Electric field and the charge distribution on the surface of an insulator in a vacuum

The free charge steady-state distribution over the insulator surface that arises in a strong electric field in a vacuum can be found by solving the boundary-value problem for the electrostatic field strength if the angle between the field vector and vacuum-insulator interface is given. A general solution to this boundary-value problem is derived for the case of an in-plane field and rectilinear interfaces. Laws of charge and field formation that follow from the solution obtained are considered. Formulas for the electric field strength and charge density in terms of elementary functions are obtained for a number of particular cases. Power-type expressions for the electric field and a critical angle between the electrode and insulator surface that describe the field behavior and charge distribution near the vacuum-insulator-electrode contact are derived.     

An ampere-like law for displacement vector field and near-field optical microscopy

We make up a novel and simple theory for near field and near-field optical microscopy (NOM). Our theory is composed of two parts. The first is a formulation to calculate the scattered near field of light by a small dielectric. We state that a wavenumber-vector-independent picture appears in the theory of the near field, and we find that this is expressed by an Ampere-like law for the displacement vector field. The second part is a formulation of field intensity for far field observation and near field observation from a unified point of view. We suggest a theoretical formula for the field intensity corresponding to the NOM image and demonstrate how to understand the relation between the near field and this image.     

Regular Electric Field in Electromagnetic Coupled to a Scalar Field

In the framework of an electromagnetic field coupled nonminimally with a scalar field in flat spacetime, the existence of a non-singular electric field is proved for a point electric charge or electric monopole. In analogy with the Maxwell-dilaton system introduced by Gibbons and Wells, first, a Maxwell-anti-dilaton system is constructed where the radial electric field of a static electric monopole is coupled to an anti-dilaton. The field equations are solved analytically for the electric and dilaton fields and observe the nonsingular electric field. Also, the self-energy of the electric monopole is found to be finite. Furthermore, the formalism to a Maxwell-scalar field is generalized where a mechanism is introduced upon which the coupled regular-electric field and scalar field is obtained. The formalism shows that for a given regular electric field there are two supersymmetric coupling functions corresponding to a scalar and a phantom field.     

Electric Field in a Gravitational Field

The potential of a static electric charge located in a Schwarzschild gravitational field is given by Linet. The expressions for the field lines derived from this potential are calculated by numerical integration and drawn for different locations of the static charge in the gravitational field. The field lines calculated for a charge located very close to the central mass can be compared to those calculated by Hanni–Ruffini. Maxwell equations are used to analyze the dynamics of the falling electric field in a gravitational field.     

Calculation of critical states of superconducting multilayers based on numerical solution of the Ginzburg-Landau equations for superconducting plates

Numerical methods are used to analyze the Ginzburg-Landau equations for a superconducting plate carrying transport current in a magnetic field. Critical current is calculated as a function of the applied magnetic field strength for superconducting plates with different thicknesses. The relations between the field dependence of critical current and the distributions of order parameter, magnetic field, and supercurrent in a plate are analyzed. The field-dependent critical currents computed for plates are used to determine the critical current as a function of the applied magnetic field strength and local magnetic field and current distributions for multilayers in parallel magnetic fields. The constituent superconducting layers are assumed to interact only via magnetic field. A simple method is proposed for analyzing the critical states of multilayers in magnetic fields of arbitrary strength, based on elementary transformations of the critical current-density distribution over individual layers in zero applied magnetic field. The method can be used to analyze experimental results.     

耦合双原子Jaynes-Cummings模型的腔场谱H

研究了处于激发态的两原子与高Q腔场相互作用单光子过程的腔场谱,给出了初始光场为光子数态、相干态、压缩真空态时的腔场谱数值计算结果,分析了原子间偶极-偶极相互作用强度gα对腔场谱结构的影响.发现真空场Rabi峰,当gα较弱时为4峰,gα较强时为3峰结构;弱场数态(n＞0)时为5峰,强场时为3峰结构.相干态和压缩真空态时,谱结构与光子数分布有关,一般为复杂的多峰结构.结果表明,gα对峰位峰高都有影响,破坏了谱结构的对称性,但这种影响只在真空场和弱场时才较明显.     

