Solution of Spin and Pseudo-Spin Symmetric Dirac Equation in (1+1) Space-Time Using Tridiagonal Representation Approach

The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.     

Janossy Densities. I. Determinantal Ensembles

We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for =2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I can be expressed in terms of the Christoffel–Darboux kernel for the orthogonal polynomials on the complement of I.     

Realization of a unique time evolution unitary operator in Klein Gordon theory

The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hubert spaceL ²(R ³) and the Einstein’s relativistic equation in the spaceL ²(R ³, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL ²(R ³) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite dimensional Hubert spaceL ²(R ³).     

Exact Solutions with Arbitrary Permutation Symmetry in a Three-Body Harmonic Oscillator

The exact solutions with arbitrary permutation symmetry to the threebody Schrödinger equation for the harmonic oscillator are presented completely.     

Continuous symmetry reduction and return maps for high-dimensional flows

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a five-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.     

Structural, electronic and optical properties of SrCl2 under hydrostatic stress

The results of first-principles theoretical study of the structural, electronic and optical properties of SrCl₂ in its cubic structure, have been performed using the full-potential linear augmented plane-wave method plus local orbitals (FP-APW+lo) as implemented in the WIEN2k code. In this approach both the local density approximation (LDA) and the generalized gradient approximation (GGA) are used for the exchange-correlation (XC) potential. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. We performed these calculations with and without spin-orbit interactions. Including spin-orbit coupling cause to lifts the triple degeneracy at Γ point and a double degeneracy at X point. Results are given for structural properties. The pressure dependence of elastic constants and band gaps are investigated. The dielectric function, reflectivity spectra and refractive index are calculated up to 30 eV. Also we calculated the pressure and volume dependence of the static optical dielectric constant.     

基于Zernike多项式的波前传感器的光子受限的研究

应用基于Zernike多项式的波前探测和重构方法2,利用蒙特卡罗法,可求出探测器在不同的光子数下,其探测精度的变化。文章还给出了由不同的探测器组成的传感器,探测星等的变化情况。