Gravitational Lensing Statistics as a Probe of Dark Energy

By using the comoving distance, we derive an analytic expression for the optical depth of gravitational lensing, which depends on the redshift to the source and the cosmological model characterized by the cosmic mass density parameter $\Omega_m$, the dark energy density parameter $\Omega_x$ and its equation of state $\omega_x = p_x/\rho_x$. It is shown that, the larger the dark energy density is and the more negative its pressure is, the higher the gravitational lensing probability is. This fact can provide an independent constraint for dark energy.Comment: 9 pages, 2 figure

Gravitational lensing statistical properties in general FRW cosmologies with dark energy component(s): analytic results

Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in gravitational lensing statistics and other cosmological tests. By using the comoving distance we derive analytic but simple expressions for the optical depth of multiple image, the expected value of image separation and the probability distribution of image separation caused by an assemble of singular isothermal spheres in general FRW cosmological models with dark energy component(s). We also present the kinematical and dynamical properties of these kinds of cosmological models and calculate the age of the universe and the distance measures, which are often used in classical cosmological tests. In some cases we are able to give formulae that are simpler than those found elsewhere in the literature, which could make the cosmological tests for dark energy component(s) more convenient.Comment: 14 pages, no figure, Latex fil

Differential quadrature method for space-fractional diffusion equations on 2D irregular domains

In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature (DQ) methods for solving the 2D space-fractional diffusion equations on irregular domains. The methods in presence reduce the original equation into a set of ordinary differential equations (ODEs) by introducing valid DQ formulations to fractional directional derivatives based on the functional values at scattered nodal points on problem domain. The required weighted coefficients are calculated by using radial basis functions (RBFs) as trial functions, and the resultant ODEs are discretized by the Crank-Nicolson scheme. The main advantages of our methods lie in their flexibility and applicability to arbitrary domains. A series of illustrated examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table

Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana bound states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark state subspace.Comment: 4 pages; Add detailed discussion of feasibility of the scheme;add ref

Central Unification versus Local Diversity: China’s Tax Regime, 1980s-2000s

This article firstly present a systematic overview on national tax regime by classifying China’s tax regime into three broad phases in context of underpinning market-oriented institutional development during last two decades and, then, in supplement to previous literatures that largely stop at provincial level, unveil the complex and obscure local tax regime based on sub-provincial field research in Zhejiang and Jiangsu province. The authors observed dual existing tax regimes: the hard and standardized state tax regime under central custody versus de facto soft and flexible local tax regime under local promotion and argue that despite central persisting initiatives in unifying tax regime and recentralization, local variation and divergence continue to play indispensable role in implementation of central reform due to China’s sheer size, geographical, cultural and resource endowment disparity as well as local state’s self-interest seeking inevitably induces localized adaptation of central policy and, consequently, calls for further decentralization