外尔费米子的奇特热电性质

<正>世界由各种微观粒子组成。这些粒子可以分为两大类,玻色子和费米子。费米子组成了物质,而玻色子传递物质之间的相互作用。1928年,为了精确计算原子的能谱,狄拉克基于量子力学的原理,同时考虑电子的相对论性运动,提出一个波函数方程来描述电子的行为。这个方程后来被称为狄拉克方程。该方程的意义远远超出了狄拉克的初衷。它不但给出了自旋的理论解     

势垒高度对Cl+H2(D2)反应的影响

使用三维含时波包方法在两个势能面上研究了Cl+H2(D2)反应．所使用的两个势能面都是从CW(Capecchi和Wener)势能面得到的，第一个是CW势能面的基态面加自旋轨道耦合修正，第二个是CW势能面的基态面没有自旋轨道耦合修正．在这两个势能面上得到了碰撞能从0.1到1.4 eV的积分截面以及反应几率．对于Cl与D2反应，考虑自旋轨道耦合后由于势垒高度的增加反应截面向高能处有一个平移，但Cl与H2反应在低能处的反应活性反而增大了，原因是虽然自旋轨道耦合效应增加了势垒高度，同时减小了势垒宽度，隧道效应更加明显，而隧道效应在低能处起着比较重要的作用，所以反应活性比较大．当碰撞能大于0.7 eV时，没有考虑自旋轨道耦合时势垒高度较低，因而反应活性较大．     

与量子输运方程相一致的夸克经典输运方程

用Sμν作为描述夸克自旋的动力学变量建立了它的经典输运方程，并讨论了该方程与量子输运方程的一致性，通过一致性的比较探讨了经典分布函数在色空间和自旋空间的一些特性.     

从Schroedinger方程引申到Dirac方程的一种简单方法

从Schroedinger方程出发，结合自旋的唯象描述、简单的相对论考虑和适当的猜测，写出了Dirac方程的正确形式     

希格斯（Higgs）粒子

在现有的弱电统一理论中，认为应当存在自旋为零的粒子（Ｈｉｇｇｓ粒 ），并且通过“Ｈｉｇｇｓ机制”实现真空对称性自发破缺．这个理论的许多重要预言都得到了实验上广泛的证实，但始终没有找到在理论上起核心作用的Ｈｉｇｇｓ粒子本身．粒子物理学面临一个十分重要的课题．本文从理论和实验两个方面就这个问题进行了评述，其中包括介绍Ｈｉｇｇｓ机制和寻找Ｈｉｇｇｓ粒子的现状及意义．     

Vaidya-Bonner-de Sitter黑洞对狄拉克粒子的热辐射

分析讨论了Vaidya-Bonner-de Sitter黑洞视界附近的狄拉克方程,准确地定出了Vaidya-Bonner-de Sitter黑洞的Hawking温度和辐射谱，同时计算出事件视界方程，所得结果与用零曲面方程得到的结果一致. 关键词： 黑洞 视界 狄拉克方程 热辐射     

直接优化法同时反演声波方程的两个系数

本文在时域范围内考虑一个层状半无限空间的声波方程两个系数同时反演的问题。通过构造一个偏差的平方和形式的目标泛函，声波方程系数的反演问题可以转化为一个由双曲型偏微分方程控制的优化问题。在本文中，一种直接优化的技术被用来解这个优化问题。通过寻找目标泛函的极小点，声波方程的两个系数可以方便地得到同时反演。由于直接优化法只使用了目标泛函的函数值而不用它的梯度信息，因此这种算法具有稳定、精确的优点。文中同时还给出了这种算法的稳定性定理以及数值解的例子。从数值解的情况上看，这种直接优化法反演声波方程系数的结果是令人满意的。     

相对论自旋流体力学

近年来,随着重离子碰撞实验中超子自旋极化与矢量介子自旋排列现象的发现,关于夸克胶子物质中自旋输运的理论研究也得到蓬勃发展,其中包括相对论自旋流体力学,它是描述自旋输运的流体力学理论.本文对相对论自旋流体力学的近期发展进行了综述,主要包括以下内容:1)相对论自旋流体力学基本方程的推导,包括宏观的唯象学推导、基于有效场论的推导以及基于输运理论的推导; 2)该理论框架的一些特殊性质,包括能动量张量中的反对称结构以及赝规范变换性质等; 3)在Bjorken和Gubser膨胀体系中的解析解及其对于重离子碰撞物理的意义.     

