Does Amati Relation Depend on Luminosity of GRB's Host Galaxies?

In order to test systematic of the Amati relation, the 24 long-duration GRBs with firmly determined $E_{\gamma,\mathrm{iso}}$ and $E_{\mathrm p}$ are separated into two sub-groups according to B-band luminosity of their host galaxies. The Amati relations in the two subgroups are found to be in agreement with each other within uncertainties. Taking into account of the well established luminosity - metallicity relation of galaxies, no strong evolution of the Amati relation with GRB's environment metallicity is implied in this study.Comment: 7 pages, 3 figures and 1 table, accepted by ChJA

Classical correlation and quantum discord sharing of Dirac fields in noninertial frames

The classical and quantum correlations sharing between modes of the Dirac fields in the noninertial frame are investigated. It is shown that: (i) The classical correlation for the Dirac fields decreases as the acceleration increases, which is different from the result of the scalar field that the classical correlation is independent of the acceleration; (ii) There is no simple dominating relation between the quantum correlation and entanglement for the Dirac fields, which is unlike the scalar case where the quantum correlation is always over and above the entanglement; (iii) As the acceleration increases, the correlations between modes $I$ and $II$ and between modes $A$ and $II$ increase, but the correlations between modes $A$ and $I$ decrease.Comment: 15 pages, 6 figures; Accepted for publication in Phys. Rev.

Explicit calculation of strong solution on linear parabolic equation

In this paper, we give the existence and uniqueness of the strong solution of one dimensional linear parabolic equation with mixed boundary conditions. The boundary conditions can be any kind of mixed Dirichlet, Neumann and Robin boundary conditions. We use the extension method to get the unique solution. Furthermore, the method can also be easily implemented as a numerical method. Some simple examples are presented.Comment: 10 page

All-versus-nothing violation of local realism in the one-dimensional Ising model

We show all-versus-nothing proofs of Bell's theorem in the one-dimensional transverse-field Ising model, which is one of the most important exactly solvable models in the field of condensed matter physics. Since this model can be simulated with nuclear magnetic resonance, our work might lead to a fresh approach to experimental test of the Greenberger-Horne-Zeilinger contradiction between local realism and quantum mechanics.Comment: 4 page

Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes

This paper provides a finite difference discretization for the backward Feynman-Kac equation, governing the distribution of functionals of the path for a particle undergoing both reaction and diffusion [Hou and Deng, J. Phys. A: Math. Theor., {\bf51}, 155001 (2018)]. Numerically solving the equation with the time tempered fractional substantial derivative and tempered fractional Laplacian consists in discretizing these two non-local operators. Here, using convolution quadrature, we provide a first-order and second-order schemes for discretizing the time tempered fractional substantial derivative, which doesn't require the assumption of the regularity of the solution in time; we use the finite difference method to approximate the two-dimensional tempered fractional Laplacian, and the accuracy of the scheme depends on the regularity of the solution on $\bar{\Omega}$ rather than the whole space. Lastly, we verify the predicted convergence orders and the effectiveness of the presented schemes by numerical examples.Comment: 37 pages, 7 table

Tight Correlation-Function Bell Inequality for Multipartite dd-Dimensional System

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to multipartite d-dimensional systems. All the Bell inequalities based on this generalization take the same simple form as the CHSH inequality. For small systems, numerical results show that the new inequalities are tight and we believe this is also valid for higher dimensional systems. Moreover, the new inequalities are relevant to the previous ones and for bipartite system, our inequality is equivalent to the Collins-Gisin-Linden-Masser-Popescu (CGLMP) inequality.Comment: 4 pages; Accepted by PR

Dependence of entanglement on initial states under amplitude damping channel in non-inertial frames

Under amplitude damping channel, the dependence of the entanglement on the initial states $|\Theta>_{1}$ and $|\Theta>_{2}$, which reduce to four orthogonal Bell states if we take the parameter of states $\alpha=\pm 1/\sqrt{2}$ are investigated. We find that the entanglements for different initial states will decay along different curves even with the same acceleration and parameter of the states. We note that, in an inertial frame, the sudden death of the entanglement for $|\Theta>_{1}$ will occur if $\alpha>1/\sqrt{2}$, while it will not take place for $|\Theta>_{2}$ for any $\alpha$. We also show that the possible range of the sudden death of the entanglement for $|\Theta>_{1}$ is larger than that for $|\Theta>_{2}$. There exist two groups of Bell state here we can't distinguish only by concurrence.Comment: 5 pages, 2 figure

Revisiting Optimal Power Control: its Dual Effect on SNR and Contention

In this paper we study a transmission power tune problem with densely deployed 802.11 Wireless Local Area Networks (WLANs). While previous papers emphasize on tuning transmission power with either PHY or MAC layer separately, optimally setting each Access Point's (AP's) transmission power of a densely deployed 802.11 network considering its dual effects on both layers remains an open problem. In this work, we design a measure by evaluating impacts of transmission power on network performance on both PHY and MAC layers. We show that such an optimization problem is intractable and then we investigate and develop an analytical framework to allow simple yet efficient solutions. Through simulations and numerical results, we observe clear benefits of the dual-effect model compared to solutions optimizing solely on a single layer; therefore, we conclude that tuning transmission power from a dual layer (PHY-MAC) point of view is essential and necessary for dense WLANs. We further form a game theoretical framework and investigate above power-tune problem in a strategic network. We show that with decentralized and strategic users, the Nash Equilibrium (N.E.) of the corresponding game is in-efficient and thereafter we propose a punishment based mechanism to enforce users to adopt the social optimal strategy profile under both perfect and imperfect sensing environments

Numerical scheme for the Fokker-Planck equations describing anomalous diffusions with two internal states

Recently, the fractional Fokker-Planck equations (FFPEs) with multiple internal states are built for the particles undergoing anomalous diffusion with different waiting time distributions for different internal states, which describe the distribution of positions of the particles [Xu and Deng, Math. Model. Nat. Phenom., $\mathbf{13}$, 10 (2018)]. In this paper, we first develop the Sobolev regularity of the FFPEs with two internal states, including the homogeneous problem with smooth and nonsmooth initial values and the inhomogeneous problem with vanishing initial value, and then we design the numerical scheme for the system of fractional partial differential equations based on the finite element method for the space derivatives and convolution quadrature for the time fractional derivatives. The optimal error estimates of the scheme under the above three different conditions are provided for both space semidiscrete and fully discrete schemes. Finally, one- and two-dimensional numerical experiments are performed to confirm our theoretical analysis and the predicted convergence order.Comment: 30 page

Algorithm implementation and numerical analysis for the two-dimensional tempered fractional Laplacian

Tempered fractional Laplacian is the generator of the tempered isotropic L\'evy process [W.H. Deng, B.Y. Li, W.Y. Tian, and P.W. Zhang, Multiscale Model. Simul., 16(1), 125-149, 2018]. This paper provides the finite difference discretization for the two dimensional tempered fractional Laplacian $(\Delta+\lambda)^{\frac{\beta}{2}}$. Then we use it to solve the tempered fractional Poisson equation with Dirichlet boundary conditions and derive the error estimates. Numerical experiments verify the convergence rates and effectiveness of the schemes.Comment: 27 pages, 4 figure