Effects of phase decoherence on the entanglement of a two-qubit anisotropic Heisenberg XYZ chain with an in-plane magnetic field

We investigate the phase decoherence effects on the entanglement of a two-qubit anisotropic Heisenberg model with a nonuniform magnetic field in the x–z-plane. As a measure of the entanglement, the concurrence of the system is calculated. It is shown that when the magnetic field is along the z-axis, the nonuniform and uniform components of the field have no influence on the entanglement for the cases of and , respectively. But when the magnetic field is not along the z-axis, both the uniform and the nonuniform components of the field will introduce the decoherence effects. It is found that the effects of the Heisenberg chain's anisotropy in the Z-direction on the entanglement are dependent on the direction of the field. Moreover, the larger the initial concurrence is, the higher value it will exhibit during the time evolution of the system for a proper set of the parameters ν, Δ, θ, γ , B and b.     

Multi-way dual Cheeger constants and spectral bounds of graphs

We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces. We further extend those results to a general reversible Markov operator and find applications in characterizing its essential spectrum.     

Robust output feedback cruise control for high-speed train movement with uncertain parameters

In this paper,the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated.The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers,which is subject to rolling mechanical resistance,aerodynamic drag and wind gust.Based on Lyapunov’s stability theory,the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities(LMIs),under which the high-speed train tracks the desired speed,the relative spring displacement between the two neighboring cars is stable at the equilibrium state,and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed.One numerical example is given to illustrate the effectiveness of the proposed methods.     

k-Edge Failure Resilient Network Design

We design a network that supports a feasible multicommodity flow even after the failures of any k edges. We present a mixed-integer linear program (MILP), a cutting plane algorithm, and a column-and-cut algorithm. The algorithms add constraints to repair vulnerabilities in partial network designs. Empirical studies on previously unsolved instances of SNDlib demonstrate their effectiveness.     

The bound of entanglement of superpositions with more than two components

A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition state which can be expressed according to entanglements of its component states. Especially, if the component states are mutually bi-orthogonal, the entanglement of the superposition state can be exactly given in terms of the entanglements of the states being superposed.     

Analysis of a recent experiment seemingly favouring local realism against quantum mechanics

A recent experiment by Brida et al. [Eur. Phys. J. D 44, 547 (2007)] is analyzed with the conclusion that the results disagree with standard quantum predictions but fit a simple local hidden variables model. New experiments are proposed which might throw new light on the anomaly.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Infinitely Many Critical Points of Non-Differentiable Functions and Applications to a Neumann-Type Problem Involving the p-Laplacian

For a family of functionals in a Banach space, which are possibly non-smooth and depend also on a positive real parameter, the existence of a sequence of critical points (according to Motreanu and Panagiotopoulos (“Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities,” Nonconvex Optimization Applications, Vol. 29, Kluwer, Dordrecht, 1998, Chap. 3)) is established by mainly adapting a new technique due to Ricceri (2000, J. Comput. Appl. Math.113, 401-410). Two applications are then presented. Both of them treat the Neumann problem for an elliptic variational-hemivariational inequality with p-Laplacian.     

A Class of Projection Methods for General Variational Inequalities

In this paper, we consider and analyze a new class of projection methods for solving pseudomonotone general variational inequalities using the Wiener-Hopf equations technique. The modified methods converge for pseudomonotone operators. Our proof of convergence is very simple as compared with other methods. The proposed methods include several known methods as special cases.     

MERIT FUNCTION AND GLOBAL ALGORITHM FOR BOX CONSTRAINED VARIATIONAL INEQUALITIES

1 IntroductionWe consider tlie variational inequality problelll, deuoted by VIP(X, F), wliicli is to find avector x* E X such thatF(X*)"(X -- X-) 2 0, VX E X, (1)where F: R" - R" is any vector-valued f11uction and X is a uonelllpty subset of R'.This problem has important applicatiolls. in equilibriun1 modeIs arising in fields such asecououtics, transportatioll scieuce alld operations research. See [1]. There exist mauy lllethodsfor solviug tlie variational li1equality problem VIP(X. …