generate selfconsistent Abelian Drinfeld twists in a background independent manner and study their discrete and gauge symmetries. They naturally give rise to dark matter candidates, possibly including ground state condensates. First order deformed Maxwell equations are derived and yield negligible cosmological dispersion and produce a propagation horizon only for photons approaching Planck energies. This model incorporates dark matter without any appeal to extra dimensions, supersymmetry, strings, branes, mirror worlds, or modifications of Newtonian dynamics.
Nonlocal Nambu-Jona-Lasinio model and chiral chemical potential
Frasca, Marco
2016-01-01
We derive the critical temperature in a nonlocal Nambu-Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the gluon propagator in Yang-Mills theory and has the property to fit in excellent way the form factor arising from the instanton liquid picture for the vacuum of the theory. Nambu-Jona-Lasinio model is derived form quantum chromodynamics providing all the constants of the theory without any need for fits. We show that the critical temperature in this case always exists and increases as the square of the chiral chemical potential. The expression we obtain for the critical temperature depends on the mass gap that naturally arises from Yang-Mills theory at low-energy as also confirmed by lattice computations.
The frustrated Brownian motion of nonlocal solitary waves
Folli, Viola
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 non-paraxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equation
The non-local content of quantum operations
Collins, D; Popescu, S; Collins, Daniel; Linden, Noah; Popescu, Sandu
2000-01-01
We show that quantum operations on multi-particle systems have a non-local content; this mirrors the non-local content of quantum states. We introduce a general framework for discussing the non-local content of quantum operations, and give a number of examples. Quantitative relations between quantum actions and the entanglement and classical communication resources needed to implement these actions are also described. We also show how entanglement can catalyse classical communication from a quantum action.
A Nonlocal Model for Carbon Nanotubes under Axial Loads
Directory of Open Access Journals (Sweden)
Raffaele Barretta
2013-01-01
Full Text Available Various beam theories are formulated in literature using the nonlocal differential constitutive relation proposed by Eringen. A new variational framework is derived in the present paper by following a consistent thermodynamic approach based on a nonlocal constitutive law of gradient-type. Contrary to the results obtained by Eringen, the new model exhibits the nonlocality effect also for constant axial load distributions. The treatment can be adopted to get new benchmarks for numerical analyses.
Proposal for revealing quantum nonlocality via local contextuality.
Cabello, Adán
2010-06-04
Two distant systems can exhibit quantum nonlocality even though the correlations between them admit a local model. This nonlocality can be revealed by testing extra correlations between successive measurements on one of the systems which do not admit a noncontextual model whatever the reduced state of this system is. This shows that quantum contextuality plays a fundamental role in quantum nonlocality, and allows an experimental test of the Kochen-Specker with locality theorem.
Kiani, Keivan
2011-10-01
The potential applications of nanoplates in energy storage, chemical and biological sensors, solar cells, field emission, and transporting of nanocars have been attracted the attentions of the nanotechnology community to them during recent years. Herein, the later application of nanoplates from nonlocal elastodynamic point of view is of interest. To this end, dynamic response of a nanoplate subjected to a moving nanoparticle is examined within the context of nonlocal continuum theory of Eringen. The fully simply supported nanoplate is modeled based on the nonlocal Kirchhoff, Mindlin, and higher-order plate theories. The non-dimensional equations of motion of the nonlocal plate models are established. The effects of moving nanoparticle's weight and existing friction between the surfaces of the moving nanoparticle and nanoplate on the in-plane and out-of-plane vibrations of the nanoplate are incorporated into the formulations of the proposed models. The eigen function expansion and the Laplace transform methods are employed for discretization of the governing equations in the spatial and the time domains, respectively. The analytical expressions of the dynamic deformation field associated with each nonlocal plate theory are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight path (an opened path) as well as an ellipse path (a closed path). The dynamic in-plane forces and moments of each nonlocal plate model are also derived. Furthermore, the critical velocity and the critical angular velocity of the moving nanoparticle for the proposed models are expressed analytically for the aforementioned paths. Part II of this work consists in a comprehensive parametric study where the effects of influential parameters on dynamic response of the proposed nonlocal plate models are scrutinized in some detail.
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.
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.
Implementation of nonlocal quantum swap operation on two entangled pairs
Institute of Scientific and Technical Information of China (English)
郑亦庄; 顾永建; 陈立冰; 郭光灿
2002-01-01
We propose a scheme for the implementation of nonlocal quantum swap operation on two spatially separated entangled pairs and we show that the operation can swap two qubits of these entangled pairs. We discuss the resourcesof the entangled qubits and classical communication bits required for the optimal implementation of the nonlocal quantum swap operation. We also put forward a scheme for probabilistic implementation of nonlocal swap operation via a nonmaximally entangled quantum channel. The probability of a successful nonlocal swap operation is obtained by introducing a collective unitary transformation.
Nonlocality Sudden Birth and Transfer in System and Environment
Institute of Scientific and Technical Information of China (English)
QIU Liang
2011-01-01
Dynamics of the nonlocality measured by the violation of Svetlichny's Bell-type inequality is investigated in the non-Markovian model. The phenomenon of nonlocality sudden birth for the atoms and the reservoirs is obtained.The evolution of the nonlocality among the atoms or the reservoirs depends on the choice of the atom detuning from the cavity pseudomode, the cavity pseudomode decay and the rotation angles. For the small pseudomode decay in the near-resonance regime, the initial atomic nonlocality is completely transferred to the reservoirs ultimately.
On a Nonlocal Problem Modelling Ohmic Heating in Planar Domains
Institute of Scientific and Technical Information of China (English)
Fei LIANG; Qi Lin LIU; Yu Xiang LI
2013-01-01
In this paper, we consider the nonlocal problem of the form ut-△u=λe-u/(∫Ωe-udx)2,x∈Ω,t>0 and the associated nonlocal stationary problem -△v=λe-v/(∫Ωe-vdx)2,x∈Ω, where A is a positive parameter. For Ω to be an annulus, we prove that the nonlocal stationary problem has a unique solution if and only if λ < 2|(6)Ω|2, and for A = 2|(6)Ω|2, the solution of the nonlocal parabolic problem grows up globally to infinity as t → ∞.
Nonlocal optical properties in periodic lattice of graphene layers.
Chern, Ruey-Lin; Han, Dezhuan
2014-02-24
Based on the effective medium model, nonlocal optical properties in periodic lattice of graphene layers with the period much less than the wavelength are investigated. Strong nonlocal effects are found in a broad frequency range for TM polarization, where the effective permittivity tensor exhibits the Lorentzian resonance. The resonance frequency varies with the wave vector and coincides well with the polaritonic mode. Nonlocal features are manifest on the emergence of additional wave and the occurrence of negative refraction. By examining the characters of the eigenmode, the nonlocal optical properties are attributed to the excitation of plasmons on the graphene surfaces.
Mélin, R.
2006-05-01
In connection with a recent experiment [Russo , Phys. Rev. Lett. 95, 027002 (2005)], we investigate the effect of weak localization on nonlocal transport in normal metal / insulator/superconductor / insulator / normal metal (NISIN) trilayers, with extended interfaces. The negative weak localization contribution to the crossed resistance can exceed in absolute value the positive elastic cotunneling contribution if the normal metal phase coherence length or the energy are large enough.
Webb, G M; McKenzie, J F; Hu, Q; Zank, G P
2013-01-01
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabelling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A nonlocal conservation law for fluid helicity applicable for a non-barotropic fluid involving Clebsch variables is derived using Noether's theorem, in conjunction with a fluid relabelling symmetry and a gauge transformation. A nonlocal cross helicity conservation law involving Clebsch potentials, and the MHD energy conservation law are derived by the same method. An Euler Poincar\\'e variational approach is also used to derive conservation laws associated with fluid relabelling symmetries using Noether's second theorem.
Generating functional and large N limit of nonlocal 2D generalized Yang-Mills theories (nlgYM 2's)
Saaidi, K.; Sajadi, H. M.
2001-01-01
Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) on nonlocal generalized 2D Yang Mills theories (nlgYM_2's), which are nonlocal in the auxiliary field. This has been considered before by Saaidi and Khorrami. Our calculations are done for general surfaces. We find a general expression for the free energy of W(φ) =φ^{2k} in nlgYM_2 theories at the strong coupling phase (SCP) regime (A > A_c) for large groups. In the specific φ^4 model, we show that the theory has a third order phase transition.
Kaganovich, Igor D; Polomarov, Oleg
2003-08-01
In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. 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 nonlocal 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, nonuniform, 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 nonuniform plasma density profile on both the current density profile and the EEDF is demonstrated.
Spin-Hall Non-Local Transport Mediated by a Magnetic Insulator
Ramezani Masir, Massoud; Chen, Hua; Sodemann, Inti; MacDonald, Allan. H.
Magnetic systems with easy-plane order support dissipationless spin supercurrents that can lead to non-local coupling between electrically separated conductors. Recently the electrical properties of a system containing two magnetic multilayer stacks with perpendicular magnetic anisotropy electrodes and a shared easy-plane magnetic layer have been discussed. In this research we discuss a closely related system in which the two conducting channels that are coupled by the easy-plane magnetic layer are co-planar thin film metals with large spin Hall effects. We theoretically explained the non-local relationship between the current-voltage relationships of two thin film metallic conductors. Coupling occurs because both conductors inject spins into the magnetic insulator and because this information is communicated between conductors via exchange interactions within the magnetic system. We investigate the non-local transport properties of the system in the macrospin and long thin nanomagnet limits, deriving conditions for the critical currents and using solutions to the Landau-Liftshitz-Gilbert equation to characterize the dynamic steady state case. This work was supported by as part of SHINES, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # SC0012670.
Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation
Institute of Scientific and Technical Information of China (English)
金艳; 贾曼; 楼森岳
2012-01-01
Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group Jnvariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.
A mixed SOC-turbulence model for nonlocal transport and Lévy-fractional Fokker–Planck equation
DEFF Research Database (Denmark)
Juul Rasmussen, Jens; Milovanov, Alexander V.
2014-01-01
The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid turbulence, and the ideas of avalanching behavior, associable...... with self-organized critical (SOC) behavior. Using statistical arguments, it is shown that an amplification mechanism is needed to introduce nonlocality into dynamics. We obtain a consistent derivation of nonlocal Fokker-Planck equation with space-fractional derivatives from a stochastic Markov process...... with the transition probabilities defined in reciprocal space. The hybrid model observes the Sparre Andersen universality and defines a new universality class of SOC. (C) 2014 Elsevier B.V. All rights reserved....
Directory of Open Access Journals (Sweden)
Obidjon Kh. Abdullaev
2016-06-01
Full Text Available In this work, we study the existence and uniqueness of solutions to non-local boundary value problems with integral gluing condition. Mixed type equations (parabolic-hyperbolic involving the Caputo fractional derivative have loaded parts in Riemann-Liouville integrals. Thus we use the method of integral energy to prove uniqueness, and the method of integral equations to prove existence.
Nonlocal Transport in the Reversed Field Pinch
Energy Technology Data Exchange (ETDEWEB)
Spizzo, G.; White, R. B.; Cappello, S.; Marrelli, L.
2009-09-21
Several heuristic models for nonlocal transport in plasmas have been developed, but they have had a limited possibility of detailed comparision with experimental data. Nonlocal aspects introduced by the existence of a known spectrum of relatively stable saturated tearing modes in a low current reversed field pinch offers a unique possibility for such a study. A numerical modelling of the magnetic structure and associated particle transport is carried out for the reversed-field pinch experiment at the Consorzio RFX, Padova, Italy. A reproduction of the tearing mode spectrum with a guiding center code1 reliably reproduces the observed soft X-ray tomography. Following particle trajectories in the stochastic magnetic field shows the transport across the unperturbed flux surfaces to be due to a spectrum of Levy flights, with the details of the spectrum position dependent. The resulting transport is subdiffusive, and cannot be described by Rechester-Rosenbluth diffusion, which depends on a random phase approximation. If one attempts to fit the local transport phenomenologically, the subdiffusion can be fit with a combination of diffusion and inward pinch2. It is found that whereas passing particles explore the stochastic field and hence participate in Levy flights, the trapped particles experience normal neoclassical diffusion. A two fluid nonlocal Montroll equation is used to model this transport, with a Levy flight defined as the motion of an ion during the period that the pitch has one sign. The necessary input to the Montroll equation consists of a time distribution for the Levy flights, given by the pitch angle scattering operator, and a distribution of the flight distances, determined numerically using a guiding center code. Results are compared to experiment. The relation of this formulation to fractional kinetics is also described.
Nonlocal Crowd Dynamics Models for several Populations
Colombo, Rinaldo M
2011-01-01
This paper develops the basic analytical theory related to some recently introduced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of $\\reali^+$. The results on the stability with respect to the equations are improved. Moreover, here the case of several populations is considered, obtaining the well posedness of systems of multi-D non-local conservation laws. The basic analytical tools are provided by the classical Kruzkov theory of scalar conservation laws in several space dimensions.
The nonlocal elastomagnetoelectrostatics of disordered micropolar media
Energy Technology Data Exchange (ETDEWEB)
Kabychenkov, A. F.; Lisiovskii, F. V., E-mail: lisf@rambler.ru [Russian Academy of Sciences, Kotel’nikov Institute of Radio Engineering and Electronics (Fryazino Branch) (Russian Federation)
2016-08-15
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.
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...
Uncertainty, non-locality and Bell's inequality
Pati, A K
1998-01-01
We derive a Bell-like inequality involving all correlations in local observables with uncertainty free states and show that the inequality is violated in quantum mechanics for EPR and GHZ states. If the uncertainties are allowed in local observables then the statistical predictions of hidden variable theory is well respected in quantum world. We argue that the uncertainties play a key role in understanding the non-locality issues in quantum world. Thus we can not rule out the possibility that a local, realistic hidden variable theory with statistical uncertainties in the observables might reproduce all the results of quantum theory.
NONLOCAL CROWD DYNAMICS MODELS FOR SEVERAL POPULATIONS
Institute of Scientific and Technical Information of China (English)
Rinaldo M. Colombo; Magali Lécureux-Mercier
2012-01-01
This paper develops the basic analytical theory related to some recently introduced crowd dynamics models.Where well posedness was known only locally in time,it is here extended to all of R+.The results on the stability with respect to the equations are improved.Moreover,here the case of several populations is considered,obtaining the well posedness of systems of multi-D non-local conservation laws.The basic analytical tools are provided by the classical Kru(z)kov theory of scalar conservation laws in several space dimensions.
Nonlocal calculation for nonstrange dibaryons and tribaryons
Mota, R D; Fernández, F; Entem, D R; Garcilazo, H
2002-01-01
We study the possible existence of nonstrange dibaryons and tribaryons by solving the bound-state problem of the two- and three-body systems composed of nucleons and deltas. The two-body systems are $NN$, $N\\Delta$, and $\\Delta\\Delta$, while the three-body systems are $NNN$, $NN\\Delta$, $N\\Delta\\Delta$, and $\\Delta\\Delta\\Delta$. We use as input the nonlocal $NN$, $N\\Delta$, and $\\Delta\\Delta$ potentials derived from the chiral quark cluster model by means of the resonating group method. We compare with previous results obtained from the local version based on the Born-Oppenheimer approximation.
Nonlocal formalism for nanoplasmonics: Phenomenological and semi-classical considerations
DEFF Research Database (Denmark)
Mortensen, N. Asger
2013-01-01
The plasmon response of metallic nanostructures is anticipated to exhibit nonlocal dynamics of the electron gas when exploring the true nanoscale. We extend the local-response approximation (based on Ohm's law) to account for a general short-range nonlocal response of the homogeneous electron gas...
Geometric reduction of dynamical nonlocality in nanoscale quantum circuits
Strambini, E.; Makarenko, K. S.; Abulizi, G.; de Jong, M. P.; van der Wiel, W. G.
2016-01-01
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young’s double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for quantum information processing. Here, we present a fundamentally different pathway of losing dynamical nonlocality, demonstrating that the detailed geometry of the detection scheme is crucial to preserve nonlocality. By means of a solid-state quantum-interference experiment we quantify this effect in a diffusive system. We show that interference is not only affected by decoherence, but also by a loss of dynamical nonlocality based on a local reduction of the number of quantum conduction channels of the interferometer. With our measurements and theoretical model we demonstrate that this mechanism is an intrinsic property of quantum dynamics. Understanding the geometrical constraints protecting nonlocality is crucial when designing quantum networks for quantum information processing.
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.
Solutions to nonlocal fractional differential equations using a noncompact semigroup
Directory of Open Access Journals (Sweden)
Shaochun Ji
2013-10-01
Full Text Available This article concerns the existence of solutions to nonlocal fractional differential equations in Banach spaces. By using a type of newly-defined measure of noncompactness, we discuss this problem in general Banach spaces without any compactness assumptions to the operator semigroup. Some existence results are obtained when the nonlocal term is compact and when is Lipschitz continuous.
Geometric reduction of dynamical nonlocality in nanoscale quantum circuits
Strambini, E.; Makarenko, K. S.; Abulizi, G.; de Jong, M. P.; van der Wiel, W. G.
2016-01-01
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young’s double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for quantum information processing. Here, we present a fundamentally different pathway of losing dynamical nonlocality, demonstrating that the detailed geometry of the detection scheme is crucial to preserve nonlocality. By means of a solid-state quantum-interference experiment we quantify this effect in a diffusive system. We show that interference is not only affected by decoherence, but also by a loss of dynamical nonlocality based on a local reduction of the number of quantum conduction channels of the interferometer. With our measurements and theoretical model we demonstrate that this mechanism is an intrinsic property of quantum dynamics. Understanding the geometrical constraints protecting nonlocality is crucial when designing quantum networks for quantum information processing. PMID:26732751
Geometric reduction of dynamical nonlocality in nanoscale quantum circuits
Strambini, E.; Makarenko, K.S.; Abulizi, G.; Jong, de M.P.; Wiel, van der W.G.
