Nonlocal Gate of a Quantum Network via Cavity Quantum Electrodynamics

We propose an experimentally feasible scheme to realize the nonlocal gate between two different nodes of a quantum network. With an entanglement-qubit acts as a quantum channel, our scheme is resist to actual environment noise and can get a high fidelity in current cavity quantum electrodynamics （C-QED） system.     

二阶总广义变分图像放大

为了在图像放大中获得更好的视觉效果,提出了一种基于总广义变分性质的变分放大模型.该模型将原始低分辨图像作为被估计的高分辨放大图像到所在空间的某个子空间的投影,利用二阶总广义变分正则化迭代处理得到被估计放大图像.通过分析新模型的性质,给出了一种有效的原始对偶放大算法.实验结果表明:该方法能去除总变分放大方法产生的图像阶梯块效应,恢复更多的细节边缘及纹理信息,从而重构出高质量的图像;相比于总变分图像放大方法和小波图像放大方法,该方法具有更高的峰值信噪比和更小的均方误差.     

Unpolarized Fragmentation Function for the Pion and Kaon via the Nonlocal Chiral-Quark Model

In this talk we present our recent studies for the unpolarized fragmentation functions for the pion and kaon, employing the nonlocal chiral quark model, which manifests the nonlocal interaction between the quarks and pseudoscalar mesons, in the light-cone frame. It turns out that the nonlocal interaction produces considerable differences in comparison to typical local-interaction models.     

Nonlocal quantum cloning via quantum dots trapped in distant cavities

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.     

体积约束的非局部扩散问题的加罚有限元方法

针对非齐次和齐次体积约束的非局部扩散问题设计了新的有限元方法——加罚有限元方法,并给出该方法的误差分析.数值算例验证了加罚有限元方法的稳定性和有效性.     

Slow Motion and Metastability for a Nonlocal Evolution Equation

In this paper we consider a nonlocal evolution equation in one dimension, which describes the dynamics of a ferromagnetic system in the mean field approximation. In the presence of a small magnetic field, it admits two stationary and homogeneous solutions, representing the stable and metastable phases of the physical system. We prove the existence of an invariant, one dimensional manifold connecting the stable and metastable phases. This is the unstable manifold of a distinguished, spatially nonhomogeneous, stationary solution, called the critical droplet.^{(4, 10)} We show that the points on the manifold are droplets longer or shorter than the critical one, and that their motion is very slow in agreement with the theory of metastable patterns. We also obtain a new proof of the existence of the critical droplet, which is supplied with a local uniqueness result.     

An Isoperimetric Inequality for Fundamental Tones of Free Plates

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given τ > 0, the free plate eigenvalues ω and eigenfunctions u are determined by the equation ΔΔu − τΔu = ωu together with certain natural boundary conditions. The boundary conditions are complicated but arise naturally from the plate Rayleigh quotient, which contains a Hessian squared term |D ² u|².     

Nonlocal transformations for accelerated observers

According to the locality postulate of special relativity, the measurements of physical fields by accelerated observers at a given event in Minkowski spacetime are related to each other by the representations of the Lorentz group. Nonlocal extensions of these representations are necessary, however, once acceleration‐induced nonlocality is taken into account. The particular case of Dirac spinors is treated in detail and the corresponding nonlocal transformation group is studied.     

A Second Quantized Approach to the Rabi Problem

In the present work, the Rabi Problem, involving the response of a spin 1/2 particle subjected to a magnetic field, is considered in a second quantized approach. In this concrete physical scenario, we show that the second quantization procedure can be applied directly in a non-covariant theory. The proposed development explicits not only the relation between the full quantum treatment of the problem and the semiclassical Rabi model, but also the connection of these approaches with the Jaynes-Cummings model. The consistency of the method is checked in the semiclassical limit. The treatment is then extended to the matter component of the Rabi problem so that the Schrödinger equation is directly quantized. Considering the spinorial field, the appearance of a negative energy sector implies a specific identification between Schrödinger’s and Maxwell’s theories. The generalized theory is consistent, strictly quantum and non-relativistic.     

Nonlocal interactions: a jammerian analysis

It is general practice to describe a microsystem by means of a model characterized by probability amplitudes possessed at each spacetime point between preparation and measurement events. Recent developments initiated by Bell's theorem indicate that any such model must in some cases be considered as participating in nonlocal interactions. Adapting ideas originated by Jammer, this paper asserts that that conclusion may be indicative only of limitations in the applicability of physical properties in the modelling of microsystems and thus might not lead to inferences about the microsystems in themselves. Recent discussions of the Aharanov-Bohm effect further exemplify the difference in these alternative interpretations of nonlocality.     

