Expansions for the eigenvalues of three-term recurrence relations. Two applications in molecular physics

Approximate expressions for the eigenvalue of a three-term recurrence relation with a general form describing various physical problems are proposed. Their range of availability is examined by comparison with exact values for two different problems: the bound and continuum states of monoelectronic diatomic ions and the Schr?dinger equation describing molecular alignment in intense laser fields. For each case, very good predictions have been obtained, which may be useful as initial values in iterative procedures for deriving exact solutions. Received: 30 January 1998 / Received in final form: 10 April 1998 / Accepted: 25 May 1998     

The recurrence relations for the spheroidal functions

The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the extension of the recurrence relation of the Legendre polynomials.     

Nonequilibrium work relations: foundations and applications

When a macroscopic system in contact with a heat reservoir is driven away from equilibrium, the second law of thermodynamics places a strict bound on the amount of work performed on the system. With a microscopic system the situation is more subtle, as thermal fluctuations give rise to a statistical distribution of work values. In recent years it has been realized that such distributions encode surprisingly more information than one might expect from traditional thermodynamic arguments. I will discuss a number of exact results that relate equilibrium properties of the system, in particular free energy differences, to the fluctuations in the work performed during such a nonequilibrium process. I will describe the theoretical foundations of these relations, connections with irreversibility and the second law of thermodynamics, and potential experimental and computational applications.     

Configuration space based recurrence relations for sunset-type diagrams

We derive recurrence relations for the calculation of multiloop sunset-type diagrams with large powers of massive propagators. The technique is formulated in configuration space and exploits the explicit form of the massive propagator raised to a given power. We write down and evaluate a convenient set of basis integrals. The method is well suited for a numerical evaluation of this class of diagrams. We give explicit analytical formulae for the basis integrals in the asymptotic regime. Received: 30 April 1999 / Revised version: 2 July 1999 / Published online: 14 October 1999     

Algebraic recurrence relations for the finite-order scattering and transmission functions

In preceding papers (cf. Bellmanet al.(^1,2,3,), integral recurrence for the finite-order scattering and transmission functions have been given in connection with integral recurrence relations for the finite order X- and Y-functions with the aid of an initial-value method. In the present paper, it is shown how to find algebraic recurrence relations for the finite-order scattering and transmission functions in terms of finite-order X- and Y-functions without referring to an initial-value method. These recurrence relations are suitable for the numerical computation of the finite-order scattering and transmission functions by use of a digital computer. Furthermore, in Tables 1–3, a numerical example of the finite-order reflection functions for optical thickness 0·2 with albedo = 1 is listed. Table 4 furnishes an example of the cumulative reflection functions for optical thickness 0·2 with three different albedos.     

Dispersion relations of vector and scalar bosons in material media

Bulletin of the Lebedev Physics Institute - The dispersion relations of vector, scalar, and pseudo-scalar bosons of a dielectric medium are determined taking into account their resonant interaction...     

Analytical solutions of weakly coupled map lattices using recurrence relations

By using asymptotic methods recurrence relations are found that rule weakly CML evolution, with both global and diffusive coupling. The solutions obtained from these relations are very general because they do not hold restrictions about boundary conditions, initial conditions and number of oscilators in the CML. Furthermore, oscillators are ruled by an arbitraty C² function.     

Differential calculi on quantum vector spaces with Hecke-type relations

From a vector spaceV equipped with a Yang-Baxter operatorR one may form the r-symmetric algebraS _R V=TV/v w–R(v w), which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebraM _R V=T(End(V))/f g–R(f g)R ^-1. In the case whenR satisfies a Hecke-type identityR ²=(1–q)R+q, we construct a differential calculus _R V forS _R V which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino whenR is essentially theR-matrix of GL _q (n). Elements of _R V may be regarded as differential forms on the quantum vector spaceS _R V. We show that _R V isM _R V-covariant in the sense that there is a coaction _*: _R V M _R V _R V with _*d=(1 d)_* extending the natural coaction :S _R V M _R V S _R V.     

也谈径向矩阵元的递推关系

利用超位力定理及其推广形式给出了一维、二维和三维系统径向矩阵元递推关系的一般表示式,并具体求出了谐振子系统及非相对论氢原子系统中径向矩阵元的递推关系．     

Factor structure of the Tomimatsu‐Sato solutions and their recurrence relations

We consider stationary axisymmetric vacuum solutions of Einstein's equations for which the Ernst potential is rational in prolate spheroidal coordinates. Extending an earlier study we show that there are several new expressions which are factorizable. In particular, we concentrate on the Tomimatsu‐Sato solutions and their recurrence relations. Various continuum limits of the recurrence relations will be discussed.     