2016-01-01
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young’s double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is we
A Note on a Nonlocal Nonlinear Reaction-Diffusion Model
Walker, Christoph
2011-01-01
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.
Nonlocal thin films in calculations of the Casimir force
Esquivel-Sirvent, R.; Svetovoy, V.B.
2005-01-01
The Casimir force is calculated between plates with thin metallic coating. Thin films are described with spatially dispersive (nonlocal) dielectric functions. For thin films the nonlocal effects are more relevant than for half-spaces. However, it is shown that even for film thickness smaller than th
Anomalous interaction of nonlocal solitons in media with competing nonlinearities
DEFF Research Database (Denmark)
Esbensen, B. K.; Bache, Morten; Bang, Ole
2012-01-01
We theoretically investigate properties of individual bright spatial solitons and their interaction in nonlocal media with competing focusing and defocusing nonlinearities. We consider the general case with both nonlinear responses characterized by different strengths and degrees of nonlocality. We...... and interaction of solitons using numerical simulations of the full model of beam propagation. The numerical simulations fully confirm our analytical results....
Spectral dimension from nonlocal dynamics on causal sets
Belenchia, Alessio; Benincasa, Dionigi M. T.; Marcianò, Antonino; Modesto, Leonardo
2016-02-01
We investigate the spectral dimension obtained from nonlocal continuum d'Alembertians derived from causal sets. We find a universal dimensional reduction to two dimensions, in all dimensions. We conclude by discussing the validity and relevance of our results within the broader context of quantum field theories based on these nonlocal dynamics.
Multi-Scale Analysis of Energy Transfer in Scalar Turbulence
Institute of Scientific and Technical Information of China (English)
FANG Le; CUI Gui-Xiang; XU Chun-Xiao; ZHANG Zhao-Shun
2005-01-01
@@ The energy transfer of homogeneous scalar turbulence is studied numerically by triad interaction in spectral space.The different transfer properties between turbulent kinetic energy and turbulent scalar energy reveal that nonlocal energy transfer exists as important as the local energy transfer in scalar turbulence. The non-local energy transfer of scalar turbulence results from non-local triad interaction. As a result there will be longer inertiaconvective range in scalar turbulence than the inertial subrange in turbulent kinetic transfer at Reλ = Peλ. The non-local transfer of turbulent scalar energy generates more energy transfer into dissipation range. The discovery of non-local transfer of turbulent scalar energy indicates that this phenomenon should be concerned carefully in numerical scheme and subgrid modelling of direct numerical simulation or large eddy simulation scalar turbulence.
Origin and effect of nonlocality in a layered composite.
Energy Technology Data Exchange (ETDEWEB)
Silling, Stewart Andrew
2014-01-01
A simple demonstration of nonlocality in a heterogeneous material is presented. By analysis of the microscale deformation of a two-component layered medium, it is shown that nonlocal interactions necessarily appear in a homogenized model of the system. Explicit expressions for the nonlocal forces are determined. The way these nonlocal forces appear in various nonlocal elasticity theories is derived. The length scales that emerge involve the constituent material properties as well as their geometrical dimen- sions. A peridynamic material model for the smoothed displacement eld is derived. It is demonstrated by comparison with experimental data that the incorporation of non- locality in modeling dramatically improves the prediction of the stress concentration in an open hole tension test on a composite plate.
Modulational instability in the nonlocal chi(2)-model
DEFF Research Database (Denmark)
Wyller, John Andreas; Krolikowski, Wieslaw; Bang, Ole
2007-01-01
We investigate in detail the linear regime of the modulational instability (MI) properties of the plane waves of the nonlocal model for chi((2))- media formulated in Nikolov et al. [N.I. Nikolov, D. Neshev, O. Bang, W.Z. Krolikowski, Quadratic solitons as nonlocal solitons, Phys. Rev. E 68 (2003...... in the parameter space for which a fundamental gain band exists, and regions for which higher order gain bands and modulational stability exist. We also show that the MI analysis for the nonlocal model is applicable in the finite walk-off case. Finally, we show that the plane waves of the nonlocal chi((2))-model...... of the nonlocal chi((2))-model, by using the singular perturbational approach. The other branch of the plane waves (i.e. the nonadiabatic branch or the optical branch) is always modulationally unstable. We compare the MI results for the adiabatic branch with the predictions obtained from the full chi((2))-model...
Origin and effect of nonlocality in a layered composite.
Energy Technology Data Exchange (ETDEWEB)
Silling, Stewart Andrew
2014-01-01
A simple demonstration of nonlocality in a heterogeneous material is presented. By analysis of the microscale deformation of a two-component layered medium, it is shown that nonlocal interactions necessarily appear in a homogenized model of the system. Explicit expressions for the nonlocal forces are determined. The way these nonlocal forces appear in various nonlocal elasticity theories is derived. The length scales that emerge involve the constituent material properties as well as their geometrical dimen- sions. A peridynamic material model for the smoothed displacement eld is derived. It is demonstrated by comparison with experimental data that the incorporation of non- locality in modeling dramatically improves the prediction of the stress concentration in an open hole tension test on a composite plate.
Notes on nonlocal projective measurements in relativistic systems
Lin, Shih-Yuin
2013-01-01
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 suppres...
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.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-01
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.
Nonlocalized cluster dynamics and nuclear molecular structure
Zhou, Bo; Horiuchi, Hisashi; Ren, Zhongzhou; Röpke, Gerd; Schuck, Peter; Tohsaki, Akihiro; Xu, Chang; Yamada, Taiichi
2013-01-01
A container picture is proposed for understanding cluster dynamics where the clusters make nonlocalized motion occupying the lowest orbit of the cluster mean-field potential characterized by the size parameter $``B"$ in the THSR (Tohsaki-Horiuchi-Schuck-R\\"{o}pke) wave function. The nonlocalized cluster aspects of the inversion-doublet bands in $^{20}$Ne which have been considered as a typical manifestation of localized clustering are discussed. So far unexplained puzzling features of the THSR wave function, namely that after angular-momentum projection for two cluster systems the prolate THSR wave function is almost 100$\\%$ equivalent to an oblate THSR wave function is clarified. It is shown that the true intrinsic two-cluster THSR configuration is nonetheless prolate. The proposal of the container picture is based on the fact that typical cluster systems, 2$\\alpha$, 3$\\alpha$, and $\\alpha$+$^{16}$O, are all well described by a single THSR wave function. It will be shown for the case of linear-chain states w...
Nonlinear structure formation in Nonlocal Gravity
Barreira, Alexandre; Hellwing, Wojciech A; Baugh, Carlton M; Pascoli, Silvia
2014-01-01
We study the nonlinear growth of structure in nonlocal gravity models with the aid of N-body simulation and the spherical collapse and halo models. We focus on a model in which the inverse-squared of the d'Alembertian operator acts on the Ricci scalar in the action. For fixed cosmological parameters, this model differs from $\\Lambda{\\rm CDM}$ by having a lower late-time expansion rate and an enhanced and time-dependent gravitational strength ($\\sim 6\\%$ larger today). Compared to $\\Lambda{\\rm CDM}$ today, in the nonlocal model, massive haloes are slightly more abundant (by $\\sim 10\\%$ at $M \\sim 10^{14} M_{\\odot}/h$) and concentrated ($\\approx 8\\%$ enhancement over a range of mass scales), but their linear bias remains almost unchanged. We find that the Sheth-Tormen formalism describes the mass function and halo bias very well, with little need for recalibration of free parameters. The fitting of the halo concentrations is however essential to ensure the good performance of the halo model on small scales. For...
Entanglement: A myth introducing non-locality in any quantum theory
Prikas, Athanasios
2007-01-01
The purposes of the present article are: a) To show that non-locality leads to the transfer of certain amounts of energy and angular momentum at very long distances, in an absolutely strange and unnatural manner, in any model reproducing the quantum mechanical results. b) To prove that non-locality is the result only of the zero spin state assumption for distant particles, which explains its presence in any quantum mechanical model. c) To reintroduce locality, simply by denying the existence of the zero spin state in nature (the so-called highly correlated, or EPR singlet state) for particles non-interacting with any known field. d) To propose a realizable experiment to clarify if two remote (and thus non-interacting with a known field) particles, supposed to be correlated as in Bell-type experiments, are actually in zero spin state.
Band Structure Calculation of Si and Ge by Non-Local Empirical Pseudo-Potential Technique
Institute of Scientific and Technical Information of China (English)
CHEN Yong; RAVAIOLI Umberto
2005-01-01
In this paper, the princ iple of spatial nonlocal empirical pseudopotential and its detailed calculation procedure is presented. Consequently, this technique is employed to calculate the band structuresof Silicon and Germaniun. By comparing the results with photoemission experimental data, the validity and accuracy of this calculation are fully conformed for valence or conductance band,respectively. Thus it can be concluded that the spin-orbit Hamiltonian will only affect the energy band gap and another conductance or valence band structure. Therefore, this nonlocal approach without spin-orbit part is adequate for the device simulation of only one carrier transport such as metal oxide semiconductor field effect transistors (MOSFET)'s, and it can significantly reduce the complication of band structure calculation.
Shock Waves Propagation in Scope of the Nonlocal Theory of Dynamical Plasticity
Khantuleva, Tatyana A.
2004-07-01
From the point of view of the modern statistical mechanics the problems on shock compression of solids require a reformulation in terms of highly nonequilibrium effects arising inside the wave front. The self-organization during the multiscale and multistage momentum and energy exchange are originated by the correlation function. The theory of dynamic plasticity has been developed by the author on the base of the self-consistent nonlocal hydrodynamic approach had been applied to the shock wave propagation in solids. Nonlocal balance equations describe both the reversible wave type transport at the initial stage and the diffusive (dissipative) one in the end. The involved inverse influence of the mesoeffects on the wave propagation makes the formulation of problems self-consistent and involves a concept of the cybernetic control close-loop.
Nonlocal Coulomb interaction in the two-dimensional spin-1/2 Falicov–Kimball model
Indian Academy of Sciences (India)
S K Bhowmick; N K Ghosh
2012-02-01
The two-dimensional (2D) extended Falicov–Kimball model has been studied to observe the role of nonlocal Coulomb interaction (nc) using an exact diagonalization technique. The f-state occupation ($n^f$), the f–d intersite correlation function (fd), the speciﬁc heat (), entropy () and the speciﬁc heat coefﬁcient () have been examined. Nonlocal Coulomb interaction-induced discontinuous insulator-to-metal transition occurs at a critical f-level energy. More ordered state is obtained with the increase of nc. In the speciﬁc heat curves, two-peak structure as well as a singlepeak structure appears. At low-temperature region, a sharp rise in the speciﬁc heat coefﬁcient is observed. The peak value of shifts to the higher temperature region with nc.
Non-localized deformation in Cu−Zr multi-layer amorphous films under tension
Energy Technology Data Exchange (ETDEWEB)
Zhong, C. [International Center for New-Structured Materials (ICNSM), Laboratory of New-Structured Materials, State Key Laboratory of Silicon Materials, and School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027 (China); Zhang, H. [International Center for New-Structured Materials (ICNSM), Laboratory of New-Structured Materials, State Key Laboratory of Silicon Materials, and School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027 (China); Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9 (Canada); Cao, Q.P.; Wang, X.D. [International Center for New-Structured Materials (ICNSM), Laboratory of New-Structured Materials, State Key Laboratory of Silicon Materials, and School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027 (China); Zhang, D.X. [State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027 (China); Hu, J.W. [Hangzhou Workers Amateur University, Hangzhou 310027 (China); Liaw, P.K. [Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996 (United States); Jiang, J.Z., E-mail: jiangjz@zju.edu.cn [International Center for New-Structured Materials (ICNSM), Laboratory of New-Structured Materials, State Key Laboratory of Silicon Materials, and School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027 (China)
2016-09-05
In metallic glasses (MGs), plastic deformation at room temperature is dominated by highly localized shear bands. Here we report the non-localized deformation under tension in Cu−Zr multi-layer MGs with a pure amorphous structure using large-scale atomistic simulations. It is demonstrated that amorphous samples with high layer numbers, composed of Cu{sub 64}Zr{sub 36} and Cu{sub 40}Zr{sub 60}, or Cu{sub 64}Zr{sub 36} and Cu{sub 50}Zr{sub 50}, present obviously non-localized deformation behavior. We reveal that the deformation behavior of the multi-layer-structured MG films is related but not determined by the deformation behavior of the composed individual layers. The criterion for the deformation mode change for MGs with a pure amorphous structure, in generally, was suggested, i.e., the competition between the elastic-energy density stored and the energy density needed for forming one mature shear band in MGs. Our results provide a promising strategy for designing tensile ductile MGs with a pure amorphous structure at room temperature. - Highlights: • Tensile deformation behaviors in multi-layer MG films. • Films with high layer numbers confirmed with a non-localized deformation behavior. • The deformation mode is reasonably controlled by whether U{sub p} larger than U{sub SB.}.
Theoretical study on stability of hybrid bilayers
Silva, Thiago S.; de Lima Bernardo, Bertúlio; Azevedo, Sèrgio
2015-04-01
Motivated by the recent experimental realization of the hybrid nanostructure of graphene and boron nitride (h-BN) sheet, and studies of gap modulation by strain, we use first principles calculations based on density functional theory to investigate the effects of strain in hybrid bilayers composed of two monolayers of graphene with a nanodomain of {{B}3}{{N}3}. The calculations were made with two different approximations for the functional exchange-correlation, GGA and VDW-DF. We investigate the modification in the electronic structure and structural properties of various configurations of the hybrid bilayers. Among the configurations, those with Bernal stacking are found to be more stable when compared to the others. Studies of the compressive strain influence were made only in the structure that has been shown to be the most stable. We have found that the two approximations used in the calculations exhibit the same results for the electronic properties of all structures. The opening of the energy gap due to strain was possible in the calculations by using the GGA approximation, but the same does not happen in the calculations using the VDW-DF approximation. Our analysis shows that the VDW-DF approximation is better suited for studies involving surfaces.
Nonlocal Mumford-Shah regularizers for color image restoration.
Jung, Miyoun; Bresson, Xavier; Chan, Tony F; Vese, Luminita A
2011-06-01
We propose here a class of restoration algorithms for color images, based upon the Mumford-Shah (MS) model and nonlocal image information. The Ambrosio-Tortorelli and Shah elliptic approximations are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, texture is nonlocal in nature and requires semilocal/non-local information for efficient image denoising and restoration. Inspired from recent works (nonlocal means of Buades, Coll, Morel, and nonlocal total variation of Gilboa, Osher), we extend the local Ambrosio-Tortorelli and Shah approximations to MS functional (MS) to novel nonlocal formulations, for better restoration of fine structures and texture. We present several applications of the proposed nonlocal MS regularizers in image processing such as color image denoising, color image deblurring in the presence of Gaussian or impulse noise, color image inpainting, color image super-resolution, and color filter array demosaicing. In all the applications, the proposed nonlocal regularizers produce superior results over the local ones, especially in image inpainting with large missing regions. We also prove several characterizations of minimizers based upon dual norm formulations.
Degenerate-band-edge engineering inspired by nonlocal transformation optics
Directory of Open Access Journals (Sweden)
Moccia Massimo
2016-01-01
Full Text Available We address the engineering of degenerate-band-edge effects in nonlocal metamaterials. Our approach, inspired by nonlocal-transformation-optics concepts, is based on the approximation of analytically-derived nonlocal constitutive “blueprints”. We illustrate the synthesis procedure, and present and validate a possible implementation based on multilayered metamaterials featuring anisotropic constituents. We also elucidate the physical mechanisms underlying our approach and proposed configuration, and highlight the substantial differences with respect to other examples available in the topical literature.
Degenerate-band-edge engineering inspired by nonlocal transformation optics
Directory of Open Access Journals (Sweden)
Moccia Massimo
2016-01-01
Full Text Available We address the engineering of degenerate-band-edge effects in nonlocal metamaterials. Our approach, inspired by nonlocal-transformation-optics concepts, is based on the approximation of analytically-derived nonlocal constitutive “blueprints”. We illustrate the synthesis procedure, and present and validate a possible implementation based on multilayered metamaterials featuring anisotropic constituents. We also elucidate the physical mechanisms underlying our approach and proposed configuration, and highlight the substantial differences with respect to other examples available in the topical literature.
Large nonlocal nonlinear optical response of castor oil
Souza, Rogério F.; Alencar, Márcio A. R. C.; Meneghetti, Mario R.; Hickmann, Jandir M.
2009-09-01
The nonlocal nonlinearity of castor oil was investigated using the Z-scan technique in the CW regime at 514 nm and in femtosecond regime at 810 nm. Large negative nonlinear refractive indexes of thermal origin, thermo-optical coefficients and degree of nonlocality were obtained for both laser excitation wavelengths. The results indicate that the electronic part of the nonlinear refractive index and nonlinear absorption were negligible. Our results suggest that castor oil is promising candidate as a nonlinear medium for several nonlocal optical applications, such as in spatial soliton propagation, as well as a dispersant agent in the measurement of absorptive properties of nanoparticles.
Generic features of modulational instability in nonlocal Kerr media
DEFF Research Database (Denmark)
Wyller, John; Krolikowski, Wieslaw; Bang, Ole
2002-01-01
The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general response function. Several generic properties are proven mathematically, with emphasis on how new gain bands are formed through a bifurcation process when the degree of nonlocality, sigma, passes...... the nonlocality tends to suppress MI, but can never remove it completely, irrespectively of the shape of the response function. For a defocusing nonlinearity the stability properties depend sensitively on the profile of the response function. For response functions with a positive-definite spectrum...
