现代数字物理教学连载②——关于电流磁场的数字教学研究

以电磁场的教学为例,介绍了数字物理教学的重要作用,并借助现代数字技术,解决了长期以来基础物理教学未能处理好的环形电流及螺线管磁场和交变电磁场的问题,丰富了电磁学的教学内容,提高了学生处理实际问题的能力．     

Oscillator strengths of optical transitions of a cylindrical shell: Crossed static electric and magnetic fields

The single-electron eigenstates of a cylindrical shell are determined as functions of the applied crossed electric and magnetic fields in the effective-mass approximation. The system considered consists of donor charges taken to be uniformly distributed within an inner core of infinitely long length. The core is concentrically enveloped by a semiconducting material of finite thickness; which is essentially the host material. This configuration of the donor charges sets up a spatially varying electric field nonetheless with only the radial component. In addition, a uniform magnetic field is applied parallel to the axis of symmetry of the inner core. As is well known, the axial applied magnetic field lifts the double degeneracies of the electron’s subbands characterized by the same azimuthal quantum numbers which differ only in sign. The main effect of increasing the external electric field is to elevate the various energy subbands, more or less to the same extent, to higher values. Further, evaluations of the oscillator strengths of optical transitions of the cylindrical shell are carried out within the dipole approximation. The radiation field is taken to be that of circularly polarized light incident along the axis of the core. The oscillator strengths of optical transitions are found to increase with an increase of the applied magnetic field, particularly in the regime of small magnetic fields. In contrast, the oscillator strengths of these optical interactions become suppressed as the donor charge density is increased.     

Effects of strong electric fields in a polyacetylene chain

In this work, we study the effects related to the creation of electron/hole pairs via application of an external electric field that acts on a pristine trans-polyacetylene molecular chain at zero-temperature. This phenomenon is termed Schwinger–Landau–Zener (SLZ) effect and arises when a physical system, which can even be the vacuum, is under the action of a strong, static and spatially homogeneous electric field. Initially, we investigate how the electrical conductivity of the polyacetylene changes with the applied field, by considering the carriers production as well as the variation of the interband gap according to certain ab initio models. Next, we analyse the competition between the SLZ effect and another one associated with the incidence of an uniform electric field on one-dimensional crystals – the Bloch oscillations. We evaluate the conditions in which these latter can be destroyed by the particles created through the same field that induces them, and verify the possibility of occurrence of the Bloch oscillations inside the trans-polyacetylene with frequencies equal to or higher than the terahertz scale.     

平行电磁场中里德堡氢原子的自相似结构研究

利用半经典方法研究了平行电磁场中里德堡氢原子的分形自相似现象. 通过研究平行电磁场中里德堡氢原子的逃逸时间和初始出射角间的关系, 发现了逃逸时间图的自相似结构, 并通过研究与图中冰柱对应的逃逸轨道, 得到了自相似结构和逃逸轨道之间的关系, 发现了该类自相似逃逸轨道满足的规律. 进一步研究了标度能量和标度磁场对体系动力学的影响, 表明标度能量和标度磁场均控制体系的分形自相似结构. 当标度能量或标度磁场比较小时, 没有自相似现象, 随着标度能量或标度磁场的增大, 自相似出现, 体系变复杂.     

带电粒子在相互垂直的匀强电场和磁场中的运动轨迹

推导出带电粒子在相互垂直的匀强电场和磁场中普遍情况下的运动方程,给出了几种典型情况下的轨迹,并对轨迹的形状和性质,结点的出现进行了讨论.     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters $E_r}$ and $\Ga/2$ of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of $10^{-9}-10^{-12}$ for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.     

平行电磁场中的Rydberg锂原子吸收谱的模型势计算

用B样条基组展开方法结合模型势计算了Rydberg锂原子在平行电磁场下的振子强度谱. 径向和角向均采用高阶Ｂ样条基组.计算结果与已有的实验结果符合得很好.利用分波分析法,对部分谱线的振子强度的强弱进行了分析. 本文方法简单有效，易于推广到交叉电磁场中Rydberg原子的精确谱的计算. 关键词： B样条 能谱 振子强度 平行电磁场 Rydberg原子     

垂直电磁场中He原子的吸收谱和回归谱的理论计算

半经典闭合轨道理论已经成功地计算了在外加磁场和平行电磁场中的里德堡原子的回归谱.但对于垂直电磁场中的里德堡原子,理论和计算都变得更为复杂.本文把闭合轨道理论推广到三维情况,采用 B.Hüpper的模型势计算了ε=-0.03,主量子数n≈ 40,m=0下He原子在垂直电磁场中的光吸收谱和回归谱,并和H原子在垂直电磁场中的回归谱作比较,突出了实散射的贡献.计算中应用了离子实散射的分区自洽迭代方法,并考虑到轨道的多次重复和离子实的多次散射效应.这是对闭合轨道理论的验证和进一步推广.     

