The sub-millimeter and Fourier transform microwave spectrum of HZnCl (X Σ)

The pure rotational spectrum of HZnCl (X ¹Σ⁺) has been recorded using sub-millimeter direct-absorption methods in the range of 439-540 GHz and Fourier transform microwave (FTMW) techniques from 9 to 39 GHz. This species was produced by the reaction of zinc vapor and chlorine gas with H₂ or D₂ in a d.c. glow discharge for the sub-millimeter studies. In the FTMW measurements, HZnCl was created in a discharge nozzle from Cl₂ and (CH₃)₂Zn. Between 5 and 10 rotational transitions were measured in the sub-millimeter regime for four zinc and two chlorine isotopologues; four transitions were recorded with the FTMW machine for the main isotopologue, each consisting of several chlorine hyperfine components. The data are consistent with a linear molecule and a ¹Σ⁺ ground electronic state. Rotational and chlorine quadrupole constants were established from the spectra, as well as an r_m⁽²⁾ structure. The Zn-Cl and Zn-H bond lengths were determined to be 2.0829 and 1.5050 Å, respectively; in contrast, the Zn-Cl bond distance in ZnCl is 2.1300 Å, longer by ∼0.050 Å. The zinc-chlorine bond distance therefore shortens with the addition of the H atom. The ³⁵Cl electric quadrupole coupling constant of eQq = −27.429 MHz found for HZnCl suggests that this molecule is primarily an ionic species with some covalent character for the Zn-Cl bond.     

The equilibrium limit of a constitutive model for two-phase granular mixtures and its numerical approximation

In this paper we analyze the equilibrium limit of the constitutive model for two-phase granular mixtures introduced in Papalexandris (2004) [13], and develop an algorithm for its numerical approximation. At, equilibrium, the constitutive model reduces to a strongly coupled, overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase. First we carry a perturbation analysis based on standard hydrostatic-type scaling arguments which reduces the complexity of the coupling of the equations. The perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator. Further, based on the Helmholtz decomposition and Ladyzhenskaya’s decomposition theorem, we develop a projection-type, Successive-Over-Relaxation numerical method. This method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro-structure. We also prove that this method is both stable and consistent hence, under standard assumptions, convergent. The paper concludes with the presentation of representative numerical results.     

反射式离轴无透镜傅里叶变换数字全息实验初探

实验研究中,设计了反射式离轴无透镜傅里叶变换实验光路图,并成功进行了记录和再现,记录并分析了实验要点。     

Symmetry-improved CJT effective action

The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward Identities due to global symmetries. By considering a simple O(2)$\mathbb{O}(2)$ scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O(2)$\mathbb{O}(2)$ is massless and the phase transition is a second-order one, already in the Hartree–Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree–Fock approximated CJT effective action, we calculate the corresponding symmetry-improved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.     

基于电光调制提高静态傅里叶干涉具光谱分辨率的研究

在静态干涉系统中,采用电光调制可变折射率晶体LiNbO₃做静态傅里叶干涉具的材料,两侧分别加载相位相反的调制信号,从而在不改变静态傅里叶干涉具尺寸的条件下提高光谱分辨率。通过推导光程差函数与折射率调制度的函数关系,计算得在折射率调制度为0.030的条件下,比同尺寸干涉具光谱分辨率提高了16.7倍,达到2.836 cm-1。仿真结果表明折射率调制度会因波长增大而减小,光程差函数会随干涉位置的增大而产生偏大的现象。实际探测过程中,由于光谱范围500～1 100 nm相对较窄,波长变化造成的光谱探测失真不大,可以通过标定补偿,所以应用该方法可以有效地提高静态干涉系统的光谱分辨率。     

基于正弦光栅调制的相位恢复

提出一种基于正弦光栅调制的相位恢复方法.首先,在空间光调制器上加载两个不同方向的正弦光栅对光场复振幅进行调制;然后,推导强度信息和相位偏导数之间的关系式;最后由强度信息计算相位偏导数,进而恢复相位.实验分别测试了该方法对简单图像、复杂图像以及含噪声图像的恢复能力.实验结果表明,该方法可以通过方便地控制图像移动量来有效恢复相位信息,适用于不同尺度的相位物体的计算.     

基于多级微镜的傅里叶变换成像光谱仪干涉成像系统分析与设计

为了实现傅里叶变换成像光谱仪的静态化与高通量,提出一种基于多级微镜的时空混合调制成像光谱仪,其干涉系统是利用一个多级微镜代替迈克尔逊干涉仪中的平面镜,其显著特点是无运动部件和限制系统光通量的狭缝,可同时获得目标的干涉图与二维空间图像。该成像光谱仪利用前置成像系统将目标成像到干涉系统的平面镜与多级微镜上,利用多级微镜的结构特点对两成像光束的光程差进行调制,然后通过后置成像系统获得不同干涉级次的目标图像。首先通过对该成像光谱仪干涉系统光谱信噪比的分析,明确了光谱信噪比与图像信噪比之间的关系,确定了多级微镜的特征参数。为了确保每个阶梯面所对应光程差的恒定性,通过对前置成像系统成像过程的分析,确定了前置成像系统像方远心的光路结构;通过对系统视场角与光程差之间关系的分析和计算,确定了前置成像系统的设计指标并完成了光学设计。为了保证后置成像系统不引入额外的光程差,通过对后置成像系统成像特点的分析,确定了后置成像系统双远心的光路结构;通过对系统入射孔径角与阶梯级数之间关系的分析和计算,最终设计出满足系统性能需求的后置成像系统。通过对各单元系统的理论分析与光学设计,为静态化与高通量成像光谱仪的发展提供了一种新的思路。     

The minimal excludant and Schmidt's partition theorem

In this work, we study Schmidt's partition theorem in a combinatorial manner, and find a strong refinement which connects the minimal excludant of ordinary partitions to the length of Schmidt's partitions. As a byproduct, we obtain a bivariate form of an identity recorded in Ramanujan's lost notebook.     

HOW REYE'S CONFIGURATION HELPS IN PROVING THE BELL–KOCHEN–SPECKER THEOREM: A CURIOUS GEOMETRICAL TALE

It is shown that the 24 quantum states or rays used by Peres (J. Phys. A 24, 174-8 (1991)) to give a proof of the Bell–Kochen–Specker (BKS) theorem have a close connection with Reye's configuration, a system of twelve points and sixteen lines known to projective geometers for over a century. The interest of this observation stems from the fact that it provides a ready explanation for many of the regularities exhibited by the Peres rays and also permits a systematic construction of all possible non-coloring proofs of the BKS theorem based on these rays. An elementary exposition of the connection between the Peres rays and Reye's configuration is given, following which its applications to the BKS theorem are discussed.     

动力系统的正则量子对称性质

分别从正规和奇异拉氏量系统的相空间生成泛函出发,导出了增广相空间中整体对称下的正则形式Ward恒等式.考虑对应的定域交换,得到了量子水平的守恒荷,给出了正则形式的量子Noether定理.讨论了在核子和π介子相互作用中的初步应用.