Unusual resonances in nanoplasmonic structures due to nonlocal response
DEFF Research Database (Denmark)
Raza, Søren; Toscano, Giuseppe; Jauho, Antti-Pekka
2011-01-01
We study the nonlocal response of a confined electron gas within the hydrodynamical Drude model. We address the question as to whether plasmonic nanostructures exhibit nonlocal resonances that have no counterpart in the local-response Drude model. Avoiding the usual quasistatic approximation, we...... find that such resonances do indeed occur, but only above the plasma frequency. Thus the recently found nonlocal resonances at optical frequencies for very small structures, obtained within quasistatic approximation, are unphysical. As a specific example we consider nanosized metallic cylinders...
Theory of nonlocal soliton interaction in nematic liquid crystals
DEFF Research Database (Denmark)
Rasmussen, Per Dalgaard; Bang, Ole; Krolikowski, Wieslaw
2005-01-01
We investigate interactions between spatial nonlocal bright solitons in nematic liquid crystals using an analytical “effective particle” approach as well as direct numerical simulations. The model predicts attraction of out-of-phase solitons and the existence of their stable bound state....... This nontrivial property is solely due to the nonlocal nature of the nonlinear response of the liquid crystals. We further predict and verify numerically the critical outwards angle and degree of nonlocality which determine the transition between attraction and repulsion of out-of-phase solitons....
Strain analysis of nonlocal viscoelastic Kelvin bar in tension
Institute of Scientific and Technical Information of China (English)
ZHAO Xue-chuan; LEI Yong-jun; ZHOU Jian-ping
2008-01-01
Based on viscoelastic Kelvin model and nonlocal relationship of strain and stress, a nonlocal constitutive relationship of viscoelasticity is obtained and the strain response of a bar in tension is studied. By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the closed-form solution of strain field of the bar is obtained. The creep process of the bar is presented. When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity.
Stochastic waves in a Brusselator model with nonlocal interaction.
Biancalani, Tommaso; Galla, Tobias; McKane, Alan J
2011-08-01
We show that intrinsic noise can induce spatiotemporal phenomena such as Turing patterns and traveling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these stochastic waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the stochastic waves analytically and the outcome is tested successfully against simulations. We discuss the possibility that nonlocal models in other areas, such as epidemic spread or social dynamics, may contain similar stochastically induced patterns.
Non-local thin films in Casimir force calculations
Esquivel, R
2005-01-01
he Casimir force is calculated between plates with thin metallic coating. Thin films are described with spatially dispersive (nonlocal) dielectric functions. For thin films the nonlocal effects are more relevant than for half-spaces. However, it is shown that even for film thickness smaller than the mean free path for electrons, the difference between local and nonlocal calculations of the Casimir force is of the order of a few tenths of a percent. Thus the local description of thin metallic films is adequate within the current experimental precision and range of separations.
Nonlocality Distillation and Trivial Communication Complexity for High-Dimensional Systems
Institute of Scientific and Technical Information of China (English)
Yan Li; Xiang-Jun Ye; Jing-Ling Chen
2016-01-01
A nonlocality distillation protocol for arbitrary high-dimensional systems is proposed.We study the nonlocality distillation in the 2-input d-output bi-partite case.Firstly,we give the one-parameter nonlocal boxes and their correlated distilling protocol.Then,we generalize the one-parameter nonlocality distillation protocol to the two-parameter case.Furthermore,we introduce a contracting protocol testifying that the 2-input d-output nonlocal boxes make communication complexity trivial.
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.
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.
Understanding quantum interference in General Nonlocality
Wanng, Hai-Jhun
2010-01-01
In this paper we attempt to give an 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-interaction of matter wave. From the metric of the GN, we derive a special formalism to interpret the interference contrast when the self-interaction 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 Schr\\"odinger current and Dirac current respectively, both of which are relevant to topology. The gap between these two cases corresponds to a spin-current effect, which is possible to test in the near future. In addition, a general interference formalism for both perturbative and non-perturbative self-interactions is presented. By analyzing the general formalism we predict that in the nonperturbative limit there is no interference at all.
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.
Photonic multipartite entanglement conversion using nonlocal operations
Tashima, T.; Tame, M. S.; Özdemir, Ş. K.; Nori, F.; Koashi, M.; Weinfurter, H.
2016-11-01
We propose a simple setup for the conversion of multipartite entangled states in a quantum network with restricted access. The scheme uses nonlocal operations to enable the preparation of states that are inequivalent under local operations and classical communication, but most importantly does not require full access to the states. It is based on a flexible linear optical conversion gate that uses photons, which are ideally suited for distributed quantum computation and quantum communication in extended networks. In order to show the basic working principles of the gate, we focus on converting a four-qubit entangled cluster state to other locally inequivalent four-qubit states, such as the Greenberger-Horne-Zeilinger and symmetric Dicke states. We also show how the gate can be incorporated into extended graph state networks and can be used to generate variable entanglement and quantum correlations without entanglement but nonvanishing quantum discord.
A quantum loophole to Bell nonlocality
Romero-Rochin, Victor
2015-01-01
We argue that the conclusion of Bell theorem, namely, that there must be spatial non-local correlations in certain experimental situations, does not apply to typical individual measurements performed on entangled EPR pairs. Our claim is based on three points, (i) on the notion of quantum {\\it complete measurements}; (ii) on Bell results on local yet distant measurements; and (iii) on the fact that perfect simultaneity is banned by the quantum mechanics. We show that quantum mechanics indicates that, while the measurements of the pair members are indeed space-like separated, the pair measurement is actually a sequence of two complete measurements, the first one terminating the entanglement and, therefore, the second one becoming unrelated to the initial preparation of the entangled pair. The outstanding feature of these measurements is that neither of them violates the principle of locality. We discuss that the present measurement viewpoint appears to run contrary to the usual interpretation of "superposition"...
Construction of nonlocal multipartite quantum states
Zhang, Zhi-Chao; Zhang, Ke-Jia; Gao, Fei; Wen, Qiao-Yan; Oh, C. H.
2017-05-01
For general bipartite quantum systems, many sets of locally indistinguishable orthogonal product states have been constructed so far. Here, we first present a general method to construct multipartite orthogonal product states in d1⊗d2⊗⋯⊗dn(d1 ,2 ,⋯,n≥3 ,n ≥4 ) by using some locally indistinguishable bipartite orthogonal product states. And we prove that these multipartite orthogonal quantum states cannot be distinguished by local operations and classical communication. Furthermore, in d1⊗d2⊗⋯⊗dn(d1 ,2 ,⋯,n≥3 ,n ≥5 ) , we give a general method to construct a much smaller number of locally indistinguishable multipartite orthogonal product states for even and odd n separately. In addition, we also present a general method to construct complete orthogonal product bases for the multipartite quantum systems. Our results demonstrate the phenomenon of nonlocality without entanglement for the multipartite quantum systems.
Nonlocal correlations and spectral properties of the Falicov-Kimball model
Ribic, T.; Rohringer, G.; Held, K.
2016-05-01
We derive an analytical expression for the local two-particle vertex of the Falicov-Kimball model, including its dependence on all three frequencies, the full vertex, and all reducible vertices. This allows us to calculate the self-energy in diagrammatic extensions of dynamical mean field theory, specifically in the dual fermion and the one-particle irreducible approach. Nonlocal correlations are thence included and originate here from charge-density wave fluctuations. At low temperatures and in two dimensions, they lead to a larger self-energy contribution at low frequencies and a more insulating spectrum.
Non-local separable solutions of two interacting particles in a harmonic trap
Energy Technology Data Exchange (ETDEWEB)
Gonzalez-Santander, C., E-mail: cglezsantander@fis.ucm.e [GISC, Departamento de Fisica de Materiales, Universidad Complutense, E-28040 Madrid (Spain); Dominguez-Adame, F. [GISC, Departamento de Fisica de Materiales, Universidad Complutense, E-28040 Madrid (Spain)
2011-01-17
We calculate the energy levels of two particles trapped in a harmonic potential. The actual two-body potential, assumed to be spherically symmetric, is replaced by a projective operator (non-local separable potential) to determine the energy levels in a closed form. This approach overcomes the limitations of the regularized Fermi pseudopotential when the characteristic length of the two-body interaction potential is of the order of the size of the harmonic trap. In addition, we recover the results obtained with the Fermi pseudopotential when the length of the interaction is much smaller than the size of the trap.
Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization
Correas-Serrano, D.; Gomez-Diaz, J. S.; Alvarez Melcon, A.; Alù, Andrea
2016-10-01
We investigate unusual surface plasmons polariton (SPP) propagation and light-matter interactions in ultrathin black phosphorus (BP) films, a 2D material that exhibits exotic electrical and physical properties due to its extremely anisotropic crystal structure. Recently, it has been speculated that the ultra-confined surface plasmons supported by BP may present various topologies of wave propagation bands, ranging from anisotropic elliptic to hyperbolic, across the mid- and near-infrared regions of the electromagnetic spectrum. By carefully analyzing the natural nonlocal anisotropic optical conductivity of BP, derived using the Kubo formalism and an effective low-energy Hamiltonian, we demonstrate here that the SPP wavenumber cutoff imposed by nonlocality prohibits that they acquire an arbitrary hyperbolic topology, forcing operation in the canalization regime. The resulting nonlocality-induced canalization presents interesting properties, as it is inherently broadband, enables large light-matter interactions in the very near field, and allows extreme device miniaturization. We also determine fundamental bounds to the confinement of BP plasmons, which are significantly weaker than for graphene, thus allowing a larger local density of states. Our results confirm the potential of BP as a promising reconfigurable plasmonic platform, with exciting applications, such as planar hyperlenses, optoelectronic components, imaging, and communication systems.
Nonlocal response of metallic nanospheres probed by light, electrons, and atoms.
Christensen, Thomas; Yan, Wei; Raza, Søren; Jauho, Antti-Pekka; Mortensen, N Asger; Wubs, Martijn
2014-02-25
Inspired by recent measurements on individual metallic nanospheres that cannot be explained with traditional classical electrodynamics, we theoretically investigate the effects of nonlocal response by metallic nanospheres in three distinct settings: atomic spontaneous emission, electron energy loss spectroscopy, and light scattering. These constitute two near-field and one far-field measurements, with zero-, one-, and two-dimensional excitation sources, respectively. We search for the clearest signatures of hydrodynamic pressure waves in nanospheres. We employ a linearized hydrodynamic model, and Mie-Lorenz theory is applied for each case. Nonlocal response shows its mark in all three configurations, but for the two near-field measurements, we predict especially pronounced nonlocal effects that are not exhibited in far-field measurements. Associated with every multipole order is not only a single blueshifted surface plasmon but also an infinite series of bulk plasmons that have no counterpart in a local-response approximation. We show that these increasingly blueshifted multipole plasmons become spectrally more prominent at shorter probe-to-surface separations and for decreasing nanosphere radii. For selected metals, we predict hydrodynamic multipolar plasmons to be measurable on single nanospheres.
Non-local plasticity effects on fracture toughness
DEFF Research Database (Denmark)
Niordson, Christian Frithiof
2002-01-01
The Mode I fracture strength in a nonlocal elastic-plastic material is analyzed under quasi-static steady crack growth. The plastic deformations are modelled using a constitutive model, where nonlocal plasticity effects are included in the instantaneous hardening moduli through a gradient measure...... of the effective plastic strain. Fracture is modelled by a cohesive zone criterion. Results on the numerically obtained stress fields are presented, as well as results on the steady-state fracture toughness. It is shown that the nonlocal theory predicts lower steady-state fracture toughness compared to predictions...... by conventional J2-flow theory, since higher normal stresses in front of the crack tip are predicted. Furthermore, the nonlocal material description increases the range of applicability of the cohesive zone model, since steady-state crack growth is possible for significantly larger values of the maximum stress...
Discrete model of dislocations in fractional nonlocal elasticity
National Research Council Canada - National Science Library
Tarasov, Vasily E
2016-01-01
Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used...
Nonlocal viscous transport and the effect on fluid stress.
Todd, B D; Hansen, J S
2008-11-01
We demonstrate that, in general, only for fluid flows in which the gradient of the strain rate is constant or zero can the classical Navier-Stokes equations with constant transport coefficients be considered exact. This is typical of two of the most common types of flow: Couette and Poiseuille. For more complicated flow fields in which the streaming velocity involves higher order nonlinear terms, the use of nonlocal constitutive equations gives an exact description of the flow. These constitutive equations involve nonlocal transport kernels. For momentum transport we demonstrate that nonlocality will be significant for any particular flow field if the even moments of the nonlocal viscosity kernel are non-negligible. This corresponds to the condition that the strain rate varies appreciably over the width of the kernel in real space. Such conditions are likely to be dominant for nanofluidic flows.
NONDENSELY DEFINED IMPULSIVE NEUTRAL FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS
Institute of Scientific and Technical Information of China (English)
Yueju Cao; Xianlong Fu
2009-01-01
In this paper, using a fixed point theorem for condensing multi-valued maps, we investigate the existence of integral solutions to a class of nondensely defined neutral evolution impulsive differential inclusions with nonlocal conditions in Banach spaces.
Controllability of semilinear integrodifferential equations with nonlocal conditions
Directory of Open Access Journals (Sweden)
Rahima Atmania
2005-07-01
Full Text Available We establish sufficient conditions for the controllability of some semilinear integrodifferential systems with nonlocal condition in a Banach space. The results are obtained using the Schaefer fixed-point theorem and semigroup theory.
Tests of quantum-gravity-induced nonlocality via optomechanical experiments
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2017-01-01
The nonrelativistic limit of nonlocal modifications to the Klein-Gordon operator is studied, and the experimental possibilities of casting stringent constraints on the nonlocality scale via planned and/or current optomechanical experiments are discussed. Details of the perturbative analysis and semianalytical simulations leading to the dynamic evolution of a quantum harmonic oscillator in the presence of nonlocality reported in [A. Belenchia, D. M. T. Benincasa, S. Liberati, F. Marin, F. Marino, and A. Ortolan, Phys. Rev. Lett. 116, 161303 (2016), 10.1103/PhysRevLett.116.161303] are given, together with a comprehensive account of the experimental methodology with particular regard to sensitivity limitations related to thermal decoherence time and active cooling of the oscillator. Finally, a strategy for detecting nonlocality scales of the order of 10-22÷10-26 m by means of the spontaneous time-periodic squeezing of quantum-coherent states is provided.
Controllability of impulsive functional differential systems with nonlocal conditions
Directory of Open Access Journals (Sweden)
Yansheng Liu
2013-08-01
Full Text Available In this article, we study the controllability of impulsive functional differential equations with nonlocal conditions. We establish sufficient conditions for controllability, via the measure of noncompactness and Monch fixed point theorem.
Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation
Broadbent, Anne
2016-08-01
In instantaneous nonlocal quantum computation, two parties cooperate in order to perform a quantum computation on their joint inputs, while being restricted to a single round of simultaneous communication. Previous results showed that instantaneous nonlocal quantum computation is possible, at the cost of an exponential amount of prior shared entanglement (in the size of the input). Here, we show that a linear amount of entanglement suffices, (in the size of the computation), as long as the parties share nonlocal correlations as given by the Popescu-Rohrlich box. This means that communication is not required for efficient instantaneous nonlocal quantum computation. Exploiting the well-known relation to position-based cryptography, our result also implies the impossibility of secure position-based cryptography against adversaries with nonsignaling correlations. Furthermore, our construction establishes a quantum analog of the classical communication complexity collapse under nonsignaling correlations.
Non-local plasticity effects on fracture toughness
DEFF Research Database (Denmark)
Niordson, Christian Frithiof
2002-01-01
The Mode I fracture strength in a nonlocal elastic-plastic material is analyzed under quasi-static steady crack growth. The plastic deformations are modelled using a constitutive model, where nonlocal plasticity effects are included in the instantaneous hardening moduli through a gradient measure...... of the effective plastic strain. Fracture is modelled by a cohesive zone criterion. Results on the numerically obtained stress fields are presented, as well as results on the steady-state fracture toughness. It is shown that the nonlocal theory predicts lower steady-state fracture toughness compared to predictions...... by conventional J2-flow theory, since higher normal stresses in front of the crack tip are predicted. Furthermore, the nonlocal material description increases the range of applicability of the cohesive zone model, since steady-state crack growth is possible for significantly larger values of the maximum stress...
Entanglement and nonlocality in multi-particle systems
Reid, M D; Drummond, P D
2011-01-01
Entanglement, the Einstein-Podolsky-Rosen (EPR) paradox and Bell's failure of local-hidden-variable (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.
Self-adjoint integral operator for bounded nonlocal transport
Maggs, J. E.; Morales, G. J.
2016-11-01
An integral operator is developed to describe nonlocal transport in a one-dimensional system bounded on both ends by material walls. The "jump" distributions associated with nonlocal transport are taken to be Lévy α -stable distributions, which become naturally truncated by the bounding walls. The truncation process results in the operator containing a self-consistent, convective inward transport term (pinch). The properties of the integral operator as functions of the Lévy distribution parameter set [α ,γ ] and the wall conductivity are presented. The integral operator continuously recovers the features of local transport when α =2 . The self-adjoint formulation allows for an accurate description of spatial variation in the Lévy parameters in the nonlocal system. Spatial variation in the Lévy parameters is shown to result in internally generated flows. Examples of cold-pulse propagation in nonlocal systems illustrate the capabilities of the methodology.
