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 methods for reconstruction of source term of heat equation from the final overdetermination

This paper deals with the numerical methods for the reconstruction of source term in linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the uniqueness of the inverse problem for determining the source term $f(x)$ from final overdetermination. We present the numerical methods for both free boundary and Neumann boundary situations. Moreover, we show that the solution of the boundary conditions problem has the form of the free boundary solution problem by using the extension method. Numerical experiments are done for the inverse problem with the boundary conditions.Comment: 15 pages, 7 figure

Space-Time Phononic Crystals with Anomalous Topological Edge States

It is well known that an interface created by two topologically distinct structures could host nontrivial edge states that are immune to defects. In this letter, we introduce a one-dimensional space-time phononic crystal and study the associated anomalous topological edge states. A space-decoupled time modulation is assumed. While preserving the key topological feature of the system, such a modulation also duplicates the edge state mode across the spectrum, both inside and outside the band gap. It is shown that, in contrast to conventional topological edge states which are excited by frequencies in the Bragg regime, the time-modulation-induced frequency conversion can be leveraged to access topological edge states at a deep subwavelength scale where the entire phononic crystal size is merely 1/5.1 of the wavelength. This remarkable feature could open a new route for designing miniature devices that are based on topological physics