库仑波函数的束缚连续跃迁矩阵元的解析计算公式和递推关系

给出了库仑波函数的束缚连续跃迁矩阵元的解析计算公式,并获得了不同幂次矩阵元之间所满足的递推关系.这些结果可广泛的用于原子和分子的散射问题.     

On general relations in relativistic kinematics and some of their applications

Two vector fields are considered, a timelike one,u , and an arbitrary one, . The relative expansion and rotation are defined with respect to these fields, their mutual relations are studied, and some general formulas obtained. Applications are made, first to vector fields which are mutually nonrotating in a plane-symmetric metric, then to the electromagnetic field of an arbitrary magnetohydrodynamic fluid.     

紧聚焦轴对称矢量光场波前调控及应用

作为光波最重要的本征物理属性之一,光场偏振态在研究光与物质相互作用中占有重要地位。矢量光场的波前调控为其聚焦场提供了更加复杂、更加灵活可控的振幅、相位以及偏振态分布,丰富了光与物质相互作用的手段,为材料表征提供了传统线偏振、圆偏振光场所不可替代的研究方法,具有重要的物理意义和实际应用价值。本文将综述矢量光场最新的研究进展,详细介绍矢量光场的偏振态特性、产生方法,以及紧聚焦轴对称矢量光场波前调控在远场小尺度光斑的产生、磁光记录、单分子/颗粒取向探测、任意三维偏振态的产生、高密度数据存储、信息加密以及矢量光场波前重构等方面的重要应用。     

Block tridiagonal matrix inversion and fast transmission calculations

A method for the inversion of block tridiagonal matrices encountered in electronic structure calculations is developed, with the goal of efficiently determining the matrices involved in the Fisher–Lee relation for the calculation of electron transmission coefficients. The new method leads to faster transmission calculations compared to traditional methods, as well as freedom in choosing alternate Green’s function matrix blocks for transmission calculations. The new method also lends itself to calculation of the tridiagonal part of the Green’s function matrix. The effect of inaccuracies in the electrode self-energies on the transmission coefficient is analyzed and reveals that the new algorithm is potentially more stable towards such inaccuracies.     

Reproduction of distance matrices and original time series from recurrence plots and their applications

We propose a method to reproduce distance matrices and original time series from recurrence plots. The procedure is to (i)convert a recurrence plot to a weighted graph and (ii)calculate a distance between each pair of nodes on this weighted graph. We demonstrate this method by reproducing the topological shape of original time series. We also propose two applications. The first application is to obtain the maximal Lyapunov exponent from a recurrence plot without reproducing the shapes of original time series. The second application is to reconstruct a common deterministic driving force from observations of forced systems. Thus, the method opens new fields in data analysis.     

Exact series expansions, recurrence relations, properties and integrals of the generalized exponential integral functions

Generalized exponential integral functions (GEIF) are encountered in multi-dimensional thermal radiative transfer problems in the integral equation kernels. Several series expansions for the first-order generalized exponential integral function, along with a series expansion for the general nth order GEIF, are derived. The convergence issues of these series expansions are investigated numerically as well as theoretically, and a recurrence relation which does not require derivatives of the GEIF is developed. The exact series expansions of the two dimensional cylindrical and/or two-dimensional planar integral kernels as well as their spatial moments have been explicitly derived and compared with numerical values.     

原子模型势中任意算符矩阵元的递推关系

运用升降算子和超维里定理计算出原子模型势中任意算符Af^U2(r)的矩阵元〈n′1l′1|Af^U2(r)|n1l1〉的递推关系.     

Highly linear transmission and EVM improvement of vector modulation signals for radio-over-fiber applications

The principle of error vector magnitude (EVM) against modulator nonlinearity for vector modulation signal (VMS) transmission in radio-over-fiber (RoF) systems is theoretically and experimentally investigated. A highly linear modulation scheme is proposed and demonstrated using a single-drive dual parallel Mach-Zehnder modulator (MZM). This method improves EVM performance and enlarges the linear input dynamic range of the VMS transmission. An index of maximum allowable input power difference (MAIPD) that reflects the difference of upper input power limits between these two schemes is measured. An EVM limitation of 5% MAIPD has 5 dB. Both 16and 64-QAM results indicate that the proposed scheme supports VMS transmission better than the MZM one.     

双变量厄米多项式递推关系与积分公式的简捷推导

基于正规乘积和反正规乘积性质与双变量厄米多项式的母函数形式,利用相干态表象完备性的高斯积分形式,系统而全面的导出双变量厄米多项式的算符恒等式、递推关系与积分公式,此推导方法简捷明了.