Understanding quantum non-locality through pseudo-telepathy game
Kunkri, Samir
2006-11-01
Usually by quantum non-locality we mean that quantum mechanics can not be replaced by local realistic theory. On the other hand this nonlocal feature of quantum mechanics can not be used for instantaneous communication and hence it respect Einstein's special theory of relativity. But still it is not trivial as proved by various quantum information processing using entangled states. Recently there have been studies of hypothetical non-local system again respecting no-signalling which is beyond quantum mechanics. Here we study the power of such a hypothetical nonlocal box first suggested by Popescu et.al. in the context of recently suggested pseudo-telepathy game constructed from a Kochen-Specker set.
Local orthogonality provides a tight upper bound for Hardy's nonlocality
Das, Subhadipa; Banik, Manik; Gazi, Md. Rajjak; Rai, Ashutosh; Kunkri, Samir
2013-12-01
The amount of nonlocality in quantum theory is limited compared to that allowed in generalized no-signaling theory [S. Popescu and D. Rohrlich, Found. Phys.FNDPA40015-901810.1007/BF02058098 24, 379 (1994)]. This feature, for example, gets manifested in the amount of Bell inequality violation as well as in the degree of success probability of Hardy's (Cabello's) nonlocality argument. Physical principles like information causality and macroscopic locality have been proposed for analyzing restricted nonlocality in quantum mechanics, viz. explaining the Cirel'son bound. However, these principles are not very successful in explaining the maximum success probability of Hardy's as well as Cabello's argument in quantum theory. Here we show that a recently proposed physical principle, namely local orthogonality, does better by providing a tighter upper bound on the success probability for Hardy's nonlocality. This bound is relatively closer to the corresponding quantum value compared to the bounds achieved from other principles.
Causal Set theory, non-locality and phenomenology
Belenchia, Alessio
2015-01-01
This proceeding is based on a talk prepared for the XIV Marcel Grossmann meeting. We review some results on causal set inspired non-local theories as well as work in progress concerning their phenomenology.
Observation of two-dimensional nonlocal gap solitons
DEFF Research Database (Denmark)
Rasmussen, Per Dalgaard; Bennett, Francis H.; Neshev, Dragomir N.
2009-01-01
We demonstrate, both theoretically and experimentally, the existence of nonlocal gap solitons in twodimensional periodic photonic structures with defocusing thermal nonlinearity. We employ liquid-infiltrated photonic crystal fibers and show how the system geometry can modify the effective respons...
Nonlocal quintic nonlinearity by cascaded THG in dispersive media
DEFF Research Database (Denmark)
Eilenberger, F.; Bache, Morten; Minardi, S.;
2011-01-01
We discuss a perturbed nonlocal cubicquintic equation describing the propagation of light pulses in a dispersive, cubic nonlinearmedium in the presence of phase and velocity mismatched third harmonic generation....
Nonlocal scalar quantum field theory from causal sets
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano
2015-03-01
We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.
Nonlocal Scalar Quantum Field Theory from Causal Sets
Belenchia, Alessio; Liberati, Stefano
2014-01-01
We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.
Local implementation of nonlocal operations with block forms
Zhao, Ning Bo; Wang, An Min
2008-07-01
We investigate the local implementation of nonlocal operations with the block matrix form, and propose a protocol for any diagonal or offdiagonal block operation. We generalize this method to the two-party multiqubit case and the multiparty case. We also compare the local implementation of nonlocal block operations with the remote implementation of local operations [Huelga , Phys. Rev. A 63, 042303 (2001)], and point out a relation between them.
Acceleration-Induced Nonlocal Electrodynamics in Minkowski Spacetime
Muench, U; Mashhoon, B; Muench, Uwe; Hehl, Friedrich W.; Mashhoon, Bahram
2000-01-01
We discuss two nonlocal models of electrodynamics in which the nonlocality is induced by the acceleration of the observer. Such an observer actually measures an electromagnetic field that exhibits persistent memory effects. We compare Mashhoon's model with a new ansatz developed here in the framework of charge & flux electrodynamics with a constitutive law involving the Levi-Civita connection as seen from the observer's local frame and conclude that they are in partial agreement only for the case of constant acceleration.
Nonlocal correlations: Fair and Unfair Strategies in Bayesian Game
Roy, Arup; Mukherjee, Amit; Guha, Tamal; Ghosh, Sibasish; Bhattacharya, Some Sankar; Banik, Manik
2016-01-01
Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform classical equilibrium strategies in common interest Bayesian games and also in conflicting interest games. However, classical equilibrium strategies can be of two types, fair and unfair. Whereas in fair equilibrium payoffs of different players are same, in unfair case they ...
Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation
Broadbent, Anne
2015-01-01
In instantaneous nonlocal quantum computation, two parties cooperate in order to perform a quantum computation on their joint inputs, while being restricted to a single round of simultaneous communication. Previous results showed that instantaneous nonlocal quantum computation is possible, at the cost of an exponential amount of prior shared entanglement (in the size of the input). Here, we show that a linear amount of entanglement suffices, (in the size of the computation), as long as the pa...
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.
Twisted Backgrounds, PP-Waves and Nonlocal Field Theories
Alishahiha, M; Alishahiha, Mohsen; Ganor, Ori J.
2003-01-01
We study partially supersymmetric plane-wave like deformations of string theories and M-theory on brane backgrounds. These deformations are dual to nonlocal field theories. We calculate various expectation values of configurations of closed as well as open Wilson loops and Wilson surfaces in those theories. We also discuss the manifestation of the nonlocality structure in the supergravity backgrounds. A plane-wave like deformation of little string theory has also been studied.
Nonlocal Problems for Fractional Differential Equations via Resolvent Operators
Directory of Open Access Journals (Sweden)
Zhenbin Fan
2013-01-01
Full Text Available We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. An example is also given to illustrate our theory.
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.
Nonlocality and purity in atom-field coupling system
Institute of Scientific and Technical Information of China (English)
Cai Xin; Huang Guang-Ming; Li Gao-Xiang
2005-01-01
The effects of initial field state and thermal environment on quantum nonlocality and linear entropy in an atomfield coupling system are investigated. We found that if the cavity is lossless and the reservoir is in vacuum, the atom-field state can exhibit quantum nonlocality periodically and the linear entropies of the atom and the field also oscillate periodically with a period the same as that of quantum nonlocality. And if the cavity dissipation is very weak and the average photon number of the reservoir is very small, the quantum nonlocality will be lost and the linear entropies of the atom and the field oscillate with a decreasing amplitude. The rapidity of the loss of the quantum nonlocality depends on the amplitude of the initial squeezed coherent state, the cavity damping constant κ and the average photon number N of the thermal reservoir. The stronger the field and the larger the constant κ and the average photon number N could be, the more rapidly the nonlocality decreases.
On the power of non-local boxes
Broadbent, A J
2005-01-01
A non-local box is a virtual device that has the following property: given that Alice inputs a bit at her end of the device and that Bob does likewise, it produces two bits, one at Alice's end and one at Bob's end, such that the XOR of the outputs is equal to the AND of the inputs. This box, inspired from the CHSH inequality, was first proposed by Popescu and Rohrlich to examine the question: given that a maximally entangled pair of qubits is non-local, why is it not maximally non-local? We believe that understanding the power of this box will yield insight into the non-locality of quantum mechanics. It was shown recently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able to simulate correlations from any measurement on a singlet state. Here, we show that the non-local box can in fact do much more: through the simulation of the magic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we show that the non-local box can simulate quantum correlations that no entangled pair...
Farkašovský, Pavol
2017-04-01
We study the combined effects of local and nonlocal hybridization on the formation and condensation of the excitonic bound states in the extended Falicov-Kimball model by the density-matrix-renormalization-group (DMRG) method. Analysing the resultant behaviours of the excitonic momentum distribution N(q) we found, that unlike the local hybridization V, which supports the formation of the q=0 momentum condensate, the nonlocal hybridization Vn supports the formation of the q = π momentum condensate. The combined effect of local and nonlocal hybridization further enhances the excitonic correlations in q=0 as well as q = π state, especially for V and Vn values from the charge-density-wave (CDW) region. Strong effects of local and nonlocal hybridization are observed also for other ground-state quantities of the model such as the f-electron density, or the density of unbound d-electrons, which are generally enhanced with increasing V and Vn. The same calculations performed for nonzero values of f-level energy Ef revealed that this model can yield a reasonable explanation for the pressure-induced resistivity anomaly observed experimentally in TmSe0.45Te0.55 compound.
Glaucoma progression detection using nonlocal Markov random field prior.
Belghith, Akram; Bowd, Christopher; Medeiros, Felipe A; Balasubramanian, Madhusudhanan; Weinreb, Robert N; Zangwill, Linda M
2014-10-01
Glaucoma is neurodegenerative disease characterized by distinctive changes in the optic nerve head and visual field. Without treatment, glaucoma can lead to permanent blindness. Therefore, monitoring glaucoma progression is important to detect uncontrolled disease and the possible need for therapy advancement. In this context, three-dimensional (3-D) spectral domain optical coherence tomography (SD-OCT) has been commonly used in the diagnosis and management of glaucoma patients. We present a new framework for detection of glaucoma progression using 3-D SD-OCT images. In contrast to previous works that use the retinal nerve fiber layer thickness measurement provided by commercially available instruments, we consider the whole 3-D volume for change detection. To account for the spatial voxel dependency, we propose the use of the Markov random field (MRF) model as a prior for the change detection map. In order to improve the robustness of the proposed approach, a nonlocal strategy was adopted to define the MRF energy function. To accommodate the presence of false-positive detection, we used a fuzzy logic approach to classify a 3-D SD-OCT image into a "non-progressing" or "progressing" glaucoma class. We compared the diagnostic performance of the proposed framework to the existing methods of progression detection.
Nonlocal Polarization Feedback in a Fractional Quantum Hall Ferromagnet.
Hennel, Szymon; Braem, Beat A; Baer, Stephan; Tiemann, Lars; Sohi, Pirouz; Wehrli, Dominik; Hofmann, Andrea; Reichl, Christian; Wegscheider, Werner; Rössler, Clemens; Ihn, Thomas; Ensslin, Klaus; Rudner, Mark S; Rosenow, Bernd
2016-04-01
In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back locally, modifying the local electronic Zeeman energy. Here we report a nonlocal effect arising from the interplay between nuclear polarization and the spatial structure of electronic domains in a ν=2/3 fractional quantum Hall state. In our experiments, we use a quantum point contact to locally control and probe the domain structure of different spin configurations emerging at the spin phase transition. Feedback between nuclear and electronic degrees of freedom gives rise to memristive behavior, where electronic transport through the quantum point contact depends on the history of current flow. We propose a model for this effect which suggests a novel route to studying edge states in fractional quantum Hall systems and may account for so-far unexplained oscillatory electronic-transport features observed in previous studies.
Energy Technology Data Exchange (ETDEWEB)
Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan); Itoh, Sanae-I.; Yagi, Masatoshi [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics
2002-09-01
Nonlocal properties of fluctuations in confined plasmas are briefly surveyed. Contributions to understanding the bifurcation phenomena, improved confinement, and transient transport problem are explained. The theoretical progress in this aspect is addressed: Namely, the fluctuations are not excited by linear instabilities but are dressed with other turbulent fluctuations or fluctuations of meso-scale. Nonlinear interactions of fluctuations with different scale lengths are essential in dictating the dynamics of turbulence and turbulent transport. There are activators and suppressers in global inhomogeneities for evolution of turbulence. Turbulent fluctuations, on the other hand, induce or destroy these global inhomogeneities. Finally, statistical nature of turbulence is addressed. (author)
Lorentz Invariant CPT Violating Effects for a Class of Gauge-invariant Nonlocal Thirring Models
Patra, Pinaki
2013-01-01
CPT violation and Lorentz invariance can coexist in the framework of non-local field theory. Local gauge-invariance may not hold for the few non-local interaction terms. However, the gauge-invariance for the non-local interaction term can be formulated by the inclusion of Swinger non-integrable phase factor. In this article we have proposed a class of CPT violating Lorentz invariant Nonlocal Gauge-invariant models which can be termed as non-local gauge-invariant Thirring models. The inclusion of non-locality will modify the current conservation laws. Also, the possible particle antiparticle mass-splitting in this respect is discussed.
Diagnostics of nonlocal plasmas: advanced techniques
Mustafaev, Alexander; Grabovskiy, Artiom; Strakhova, Anastasiya; Soukhomlinov, Vladimir
2014-10-01
This talk generalizes our recent results, obtained in different directions of plasma diagnostics. First-method of flat single-sided probe, based on expansion of the electron velocity distribution function (EVDF) in series of Legendre polynomials. It will be demonstrated, that flat probe, oriented under different angles with respect to the discharge axis, allow to determine full EVDF in nonlocal plasmas. It is also shown, that cylindrical probe is unable to determine full EVDF. We propose the solution of this problem by combined using the kinetic Boltzmann equation and experimental probe data. Second-magnetic diagnostics. This method is implemented in knudsen diode with surface ionization of atoms (KDSI) and based on measurements of the magnetic characteristics of the KDSI in presence of transverse magnetic field. Using magnetic diagnostics we can investigate the wide range of plasma processes: from scattering cross-sections of electrons to plasma-surface interactions. Third-noncontact diagnostics method for direct measurements of EVDF in remote plasma objects by combination of the flat single-sided probe technique and magnetic polarization Hanley method.
Exploring nonlocal observables in shock wave collisions
Ecker, Christian; Stanzer, Philipp; Stricker, Stefan A; van der Schee, Wilke
2016-01-01
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: hi...
Nonperturbative embedding for highly nonlocal Hamiltonians
Subaşı, Yiǧit; Jarzynski, Christopher
2016-07-01
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with at most two-body interactions. Although valid for arbitrary k -body interactions, their use is limited to small k because the strength of interaction is k th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective k -body interactions using Hamiltonians consisting of at most l -body interactions with l effect of this procedure is shown to be equivalent to evolving the system with the original nonlocal Hamiltonian. This technique does not suffer from the aforementioned shortcoming of perturbative methods and requires only one ancilla qubit for each k -body interaction irrespective of the value of k . It works best for Hamiltonians with a few many-body interactions involving a large number of qubits and can be used together with perturbative gadgets to embed Hamiltonians of considerable complexity in proper subspaces of two-local Hamiltonians. We describe how our technique can be implemented in a hybrid (gate-based and adiabatic) as well as solely adiabatic quantum computing scheme.
Off-shell and nonlocal effects in proton-nucleus elastic scattering
Energy Technology Data Exchange (ETDEWEB)
Picklesimer, A.; Tandy, P.C.; Thaler, R.M.; Wolfe, D.H.
1984-04-01
The influence of off-shell and nonlocal effects in the first-order nonrelativistic microscopic optical potential is investigated for elastic proton scattering above 100 MeV. With the free nucleon-nucleon t matrix taken from the model of Love and Franey, these effects are significant only for scattering angles greater than about 60/sup 0/ and energies below about 300 MeV. The inadequacy of the standard first-order theory for predictions of spin observables at forward scattering angles remains unchanged when these effects are included and the need for higher order processes including medium and relativistic effects is reinforced.
Off-shell and nonlocal effects in proton-nucleus elastic scattering
Picklesimer, A.; Tandy, P. C.; Thaler, R. M.; Wolfe, D. H.
1984-04-01
The influence of off-shell and nonlocal effects in the first-order nonrelativistic microscopic optical potential is investigated for elastic proton scattering above 100 MeV. With the free nucleon-nucleon t matrix taken from the model of Love and Franey, these effects are significant only for scattering angles greater than about 60° and energies below about 300 MeV. The inadequacy of the standard first-order theory for predictions of spin observables at forward scattering angles remains unchanged when these effects are included and the need for higher order processes including medium and relativistic effects is reinforced.
Global well-posedness for nonlinear nonlocal Cauchy problems arising in elasticity
Directory of Open Access Journals (Sweden)
Hantaek Bae
2017-02-01
Full Text Available In this article, we prove global well-posedness for a family of one dimensional nonlinear nonlocal Cauchy problems arising in elasticity. We consider the equation $$ u_{tt}-\\delta Lu_{xx}=\\big(\\beta \\ast [(1-\\deltau+u^{2n+1}]\\big_{xx}\\,, $$ where $L$ is a differential operator, $\\beta$ is an integral operator, and $\\delta =0$ or 1. (Here, the case $\\delta=1$ represents the additional doubly dispersive effect. We prove the global well-posedness of the equation in energy spaces.
Implicit for local effects and explicit for nonlocal effects is unconditionallly stable.
Energy Technology Data Exchange (ETDEWEB)
Anitescu, M.; Layton, W. J.; Pahlevani, F.; Mathematics and Computer Science; Univ. of Pittsburgh
2004-01-01
A combination of implicit and explicit timestepping is analyzed for a system of ordinary differential equations (ODEs) motivated by ones arising from spatial discretizations of evolutionary partial differential equations (PDEs). Loosely speaking, the method we consider is implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numerical scheme are proved by the energy method and by algebraic techniques. This stability result is surprising because usually when different methods are combined, the stability properties of the least stable method plays a determining role in the combination.
Fukukawa, K.; Fujiwara, Y.
2011-05-01
The S-wave effective-range parameters of the neutron-deuteron (nd) scattering are calculated in the Faddeev formalism using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-body force, yielding almost correct values of the scattering length and the triton binding energy without the three-nucleon force. This feature is due to the strong distortion effect of the deuteron in this spin channel, which is very sensitive to the nonlocal description of the short-range repulsion in the quark-model nucleon-nucleon interaction. We incorporate the Coulomb force by extending the framework of the Coulomb externally corrected approximation and calculate the differential cross sections of the pd scattering.
