薄壁量子化方法进展

微纳加工技术的快速发展实现了具有非平庸几何结构的低维材料与结构的制备,使得受几何性质影响的有效动力学问题受到关注。作为研究低维弯曲系统中量子力学的有效方法,薄壁量子化方法,它给出的几何势和几何动量也得到实验的证实。本文将回顾薄壁量子化方法,简述其基本计算框架,明确给出几何量子效应是来自于微分同胚变换和局域标架间的旋转变换。这对于理解引力规范场,演生规范场很有帮助,对理解人工规范场所隐含的几何结构也很有帮助。在特定的量子体系中,几何量子效应可表现为共振隧穿、量子阻塞、量子霍尔效应、量子霍尔黏性、量子自旋霍尔效应和单极磁场等,这些结果从不同角度展示了几何与新奇的物理现象之间的联系。     

匀质悬链几何形状的力学研究

本文研究了匀质悬链的几何形状为悬链线和抛物线的力学条件;探讨了悬链形状与外力作用分布的一般关系;得到了一系列与悬链线有关的参数计算公式.     

高阶微商场论中奇异拉氏量系统的量子正则对称性

给出了高阶徽商场论中奇异拉氏量系统规范生成元的构成.从相空间中Green函数的生成泛函出发,导出了约束Hamilton系统正则形式的Ward恒等式.指出该系统的量子正则方程与由Dirac猜想得到的经典正则方程不同.给出了与Chern-Simons理论等价的一个广义动力学系统的量子化.将正则Ward恒等式初步应用于该系统,不作出对正则动量的路径积分,也可导出场的传播子与正规顶角之间的某些关系.     

三维各向同性谐振子的几何动量分布

尽管几何动量最初的引入是为了描述超面上的运动粒子的动量,却不需要限制在真实的曲面上.如果一个曲线坐标系包含了超面族和超面上的法向矢量作为一个坐标轴的单位矢量,几何动量可以定义在超面族上,并参与构造对易力学量完全集.在三维各向同性谐振子中,采用球坐标描述,存在等效球面,并在球面族上建立对易力学量完全集.因此,三维各向同性谐振子同时具有动量和几何动量分布.这两个动量的差,可以定义为径向动量,从而使得径向动量可以测量.那么,通过几何动量,可以显示出狄拉克引进的径向动量的物理意义,而不是一直认为的那样完全不具有观测意义.     

20年大学物理教学研究成果回顾展正则动量的量子化

回顾了历年来《大学物理》上有关广义坐标下正则动量如何量子化问题的讨论，并对此问题发表了作者的看法.     

有限空间中经典场的正则量子化

从离散的角度研究带边界的1+1维经典标量场和Dirac场的正则量子化问题. 与以往不同的是, 这里将时间和空间两个变量同时进行变步长的离散, 应用变步长离散的变分原理, 得到离散形式的运动方程、边界条件和能量守恒的表达式. 然后, 根据Dirac理论, 将边界条件当作初级约束, 将边界条件和内在约束统一处理. 研究表明, 采用此方法, 不仅在每个离散的时空格点上能够建立起Dirac括号, 从而可以完成该模型的正则量子化;而且, 该方法还保持了离散情况下的能量守恒.     

氢原子在红外激光和极紫外脉冲组合场中的阈上电离

通过求解氢原子在强红外(IR)激光和极紫外（XUV）脉冲组合场中的三维含时薛定谔方程(TDSE),理论研究了XUV脉冲的加入对光电子能谱和二维光电子动量分布的影响.计算结果表明,与仅由红外场驱动的情况相比,组合场驱动下的光电子能谱和二维光电子动量分布中呈现出明显的干涉增强结构,干涉结构对XUV脉冲的强度、光子能量和时间延迟都有很强的依赖,该方案可实现高能阈上电离谱的选择性增强.     