Effects of external electric and magnetic fields on the linear and nonlinear intersubband optical properties of finite semi-parabolic quantum dots

In this work, influences of external electric and magnetic fields on the optical rectification coefficient, the linear and the third-order nonlinear optical absorption coefficients as well as refractive index changes of finite semi-parabolic quantum dots are investigated. In this regard, energy eigenvalues and eigenfunctions of the system are calculated numerically, and optical properties are obtained using the compact density matrix approach. The results show that external electric and magnetic fields have a great influence on these optical quantities.     

用杂化CIS-DFT方法研究外电场对乙烯激发态的影响

采用杂化CIS-DFT方法研究了外电场对乙烯分子基态和激发态性质的影响,结果表明外电场对分子几何结构,总能量,偶极矩,极化率,振子强度和激发能有显著影响.CIS-DFT的优点在于能确定外场下分子的对称性,给出正确的激发顺序以及分子轨道的电子组态,由此导出乙烯分子的激发态,结果与实验一致.首次研究了乙烯分子的外电场效应.与其他从头算方法相比,杂化CIS-DFT方法计算精确和效率相对较高,可用于研究大分子体系.     

外场调控下硼磷烯量子点的电子结构和光学性质研究

采用紧束缚近似方法对锯齿状六边形硼磷烯量子点在平面电场和垂直磁场调控下的电子结构和光学性质进行了研究. 研究表明,硼磷烯量子点作为直接带隙半导体,在无外加电场和磁场作用时,能隙不随尺寸的改变而变化. 在平面电场调控下,能隙随电场强度的增加逐渐减小直至消失,平面电场方向几乎不会对硼磷烯量子点体系产生影响, 且随量子点尺寸的增大,能隙消失所需电场强度逐渐减小. 在垂直磁场调控下,表现为体态的能级在磁场作用下形成朗道能级,而能隙边缘处的朗道能级近似为一个平带,不随磁通量的改变而变化,态密度主要分布于朗道能级处. 另外,垂直磁场作用下的光吸收主要是由朗道能级之间的跃迁引起的.     

不同维度ZnO能带结构和电子态密度的研究

本文采用基于密度泛函理论的第一性原理计算方法来研究不同维度ZnO的能带结构和电子态密度.参考实验上的ZnO晶格参数构建不同维度的ZnO模型并进行结构优化后再计算能带结构和电子态密度.研究结果表明二维和三维ZnO都属于直接带隙半导体且二维ZnO的禁带宽度大于三维ZnO;从三维变到二维,ZnO的电子局域化程度变高且Zn 3d轨道电子从能量较低的能级向能量较高的能级跃迁.本文的研究展示了二维和三维ZnO能带结构和电子态密度的异同,为二维ZnO基的器件研究提供了一定的理论参考价值.     

Effects of the edge shape and the width on the structural and electronic properties of silicene nanoribbons

Under the generalized gradient approximation (GGA), the structural and electronic properties are studied for H-terminated silicene nanoribbons (SiNRs) with either zigzag edge (ZSiNRs) or armchair edge (ASiNRs) by using the first-principles projector-augmented wave potential within the density function theory (DFT) framework. The results show that the length of the Si-H bond is always 1.50 Å, but the edge Si-Si bonds are shorter than the inner ones with identical orientation, implying a contraction relaxation of edge Si atoms. An edge state appears at the Fermi level E_F in broader ZSiNRs, but does not appear in all ASiNRs due to their dimer Si-Si bond at edge. With increasing width of ASiNRs, the direct band gaps exhibit not only an oscillation behavior, but also a periodic feature of Δ_3n > Δ_3n+1 > Δ_3n+2 for a certain integer n. The charge density contours analysis shows that the Si-H bond is an ionic bond due to a relative larger electronegativity of H atom. However, all kinds of the Si-Si bonds display a typical covalent bonding feature, although their strength depends on not only the bond orientation but also the bond position. That is, the larger deviation of the Si-Si bond orientation from the nanoribbon axis as well as the closer of the Si-Si bond to the nanoribbon edge, the stronger strength of the Si-Si bond. Besides the contraction of the nanoribbon is mainly in its width direction especially near edge, the addition contribution from the terminated H atoms may be the other reason.     

