可积系统棗求迹公式和h逆谱分析

研究了二维无关联四次振子系统,有理环面上积分Hamiltonian运动方程给出了系统一系列周期轨道和经典物理量,使用半经典近似下的Berry-Tabor求迹公式,得到了半经典的态密度．应用Fourier变换分析了每条周期轨道对态密度的贡献,并与量子态密度的Fourier变换结果比较证实了半经典求迹公式的有效性．     

实际光栅系统的分辨本领

本文指出了传统的光栅分辨本领Ｒ＝ｋＮ只是在光源狭缝无限细的情况下的极限值。当光源狭缝还有一定宽度Ｗ时，衍射条纹将增宽，相应最小分辨角Δθｋ将增大，实际光栅系统的分辨本领将减小。文章运用衍射理论，给出了实际光栅系统分辨本领的修正公式。在实验中，在不同光栅宽度Ｄ的情况下，用ｋ＝１级衍射条纹，当测量恰能分辨钠黄光的双线结构的光源缝宽Ｗ时，这时光栅系统的分辨本领是λ／δλ≈１０００，与修正公式计算的理论值一致。     

莫比乌斯变换及其物理应用

北京科技大学陈难先教授把数论中的一条古老定理:莫比乌斯变换推广到普通函数并创造性地用之于物理学中许多反问题,取得了巨大成功。在此以更直观和易于理解的方式导出陈氏定理,并通过一些具体实例展示其应用前景。     

Maxwell–Chern–Simons场的Casimir效应

利用约束理论对AbelMaxwell-Chem-Simons场进行路径积分量子化. 并利用复变函数论中Plana求和公式,计算(2+1)维空间中两个平行导线型边界的Casimir效应. 不引任何截断参数,而得出有限的解析表达式.     

Harris公式和ab公式对超形变核转动带的适用性的比较

对A≈190区超变形转动带分别用Harris二参数公式和ab公式进行了系统分析.分析结果表明,与正常变形核动带的情况相似,Harris公式与实验有明显的系统偏离,而ab公式则与实验很接近,可以相当精确和方便地描述超变形转动带.     

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.     

Microwave absorption properties regulation and bandwidth formula of oriented Y2Fe17N3-δ@SiO2/PU composite synthesized by reduction-diffusion method

As concepts closely related to microwave absorption properties, impedance matching and phase matching were rarely combined with material parameters to regulate properties and explore related mechanisms. In this work, reduction-diffusion method was innovatively applied to synthesize rare earth alloy Y$_{2}$Fe$_{17}$. In order to regulate the electromagnetic parameters of absorbers, the Y$_{2}$Fe$_{17}$N$_{3-\delta }$ particles were coated with silica (Y$_{2}$Fe$_{17}$N$_{3-\delta }$@SiO$_{2}$) and absorbers with different volume fractions were prepared. The relationship between impedance matching, matching thickness, and the strongest reflection loss peak (${\rm RL}_{\rm min}$) was presented obviously. Compared to the microwave absorption properties of Y$_{2}$Fe$_{17}$N$_{3-\delta }$/PU absorber, Y$_{2}$Fe$_{17}$N$_{3-\delta }$@SiO$_{2}$/PU absorbers are more conducive to the realization of microwave absorption material standards which are thin thickness, light weight, strong absorbing intensity, and broad bandwidth. Based on microwave frequency bands, the microwave absorption properties of the absorbers were analyzed and the related parameters were listed. As an important parameter related to perfect matching, reflection factor ($\sqrt {ărepsilon_{\rm r}/\mu_{\rm r}}$) was discussed combined with microwave amplitude attenuation. According to the origin and mathematical model of bandwidth, the formula of EAB (${\rm RL}<-10$ dB) was derived and simplified. The calculated bandwidths agreed well with experimental results.     

芴二聚体三重激发态能量转移的理论研究

利用电子结构计算和电子转移速率理论,研究了芴二聚体的三重激发态能量转移过程. 应用限制性密度泛函理论构造得到非绝热态后,计算了控制能量转移的两个重要参数{电子耦合强度和重组能. 电子耦合强度的波动利用电子动力学模拟计算. 通过对上述参数相关函数的计算,成功得到了体系哈密顿量的对角元和非对角元波动,并应用微扰理论和波包扩散方法得到了能量转移速率. 结果表明,静态和动态的波动都明显地增加了能量转移速率,但是动态波动导致的速度增加却小于静态波动.     

New microscopic wave function of ��-condensation

We explain how to treat a microscopic wave function of ??-condensation taking a 3??-nucleus as a typical example. The wave function has been originally proposed ten years before by Horiuchi, R?pke, Schuck and the present author (Phys. Rev. Lett., 2001, 87: 192501). The microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons, effective internucleon forces and the Coulomb force, can play an important role in reproducing an ??-gas nature thanks to ??-condensation as an excited state of ??-like nuclei. An essential point of the wave function is to describe their ground state simultaneously. We study its typical features by giving an analytical formula of the norm kernel and the kernel concerning the one-body operator for 3??-condensation.