Gravitational Lensing and Anisotropies of CBR on the Small Angular Scales

We investigate the effect of gravitational lensing, produced by linear density perturbations, for anisotropies of the Cosmic Background Radiation (CBR) on scales of arcminutes. In calculations, a flat universe ($\Omega=1$) and the Harrison-Zel'dovich spectrum ($n=1$) are assumed. The numerical results show that on scales of a few arcminutes, gravitational lensing produces only negligible anisotropies in the temperature of the CBR. Our conclusion disagrees with that of Cay\'{o}n {\it et al.} who argue that the amplification of $\Delta T/T$ on scales $\le 3'$ may even be larger than 100\%.Comment: Accepted by MNRAS. 16 pages, 2 figures, tarred, compressed and uuencoded Postscript file

Limit Cycle Bifurcations from Centers of Symmetric Hamiltonian Systems Perturbing by Cubic Polynomials

In this paper, we consider some cubic near-Hamiltonian systems obtained from perturbing the symmetric cubic Hamiltonian system with two symmetric singular points by cubic polynomials. First, following Han [2012] we develop a method to study the analytical property of the Melnikov function near the origin for near-Hamiltonian system having the origin as its elementary center or nilpotent center. Based on the method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Then, we consider the symmetric singular points and present the conditions for one of them to be elementary center or nilpotent center. Under the condition for the singular point to be a center, we obtain the normal form of the Hamiltonian systems near the center. Moreover, perturbing the symmetric cubic Hamiltonian systems by cubic polynomials, we consider limit cycles bifurcating from the center using the algorithm to compute the coefficients of Melnikov function. Finally, perturbing the symmetric hamiltonian system by symmetric cubic polynomials, we consider the number of limit cycles near one of the symmetric centers of the symmetric near-Hamiltonian system, which is same to that of another center

Probabilistic teleportation of unknown two-particle state via POVM

We propose a scheme for probabilistic teleportation of unknown two-particle state with partly entangled four-particle state via POVM. In this scheme the teleportation of unknown two-particle state can be realized with certain probability by performing two Bell state measurements, a proper POVM and a unitary transformation.Comment: 5 pages, no figur

Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians

The Projected Configuration Interaction (PCI) method starts from a collection of mean-field wave functions, and builds up correlated wave functions of good symmetry. It relies on the Generator Coordinator Method (GCM) techniques, but it improves the past approaches by a very efficient method of selecting the basis states. We use the same realistic Hamiltonians and model spaces as the Configuration Interaction (CI) method, and compare the results with the full CI calculations in the sd and pf shell. Examples of 24Mg, 28Si, 48Cr, 52Fe and 56Ni are discussed.Comment: 10 pages, 10 figures. Revised version. To be published in Physical Review

Effects of spin imbalance on the electric-field driven quantum dissipationless spin current in pp-doped Semiconductors

It was proposed recently by Murakami et al. [Science \textbf{301}, 1348(2003)] that in a large class of $p$-doped semiconductors, an applied electric field can drive a quantum dissipationless spin current in the direction perpendicular to the electric field. In this paper we investigate the effects of spin imbalance on this intrinsic $spin$ Hall effect. We show that in a real sample with boundaries, due to the presence of spin imbalance near the edges of the sample, the spin Hall conductivity is not a constant but a sensitively $position$-$dependent$ quantity, and due to this fact, in order to take the effects of spin imbalance properly into account, a microscopic calculation of both the quantum dissipationless spin Hall current and the spin accumulation on an equal footing is thus required. Based on such a microscopic calculation, a detailed discussion of the effects of spin imbalance on the intrinsic spin Hall effect in thin slabs of $p$-doped semiconductors are presented.Comment: 8 pages, 2 figures, An extended version with detailed calculations To appear in Phys. Rev.