Anitescu, Mihai; Layton, William J.; Pahlevani, Faranak
2003-01-01
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numerical scheme are proven by the energy method and by algebraic techniques. This stability result is sur...
Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality
Directory of Open Access Journals (Sweden)
Y. Jack Ng
2008-10-01
Full Text Available Due to quantum fluctuations, spacetime is foamy on small scales. The degree of foaminess is found to be consistent with holography, a principle prefigured in the physics of black hole entropy. It has bearing on the ultimate accuracies of clocks and measurements and the physics of quantum computation. Consistent with existing archived data on active galactic nuclei from the Hubble Space Telescope, the application of the holographic spacetime foam model to cosmology requires the existence of dark energy which, we argue, is composed of an enormous number of inert Ã¢Â€ÂœparticlesÃ¢Â€Â of extremely long wavelength. We suggest that these Ã¢Â€ÂœparticlesÃ¢Â€Â obey infinite statistics in which all representations of the particle permutation group can occur, and that the nonlocality present in systems obeying infinite statistics may be related to the nonlocality present in holographic theories. We also propose to detect spacetime foam by looking for halos in the images of distant quasars, and argue that it does not modify the GZK cutoff in the ultra-high energy cosmic ray spectrum and its contributions to time-offlight differences of high energy gamma rays from distant GRB are too small to be detectable.
Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud
2016-09-01
The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.
Ansari, R.; Norouzzadeh, A.
2016-10-01
The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin-Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material properties vary in the thickness direction and are evaluated using the Mori-Tanaka homogenization scheme. The governing equations of buckled nanoplate are achieved by the minimum total potential energy principle. To perform the isogeometric analysis as a solution methodology, a novel matrix-vector form of formulation is presented. Numerical examples are given to study the effects of surface stress as well as other important parameters on the critical buckling loads of functionally graded nanoplates. It is found that the buckling configuration of nanoplates at small scales is significantly affected by the surface free energy.
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.
Examining the effect of nonlocality in (d ,n ) transfer reactions
Ross, A.; Titus, L. J.; Nunes, F. M.
2016-07-01
Background: In the past year we have been exploring the effect of the explicit inclusion of nonlocality in (d ,p ) reactions. Purpose: The goal of this paper is to extend previous studies to (d ,n ) reactions, which, although similar to (d ,p ) reactions, have specific properties that merit inspection. Method: We apply our methods (both the distorted-wave Born approximation and the adiabatic wave approximation) to (d ,n ) reactions on 16O,40Ca,48Ca,126Sn,132Sn , and 208Pb at 20 and 50 MeV. Results: We look separately at the modifications introduced by nonlocality in the final bound and scattering states as well as the consequences reflected on the differential angular distributions. The cross sections obtained when using nonlocality explicitly are significantly different than those using the local approximation, just as in (d ,p ) reactions. Due to the particular role of the Coulomb force in the bound state, often we found the effects of nonlocality to be larger in (d ,n ) than in (d ,p ) reactions. Conclusions: Our results confirm the importance of including nonlocality explicitly in deuteron-induced reactions.
Nonlocal dielectric effects in core-shell nanowires.
Energy Technology Data Exchange (ETDEWEB)
McMahon, J. M.; Gray, S. K.; Schatz, G. C. (Center for Nanoscale Materials); ( CSE); (Northwestern Univ.)
2010-01-01
We study the optical spectra and near fields of core-shell nanowires (nanoshells), using a recently developed finite-difference method that allows for a spatially nonlocal dielectric response. We first analyze the parameters of the nonlocal model by making comparisons with related experimental data and previous theoretical work. We then investigate how nonlocal effects are dependent on nanoshell features, such as shell thickness, overall size, and the ratio of core radius to shell radius. We demonstrate that the shell thickness along the longitudinal direction of the incident light is the primary controlling factor of nonlocal effects, which appear as anomalous absorption resonances and blueshifts in the localized surface plasmon resonance (LSPR) positions, relative to local theory. In addition, we show that the amount of blueshift depends on the order of the LSPR. The optical responses of nanoshells immersed in various refractive index (RI) environments are also studied. We show that the nonlocal anomalous absorption features are relatively insensitive to RI changes, but the blueshift of the dipolar LSPR varies nonlinearly.
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.
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.
Nonlocal Total Variation Subpixel Mapping for Hyperspectral Remote Sensing Imagery
Directory of Open Access Journals (Sweden)
Ruyi Feng
2016-03-01
Full Text Available Subpixel mapping is a method of enhancing the spatial resolution of images, which involves dividing a mixed pixel into subpixels and assigning each subpixel to a definite land-cover class. Traditionally, subpixel mapping is based on the assumption of spatial dependence, and the spatial correlation information among pixels and subpixels is considered in the prediction of the spatial locations of land-cover classes within the mixed pixels. In this paper, a novel subpixel mapping method for hyperspectral remote sensing imagery based on a nonlocal method, namely nonlocal total variation subpixel mapping (NLTVSM, is proposed to use the nonlocal self-similarity prior to improve the performance of the subpixel mapping task. Differing from the existing spatial regularization subpixel mapping technique, in NLTVSM, the nonlocal total variation is used as a spatial regularizer to exploit the similar patterns and structures in the image. In this way, the proposed method can obtain an optimal subpixel mapping result and accuracy by considering the nonlocal spatial information. Compared with the classical and state-of-the-art subpixel mapping approaches, the experimental results using a simulated hyperspectral image, two synthetic hyperspectral remote sensing images, and a real hyperspectral image confirm that the proposed algorithm can obtain better results in both visual and quantitative evaluations.
Discrete Solitary Waves in Systems with Nonlocal Interactions and the Peierls-Nabarro Barrier
Jenkinson, M.; Weinstein, M. I.
2017-04-01
We study a class of discrete focusing nonlinear Schrödinger equations (DNLS) with general nonlocal interactions. We prove the existence of onsite and offsite discrete solitary waves, which bifurcate from the trivial solution at the endpoint frequency of the continuous spectrum of linear dispersive waves. We also prove exponential smallness, in the frequency-distance to the bifurcation point, of the Peierls-Nabarro energy barrier (PNB), as measured by the difference in Hamiltonian or mass functionals evaluated on the onsite and offsite states. These results extend those of the authors for the case of nearest neighbor interactions to a large class of nonlocal short-range and long-range interactions. The appearance of distinct onsite and offsite states is a consequence of the breaking of continuous spatial translation invariance. The PNB plays a role in the dynamics of energy transport in such nonlinear Hamiltonian lattice systems. Our class of nonlocal interactions is defined in terms of coupling coefficients, J m , where {min{Z}} is the lattice site index, with {J_m˜eq m^{-1-2s}, sin[1,∞)} and {J_m˜ e^{-γ|m|}, s=∞, γ > 0,} (Kac-Baker). For {s≥1}, the bifurcation is seeded by solutions of the (effective/homogenized) cubic focusing nonlinear Schrödinger equation (NLS). However, for {1/4 equation, FNLS, with {(-Δ)^s} replacing {-Δ}. The proof is based on a Lyapunov-Schmidt reduction strategy applied to a momentum space formulation. The PN barrier bounds require appropriate uniform decay estimates for the discrete Fourier transform of DNLS discrete solitary waves. A key role is also played by non-degeneracy of the ground state of FNLS, recently proved by Frank, Lenzmann and Silvestrie.
Collapse suppression and soliton stabilization through nonlocality in bulk Kerr media
DEFF Research Database (Denmark)
Bang, Ole; Chemineau, E. T.; Krolikowski, Wieslaw
2000-01-01
We show that self-focusing cannot occur in bulk Kerr media with a nonlocal nonlinear response. We find the stationary solutions and show that nonlocality makes them stable. The results are verified numerically....
Nonlocal means filter-based speckle tracking.
Afsham, Narges; Rasoulian, Abtin; Najafi, Mohammad; Abolmaesumi, Purang; Rohling, Robert
2015-08-01
The objective of sensorless freehand 3-D ultrasound imaging is to eliminate the need for additional tracking hardware and reduce cost and complexity. However, the accuracy of current out-of-plane pose estimation is main obstacle for full 6-degree-of-freedom (DoF) tracking. We propose a new filter-based speckle tracking framework to increase the accuracy of out-of-plane displacement estimation. In this framework, we use the displacement estimation not only for the specific speckle pattern, but for the entire image. We develop a nonlocal means (NLM) filter based on a probabilistic normal variance mixture model of ultrasound, known as Rician-inverse Gaussian (RiIG). To aggregate the local displacement estimations, Stein's unbiased risk estimate (SURE) is used as a quality measure of the estimations. We derive an explicit analytical form of SURE for the RiIG model and use it as a weight factor. The proposed filter-based speckle tracking framework is formulated and evaluated for three commonly used noise models, including the RiIG model. The out-of-plane estimations are compared with our previously proposed model-based algorithm in a set of ex vivo experiments for different tissue types. We show that the proposed RiIG filter-based method is more accurate and less tissue-dependent than the other methods. The proposed method is also evaluated in vivo on the spines of five different subjects to assess the feasibility of a clinical application. The 6-DoF transform parameters are estimated and compared with the electromagnetic tracker measurements. The results show higher tracking accuracy for typical small lateral displacements and tilt rotations between image pairs.
Analysis of radial nonlocal effect on the structural response of carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Pradhan, S.C., E-mail: scp@aero.iitkgp.ernet.in; Mandal, U.
2013-11-01
In this Letter, finite element model is developed to study the effect of nonlocal parameter in the radial structural response of carbon nanotubes. Timoshenko beam model is employed. The influence of nonlocal parameter in the radial direction due to interaction of atoms is defined as the radial nonlocal effect. It is found that there is significant influence of radial nonlocal effect on the structural response of the carbon nanotubes.
Sheridan, J. T.; Kelly, J. V.; O'Brien, G.; Gleeson, M. R.; O'Neill, F. T.
2004-12-01
Non-local and non-linear models of photopolymer materials, which include diffusion effects, have recently received much attention in the literature. The material response is described as non-local as it is assumed that monomers are polymerized to form polymer chains and that these chains grow away from a point of initiation. The non-locality is defined in terms of a spatial non-local material response function. The material model is non-linear as a general non-linear material response to the incident light is included. Typically the numerical method of solution has involved retaining only up to four harmonics of the Fourier series of monomer concentration in the calculations. In this paper a general set of coupled first-order differential equations is derived which allow the inclusion of a higher number of harmonics. The resulting effect on the convergence of the algorithm, as the number of harmonics retained is increased, is investigated. Special care is taken to note the effect of physical parameters, i.e. the non-local material variance σ, the power-law degree k, and the rates of diffusion, D, and polymerization, F0.
Torsional wave propagation in multiwalled carbon nanotubes using nonlocal elasticity
Arda, Mustafa; Aydogdu, Metin
2016-03-01
Torsional wave propagation in multiwalled carbon nanotubes is studied in the present work. Governing equation of motion of multiwalled carbon nanotube is obtained using Eringen's nonlocal elasticity theory. The effect of van der Waals interaction coefficient is considered between inner and outer nanotubes. Dispersion relations are obtained and discussed in detail. Effect of nonlocal parameter and van der Waals interaction to the torsional wave propagation behavior of multiwalled carbon nanotubes is investigated. It is obtained that torsional van der Waals interaction between adjacent tubes can change the rotational direction of multiwalled carbon nanotube as in-phase or anti-phase. The group and escape velocity of the waves converge to a limit value in the nonlocal elasticity approach.
Bell on Bell's theorem: The changing face of nonlocality
Brown, Harvey R
2015-01-01
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates `local causality') became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical form of the local causality condition, and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be a...
Bounding the persistency of the nonlocality of W states
Diviánszky, Péter; Trencsényi, Réka; Bene, Erika; Vértesi, Tamás
2016-04-01
The nonlocal properties of the W states are investigated under particle loss. By removing all but two particles from an N -qubit W state, the resulting two-qubit state is still entangled. Hence, the W state has high persistency of entanglement. We ask an analogous question regarding the persistency of nonlocality [see N. Brunner and T. Vértesi, Phys. Rev. A 86, 042113 (2012), 10.1103/PhysRevA.86.042113]. Namely, we inquire what is the minimal number of particles that must be removed from the W state so that the resulting state becomes local. We bound this value in function of N qubits by considering Bell nonlocality tests with two alternative settings per site. In particular, we find that this value is between 2 N /5 and N /2 for large N . We also develop a framework to establish bounds for more than two settings per site.
Near field radiative heat transfer between two nonlocal dielectrics
Singer, F; Joulain, Karl
2015-01-01
We explore in the present work the near-field radiative heat transfer between two semi-infinite parallel nonlocal dielectric planes by means of fluctuational electrodynamics. We use atheory for the nonlocal dielectric permittivityfunction proposed byHalevi and Fuchs. This theory has the advantage to includedifferent models performed in the literature. According to this theory, the nonlocal dielectric function is described by a Lorenz-Drude like single oscillator model, in which the spatial dispersion effects are represented by an additional term depending on the square of the total wavevector k. The theory takes into account the scattering of the electromagneticexcitation at the surface of the dielectric material, which leads to the need of additional boundary conditions in order to solve Maxwell's equations and treat the electromagnetic transmission problem. The additional boundary conditions appear as additional surface scattering parameters in the expressions of the surface impedances. It is shown that the...
Quantum theory is classical mechanics with non-local existence
Hegseth, John
2009-01-01
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized to allow many paths due to the non-local existence of particles in phase space. This principle allows a physical system to evolve non-locally in phase space while still allowing a representation that uses many classical paths. Whereas a point in phase space represents a classical system's state, I represent the state of a non-local system by a mixed trajectory. This formulation naturally leads to the transactional interpretation for resolving the paradoxes of the measurement problem. This principle also suggests a more flexible framework for formulating theories based on invariant actions and provides a single conceptual framework for discussing many areas of science.
Extremely nonlocal optical nonlinearities in atoms trapped near a waveguide
Shahmoon, Ephraim; Stimming, Hans Peter; Mazets, Igor; Kurizki, Gershon
2014-01-01
Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms can be tailored. When the atoms are in an electromagnetically-induced transparency configuration, the atomic interactions are translated to long-range interactions between photons and thus to highly nonlocal optical nonlinearities. We derive and analyze the governing nonlinear propagation equation, finding a roton-like excitation spectrum for light and the emergence of long-range order in its output intensity. These predictions open the door to studies of unexplored wave dynamics and many-body physics with highly-nonlocal interactions of optical fields in one dimension.
Nonlocal Measurements in the Time-Symmetric Quantum Mechanics
Vaidman, L; Vaidman, Lev; Nevo, Izhar
2005-01-01
Although nondemolition, reliable, and instantaneous quantum measurements of some nonlocal variables are impossible, demolition reliable instantaneous measurements are possible for all variables. It is shown that this is correct also in the framework of the time-symmetric quantum formalism, i.e. nonlocal variables of composite quantum systems with quantum states evolving both forward and backward in time are measurable in a demolition way. The result follows from the possibility to reverse with certainty the time direction of a backward evolving quantum state. Demolition measurements of nonlocal backward evolving quantum states require remarkably small resources. This is so because the combined operation of time reversal and teleportation of a local backward evolving quantum state requires only a single quantum channel and no transmission of classical information.
A Caveat on Building Nonlocal Models of Cosmology
Tsamis, N C
2014-01-01
Nonlocal models of cosmology might derive from graviton loop corrections to the effective field equations from the epoch of primordial inflation. Although the Schwinger-Keldysh formalism would automatically produce causal and conserved effective field equations, the models so far proposed have been purely phenomenological. Two techniques have been employed to generate causal and conserved field equations: either varying an invariant nonlocal effective action and then enforcing causality by the ad hoc replacement of any advanced Green's function with its retarded counterpart, or else introducing causal nonlocality into a general ansatz for the field equations and then enforcing conservation. We point out here that the two techniques access very different classes of models, and that neither one of them may represent what would actually arise from fundamental theory.
Generalized conservation laws in non-local field theories
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Generalised conservation laws in non-local field theories
Kegeles, Alexander
2015-01-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalised conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalisation of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Modelling population growth with delayed nonlocal reaction in 2-dimensions.
Liang, Dong; Wu, Jianhong; Zhang, Fan
2005-01-01
In this paper, we consider the population growth of a single species living in a two-dimensional spatial domain. New reaction-difusion equation models with delayed nonlocal reaction are developed in two-dimensional bounded domains combining diferent boundary conditions. The important feature of the models is the reflection of the joint efect of the difusion dynamics and the nonlocal maturation delayed efect. We consider and ana- lyze numerical solutions of the mature population dynamics with some wellknown birth functions. In particular, we observe and study the occurrences of asymptotically stable steady state solutions and periodic waves for the two-dimensional problems with nonlocal delayed reaction. We also investigate numerically the efects of various parameters on the period, the peak and the shape of the periodic wave as well as the shape of the asymptotically stable steady state solution.
The Nonlocal p-Laplacian Evolution for Image Interpolation
Directory of Open Access Journals (Sweden)
Yi Zhan
2011-01-01
Full Text Available This paper presents an image interpolation model with nonlocal p-Laplacian regularization. The nonlocal p-Laplacian regularization overcomes the drawback of the partial differential equation (PDE proposed by Belahmidi and Guichard (2004 that image density diffuses in the directions pointed by local gradient. The grey values of images diffuse along image feature direction not gradient direction under the control of the proposed model, that is, minimal smoothing in the directions across the image features and maximal smoothing in the directions along the image features. The total regularizer combines the advantages of nonlocal p-Laplacian regularization and total variation (TV regularization (preserving discontinuities and 1D image structures. The derived model efficiently reconstructs the real image, leading to a natural interpolation, with reduced blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.