可控磁性量子点杂质引起的单电子自旋过滤器

本文提出一种基于电子-电子自旋交换相互作用获得自旋极化电流的模型.该方案中,需要两个距离相近的量子点.其中一个是开放系统,另一个是封闭系统.开放系统能完成单电子输运,封闭系统产生比较强的局域磁场,两个系统之间有电子-电子自旋交换相互作用.该相互作用会影响电子输运,从而可以对电子输运产生自旋过滤效应.我们用量子主方程描述开放系统的演化,在有效哈密顿量的基础上,可以得到解析结果.结果显示,在低温条件下,交换相互作用足够强的时候,系统给出的自旋过滤效率接近1.     

拉氏方程,阿贝尔方程的张量推导

本文应用线性代数、张量分析的基本概念说明拉氏方程、阿贝尔方程可以看作是牛顿方程在约束所允许的矢量空间中的协变分量形式，从而在不直接引用虚位移原理的前提下，导出这两个分析力学的基本方程．     

Spinor Representation of Electromagnetic Fields on Noncommutative Spaces

We apply Campolattaro's spinor representation of the electromagnetic field to noncommutative spaces. The spinor representation of the (self-dual) electromagnetic field on noncommutative spaces is obtained.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper.Firstly,since the Dirac equation is described as a matrix equation in phase space,it is necessary to define the Wigner function as a matrix function in spinor space.Secondly,the matrix form of the Wigner function is proven to support the Dirac equation.Thirdly,by solving the Dirac equation,energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Dynamic and Geometric Phase Formulas in the Hestenes-Dirac Theory

We examine the dynamic and geometric phases of the electron in quantum mechanics using Hestenes' spacetime algebra formalism. First the standard dynamic phase formula is translated into the spacetime algebra. We then define new formulas for the dynamic and geometric phases that can be used in Hestenes' formalism.     

Spinors, Inflation, and Non-Singular Cyclic Cosmologies

We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by a spinor field turns out to be unappealing as it leads to a blue spectrum of perturbations and requires considerable fine-tuning of parameters. We next find that, for simple, quartic spinor self-interactions, non-singular cyclic cosmologies exist with reasonable parameter choices. These solutions might eventually be incorporated into a successful past- and future-eternal cosmological model free of singularities. In an Appendix, we discuss the classical treatment of spinors and argue that certain quantum systems might be approximated in terms of such fields.     

Nodal theorems for the Dirac equation in d ≥ 1 dimensions

A single particle obeys the Dirac equation in spatial dimensions and is bound by an attractive central monotone potential that vanishes at infinity. In one dimension, the potential is even, and monotone for The asymptotic behavior of the wave functions near the origin and at infinity are discussed. Nodal theorems are proven for the cases and , which specify the relationship between the numbers of nodes n₁ and n₂ in the upper and lower components of the Dirac spinor. For , whereas for if and if where and This work generalizes the classic results of Rose and Newton in 1951 for the case Specific examples are presented with graphs, including Dirac spinor orbits      

概率波和非概率波

对于把克莱因-戈尔登方程当作是玻色子的方程的看法提出异议,认为它是所有微观粒子均要满足的方程,但它却不能成为任何一类粒子的波动方程.提出了克-戈方程中包含着概率和非概率两类波的概念,认为概率波还要遵从一个对时和空都是一阶导数的方程,这才是粒子的波动方程.不同种类粒子性质的不同则体现在他们概率波类型的不同上.     

Spin current in a spinor Bose-Einstein condensate induced by a gradient magnetic field

We develop a research of spin currents in a ²³Na spinor Bose-Einstein condensate (BEC) by applying a magnetic field gradient. The spin current is successfully induced by the spin-dependent force arising from the magnetic field gradient. The dynamics of the spin components under the magnetic force is investigated. The study is promising to be extended to produce a longer spin-coherence and to enhance the sensitivity of the spin-mixing interferometry in a spinor BEC.     

Spinor Boltzmann Equation with Two Momenta at the Fermi Level

Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The longitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.