方解石棱镜分束角高度对称性的设计

研究ｏ、ｅ双输出棱镜分束角的对称性。指出经特殊设计的双渥拉斯顿棱镜产生的ｏ、ｅ光的分束角具有高度的对称性。     

The Second Noether Theorem in the formalism of jet-bundles: Symmetries and degeneration

By means of the jet-bundle formalism, the Second Noether Theorem is formulated for a general first-order Lagrangian field theory with infinitesimal local symmetries. These symmetries are implemented by a linear differential operator acting between the sections of a vector bundle and vector fields on the configuration bundle. The problem of the degeneration of the Lagrangian system is examined from a covariant and an instantaneous (i.e. space+time split) viewpoint. It is shown that in the instantaneous approach the presence of infinitesimal local symmetries leads to degeneration of the theory. Vertical local symmetries are shown to imply degeneration also in the covariant formalism. These results can be extended to higher-order Lagrangians as well.     

Quark condensation, induced symmetry breaking and color superconductivity at high density

The phase structure of hadronic matter at high density relevant to the physics of compact stars and relativistic heavy-ion collisions is studied in a low-energy effective quark theory. The relevant phases that figure are (1) chiral condensation, (2) diquark color condensation (color superconductivity) and (3) induced Lorentz-symmetry breaking (“ISB”). For a reasonable strength for the effective four-Fermi current–current interaction implied by the low-energy effective quark theory for systems with a Fermi surface we find that the “ISB” phase sets in together with chiral symmetry restoration (with the vanishing quark condensate) at a moderate density while color superconductivity associated with scalar diquark condensation is pushed up to an asymptotic density. Consequently, color superconductivity seems rather unlikely in heavy-ion collisions although it may play a role in compact stars. Lack of confinement in the model makes the result of this analysis only qualitative but the hierarchy of the transitions we find seems to be quite robust.     

Incommensurate modulations in Ba2TiSi2O8, Sr2TiSi2O8, and Ba2TiGe2O8

Incommensurate modulations in Ba₂TiSi₂O₈, Sr₂TiSi₂O₈, and Ba₂TiGe₂O₈ are compared based on their corresponding electron diffraction patterns. The dependence of the modulations on chemical composition provides a suitable model system for the investigation of incommensurations in framework structures using high-resolution transmission electron microscopy (HRTEM). A widening of quantitative HRTEM utilising the concept of rigid units is proposed allowing for a determination of atomistic displacements responsible for the formation of incommensurately modulated structures.     

具有特殊伸缩矩阵的三元不可分正交小波的构造

多元小波分析是分析和处理多维数字信号的有力工具.不可分多元小波被广泛地应用在模式识别、纹理分析和边缘检测等领域.给出了构造具有伸缩矩阵(101-1-110-10)的紧支撑三元不可分正交小波的算法,利用该算法得到的小波函数继承了来源于尺度函数和符号函数的对称性和消失矩性质,从而为这类小波在信号处理方面的应用提供了便利.最后给出了数值算例.     

Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation j of the empirical current with a rate functional I(j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional I. We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.     

Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

Isospin symmetry violation, meson production and η-nucleus interaction studies

We have studied isospin symmetry violation in nuclear reactions by measuring simultaneously the cross-section of the following two reactionsp +d →³H π⁺ andp +d →³He π⁰. The experiment was perfomed at the cooler synchrotron accelerator COSY, Jülich at several beam energies close to the correspondingη production threshold. We also have ongoing programmes onη-nucleus final-state interaction studies viap+⁶ Li →⁷ Be +η reactions, high resolution search for dibaryonic resonances and lambda-proton final state interaction studies. The experimental details and results obtained so far are presented here     

在赝自旋对称性势场中运动的相对论粒子的束缚态

在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.     

准坐标下完整力学系统的非Noether守恒量——Hojman定理的推广

利用时间不变的无限小变换下的Lie对称性，研究准坐标下完整力学系统的一类新守恒量.建立系统的运动微分方程，给出无限小变换下的Lie对称性确定方程.将Hojman定理推广，并举例说明结果的应用. 关键词： 准坐标 完整力学系统 Lie对称性 非Noether守恒量 Hojman定理