极化自由度对分束器出射光场的量子相干性影响的研究

我们在讨论粒子数态光场在分束器上干涉后得到的输出态的量子相干性时,考虑了入射场的极化自由度.利用campos[1]等人提出的量子分束器的SU(2)理论模型,计算得到了输出光场所处状态的表达式.进而讨论了光场在两个不同的入射空间模上极化方向对两个输出空间模上光场二阶量子干涉度的影响.     

Truncation of small matrix elements based on the Euclidean norm for blocked data structures

Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree-Fock and Kohn-Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary-invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49, 032103). The Euclidean norm is unitary-invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations.     

Quantum chemical investigation of lanthanum doping effects in tetragonal and rhombohedral PZT materials

Structural and electronic properties of lead–zirconate–titanate (PZT) materials doped with a lanthanum (La) impurity are studied using a quantum‐chemical approach based on the Hartree–Fock theory. Performed geometry optimization in the defective crystals shows that the atomic movements are predominantly outward with respect to the impurity position. It is found that the La impurity enhances a covalent character in the chemical bonding between the Ti and O atoms, as well as the Zr and O atoms situated in the neighborhood of the defect despite the fact that the La‐O interaction remains purely ionic. The occurrence of local energy levels within the band gap of the material is analyzed in light of the available experimental data on La concentration influence upon dielectric and piezoelectric properties in these crystals. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

IR, Raman and SERS spectra of 2-phenoxymethylbenzothiazole

The FT-IR and FT-Raman spectra of 2-phenoxymethylbenzothiazole were recorded and analyzed. The surface enhanced Raman scattering (SERS) spectrum was recorded in a silver colloid. The vibrational wavenumbers of the compound have been computed using the Hartree–Fock/6-31G* basis and compared with the experimental values. The appearance of the Ag–O stretching mode at 237 cm⁻¹ in the SERS spectrum along with theoretically calculated atomic charge density, leads us to suggest that the molecule is adsorbed through the oxygen atom with the molecular plane tilted on the colloidal silver surface. The direction of charge transfer contribution to SERS has been discussed from the frontier orbital theory.     

A note on Schatten‐class membership of Hankel operators with antiholomorphic symbols on generalized Fock‐spaces

In this paper we investigate Hankel operators with anti‐holomorphic L²‐symbols on generalized Fock spaces A_m² in one complex dimension. The investigation of the mentioned operators was started in [4] and [3]. Here, we show that a Hankel operator with anti‐holomorphic L²‐symbol is in the Schatten‐class S_p if and only if the symbol is a polynomial with degree N satisfying 2N < m and p > . The result has been proved independently before in the recent work [2], which also considers the case of several complex variables. However, in addition to providing a different proof for the result the present work shows that the methodology developed in [4] and [3] can be adopted in order to work to characterize Schatten‐class membership. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Geometry of rank 2 distributions with nonzero Wilczynski invariants

In the famous 1910 “cinq variables” paper Cartan showed in particular that for maximally nonholonomic rank 2 distributions in ?⁵ with non-zero covariant binary biquadratic form the dimension of the pseudo-group of local symmetries does not exceed 7 and among such distributions he described the one-parametric family of distributions for which this pseudo-group is exactly 7-dimensional. Using the novel interpretation of the Cartan covariant binary biquadratic form via the classical Wilczynski invariant of curves in projective spaces associated with abnormal extremals of the distributions [4, 27, 28] one can generalize this Cartan result to rank 2 distributions in ?ⁿ satisfying certain genericity assumption, called maximality of class, for arbitrary n ≥ 5.

In the present paper for any rank 2 distribution of maximal class with at least one nonvanishing generalized Wilczynski invariants we construct the canonical frame on a (2n — 3)-dimensional bundle and describe explicitly the moduli spaces of the most symmetric models. The relation of our results to the divergence equivalence of Lagrangians of higher order is given as well.     

二次量子化中单体和两体算符的一种启发式推导

二次量子化是研究生和高年级本科生量子力学课程中的重要内容.如何从一次量子化中的多粒子哈密顿量及波函数出发,自然地导出二次量子化中由产生和湮没算符表示的单体和两体算符,是一个既关键且又使初学者较难理解的步骤.以全同费米子系统为例,本文给出该步骤的一种自然且具有启发性的推导方法.该方法仅依赖于:多粒子波函数的对称性假设,Fock空间中“真空填充”的概念,以及全反对称多粒子波函数与Fock态的等价性.     

An alternative scheme for calculating the unrestricted Hartree–Fock equation: Application to the boron and neon atoms

We present an alternative scheme for calculating the unrestricted Hartree–Fock (HF) equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity of the present scheme is confirmed by actual calculations of the boron and neon atoms. The total energy of the present scheme is lower than that of the conventional restrictive HF equation, but higher than that of the CI method. Also, the resultant wave function satisfies the electron–nucleus cusp condition.     

Comparative study of kinetics isomerization of substituted polyacetylene (Cl,F and I): Ab initio and DFT calculations

Ab initio and DFT methods were used to investigate the interconversions of substituted polyacetylene conformers C₁₀H₆X₆ (X=F, Cl and I) in the vapour phase. The rates of this geometrical isomerization have been calculated and the Arrhenius parameters evaluated. In the case of unsubstituted polyacetylene as the reference, the B3LYP Arrhenius parameters obtained are A₁=2.99 × 10¹⁷ s^–1 and E_a=17.30 kcal mol^–1. The values of the equilibrium constant for the reaction have also been determined at various temperatures between 300 and 500 K and the value of the energies change calculated. The results also suggest that the straightforward kinetics characterizing the majority of substituted polyacetylene isomerizations above 300 K. The isomerization energies are positive and the barrier heights ΔE_barrier are expected to be sensitive for the magnitude of halogens effects. According to geometries features the Cis → Trans isomerization in the gas phase occurs by a rotational mechanism.