Nonlocal quartic interactions and universality classes in perovskite manganites.
Singh, Rohit; Dutta, Kishore; Nandy, Malay K
2015-07-01
A modified Ginzburg-Landau model with a screened nonlocal interaction in the quartic term is treated via Wilson's renormalization-group scheme at one-loop order to explore the critical behavior of the paramagnetic-to-ferromagnetic phase transition in perovskite manganites. We find the Fisher exponent η to be O(ε) and the correlation exponent to be ν=1/2+O(ε) through epsilon expansion in the parameter ε=d(c)-d, where d is the space dimension, d(c)=4+2σ is the upper critical dimension, and σ is a parameter coming from the nonlocal interaction in the model Hamiltonian. The ensuing critical exponents in three dimensions for different values of σ compare well with various existing experimental estimates for perovskite manganites with various doping levels. This suggests that the nonlocal model Hamiltonian contains a wide variety of such universality classes.
Nonlocal thermal transport across embedded few-layer graphene sheets.
Liu, Ying; Huxtable, Scott T; Yang, Bao; Sumpter, Bobby G; Qiao, Rui
2014-12-17
Thermal transport across the interfaces between few-layer graphene sheets and soft materials exhibits intriguing anomalies when interpreted using the classical Kapitza model, e.g. the conductance of the same interface differs greatly for different modes of interfacial thermal transport. Using atomistic simulations, we show that such thermal transport follows a nonlocal flux-temperature drop constitutive law and is characterized jointly by a quasi-local conductance and a nonlocal conductance instead of the classical Kapitza conductance. The nonlocal model enables rationalization of many anomalies of the thermal transport across embedded few-layer graphene sheets and should be used in studies of interfacial thermal transport involving few-layer graphene sheets or other ultra-thin layered materials.
Image and video restorations via nonlocal kernel regression.
Zhang, Haichao; Yang, Jianchao; Zhang, Yanning; Huang, Thomas S
2013-06-01
A nonlocal kernel regression (NL-KR) model is presented in this paper for various image and video restoration tasks. The proposed method exploits both the nonlocal self-similarity and local structural regularity properties in natural images. The nonlocal self-similarity is based on the observation that image patches tend to repeat themselves in natural images and videos, and the local structural regularity observes that image patches have regular structures where accurate estimation of pixel values via regression is possible. By unifying both properties explicitly, the proposed NL-KR framework is more robust in image estimation, and the algorithm is applicable to various image and video restoration tasks. In this paper, we apply the proposed model to image and video denoising, deblurring, and superresolution reconstruction. Extensive experimental results on both single images and realistic video sequences demonstrate that the proposed framework performs favorably with previous works both qualitatively and quantitatively.
Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
Directory of Open Access Journals (Sweden)
Maxim A. Molchan
2007-08-01
Full Text Available On the basis of the competing cubic-quintic nonlinearity model, stability (instability of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.
Theory of genuine tripartite nonlocality of Gaussian states.
Adesso, Gerardo; Piano, Samanta
2014-01-10
We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.
Bound on Hardy's nonlocality from the principle of information causality
Ahanj, Ali; Kunkri, Samir; Rai, Ashutosh; Rahaman, Ramij; Joag, Pramod S.
2010-03-01
Recently, the principle of nonviolation of information causality [Nature 461, 1101 (2009)] has been proposed as one of the foundational properties of nature. We explore the Hardy’s nonlocality theorem for two-qubit systems, in the context of generalized probability theory, restricted by the principle of nonviolation of information causality. Applying a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy’s nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics but still much less than what the no-signaling condition permits. We also study the Cabello type nonlocality argument (a generalization of Hardy’s argument) in this context.
An improved and fully implicit multi-group non-local electron transport model and its validations
Sijoy, C. D.; Mishra, V.; Chaurasia, S.
2017-09-01
The combined effect of thermal flux inhibition and non-local electron heat flux in the radiation hydrodynamics (RHD) simulation of laser-driven systems can be accurately predicted by using non-local electron transport (NLET) models. These models can avoid commonly used space and time-independent ad-hoc flux-limiting procedures. However, the use of classical electron collision frequency in these models is rigorously valid for high temperature non-degenerate plasmas. In laser-driven systems, the electron thermal energy transport is important in regions between the critical density and ablation surface where the plasma is partially degenerate. Therefore, an improved model for electron collision frequency in this regime is required to accurately predict the thermal energy transport. Previously, we have reported an improved single group non-local electron transport model by using a wide-range electron collision frequency model valid from warm-dense matter (WDM) to fully ionized plasmas. In this work, we have extended this idea into a two-dimensional multi-group non-local electron transport (MG-NLET) model. Moreover, we have used a fully implicit numerical integration scheme in which the models for multi-group thermal radiation transport, laser absorption, electron-ion thermal energy relaxation and ion heat conduction are included in a single step. The performance of this improved MG-NLET model has been assessed by comparing the simulated foil trajectories with the reported experimental data for laser-driven plastic foils. The results indicate that the improved model yields results that are in better agreement with the experimental data.
Probing Plasmonic Nanostructures with Electron Energy - Loss Spectroscopy
DEFF Research Database (Denmark)
Raza, Søren
for nonlocal response. The experimental work comprises the use of electron energy-loss spectroscopy (EELS) to excite and study both localized and propagating surface plasmons in metal structures. Following a short introduction, we present the theoretical foundation to describe nonlocal response in Maxwell...
Non-locality of Entangled Coherent States and Its Evolution in a Thermal Reservoir
Institute of Scientific and Technical Information of China (English)
GONG Ren-Shan
2005-01-01
Regarding the necessary and sufficient condition violating Bell-CHSH's inequality as criterion for nonlocality of entangled states, we present a perturbative calculation determining non-locality of evolving entangled states.Furthermore, by means of the perturbative calculation, the non-locality and its evolution of two kinds of entangled coherent states in a thermal reservoir are discussed.
Energy Technology Data Exchange (ETDEWEB)
Tao, Jianmin [Los Alamos National Laboratory; Perdew, John P [TULANE UNIV; Staroverov, Viktor N [UNIV OF WESTERN ONTARIO; Scuseria, Gustavo E [RICE UNIV
2008-01-01
We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a 'normal' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to -1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. 'Abnormal' regions, where non locality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semi local exchange energy densities locally (i.e., with a mixing fraction that is a function of position r and a functional of the density). Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters (corresponding roughly to the four kinds of abnormal regions). Our local hybrid functional is perhaps the first accurate size-consistent density functional with full exact exchange. It satisfies other known
Application of Nonlocal Electron Kinetics to Plasma Technologies
Kaganovich, Igor D.
2011-10-01
Partially ionized plasmas are typically in a highly non-equilibrium thermodynamic state: the electrons are not in equilibrium with the neutral particle species or the ions, and the electrons are also not in equilibrium within their own ensemble, which results in a significant departure of the electron velocity distribution function (EVDF) from a Maxwellian. These non-equilibrium conditions provide considerable freedom to choose optimal plasma parameters for applications, which make gas-discharge plasmas remarkable tools for a variety of plasma applications, including plasma processing, discharge lighting, plasma propulsion, particle beam sources, and nanotechnology. Significant progress in understanding the formation of non-Maxwellian EVDF in the self-consistent electric fields has been one of the major achievements in the low-temperature plasmas during the last decade. This progress was made possible by a synergy between full-scale particle-in-cell simulations, analytical models, and experiments. Specific examples include rf discharges, dc discharges with auxiliary electrodes, Hall thruster discharges. In each example, nonlocal kinetic effects are identified as the main mechanisms responsible for the surprising degree of discharge self-organization. These phenomena include: explosive generation of cold electrons with rf power increase in low-pressure rf discharges; abrupt changes in discharge structure with increased bias voltage on a third electrode in a dc discharge with hot cathode; absence of a steady-state regime in Hall thruster discharges with intense secondary electron emission due to coupling of the sheath properties and the EVDF. In collaboration with Y. Raitses, A.V. Khrabrov, M. Campanell, V. I. Demidov, D. Sydorenko, I. Schweigert, and A. S. Mustafaev. Research supported by the U.S. Department of Energy.
Discrete model of dislocations in fractional nonlocal elasticity
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2016-01-01
Full Text Available Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used. The fractional differences allow us to describe long-range interactions in materials. In continuous limit the suggested discrete models give continuum models of dislocations in nonlocal continua. Fractional generalization of the Frenkel–Kontorova model by using long-range interactions is suggested. We also propose a fractional generalization of interacting atomic chains (IAC model of dislocations by considering long-range interacting chains.
Nonlocal plasticity effects on interaction of different size voids
DEFF Research Database (Denmark)
Tvergaard, Viggo; Niordson, Christian Frithiof
2004-01-01
A nonlocal elastic-plastic material model is used to show that the rate of void growth is significantly reduced when the voids are small enough to be comparable with a characteristic material length. For a very small void in the material between much larger voids the competition between...... an increased growth rate due to the stress concentrations around the larger voids and a reduced growth rate due to the nonlocal effects is studied. The analyses are based on an axisymmetric unit cell model with special boundary conditions, which allow for a relatively simple investigation of a full three...
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
Single-particle nonlocality and entanglement with the vacuum
Björk, G; Sánchez-Soto, L L
2001-01-01
We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell's inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process one is led to the conclusion that even a single particle can show nonlocal properties.
Accelerating cosmologies from non-local higher-derivative gravity
Capozziello, Salvatore; Nojiri, Shin'ichi; Odintsov, Sergei D
2008-01-01
We study accelerating cosmological solutions of a general class of non-linear gravities which depend on Gauss-Bonnet and other higher derivative invariants. To achieve this goal a local formulation with auxiliary scalars for arbitrary higher-derivative non-local gravity is developed. It is demonstrated that non-local Gauss-Bonnet gravity can be reduced, in the local formulation, to a model of string-inspired scalar-Gauss-Bonnet gravity. A natural unification, in the theory here developed, of the early-time inflation epoch with a late-time acceleration stage can also be realized.
Accelerating cosmologies from non-local higher-derivative gravity
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli (Italy); Elizalde, Emilio [Consejo Superior de Investigaciones Cientificas ICE/CSIC-IEEC, Campus UAB, Facultat de Ciencies, Torre C5-Parell-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Nojiri, Shin' ichi [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan)], E-mail: nojiri@phys.nagoya-u.ac.jp; Odintsov, Sergei D. [Institucio Catalana de Recerca i Estudis Avancats (ICREA) and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra, Barcelona (Spain)
2009-01-12
We study accelerating cosmological solutions of a general class of non-linear gravities which depend on Gauss-Bonnet and other higher derivative invariants. To achieve this goal a local formulation with auxiliary scalars for arbitrary higher-derivative non-local gravity is developed. It is demonstrated that non-local Gauss-Bonnet gravity can be reduced, in the local formulation, to a model of string-inspired scalar-Gauss-Bonnet gravity. A natural unification, in the theory here developed, of the early-time inflation epoch with a late-time acceleration stage can also be realized.
Genuine multipartite nonlocality of permutationally invariant Gaussian states
Xu, Buqing; Adesso, Gerardo
2016-01-01
We investigate genuine multipartite nonlocality of pure permutationally invariant multimode Gaussian states of continuous variable systems, as detected by the violation of Svetlichny inequality. We identify the phase space settings leading to the largest violation of the inequality when using displaced parity measurements, distinguishing between even and odd number of modes. We further consider pseudospin measurements and show that, for three-mode states with asymptotically large squeezing degree, particular settings of these measurements allow one to approach the maximum violation allowed by quantum mechanics. This indicates that the highest possible genuine multipartite quantum nonlocality is in principle verifiable on Gaussian states.
Localization of Nonlocal Symmetries and Symmetry Reductions of Burgers Equation
Wu, Jian-Wen; Lou, Sen-Yue; Yu, Jun
2017-05-01
The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method. The auto-Bäcklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained. Supported by the Global Change Research Program China under Grant No. 2015CB953904, the National Natural Science Foundations of China under Grant Nos. 11435005, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No. ZF1213, and K. C. Wong Magna Fund in Ningbo University
Dynamical quenching with non-local alpha and downward pumping
Brandenburg, A; Käpylä, P J
2014-01-01
In light of new results, the one-dimensional mean-field dynamo model of Brandenburg & Kapyla (2007) with dynamical quenching and a nonlocal Babcock-Leighton alpha effect is re-examined for the solar dynamo. We extend the one-dimensional model to include the effects of turbulent downward pumping (Kitchatinov & Olemskoy 2011), and to combine dynamical quenching with shear. We use both the conventional dynamical quenching model of Kleeorin & Ruzmaikin (1982) and the alternate one of Hubbard & Brandenburg (2011), and confirm that with varying levels of non-locality in the alpha effect, and possibly shear as well, the saturation field strength can be independent of the magnetic Reynolds number.
Inhomogeneous broadening in non-interacting nonlocal plasmonic ensembles
DEFF Research Database (Denmark)
Tserkezis, Christos; Maack, Johan Rosenkrantz; Liu, Z.
2016-01-01
The importance of inhomogeneous broadening due to the size dependence of plasmon resonances in few-nm metallic particle ensembles is investigated through different models describing the nonlocal optical response of plasmonic nanospheres. Modal shifts and plasmon line broadening are shown to become...... important within the first-order correction to classical electrodynamics provided by the hydrodynamic Drude model, but turn out to be less prominent once additional single-particle size-dependent damping mechanisms are accounted for through the recently developed Generalized Nonlocal Optical Response theory...
Strong field ionization and gauge dependence of nonlocal potentials
Rensink, T C
2016-01-01
Nonlocal potential models have been used in place of the Coulomb potential in the Schrodinger equation as an efficient means of exploring high field laser-atom interaction in previous works. Al- though these models have found use in modeling phenomena including photo-ionization and ejected electron momentum spectra, they are known to break electromagnetic gauge invariance. This paper examines if there is a preferred gauge for the linear field response and photoionization characteristics of nonlocal atomic binding potentials in the length and velocity gauges. It is found that the length gauge is preferable for a wide range of parameters.
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.
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.
Kirczenow, George
2015-09-01
Valley currents and nonlocal resistances of graphene nanostructures with broken inversion symmetry are considered theoretically in the linear response regime. Scattering state wave functions of electrons entering the nanostructure from the contacts represented by groups of ideal leads are calculated by solving the Lippmann-Schwinger equation and are projected onto the valley state subspaces to obtain the valley velocity fields and total valley currents in the nanostructures. In the tunneling regime when the Fermi energy is in the spectral gap around the Dirac point energy, inversion symmetry breaking is found to result in strong enhancement of the nonlocal four-terminal Büttiker-Landauer resistance and in valley currents several times stronger than the conventional electric current. These strong valley currents are the direct result of the injection of electrons from a contact into the graphene in the tunneling regime. They are chiral and occur near contacts from which electrons are injected into the nanostructure whether or not a net electric current flows through the contact. It is also pointed out that enhanced nonlocal resistances in the linear response regime are not a signature of valley currents arising from the combined effect of the electric field and Berry curvature on the velocities of electrons.
Altafini, C
2004-01-01
For the 3-qubit UPB state, i.e., the bound entangled state constructed from an Unextendable Product Basis of Bennett et al. (Phys. Rev. Lett. 82:5385, 1999), we provide a set of violations of Local Hidden Variable (LHV) models based on the particular type of reflection symmetry encoded in this state. The explicit nonlocal unitary operation needed to prepare the state from its reflected separable mixture of pure states is given, as well as a nonlocal one-parameter orbit of states with Positive Partial Transpositions (PPT) which swaps the entanglement between a state and its reflection twice during a period.
Gisin, Nicolas
2010-01-01
Observing the violation of Bell's inequality tells us something about all possible future theories: they must all predict nonlocal correlations. Hence Nature is nonlocal. After an elementary introduction to nonlocality and a brief review of some recent experiments, I argue that Nature's nonlocality together with the existence of free will is incompatible with the many-worlds view of quantum physics.
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 is o...
Acceleration-induced nonlocality: kinetic memory versus dynamic memory
Chicone, C.; Mashhoon, B.
2001-01-01
The characteristics of the memory of accelerated motion in Minkowski spacetime are discussed within the framework of the nonlocal theory of accelerated observers. Two types of memory are distinguished: kinetic and dynamic. We show that only kinetic memory is acceptable, since dynamic memory leads to divergences for nonuniform accelerated motion.
A nonlocal parabolic system with application to a thermoelastic problem
Directory of Open Access Journals (Sweden)
Y. Lin
1999-01-01
problem is first transformed into an equivalent nonlocal parabolic systems using a transformation, and then the existence and uniqueness of the solutions are demonstrated via the theoretical potential representation theory of the parabolic equations. Finally some realistic situations in the applications are discussed using the results obtained in this paper.
THE NONLOCAL INITIAL PROBLEMS OF A SEMILINEAR EVOLUTION EQUATION
Institute of Scientific and Technical Information of China (English)
王远弟; 冉启康
2004-01-01
The purpose of this paper is to investigate the existence of solutions to a nonlocal Cauchy problem for an evolution equation. The methods used here include the abstract semigroup methods in proper spaces and Schauder's theorem.And the abstract results are applied to a system of nonlinear partial differential equations with nonlinear boundary conditions.
Non-local common cause explanations for EPR
Egg, Matthias
2013-01-01
The paper argues that a causal explanation of the correlated outcomes of EPR-type experiments is desirable and possible. It shows how Bohmian mechanics and the GRW mass density theory offer such an explanation in terms of a non-local common cause.
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...... Purcell factors, and thus has important implications for quantum plasmonics....