用杂化CIS-DFT方法研究外电场对乙烯激发态的影响

采用杂化CIS-DFT方法研究了外电场对乙烯分子基态和激发态性质的影响，结果表明外电场对分子几何结构，总能量，偶极矩，极化率，振子强度和激发能有显著影响。CIS-DFT的优点在于它能确定外场下分子的对称性并且给出正确的激发顺序以及分子轨道的电子组态，由此导出乙烯分子的激发态，计算结果与实验一致。首次研究了乙烯分子的外电场效应。与其他从头算方法相比，杂化CIS-DFT方法计算精度和效率相对较高，可用于研究大分子体系。     

Calculation of electric and magnetic induced fields in humans subjected to electric power lines

In this work, analysis of the human body exposed to high voltage electric and magnetic fields is presented. The distribution of the electric field is obtained by using Laplace's equation. This relates the surface charge induced on the body to the potential in a reciprocal Laplace problem, which is then calculated by charge simulation method coupled with genetic algorithms to determine the appropriate arrangement of simulating charges inside the human body. The magnetic field intensity along the vertical center line of the human is calculated. Exposure to external electric and magnetic fields at power frequency induces electric field, magnetic field and currents inside the human body. The presented model for simulating electric and magnetic fields are a three dimensional field problem and introduced different types of charges to simulate the different elementary geometrical shapes of human body. The particular strength of the charge simulation method in this application is its ability to allow a detailed representation of the shape and posture of the human body. The results have been assessed through comparison induced current, electric field, magnetic field and there distribution over the body surface, as estimated in other experimental and computational work.     

THz spectroscopy of diluted magnetic semiconductors and semiconductor quantum structures in ultrahigh magnetic fields

Magneto-absorption spectra in ferromagnetic semiconductor In_1−xMn_xAs films and self-organized PbSe/PbEuTe quantum dot superlattices have been studied in the terahertz range at very high magnetic fields up to 500 T. Both heavy hole (HH) and light hole (LH) cyclotron resonance (CR) have been observed in bulk In_1−xMn_xAs thin films with different Mn concentrations. The detailed Landau level calculation in terms of the effective mass approximation well explained the CR peak positions, line shapes and the dependence of the circular polarization of the incident light on the CR spectra. In InMnAs/GaSb heterostructures that have higher ferromagnetic transition temperature (T_c) than the bulk samples, the observed HH and LH cyclotron masses are larger than that in the bulk thin films. We found that the CR peak position and its line shape suddenly change in the vicinity of the ferromagnetic transition temperature, suggesting the change in the electronic structure due to the ferromagnetic transition. Electron CR in PbSe/PbEuTe quantum dots has been observed and it was found that the effective mass of the electrons is considerably modified by the quantum confinement potential and the lattice strain around the dots. A large wavelength dependence of the absorption intensity was observed due to the interference effect of the radiation inside the sample.     

Instabilities in nematic elastomers in external electric and magnetic fields

In this paper we study the macroscopic behavior of nematic side-chain liquid single crystal elastomers exposed to an external electric or magnetic field. For this purpose we use the framework of a continuum model. The geometries investigated comprise the bend and the twist geometry known from the classical Frederiks transition in low molecular weight liquid crystals. For the bend geometry we find a laterally homogeneous and a two-dimensional undulatory instability, which may compete at onset. In the case of the twist geometry three instabilities can occur at onset, two of which are two dimensional and clearly show undulations. As a major result we propose how the values of the twist coefficient K(2) and the values of the material parameters D(1) and D(2) connected to relative rotations between the director field and the polymer network can be determined from experimental observations. In addition, we explain why a twist experiment is probably the most suitable set-up in order to measure the material parameter D(1).