利用Compton散射对自由电子激光器的研究

通过坐标变换的方法，利用康普顿散射对自由电子激光器(FEL)的自发辐射进行了研究，精确地推导了FEL的自发辐射的波长公式，其近似式就是经典散射理论推导的自发辐射波长公式；对自发辐射的辐射功率也进行了近似推导，结果与经典散射理论公式一致。     

非三维空间的经典气体模型

类似于三维空间中的方法，推导了一、二、四维空间中经典气体的气体动理论的相应的公式和常数，与三维空间的情况做了比较。     

基于Bohr-Sommerfeld量子理论的X射线光谱分析

基于Bohr-Sommerfeld量子理论,研究了特征X射线的产生机理,导出了一个按原子序数来计算特征X射线波长的公式.同时对计算推导的波长值做了系统的误差分析,得到了相对误差的规律.结果表明,计算推导的波长值与实验得到的波长值非常接近,并且在实际应用中该公式也更为简便. 关键词： Bohr-Sommerfeld量子理论 特征X射线 波长 误差分析     

多晶体金属疲劳寿命随晶粒尺寸变化的理论研究

在疲劳断裂非平衡统计理论框架的基础上，根据界面能模型，推导出了多晶体金属的疲劳寿 命随晶粒尺寸、应变振幅的变化公式.还与有关实验结果进行了比较，发现理论与实验较为 相符. 关键词： 疲劳寿命 晶粒尺寸 非平衡统计理论 界面能模型     

离轴照明下依赖于入射角度的矢量霍普金斯公式

应用矢量电磁场理论和波导模型推导出离轴照明下的矢量霍普金斯公式,与传统的标量霍普金斯公式不同之处在于引入了入射角及入射方位角. 通过仿真实际投影光刻工艺下三维掩模的成像效果,分析了最佳入射角范围,讨论了离轴照明时入射角对最终成像质量的影响. 关键词： 光学光刻 矢量霍普金斯公式 矢量电磁场理论 离轴照明     

微小孔衍射——近场光学理论

推导了圆孔衍射公式，该公式不受孔径大小和到屏距离的限制，可以作为近场光学的理论。它满足麦克斯韦方程标量形式和基尔霍夫边界条件，包括传播波和衰减波。数值计算表明，此结果优于用Ｂｅｔｈｅ模型所得到的近场理论的结果     

共顶点同轴圆锥形及圆盘形传输线的电参数计算公式

 用安培环路定理、高斯定理推导了共顶点同轴圆锥形及圆盘形两种重要的理想传输线电参数的计算公式，给出了电场、电感、电容及阻抗的解析表达式或数值求解方法；用实例验证了推导的公式和介绍的方法；应用验证后的公式或方法对一个设计进行了估算，得到了合理的结果。     

平顶高斯光束的模相关系数和模分解理论

利用部分相干光理论,推导出柱坐标系下平顶高斯光束模相关系数的解析表达式,基于推导出的Ｍ＾２因子的推广公式,建立了平顶高斯光束的模分解理论。     

会聚球面波的泰伯效应

运用傅里叶变换和菲涅尔-基尔霍夫衍射理论推导了会聚球面波入射二维振幅型光栅在其菲涅尔衍射区的像面光场分布表达式，分析了成像条件以及成像规律。通过实验对泰伯效应进行观测，测量数据与理论值平均误差在4.6%左右，验证了所推导公式的正确性。研究结果完善了泰伯效应相关理论，对拓展其应用具有一定参考价值。     

重焦折射系统的成像

推导了重焦系统的成像公式,并利用成像公式讨论了重焦系统的成像特性,作为理想光具组理论的补充。     

Kernresonanz-und leitfähigkeitsmessungen zu diffusion und fehlordnung in LiBr

Electrical conductivity and nuclear magnetic relaxation rates were measured with pure and doped LiBr between 400 K and the melting point (824 K). Prevalent intrinsinc disorder was observed down to 470 K. The degree of thermal disorder is 5.10⁻⁷ at 470 K and 5.10⁻³ at the melting point. From the relaxation rates of ⁷Li, which are caused by Li-diffusion and nuclear dipole interaction, mean jump frequencies of the cations are derived. Conductivities calculated from these frequencies for a jump process via neighbouing cation vacancies are in perfect agreement with directly measured conductivities. From relaxation rates of ⁸¹Br with MgBr₂-doped crystals jump frequencies of vacancies were obtained which are again in good agreement with those derived from the conductivity data. The energies resulting from the measurements are (0.43 ± 0.03) eV for migration of cation vacancies and (1.46 ± 0.05) eV for thermal disorder. From motional narrowing of the ⁸¹Br absorption line the jump frequency of the anions is obtained, which is much smaller than for the cations. Since this motional narrowing is not influenced by any doping, it is concluded that anion transport mainly occurs via pairs of cation and anion vacancies.     

Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion

Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.     

饱和光谱中带弛豫项的光学Bloch方程的微扰解法

本文利用微扰论方法,直接求解带弛豫项的光学Bloch方程,给出了计算各级微扰的递推公式,具体地给出了一级和二级微扰近似的解析表达式,并对所得结果做了物理解释。 关键词：     

Raman光激射器

本文从哈密顿量出发,导出描写受激Raman过程的方程式:Laser光、一级Stokes与反Stokes光及相干的声子场的耦合方程,并唯象地引入弛豫耗散。在分子属于远共振情形及比介电常数近似更高一级的近似下,分析了方程的性质。由平衡点稳定性的讨论给出了Raman光激射器的阈值,发现反Stokes激射光的产生并不要求附加的阈条件,即在受激Raman效应中,反Stokes光总是必然出现的。对于Raman光激射器诸工作点的性质及工作过程也作了进一步的讨论,发现在一定条件下,在强激射光源辐照下,存在着Stokes与反Stokes成分几乎各占一半的唯一的稳定平衡点(Raman光激射器的工作点)。文中也顺便讨论了声子弛豫所起的作用及有长寿命的声子时Raman光激射器的行为。     

Dependence of the magnetization relaxation time of single-domain ferromagnetic particles on damping in the Brown model

Analytical expressions for the magnetization relaxation time τ of single-domain ferromagnetic particles with cubic or uniaxial anisotropy in a static transverse magnetic field are derived. The derivation is based on calculating the escape rate of a Brownian particle from a potential well; this technique is applicable at any damping and is generalized to the case of magnetic relaxation of superparamagnetic particles. The validity of the expressions obtained for τ is checked against a numerical solution of the Landau-Lifshitz-Gilbert equation over the whole range of damping (very low, intermediate, and high damping and the crossover region between low and intermediate damping).     

Giant charge relaxation resistance in the Anderson model

We investigate the dynamical charge response of the Anderson model viewed as a quantum RC circuit. Applying a low-energy effective Fermi liquid theory, a generalized Korringa-Shiba formula is derived at zero temperature, and the charge relaxation resistance is expressed solely in terms of static susceptibilities which are accessible by Bethe ansatz. We identify a giant charge relaxation resistance at intermediate magnetic fields related to the destruction of the Kondo singlet. The scaling properties of this peak are computed analytically in the Kondo regime. We also show that the resistance peak fades away at the particle-hole symmetric point.     

Algebraic description of spin 3/2 dynamics in NMR experiments

The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix's evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments.     

Dielectric and anelastic relaxation of crystals containing point defects. II

In part I (1965, Adv. Phys., 14, 101), a theory was developed which treated the thermodynamics of dielectric and anelastic relaxation due to point defects in crystals from the viewpoint of the point symmetry of the defect as well as of the crystal. In the present paper this theory is extended to treat the kinetics of relaxation. Equations are derived which express the relaxation times of electrically and stress active modes of relaxation in terms of the rates of reorientation between one particular defect orientation and all of the other equivalent configurations. Explicit expressions are then given for these relaxation times for commonly occurring crystal and defect symmetries. The reorientation frequencies which appear in these expressions may be converted into the appropriate atom or ion jump rates; this final step can generally be carried out merely by inspection of the crystal model. The possibility that two or more relaxations due to a given point defect may be widely separated on a frequency or temperature scale (a situation which is called a ‘frozen-free split’), and the anomalies connected with such behaviour, are discussed. Finally, various examples which have been studied in the literature, of relaxations due to point defects, are reviewed in the framework of the present theory.     

A New Form of the Crystal Potential in BCC Iron

By approximating the electron density in the crystal as a sum of spherically symmetrical atomic densities using the Green's function, a new exact relation for the Coulomb potential is derived. The relation allows calculation of its values at any point of a unit cell. An attractive potential of the Coulomb hole that screens the electron long-range action is obtained. The method is applied in practice to the bcc iron for the [100], [110], and [111] directions.     

Books received

Equations are derived to enable the two components of magnetic field at a corner of a cross-section through a long straight conductor to be calculated, and it is shown how the field components at any point in or near the conductor can be obtained by combining contributions calculated using these equations.