A Stefan Problem with Surface Tension as the Sharp Interface Limit of a Nonlocal System of Phase-Field Type

A model for the evolution of phase boundaries reminiscent of the phase-field model is considered. The equation related to conservation of thermal energy is diffusive and coupled to an equation for the order parameter, which contains a nonlinear convolution operator, related to the limit of an interacting particle model with Kac-potential. Under diffusive rescaling the solutions converge to solutions of the Stefan problem with kinetic undercooling and surface tension.     

Nonlocal shear stress for homogeneous fluids

It has been suggested that for fluids in which the rate of strain varies appreciably over length scales of the order of the intermolecular interaction range, the viscosity must be treated as a nonlocal property of the fluid. The shear stress can then be postulated to be a convolution of this nonlocal viscosity kernel with the strain rate over all space. In this Letter, we confirm that this postulate is correct by a combination of analytical and numerical methods for an atomic fluid out of equilibrium. Furthermore, we show that a gradient expansion of the nonlocal constitutive equation gives a reasonable approximation to the shear stress in the small wave vector limit.     

Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory

Based on the strain gradient and Eringen’s piezoelasticity theories, wave propagation of an embedded double-walled boron nitride nanotube (DWBNNT) conveying fluid is investigated using Euler–Bernoulli beam model. The elastic medium is simulated by the Pasternak foundation. The van der Waals (vdW) forces between the inner and outer nanotubes are taken into account. Since, considering electro-mechanical coupling made the nonlinear motion equations, a numerical procedure is proposed to evaluate the upstream and downstream phase velocities. The results indicate that the effect of nonlinear terms in motion equations on the phase velocity cannot be neglected at lower wave numbers. Furthermore, the effect of fluid-conveying on wave propagation of the DWBNNT is significant at lower wave numbers.     

Nonlocal Appearance of a Macroscopic Angular Momentum

We discuss a type of measurement in which a macroscopically large angular momentum (spin) is “created” nonlocally by the measurement of just a few atoms from a double Fock state. This procedure apparently leads to a blatant nonconservation of a macroscopic variable—the local angular momentum. We argue that while this gedankenexperiment provides a striking illustration of several counter-intuitive features of quantum mechanics, it does not imply a non-local violation of the conservation of angular momentum.     

Inequalities for Means of Chords, with Application to Isoperimetric Problems

We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in $L^2(\mathbb{R}^2)We consider a pair of isoperimetric problems arising in physics. The first concerns a Schr?dinger operator in with an attractive interaction supported on a closed curve Γ, formally given by −Δ−αδ(x−Γ); we ask which curve of a given length maximizes the ground state energy. In the second problem we have a loop-shaped thread Γ in , homogeneously charged but not conducting, and we ask about the (renormalized) potential-energy minimizer. Both problems reduce to purely geometric questions about inequalities for mean values of chords of Γ. We prove an isoperimetric theorem for p-means of chords of curves when p ≤ 2, which implies in particular that the global extrema for the physical problems are always attained when Γ is a circle. The letter concludes with a discussion of the p-means of chords when p > 2.     

Nonlocal models for nonlinear, dispersive waves

Considered herein are model equations for the unidirectional propagation of small-amplitude, nonlinear, dispersive, long waves such as those governed by the classical Korteweg-de Vries equation. Of special interest are physical situations in which the linear dispersion relation is not appropriately approximated by a polynomial, so that the operator modelling dispersive effect is nonlocal. Particular cases in view here are the Benjamin-Ono equation and the intermediate long-wave equation which arise in internal-wave theory, and Smith's equation which governs certain types of continental-shelf waves.

The initial-value problem for these equations is shown to be globally well posed in the classical sense, including continuous dependence upon the initial data and, in certain cases upon the modelling of nonlinear and dispersive effects. Whilst the results are stated for the specific equations listed above, the techniques utilized are seen to have a considerable range of generality as regards application to nonlinear, dispersive evolution equations. Particularly worthy of note is our theorem implying that solutions of the intermediate long-wave equation converge strongly to solutions of the Korteweg-de Vries equation, or to solutions of the Benjamin-Ono equation, in appropriate asymptotic limits.     

Nonlocal condensate model for QCD sum rules

We include effects of nonlocal quark condensates into QCD sum rules (QSR) via the Källén–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 Q²≈10 GeV²$Q^2\approx 10{\text{GeV}}^2$. It is observed that the nonlocal quark condensate contribution descends like 1/Q²$1/Q^2$, different from the exponential decrease in Q²$Q^2$ obtained in the literature, and contrary to the linear rise in the local-condensate approximation.     

Long-Time Asymptotics for the Nonlocal MKdV Equation

In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal m KdV equation. In contrast with the classical mKdV equation,we find some new and different results on long-time asymptotics for the nonlocal mKdV equation and some additional assumptions about the scattering data are made in our main results.