Thomas rotation and the parametrization of the Lorentz transformation group

Two successive pure Lorentz transformations are equivalent to a pure Lorentz transformation preceded by a 3×3 space rotation, called a Thomas rotation. When applied to the gyration of the rotation axis of a spinning mass, Thomas rotation gives rise to the well-knownThomas precession. A 3×3 parametric, unimodular, orthogonal matrix that represents the Thomas rotation is presented and studied. This matrix representation enables the Lorentz transformation group to be parametrized by two physical observables: the (3-dimensional) relative velocity and orientation between inertial frames. The resulting parametrization of the Lorentz group, in turn, enables the composition of successive Lorentz transformations to be given by parameter composition. This composition is continuously deformed into a corresponding, well-known Galilean transformation composition by letting the speed of light approach infinity. Finally, as an application the Lorentz transformation with given orientation parameter is uniquely expressed in terms of an initial and a final time-like 4-vector.     

Long-time asymptotics in the one-dimensional trapping problem with large bias

The survival probability of a particle which moves according to a biased random walk in a one-dimensional lattice containing randomly distributed deep traps is studied at large times. Exact asymptotic expansions are deduced for fields exceeding a certain threshold, using the method of images. In order to cover the whole range of fields, we also derive the behavior of the survival probability below this threshold, using the eigenvalue expansion method. The connection with the continuous diffusion model is discussed.     

Measurement and analysis of excitation functions for alpha-induced reactions in copper

Excitation functions for the production of⁶⁸Ga,⁶⁷Ga,⁶⁶Ga,⁶⁵Ga +⁶⁵Zn and⁶¹Cu fromα-induced reactions in natural copper have been measured in the energy range ≈ 10–40 MeV using the stacked foil technique. A stack of nine copper foils was irradiated by a 40 MeVα-beam. Theγ-rays emitted from the irradiated samples were recorded. Excitation functions have also been calculated theoretically using a statistical model with and without the inclusion of pre-equilibrium emission of particles. Pre-equilibrium component simulated by exciton model shows that the inclusion of pre-equilibrium emission gives better agreement between experimental and theoretical excitation functions. Pre-equilibrium fraction depends on the incident energy and the target mass number.     

The projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise

Two models for the Freedericksz transition in a fluctuating magnetic field are considered: one is based on a dichotomic and the other on a nonlinear Gaussian noise. Both noises are characterized by a finite correlation time. It is shown that the linear response assumption leading to the best Fokker-Planck approximation in the dichotomic and nonlinear Gaussian cases can be trusted only up to the order ¹ and ⁰, respectively. The role of the corrections to the linear response approximation is discussed and it is shown how to replace the non-Fokker-Planck terms stemming from these corrections with equivalent terms of standard type. This technique is shown to produce perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise).     

3d过渡金属掺杂M_2@Si_(20)(M=Sc-Zn)团簇的密度泛函理论研究

利用密度泛函理论(DFT)研究3d过渡金属掺杂硅团簇的几何结构和稳定性,计算了绝热电子亲和能和垂直电离能,内嵌双金属间距,自旋磁矩等.结果表明内嵌的Sc、Ti、V、Mn金属二聚体和十二面体硅笼构成了稳定的富勒烯结构,随着d电子数目的增加其内嵌的富勒烯构型有部分畸变,总体而言Si_(20)团簇掺杂双金属后稳定性得到了提高.     

Na原子链表面等离激元特性的含时密度泛函研究

本文用含时密度泛函理论研究了线性Na原子链的表面等离激元机理.主要在原子尺度下模拟计算了体系随着原子数增加及原子间距变化的集体激发过程.研究发现线性原子链有一个普遍的特性——存在一个纵模和两个横模.两个横模一般在实验上很难被观测到.纵模随着原子链长度增加,能量红移的同时,该纵模主峰的强度呈线性增长.随着原子个数的增加,端点模式(TE)开始蓝移,能量和偶极强度都逐渐趋向饱和.横模能量被劈裂的原因概括如下:(一)每个位置的电子受到的势不同,在两端的电子受到的势要比在中间的电子受到的势要高,因此两端的电荷积累也比中间多;(二)端点存在悬挂键,所以中间的电子-电子间相互作用与端点的不一样,这两方面又都与原子间距d有关.     

水准折光及双波长激光效应

本文从“同温度层不完全平行于地面,且在变化”的“任意分层”假设出发,导出了水准折光修正公式,并利用光的色散效应在10~(-6)的精度要求下,求得r=r_T=h_1/h_2=(n_(01)-1)/(n_(02)-1)=常数最后指出,研制双波长激光水准仪的必要性和可能性,并提出了研制此种仪器的技术参数.     

介质薄膜不同方向折射率的计算

本文应用介电椭球理论,推导出计算介质薄膜不同方向折射率的新公式.     

氧化锌发光中心的统计力学模型

根据ZnO结构的两种空隙(四面体和多面体),提出了一种发光模型.用统计系综求得了上述两种填隙锌的数量计算公式.     

1:1分步亚微米光刻镜头

本文介绍一个数值孔径0.4、视场10×10mm~2可用于1:1分步投影光刻机的镜头的光学设计及其模型实验结果.光学设计在Wynne-Dyson的1:1折反式系统的基础上,对该系统作了某些改变.实验结果表明,该镜头具有亚微米的光刻分辨率.