广义Schwarzschild几何的引力微扰

利用Regge和Wheeler提出的方法,导出了广义Schwarzschild几何的轴扰动方程.对给定角动量L和λ参数,通过数值计算,得到了拟正则模的值.数值结果与不稳定性的解析证明相一致. 关键词：     

超球坐标下氢分子体系势能矩阵元的解析表达式

给出了在非正则超球坐标系下对氢分子薛定谔方程进行直接求解时所涉及的所有势能矩阵元的解析表达式,以及主要的推导。在推导过程中,引入了付立叶变换及９维矢量将势能各项用超球谐函数来展开,并且利用了合流超几何函数,拉卡系数和维格纳系数的一些性质。     

阻尼谐振子波函数的解

对一维阻尼受迫谐振子,根据其哈密顿量,通过正则量子化、变量代换等方法求解其薛定谔方程,得到其波函数和能量的表达式,同时分析讨论了该解的零点量子涨落问题。     

弹体尾部轴对称干扰流场数值模拟

绕弹体的超声速气流与发动机喷流相互作用,在尾部形成复杂的干扰流场。本文用有限差分法求解全N-S方程,对这一复杂流场进行了数值模拟,得到了实验观察到的各种流场结构及其随喷口压力比的变化规律。外流M_∞=1.94,R_e∞=2.2×10⁵,喷流M_j=3.0,喷口压力比p_j/p_∞分别为1.03,0.527,0.15三种。差分算法为一种改进的Beam-Warming格式。计算底部压力和激波在喷流中心的反射位置与实验数据进行了比较,吻合较好。     

Dielectric and ferroelectric properties of the mixed crystals system (CH3NH3)5Bi2(1 − x)Sb2xCl11

Dielectric and pyroelectric properties of the mixed crystals system, (CH₃NH₃)₅Bi_{2(1 − x)}Sb_2xCl₁₁ (0 < x < 0.25) were systematically investigated. Temperature dependencies of ′_c in the vicinity of ferro-paraelectric phase transition were measured for the mixed crystals with x = 0.05, 0.07, 0.11, 0.13 and 0.25 in the frequency region 1 kHz–1 MHz. The substitution of bismuth atoms by antimony drastically reduces the magnitude of ′_c and shifts the ferro-paraelectric phase transition towards higher temperatures. The dielectric dispersion of the complex electric permittivity, _c^*, in x = 0.05 crystals was studied in the frequency range from 30 to 1000 MHz. Around 321 K phase transition, two dielectric relaxators are postulated; a low-frequency one in the megahertz region showing a critical slowing down and a high-frequency one in the gigahertz region.     

Giant pressure effect in oxygen deficient YBa2Cu3Ox

The pressure effect on T_c of polycrystalline and single crystalline YBa₂Cu₃O_x investigated as a function of oxygen content x by ac-susceptibility measurements under helium pressure. In the overdoped region x> 6.93 the single crystals show a negative dT_c/d p, as expected from the charge transfer model. For optimally doped samples with x = 6.93 we find dT_c/d P = 0.4 K/GPa which points to pressure effects on T_c aside from charge transfer. In the underdoped region x < 6.93 the dT_c/d p values obtained from the experiment depend strongly on the storage temperature of the sample during the experiment. When the samples are stored at temperatures well below 240 K throughout the entire experiment including pressure application and pressure release, dT_c/d p increases to approx. 7 K/GPa at x = 6.7 but with a further decrease of the oxygen content the dT_c/d p drops to approx. 2 K/GPa at x = 6.4. These effects are intrinsic to the YBa₂Cu₃O_x structure and can be explained by considering the anisotropic structure of YBa₂Cu₃O_x. The decrease of the c-axis lattice parameter results in a charge transfer to the CuO₂-planes mainly [1], whereas the compression of the a- and b-axis lattice parameter is known to produce different pressure effects which are responsible for the peak in dT_c/d p at x = 6.7 [2]. When pressure is changed at room temperature oxygen ordering effects occur which cause a relaxation of T_c to the equilibrium value T_c(p) at this pressure with a time constant depending on the oxygen content x. A decrease x results in a peak effect in dT_c/d p at x = 6.7 again, which is enhanced to approx. 12 K/GPa. If the oxygen content is decreased further, dT_c/d p first drops to 5 K/GPa at x = 6.6, but the increases to values of more than 20 K/GPa for x < 6.42. These giant pressure effects at low oxygen contents are mainly caused by a reversible T_c increase (dT_c/d p)_O due to pressure induced oxygen ordering via oxygen motion between unit cells.     

The Arnol''d cat: Failure of the correspondence principle

The classical Hamiltonian H = p²/2m + ε(q²/2)Σδ[s-(t/T)] has an integrable mapping of the plane, [q_n+1, p_n+1]= [q_n+1+p_n, q_n+2p_n], as its equations of motion. But then by introducing periodic boundary conditions via (mod 1) applied to both q and p variables, the equations of motion become the Arnol'd cat map, [q_n+1, p_n+1] = [q_n + p_n, q_n + 2p_n], (mod 1), revealing it to be one of the simplest fully chaotic systems which can be derived from a Hamiltonian and analyzed. Consequently, we here quantize the Arnol'd cat and examine its quantum motion for signs of chaos using algorithmic complexity as the litmus. Our analysis reveals that the quantum cat is not chaotic in the deep quantum domain nor does it become chaotic in the classical limit as required by the correspondence principle. We therefore conclude that the correspondence principle, as defined herein, fails for the quantum Arnol'd cat.     