Vortex stabilization by means of spatial solitons in nonlocal media
Izdebskaya, Yana; Krolikowski, Wieslaw; Smyth, Noel F.; Assanto, Gaetano
2016-05-01
We investigate how optical vortices, which tend to be azimuthally unstable in local nonlinear materials, can be stabilized by a copropagating coaxial spatial solitary wave in nonlocal, nonlinear media. We focus on the formation of nonlinear vortex-soliton vector beams in reorientational soft matter, namely nematic liquid crystals, and report on experimental results, as well as numerical simulations.
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...
Fractional evolution equation nonlocal problems with noncompact semigroups
Directory of Open Access Journals (Sweden)
Xuping Zhang
2016-01-01
Full Text Available This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations. New existence theorems are obtained by means of the fixed point theorem for condensing maps. The results extend and improve some related results in this direction.
Nonlocal effects on localization in a void-sheet
DEFF Research Database (Denmark)
Tvergaard, Viggo; Needleman, A.
1997-01-01
solid under plane strain conditions are here used to compare with predictions of a nonlocal Version of a porous ductile material model. Both the critical strain for the onset of plastic flow localization and the slope of the stress-strain curve in the post-localization range are compared...
Theory of nonlocal heat transport in fully ionized plasma
Energy Technology Data Exchange (ETDEWEB)
Maximov, A.V. (Tesla Labs., Inc., La Jolla, CA (United States)); Silin, V.P. (P.N. Lebedev Inst., Russian Academy of Sciences, Moscow (Russia))
1993-01-25
A new analytic solution of the electron kinetic equation describing the interacting of the electromagnetic heating field with plasma is obtained in the region of plasma parameters where the Spitzer-Harm classical theory is invalid. A novel expression for the nonlocal electron thermal conductivity is derived. (orig.).
On nonlocal problems for fractional differential equations in Banach spaces
Directory of Open Access Journals (Sweden)
XiWang Dong
2011-01-01
Full Text Available In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations
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H.L. Tidke
2010-12-01
Full Text Available The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.
Stable rotating dipole solitons in nonlocal optical media
DEFF Research Database (Denmark)
Lopez-Aguayo, Servando; Desyatnikov, Anton S.; Kivshar, Yuri S.
2006-01-01
We reveal that nonlocality can provide a simplæe physical mechanism for stabilization of multihump optical solitons and present what we believe to be the first example of stable rotating dipole solitons and soliton spiraling, which we are known to be unstable in all types of realistic nonlinear...
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...
Flare loop radiative hydrodynamics. III - Nonlocal radiative transfer effects
Canfield, R. C.; Fisher, G. H.; Mcclymont, A. N.
1983-01-01
The study has three goals. The first is to demonstrate that processes exist whose intrinsic nonlocal nature cannot be represented by local approximations. The second is to elucidate the physical nature and origins of these nonlocal processes. The third is to suggest that the methods and results described here may prove useful in constructing semiempirical models of the chromosphere by means more efficient than trial and error. Matrices are computed that describe the effect of a temperature perturbation at an arbitrary point in the loop on density, hydrogen ionized fraction, total radiative loss rate, and radiative loss rate of selected hydrogen lines and continua at all other points. It is found that the dominant nonlocal radiative transfer effects can be separated into flux divergence coefficient effects and upper level population effects. The former are most important when the perturbation takes place in a region of significant opacity. Upper level population effects arise in both optically thick and thin regions in response to nonlocal density, ionization, and interlocking effects.
Numerical computation of a nonlocal double obstacle problem
Bhowmik, S.K.
2009-01-01
We consider a nonlocal double obstacle problem. This type of problems comes in various biological and physical situations, e.g., in phase transition models. We focus on numerical approximations and fast computation of such a model. We start with considering piece-wise basis functions for spatial app
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 correlations: Fair and unfair strategies in Bayesian games
Roy, Arup; Mukherjee, Amit; Guha, Tamal; Ghosh, Sibasish; Bhattacharya, Some Sankar; Banik, Manik
2016-09-01
An interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform classical equilibrium strategies in common-interest Bayesian games and also in conflicting-interest Bayesian games. Classical equilibrium strategies can be of two types, fair and unfair. Whereas in fair equilibrium payoffs of different players are equal, in the unfair case they differ. An advantage of nonlocal correlation has been demonstrated over fair strategies only. We show that quantum strategies can outperform even the unfair classical equilibrium strategies. For this purpose we consider a class of two-player Bayesian games. It becomes that such games can have only fair equilibria, both fair and unfair equilibria, or only unfair ones. We provide a simple analytic method to characterize the nonlocal correlations that are advantageous over the classical equilibrium strategies in these games. We also show that quantum advice provides a better social optimality solution (a relevant notion of equilibrium for the unfair case) over the classical one.
Inhomogeneous broadening in non-interacting nonlocal plasmonic ensembles
DEFF Research Database (Denmark)
Tserkezis, Christos; Maack, Johan Rosenkrantz; Liu, Z.
2016-01-01
important within the first-order correction to classical electrodynamics provided by the hydrodynamic Drude model, but turn out to be less prominent once additional single-particle size-dependent damping mechanisms are accounted for through the recently developed Generalized Nonlocal Optical Response theory....... Our work is therefore expected to provide insight and facilitate the design of nanoscale spectroscopy experiments....
Non-local model analysis of heat pulse propagation
Energy Technology Data Exchange (ETDEWEB)
Iwasaki, Takuya [Interdisciplinary Graduate School of Engineering Sciences, Kyushu Univ., Kasuga, Fukuoka (Japan); Itoh, Sanae-I.; Yagi, Masatoshi
1998-10-01
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)
Theoretical Foundations of Incorporating Local Boundary Conditions into Nonlocal Problems
Aksoylu, Burak; Beyer, Horst Reinhard; Celiker, Fatih
2017-08-01
We study nonlocal equations from the area of peridynamics on bounded domains. We present four main results. In our recent paper, we have discovered that, on R, the governing operator in peridynamics, which involves a convolution, is a bounded function of the classical (local) governing operator. Building on this, as main result 1, we construct an abstract convolution operator on bounded domains which is a generalization of the standard convolution based on integrals. The abstract convolution operator is a function of the classical operator, defined by a Hilbert basis available due to the purely discrete spectrum of the latter. As governing operator of the nonlocal equation we use a function of the classical operator, this allows us to incorporate local boundary conditions into nonlocal theories. As main result 2, we prove that the solution operator can be uniquely decomposed into a Hilbert-Schmidt operator and a multiple of the identity operator. As main result 3, we prove that Hilbert-Schmidt operators provide a smoothing of the input data in the sense a square integrable function is mapped into a function that is smooth up to boundary of the domain. As main result 4, for the homogeneous nonlocal wave equation, we prove that continuity is preserved by time evolution. Namely, the solution is discontinuous if and only if the initial data is discontinuous. As a consequence, discontinuities remain stationary.
ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.
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...... 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....... 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...
The relation between Hardy's non-locality and violation of Bell inequality
Xiang, Yang
2011-06-01
We give an analytic quantitative relation between Hardy's non-locality and Bell operator. We find that Hardy's non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy's non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy's non-locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the Cabello's argument of Hardy's non-locality (a generalization of Hardy's argument) and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy's non-locality under the constraint of information causality with the aid of the above derived relation between Hardy's non-locality and Bell operator.
Spectral non-uniform temperature and non-local heat transfer in the spin Seebeck effect.
Tikhonov, Konstantin S; Sinova, Jairo; Finkel'stein, Alexander M
2013-01-01
Recently discovered spin-dependent thermoelectric effects have merged spin, charge, and thermal physics, known as spin caloritronics, of which the spin Seebeck effect is its most puzzling. Here we present a theory of this effect driven by subthermal non-local phonon heat transfer and spectral non-uniform temperature. The theory explains its non-local behaviour from the fact that phonons that store the energy (thermal) and the phonons that transfer it (subthermal) are located in different parts of the spectrum and have different kinetics. This gives rise to a spectral phonon distribution that deviates from local equilibrium along the substrate and is sensitive to boundary conditions. The theory also predicts a non-magnon origin of the effect in ferromagnetic metals in agreement with observations in recent experiments. Equilibration of the heat flow from the substrate to the Pt probe and backwards leads to a vertical spin current produced by the spin-polarized electrons dragged by the thermal phonons.
Nonlocally-induced (quasirelativistic) bound states: Harmonic confinement and the finite well
Garbaczewski, Piotr
2014-01-01
Nonlocal Hamiltonian-type operators, like e.g. fractional and quasirelativistic, seem to be instrumental for a conceptual broadening of current quantum paradigms. However physically relevant properties of related quantum systems have not yet received due (and scientifically undisputable) coverage in the literature. In the present paper we address Schr\\"{o}dinger-type eigenvalue problems for $H=T+V$, where a kinetic term $T=T_m$ is a quasirelativistic energy operator $T_m = \\sqrt{-\\hbar ^2c^2 \\Delta + m^2c^4} - mc^2$ of mass $m\\in (0,\\infty)$ particle. A potential $V$ we assume to refer to the harmonic confinement or finite well of an arbitrary depth. We analyze spectral solutions of the pertinent nonlocal quantum systems with a focus on their $m$-dependence. Extremal mass $m$ regimes for eigenvalues and eigenfunctions of $H$ are investigated: (i) $m\\ll 1$ spectral affinity ("closeness") with the Cauchy-eigenvalue problem ($T_m \\sim T_0=\\hbar c |\
Directory of Open Access Journals (Sweden)
Rubing Xi
2014-01-01
Full Text Available The variational models with nonlocal regularization offer superior image restoration quality over traditional method. But the processing speed remains a bottleneck due to the calculation quantity brought by the recent iterative algorithms. In this paper, a fast algorithm is proposed to restore the multichannel image in the presence of additive Gaussian noise by minimizing an energy function consisting of an l2-norm fidelity term and a nonlocal vectorial total variational regularization term. This algorithm is based on the variable splitting and penalty techniques in optimization. Following our previous work on the proof of the existence and the uniqueness of the solution of the model, we establish and prove the convergence properties of this algorithm, which are the finite convergence for some variables and the q-linear convergence for the rest. Experiments show that this model has a fabulous texture-preserving property in restoring color images. Both the theoretical derivation of the computation complexity analysis and the experimental results show that the proposed algorithm performs favorably in comparison to the widely used fixed point algorithm.
Shen, Hao; Chen, Li; Ferrari, Lorenzo; Lin, Meng-Hsien; Mortensen, N Asger; Gwo, Shangjr; Liu, Zhaowei
2017-03-02
The advances in recent nanofabrication techniques have facilitated explorations of metal structures into nanometer scales, where the traditional local-response Drude model with hard-wall boundary conditions fails to accurately describe their optical responses. The emerging nonlocal effects in single ultrasmall silver nanoparticles have been experimentally observed in single-particle spectroscopy enabled by the unprecedented high spatial resolution of electron energy loss spectroscopy (EELS). However, the unambiguous optical observation of such new effects in gold nanoparticles has yet not been reported, due to the extremely weak scattering and the obscuring fingerprint of strong interband transitions. Here we present a nanosystem, a superlattice monolayer formed by sub-10 nm gold nanoparticles. Plasmon resonances are spectrally well-separated from interband transitions, while exhibiting clearly distinguishable blueshifts compared to predictions by the classical local-response model. Our far-field spectroscopy was performed by a standard optical transmission and reflection setup, and the results agreed excellently with the hydrodynamic nonlocal model, opening a simple and widely accessible way for addressing quantum effects in nanoplasmonic systems.
Non-local effects in a stratified glow discharge with dust particles
Energy Technology Data Exchange (ETDEWEB)
Sukhinin, G I; Fedoseev, A V [Institute of Thermophysics SB RAS, Lavrentyev Ave., 1, Novosibirsk, 630090 (Russian Federation); Ramazanov, T S; Amangaliyeva, R Zh; Dosbalayev, M K; Jumabekov, A N [Institute of Experimental and Theoretical Physics, Al Farabi Kazakh National University, Tole Bi, 96a, Almaty, 050012 (Kazakhstan)], E-mail: fedoseev@itp.nsc.ru
2008-12-21
The work is aimed at describing non-local effects in the positive column of a low-pressure stratified dc glow discharge in argon with dust particles in a vertical cylindrical discharge tube. Numerical calculations of plasma parameters in the axis of the discharge tube were performed with the help of a hybrid model based on the solution of a non-local Boltzmann equation for electron energy distribution function (EEDF). Axial distributions of optical emission from striations with dust particles were measured experimentally. Negatively charged dust particles in a low-pressure stratified gas discharge should levitate at the anode-side branch of an electric field distribution above its maximum. At the same time the experiments showed that the dust particles levitate at the cathode side of a stratum. This paradox is explained by the fact that in a low-pressure striated discharge the optical emission distribution is displaced relative to the electric field distribution that was shown both by numerical simulations and experimental measurements.
Fukukawa, Kenji
2010-01-01
The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.
Nonlocal nucleon-nucleus interactions in (d ,p ) reactions: Role of the deuteron D state
Bailey, G. W.; Timofeyuk, N. K.; Tostevin, J. A.
2017-02-01
Theoretical models of the (d ,p ) reaction are exploited for both nuclear astrophysics and spectroscopic studies in nuclear physics. Usually, these reaction models use local optical model potentials to describe the nucleon- and deuteron-target interactions. Within such a framework, the importance of the deuteron D state in low-energy reactions is normally associated with spin observables and tensor polarization effects, with very minimal influence on differential cross sections. In contrast, recent work that includes the inherent nonlocality of the nucleon optical model potentials in the Johnson-Tandy adiabatic-model description of the (d ,p ) transition amplitude, which accounts for deuteron break-up effects, shows sensitivity of the reaction to the large n -p relative momentum content of the deuteron wave function. The dominance of the deuteron D -state component at such high momenta leads to significant sensitivity of calculated (d ,p ) cross sections and deduced spectroscopic factors to the choice of deuteron wave function [Phys. Rev. Lett. 117, 162502 (2016), 10.1103/PhysRevLett.117.162502]. We present details of the Johnson-Tandy adiabatic model of the (d ,p ) transfer reaction generalized to include the deuteron D state in the presence of nonlocal nucleon-target interactions. We present exact calculations in this model and compare these to approximate (leading-order) solutions. The latter, approximate solutions can be interpreted in terms of local optical potentials, but evaluated at a shifted value of the energy in the nucleon-target system. This energy shift is increased when including the D -state contribution. We also study the expected dependence of the D -state effects on the separation energy and orbital angular momentum of the transferred nucleon. Their influence on the spectroscopic information extracted from (d ,p ) reactions is quantified for a particular case of astrophysical significance.
On wave propagation characteristics in fluid saturated porous materials by a nonlocal Biot theory
Tong, Lihong; Yu, Yang; Hu, Wentao; Shi, Yufeng; Xu, Changjie
2016-09-01
A nonlocal Biot theory is developed by combing Biot theory and nonlocal elasticity theory for fluid saturated porous material. The nonlocal parameter is introduced as an independent variable for describing wave propagation characteristics in poroelastic material. A physical insight on nonlocal term demonstrates that the nonlocal term is a superposition of two effects, one is inertia force effect generated by fluctuation of porosity and the other is pore size effect inherited from nonlocal constitutive relation. Models for situations of excluding fluid nonlocal effect and including fluid nonlocal effect are proposed. Comparison with experiment confirms that model without fluid nonlocal effect is more reasonable for predicting wave characteristics in saturated porous materials. The negative dispersion is observed theoretically which agrees well with the published experimental data. Both wave velocities and quality factors as functions of frequency and nonlocal parameter are examined in practical cases. A few new physical phenomena such as backward propagation and disappearance of slow wave when exceeding critical frequency and disappearing shear wave in high frequency range, which were not predicted by Biot theory, are demonstrated.
Nonlocal operators, parabolic-type equations, and ultrametric random walks
Energy Technology Data Exchange (ETDEWEB)
Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx [Centro de Investigacion y de Estudios Avanzados del I.P.N., Departamento de Matematicas, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico D.F., C.P. 07360 (Mexico)
2013-11-15
In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.
Dynamic crack growth in a nonlocal progressively cavitating solid
DEFF Research Database (Denmark)
Needleman, A.; Tvergaard, Viggo
1998-01-01
Dynamic crack growth is analyzed numerically using a nonlocal constitutive formulation for a porous ductile material. The delocalization relates to the void growth and coalescence mechanism and is incorporated in terms of an integral condition on the rate of increase of the void volume fraction....... The material is modeled as elastic-viscoplastic with the thermal softening due to adiabatic heating accounted for. Finite element computations are carried our for edge cracked specimens subject to tensile impact loading. Two values of the material characteristic length and two finite-element discretizations...... to increase and the crack speed to decrease with increasing values of the material characteristic length. The crack growth predictions using the nonlocal constitutive model exhibit less mesh sensitivity than the corresponding ones based on the local constitutive relation. However, for the largest value...
Quantum non-locality - It ain't necessarily so...
Zukowski, Marek
2015-01-01
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc....
Wave propagation in nanostructures nonlocal continuum mechanics formulations
Gopalakrishnan, Srinivasan
2013-01-01
Wave Propagation in Nanostructures describes the fundamental and advanced concepts of waves propagating in structures that have dimensions of the order of nanometers. The book is fundamentally based on non-local elasticity theory, which includes scale effects in the continuum model. The book predominantly addresses wave behavior in carbon nanotubes and graphene structures, although the methods of analysis provided in this text are equally applicable to other nanostructures. The book takes the reader from the fundamentals of wave propagation in nanotubes to more advanced topics such as rotating nanotubes, coupled nanotubes, and nanotubes with magnetic field and surface effects. The first few chapters cover the basics of wave propagation, different modeling schemes for nanostructures and introduce non-local elasticity theories, which form the building blocks for understanding the material provided in later chapters. A number of interesting examples are provided to illustrate the important features of wave behav...
