Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime

We study a relativistic quantum particle in cosmic string spacetime in the presence of a magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the su(1,1)$su(1,1)$ symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schrödinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.     

On the harmonic-type and linear-type confinement of a relativistic scalar particle yielded by Lorentz symmetry breaking effects

Based on the Standard Model Extension, we investigate relativistic quantum effects on a scalar particle in backgrounds of the Lorentz symmetry violation defined by a tensor field. We show that harmonic-type and linear-type confining potentials can stem from Lorentz symmetry breaking effects, and thus, relativistic bound state solutions can be achieved. We first analyse a possible scenario of the violation of the Lorentz symmetry that gives rise to a harmonic-type potential. In the following, we analyse another possible scenario of the breaking of the Lorentz symmetry that induces both harmonic-type and linear-type confining potentials. In this second case, we also show that not all values of the parameter associated with the intensity of the electric field are permitted in the search for polynomial solutions to the radial equation, where the possible values of this parameter are determined by the quantum numbers of the system and the parameters associated with the violation of the Lorentz symmetry.     

Three paths toward the quantum angle operator

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight” functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.     

Highly accurate excited-state energies from direct computation of the 2-electron reduced density matrix by the anti-Hermitian contracted Schrödinger equation

ABSTRACT

Directly solving for the 2-electron reduced density matrix (2-RDM) via the anti-Hermitian contracted Schrödinger equation (ACSE) enables computations for excited states energies without the N-electron wave function. Of particular interest are excitations and dissociation curves that exhibit strong multi-reference correlation effects. The ground and excited states of the molecules HF, H₂O, and N₂ are examined at both equilibrium and non-equilibrium geometries to compare the ability of the ACSE and widely used ab initio techniques to treat strong multi-reference electron correlation. Calculations are performed with double-ζ basis sets for calibration with full configuration interaction (FCI). Multi-reference second-order perturbation theory (MRPT2) and the ACSE both provide qualitative precision with respect to FCI data, although the ACSE's capability to include higher order correlation effects permits near-FCI accuracy for ground and excited states and excitation energies.     

Phase transition and optoelectronic properties of MgH2

In this article, structural and electronic properties of MgH₂ have been studied. The aim behind this study was to find out the ground state crystal structure of MgH₂. For the purpose, density functional theory (DFT)-based full-potential linearized augmented plane wave (FP-LAPW) calculations have been performed in three different space groups: P4₂/mnm (α-MgH₂), Pa3 (β-MgH₂) and Pbcn (γ-MgH₂). It has been found that the ground state structure of MgH₂ is α-MgH₂. The present study shows that α-MgH₂ transforms into γ-MgH₂ at a pressure of 0.41 GPa. After further increase in pressure, γ-MgH₂ transforms into β-MgH₂ at a pressure of 3.67 GPa. The obtained results are in good agreement with previously reported experimental data. In all the studied phases, the behavior of MgH₂ is insulating and its optical conductivity is around 6.0 eV. The α-MgH₂ and γ-MgH₂ are anisotropic materials while β-MgH₂ is isotropic in nature.     

类Be离子(Z=8-54)内壳层激发态1s2s~22p退激发过程的理论研究

采用基于全相对论框架的多组态Dirac-Fock方法,系统研究了类Be离子(Z=8-54)内壳层激发态1s2s22p的能量、辐射退激发和Auger退激发过程.详细讨论了电子关联效应对相关结构和退激发过程的影响.结果表明,来自于n=2和3壳层的电子关联效应最重要.另外,随着Z的增大,辐射退激发几率逐渐而平滑的增大,而Auger退激发几率的变化则不显著.本文计算结果与其它理论计算结果符合很好.     

Cr,Cu掺杂Ag电子结构和光学特性的第一性原理研究

基于密度泛函理论的第一性原理平面波超软赝势方法,分别计算了Cr、Cu掺杂Ag晶胞的电子结构和光学特性,计算结果表明,掺杂后Cr、Cu外层电子分别与Ag外层电子发生作用,价带会出现一定展宽;掺杂体系的反射谱和吸收谱在不同波段范围内会发生不同变化,体系的光谱特性发生改变.研究结果对于光电子器件制备及薄膜界面特性研究具有指导意义.     

Recasting wave functions into valence bond structures: A simple projection method to describe excited states

A method is proposed to obtain coefficients and weights of valence bond (VB) determinants from multi configurational wave functions. This reading of the wave functions can apply to ground states as well as excited states. The method is based on projection operators. Both energetic and overlap‐based criteria are used to assess the quality of the resulting VB wave function. The approach gives a simple access to a VB rewriting for low‐lying states, and it is applied to the allyl cation, to the allyl radical and to the ethene (notably to the V‐state). For these states, large overlap between VB and multi reference wave functions are easily obtained. The approach proves to be useful to propose an interpretation of the nature of the V‐state of ethene. © 2015 Wiley Periodicals, Inc.