Entanglement measures of a new type pseudo-pure state in accelerated frames

In this work we analyze the characteristics of quantum entanglement of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity N_ABI (ρ^TA_ABI) increases with F but decreases with the variable y, while the variation of the negativity N_BIBII(ρ^TA_ABI) is opposite to that of the negativity N_ABI (ρ^TA_ABI). We also study the von Neumann entropies S(ρ_ABI) and S(ρ_BIBII). We find that the S(ρ_ABI) increases with variable y but S(ρ_BIBII) is independent of it. However, both S(ρ_ABI) and S(ρ_BIBII) first decreases with F and then increases with it. The concurrences C(ρ_ABI) and C(ρ_BIBII) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it.     

Saturation and BFKL dynamics in the HERA data at small-x

We show that the HERA data for the inclusive structure function F₂(x,Q²) for x10⁻² and 0.045Q²45 GeV² can be well described within the color dipole picture, with a simple analytic expression for the dipole–proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x₀ of x at which the saturation scale Q_s equals 1 GeV, and the logarithmic derivative of the saturation momentum λ. The value of λ extracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.     

Magnetic behavior of Pr1 − xMxCo5 compounds (M = Ti, Zr and Hf)

Magnetic characteristics of Ti-, Zr- and Hf-substituted PrCo₅ alloys have been studied over the temperature range from 77 to 300 K and for applied fields up to 20 kOe. It is established that Ti, Zr and Hf substitute for Pr. Single-phase materials are formed for all values of x up to 0.2 in the system Pr_1−xZr_xCo₅ but for x only up to 0.1 for Pr_1−xTi_x Co₅ and Pr_1−xHfxCo₅ alloys. Larger amounts of Zr can be substituted if the material is made hyperstoichiometric in Co, e.g., Pr_0.7Zr_0.3Co_5.5. All the alloys show a decrease in magnetic moment and an increase in Curie temperature as x increases. Anisotropy fields decrease as x increases at 295 K. Anomalous behavior is observed at 77 K, suggested that these ternary alloys may have a cone structure at this temperature.     

Structure, oxygen stoichiometry and electrical conductivity in the system Sr-Ce-Co-O

Mixed oxides in the system S-Ce-Co-O were prepared by solid state reaction and by freeze-drying of precursor compounds followed by thermal treatment. Two types of perovskite oxides exist in the system: Solid solutions of the type Sr_{1 − y}Ce_yCoO_{3 − x} and mixed oxides of the type (1 − y)SrCeO₃ − ySrCoO_{3 − x}. Microstructures and phase compositions were determined by electron microscopy and X-ray diffraction. SrCoO_{3 − x} forms a solid solution of ceria on the A-site in the strontium cobaltite lattice up to 0.15 mol Ce. This solid solution corresponds to the high-temperature structure of pure SrCoO_{3 − x} and is characterized by high oxygen exchange and electrical conductivity. The oxygen deficiency x was measured by solid electrolyte coulometry. The oxygen deficiency of solid solutions Sr_{1 − y}Ce_yCoO_{3 − x} increases with temperature and decreases with pO₂ in the ambient atmosphere and with increasing Ce dopant concentration. The pO₂-T-x diagram of the solid solution was determined. The T, pO₂ and dopant concentration dependencies of electrical conductivity were measured by a four-point d.c. technique. By Ce doping strontium cobaltite becomes a stabilized high-conductive material (maximum conductivity: 500 S cm⁻¹ at 400 °C, E_a = 0.025 eV, p-type). Above this temperature the T-coefficient of the conductivity changes from positive (semiconducting) to negative values.     

The optimal coefficients in Daubechies wavelets

The construction of wavelets begins with a dilation equation (x) = Σc_k(2x-k). The choice of the coefficients c_k controls the accuracy and orthogonality of wavelet expansions. We show how the Daubechies coefficients, which give pth order accuracy with 2p coefficients (the minimum number), follow from orthogonality and accuracy conditions applied to the polynomial Σc_ke^ikξ.