Symmetry reduction related with nonlocal symmetry for Gardner equation
Ren, Bo
2017-01-01
Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.
Kinematical and nonlocality effects on the nonmesonic weak hypernuclear decay
Barbero, C; Galeao, A P; Krmpotic, F
2003-01-01
We derive in detail the transition potential for nonmesonic lambda-hypernuclear decay in a one-meson-exchange model involving the full pseudoscalar and vector meson octets and including two effects that have been systematically omitted in the literature, or, at best, only partially considered. These are the kinematical effects due to the difference between the lambda and nucleon masses, and the first-order nonlocality corrections, i.e., those involving up to first-order differential operators. Numerical results for $^{12}_\\Lambda$C are presented and they show that the kinematical plus nonlocal corrections have an appreciable influence on the partial decay rates. However, this is somewhat diminished in the total rate. Also the ratio of neutron-induced to proton-induced transitions is only slightly affected, and still cannot be reconciled with the available experimental data. We give indications that the combined effect should be most significant for observables that distinguish between parity-conserving and pa...
Quantum nonlocality in weak-thermal-light interferometry.
Tsang, Mankei
2011-12-30
In astronomy, interferometry of light collected by separate telescopes is often performed by physically bringing the optical paths together in the form of Young's double-slit experiment. Optical loss severely limits the efficiency of this so-called direct detection method, motivating the fundamental question of whether one can achieve a comparable performance using separate optical measurements at the two telescopes before combining the measurement results. Using quantum mechanics and estimation theory, here I show that any such spatially local measurement scheme, such as heterodyne detection, is fundamentally inferior to coherently nonlocal measurements, such as direct detection, for estimating the mutual coherence of bipartite thermal light when the average photon flux is low. This surprising result reveals an overlooked signature of quantum nonlocality in a classic optics experiment.
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.
Nonlocal excitonic–mechanical interaction in a nanosystem
Energy Technology Data Exchange (ETDEWEB)
Zabolotskii, A. A., E-mail: zabolotskii@iae.nsk.su [Russian Academy of Sciences, Institute of Automatics and Electrometry, Siberian Branch (Russian Federation)
2016-11-15
The dynamics of a nanoparticle during its dipole interaction with an excitonic excitation in an extended quasi-one-dimensional polarizable medium is investigated. Bundles of J-aggregates of dye molecules are considered as an example of the latter. The nonlocal excitonic–mechanical interaction between the field of an amplifying or absorbing nanoparticle and excitons in a bundle has been simulated numerically. It has been found that the interaction between the field of the induced nanoparticle dipole and the fields of the molecular dipoles in an aggregate can lead to a change in the particle trajectory and excitonic pulse shape. The possibility of controlling the nanoparticle by excitonic pulses and the reverse effect of the nanoparticle field on the dynamics of excitons due to the nonlocal excitonic–mechanical interaction has been demonstrated.
Deterministic error correction for nonlocal spatial-polarization hyperentanglement.
Li, Tao; Wang, Guan-Yu; Deng, Fu-Guo; Long, Gui-Lu
2016-02-10
Hyperentanglement is an effective quantum source for quantum communication network due to its high capacity, low loss rate, and its unusual character in teleportation of quantum particle fully. Here we present a deterministic error-correction scheme for nonlocal spatial-polarization hyperentangled photon pairs over collective-noise channels. In our scheme, the spatial-polarization hyperentanglement is first encoded into a spatial-defined time-bin entanglement with identical polarization before it is transmitted over collective-noise channels, which leads to the error rejection of the spatial entanglement during the transmission. The polarization noise affecting the polarization entanglement can be corrected with a proper one-step decoding procedure. The two parties in quantum communication can, in principle, obtain a nonlocal maximally entangled spatial-polarization hyperentanglement in a deterministic way, which makes our protocol more convenient than others in long-distance quantum communication.
Nonlocal spin-transport measurement of superconductor-ferromagnet nanostructures
Energy Technology Data Exchange (ETDEWEB)
Kolenda, Stefan; Wolf, Michael J.; Huebler, Florian; Beckmann, Detlef [Institut fuer Nanotechnologie, Karlsruher Institut fuer Technologie (Germany)
2015-07-01
We present measurements of the nonlocal conductance of nanostructures with several ferromagnetic electrodes lying perpendicular on a superconducting wire. In these structures nonlocal conductance is mostly given by diffusion of quasiparticles, which are injected by one of the electrodes and detected by an other one. Applying a magnetic field induces a Zeeman splitting in the quasiparticles density of states, which suppresses the relaxation of injected spin imbalance, thus spin transport over distances of several micrometers is found. While in the previous experiments the magnetic field was aligned parallel to the ferromagnetic electrodes, we also show measurements applying the magnetic field noncollinear with the magnetization of the ferromagnetic electrodes. We compare our results to the previous case.
Evidence for nonlocal electrodynamics in planar Josephson junctions.
Boris, A A; Rydh, A; Golod, T; Motzkau, H; Klushin, A M; Krasnov, V M
2013-09-13
We study the temperature dependence of the critical current modulation I(c)(H) for two types of planar Josephson junctions: a low-Tc Nb/CuNi/Nb and a high-Tc YBa2Cu3O(7-δ) bicrystal grain-boundary junction. At low T both junctions exhibit a conventional behavior, described by the local sine-Gordon equation. However, at elevated T the behavior becomes qualitatively different: the I(c)(H) modulation field ΔH becomes almost T independent and neither ΔH nor the critical field for the penetration of Josephson vortices vanish at Tc. Such an unusual behavior is in good agreement with theoretical predictions for junctions with nonlocal electrodynamics. We extract absolute values of the London penetration depth λ from our data and show that a crossover from local to nonlocal electrodynamics occurs with increasing T when λ(T) becomes larger than the electrode thickness.
Explaination of nonlocal granular fluidity in terms of microscopic fluctuations
Zhang, Qiong; Kamrin, Ken
A recently proposed granular constitutive law has shown capability to predict nonlocal granular rheology using a variable denoted ``granular fluidity''. This work is aimed at finding the microscopic physical meaning of fluidity in terms of fluctuations such as fluctuation of normalized shear stress and fluctuation of velocity. We try to predict the fluidity as a function of the fluctuation of normalized shear stress, and also test Eyring equation and kinetic theory based on the theoretical prediction proposed in other work. We find a consistent definition for the fluidity to be proportional to the product of the velocity fluctuations and some function of packing fraction divided by the average diameter of the grains. This definition shows predictive ability in multiple geometries for which flow behavior is nonlocal. It is notable that the fluidity is well-defined as a function of kinematic state variables, as one would hope for a quantity of this nature.
Uncertainty estimation in diffusion MRI using the nonlocal bootstrap.
Yap, Pew-Thian; An, Hongyu; Chen, Yasheng; Shen, Dinggang
2014-08-01
In this paper, we propose a new bootstrap scheme, called the nonlocal bootstrap (NLB) for uncertainty estimation. In contrast to the residual bootstrap, which relies on a data model, or the repetition bootstrap, which requires repeated signal measurements, NLB is not restricted by the data structure imposed by a data model and obviates the need for time-consuming multiple acquisitions. NLB hinges on the observation that local imaging information recurs in an image. This self-similarity implies that imaging information coming from spatially distant (nonlocal) regions can be exploited for more effective estimation of statistics of interest. Evaluations using in silico data indicate that NLB produces distribution estimates that are in closer agreement with those generated using Monte Carlo simulations, compared with the conventional residual bootstrap. Evaluations using in vivo data demonstrate that NLB produces results that are in agreement with our knowledge on white matter architecture.
Plasmon-enhanced fluorescence near nonlocal metallic nanospheres
DEFF Research Database (Denmark)
Tserkezis, Christos; Stefanou, N.; Wubs, Martijn
) of a dipole emitter. Here we explore the importance of hitherto disregarded nonclassical effects in the description of emitter-plasmon hybrids, focusing on the roles of metal nonlocal optical response and size-dependent plasmon damping [1]. Comparison between the common local response approximation (LRA......) and the generalized nonlocal optical response (GNOR) theory [2] shows that a significant decrease in fluorescence enhancement is obtained for emitters close to small metallic nanospheres or thin metallic nanoshells, while the optimum emitter position is also affected. In this respect, our recent work introduces...... the study of emitterplasmon coupling (in the weak-coupling limit) as a sensitive test for the validity of stateof-the-art nonclassical models. For the regime of strong emitter-plasmon coupling, we anticipate an analogously wide importance of a description beyond classical electrodynamics, particularly once...
Axial vibration analysis of nanocones based on nonlocal elasticity theory
Institute of Scientific and Technical Information of China (English)
Shu-Qi Guo; Shao-Pu Yang
2012-01-01
Carbon nanocones have quite fascinating electronic and structural properties,whose axial vibration is seldom investigated in previous studies.In this paper,based on a nonlocal elasticity theory,a nonuniform rod model is applied to investigate the small-scale effect and the nonuniform effect on axial vibration of nanocones.Using the modified Wentzel-Brillouin-Kramers (WBK) method,an asymptotic solution is obtained for the axial vibration of general nonuniform nanorods.Then,using similar procedure,the axial vibration of nanocones is analyzed for nonuniform parameters,mode number and nonlocal parameters.Explicit expressions are derived for mode frequencies of clamped-clamped and clamped-free boundary conditions.It is found that axial vibration frequencies are highly overestimated by the classical rod model because of ignorance of the effect of small length scale.
Optimizing plasmon-enhanced fluorescence with nonlocal metallic nanospheres
DEFF Research Database (Denmark)
Tserkezis, Christos; Stefanou, Nikolaos; Wubs, Martijn
nonlocal corrections, the plasmon blueshift predicted by the hydrodynamic Drude model [1] leads to a small reduction of η. If however the plasmonic mode does not coincide exactly with λem, this blueshift can tune the mode to increase η. Nevertheless, when size-dependent losses are also taken into account......The fluorescence signal η of molecules coupled to plasmonic nanoparticles (NPs) is optimized through extended simulations, taking the metal nonlocal optical response fully into account. Solid Au and Ag nanospheres, as well as SiO2/Au(Ag) core/shell NPs (of total radius R), are engineered...... to maximize the ratio of radiative to nonradiative losses and match the emitter emission wavelength, λem. For a molecule modeled as an electric dipole p, oriented parallel to the incident field E, the optimal emitter-NP distance is then identified within the local response approximation (LRA). Introducing...
Conserved nonlocal dynamics and critical behavior of uranium ferromagnetic superconductors.
Singh, Rohit; Dutta, Kishore; Nandy, Malay K
2017-01-01
A recent theoretical study [Phys. Rev. Lett. 112, 037202 (2014)10.1103/PhysRevLett.112.037202] has revealed that systems such as uranium ferromagnetic superconductors obey conserved dynamics. To capture the critical behavior near the paramagnetic to ferromagnetic phase transition of these compounds, we study the conserved critical dynamics of a nonlocal Ginzburg-Landau model. A dynamic renormalization-group calculation at one-loop order yields the critical indices in the leading order of ε=d_{c}-d, where d_{c}=4-2ρ is the upper critical dimension, with ρ an exponent in the nonlocal interaction. The predicted static critical exponents are found to be comparable with the available experimentally observed critical exponents for strongly uniaxial uranium ferromagnetic superconductors. The corresponding dynamic exponent z and linewidth exponent w are found to be z=4-ρε/4+O(ε^{2}) and w=1+ρ+3ε/4+O(ε^{2}).
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.
On the no-signaling approach to quantum nonlocality
Energy Technology Data Exchange (ETDEWEB)
Méndez, J. M., E-mail: manolo@ifisica.uaslp.mx; Urías, Jesús, E-mail: jurias@ifisica.uaslp.mx [Instituto de Física, UASLP, San Luis Potosí, San Luis Potosí (Mexico)
2015-03-15
The no-signaling approach to nonlocality deals with separable and inseparable multiparty correlations in the same set of probability states without conflicting causality. The set of half-spaces describing the polytope of no-signaling probability states that are admitted by the most general class of Bell scenarios is formulated in full detail. An algorithm for determining the skeleton that solves the no-signaling description is developed upon a new strategy that is partially pivoting and partially incremental. The algorithm is formulated rigorously and its implementation is shown to be effective to deal with the highly degenerate no-signaling descriptions. Several applications of the algorithm as a tool for the study of quantum nonlocality are mentioned. Applied to a large set of bipartite Bell scenarios, we found that the corresponding no-signaling polytopes have a striking high degeneracy that grows up exponentially with the size of the Bell scenario.
Conserved nonlocal dynamics and critical behavior of uranium ferromagnetic superconductors
Singh, Rohit; Dutta, Kishore; Nandy, Malay K.
2017-01-01
A recent theoretical study [Phys. Rev. Lett. 112, 037202 (2014), 10.1103/PhysRevLett.112.037202] has revealed that systems such as uranium ferromagnetic superconductors obey conserved dynamics. To capture the critical behavior near the paramagnetic to ferromagnetic phase transition of these compounds, we study the conserved critical dynamics of a nonlocal Ginzburg-Landau model. A dynamic renormalization-group calculation at one-loop order yields the critical indices in the leading order of ɛ =dc-d , where dc=4 -2 ρ is the upper critical dimension, with ρ an exponent in the nonlocal interaction. The predicted static critical exponents are found to be comparable with the available experimentally observed critical exponents for strongly uniaxial uranium ferromagnetic superconductors. The corresponding dynamic exponent z and linewidth exponent w are found to be z =4 -ρ ɛ /4 +O (ɛ2) and w =1 +ρ +3 ɛ /4 +O (ɛ2) .
Magnified imaging based on non-Hermitian nonlocal cylindrical metasurfaces
Savoia, Silvio; Valagiannopoulos, Constantinos A.; Monticone, Francesco; Castaldi, Giuseppe; Galdi, Vincenzo; Alà, Andrea
2017-03-01
We show that a cylindrical lensing system composed of two metasurfaces with suitably tailored non-Hermitian (i.e., with distributed gain and loss) and nonlocal (i.e., spatially dispersive) properties can perform magnified imaging with reduced aberrations. More specifically, we analytically derive the idealized surface-impedance values that are required for "perfect" magnification and imaging and elucidate the role and implications of non-Hermiticity and nonlocality in terms of spatial resolution and practical implementation. For a basic demonstration, we explore some proof-of-principle quasilocal and multilayered implementations and independently validate the outcomes via full-wave numerical simulations. We also show that the metasurface frequency-dispersion laws can be chosen so as to ensure unconditional stability with respect to arbitrary temporal excitations. These results, which extend previous studies on planar configurations, may open intriguing venues in the design of metastructures for field imaging and processing.
Entropic Tests of Multipartite Nonlocality and State-Independent Contextuality
Raeisi, Sadegh; Kurzyński, Paweł; Kaszlikowski, Dagomir
2015-05-01
We introduce a multipartite extension of an information-theoretic distance introduced by Zurek [Nature (London) 341, 119 (1989)]. We use it to develop a new tool for studying quantum correlations from an information-theoretic perspective. In particular, we derive entropic tests of multipartite nonlocality for three qubits and for an arbitrary even number of qubits as well as a test of state-independent contextuality. In addition, we rederive the tripartite Mermin inequality and a state-independent noncontextuality inequality by Cabello [Phys. Rev. Lett. 101, 210401 (2008)]. This suggests that the information-theoretic distance approach to multipartite nonlocality and state-independent contextuality can provide a more general treatment of nonclassical correlations than the orthodox approach based on correlation functions.
A histories perspective on characterising quantum non-locality
Dowker, Fay; Wallden, Petros
2013-01-01
We introduce a framework for studying non-locality and contextuality inspired by the path integral formulation of quantum theory. We prove that the existence of a strongly positive joint quantum measure -- the quantum analogue of a joint probability measure -- on a set of experimental probabilities implies the Navascues-Pironio-Acin (NPA) condition $Q^1$ and is implied by the stronger NPA condition $Q^{1+AB}$. A related condition is shown to be equivalent to $Q^{1+AB}$.
Ground state solutions for non-local fractional Schrodinger equations
Directory of Open Access Journals (Sweden)
Yang Pu
2015-08-01
Full Text Available In this article, we study a time-independent fractional Schrodinger equation with non-local (regional diffusion $$ (-\\Delta^{\\alpha}_{\\rho}u + V(xu = f(x,u \\quad \\text{in }\\mathbb{R}^{N}, $$ where $\\alpha \\in (0,1$, $N > 2\\alpha$. We establish the existence of a non-negative ground state solution by variational methods.
Nonlocal quantum cloning via quantum dots trapped in distant cavities
Institute of Scientific and Technical Information of China (English)
Yu Tao; Zhu Ai-Dong; Zhang Shou
2012-01-01
A scheme for implementing nonlocal quantum cloning via quantum dots trapped in cavities is proposed.By modulating the parameters of the system,the optimal 1 → 2 universal quantum cloning machine,1 → 2 phase-covariant cloning machine,and 1 → 3 economical phase-covariant cloning machine are constructed.The present scheme,which is attainable with current technology,saves two qubits compared with previous cloning machines.
Nonlocal Symmetries and Exact Solutions for PIB Equation
Xin, Xiang-Peng; Miao, Qian; Chen, Yong
2012-09-01
In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
Mild Solutions for Fractional Differential Equations with Nonlocal Conditions
Directory of Open Access Journals (Sweden)
Fang Li
2010-01-01
Full Text Available This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions dqx(t/dtq=−Ax(t+f(t,x(t,Gx(t, t∈[0,T], and x(0+g(x=x0, in a Banach space X, where 0