直线感应加速器加速间隙对发射度的影响

文中用解析方法计算了直线感应加速器加速间隙对发射度的影响。考虑了存在轴向引导磁场,加速电场,束流分裂以及多个加速间隙的作用。这种解析方法也适用于射频直线加速器的情形。     

On the Number of Photons in a Classical Electromagnetic Field

Relations determining the number of photons in an electromagnetic field are considered from the point of view of a classical electromagnetic field. A relativistically invariant expression is obtained for the number of emitted photons in terms of charges and currents producing the electromagnetic field. Examples are considered for calculating the numbers of photons in the electromagnetic field for the case of the electric dipole radiation field, as well as the field of a finite and spatially restricted electromagnetic pulse.     

Continuous-variable Entanglement in a Correlated Spontaneous Emission Laser

We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser in the linear regime. The master equation for the two-mode cavity field is derived and solved analytically in phase space. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two- mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.     

Zur Theorie der Bewegung geladener Teilchen in richtungskonstanten Magnetfeldern exponentieller Zeitabhängigkeit. I. Allgemeine Theorie und Einschaltvorgang

The general solution of the equations of motion for a charged particle in a magnetic field is given for the following case: the spatially homogeneous magnetic field having a constant direction is a superposition of a field constant in time and one decreasing exponentially in time; taken into account is the influence of the electric field induced by the time dependent magnetic field and a friction force proportional to the particle velocity. The higher transcendental functions appearing in the exact solution are approximated in various ways in dependence on the values of the argument and parameters. The important case of a switching process without a friction force is investigated in detail. The higher transcendential functions can be approximated by simplier functions in such a way, that the solutions for the switching process, valid for all times, differ from the solutions in the case of a linear increasing magnetic field only by factors consisting of elementary functions. Approximated formulae of a very simple form are obtained for position, velocity, kinetic energy and magnetic moment of the particle. The particle orbits are classified and their dependence on the initial values and parameters of the magnetic fields is studied. A comparison between our results and a rectangular variation of the field shows that the latter is not a good approximation for a really exponential increasing field. Finally a detailed investigation shows that the electric field induced by the time dependent magnetic field has an important influence on the particle motion.     

Electric-field-induced front deformation of Belousov-Zhabotinsky waves

Experimental evidence is given of deformations in the vertical profiles of ferroin-catalyzed Belousov-Zhabotinsky waves propagating in thin horizontal cuvettes under an imposed dc electric field. While no deformations are seen in a zero field, for low negative field, or for any positive field, a pronounced S-shaped deformation does occur when a wave is exposed to a negative field above some critical magnitude. The observed phenomena are discussed on the basis of the convective flows that are assumed to increase in the negative field resulting from changes in the longitudinal profile of the wave.     

Field penetration and band bending near semiconductor surfaces in high electric fields

The existing theory of band bending in the surface space charge region of semiconductors is adapted to problems in field emission, field ionization and field evaporation. The surface field in the space charge layers of semiconductors appropriate for these phenomena ranges from ~10^?2 V/Å to a few 10^?1 V/Å, similar to those encountered in many interface phenomena involving semiconductors. We found that the surface potential resulting from band bending may amount to a few eV. The field penetrates ~10 Å into the semiconductor surface for intrinsic cases, and ~200Å for an n-type semiconductor in a positive field, or for a p-type semiconductor in a negative field. Both the surface potential and the field penetration will affect significantly the electronic properties of the near surface layers. In particular, the photon adsorption edge will be shifted toward the red by the field penetration effect.     

Avoiding Haag’s Theorem with Parameterized Quantum Field Theory

Under the normal assumptions of quantum field theory, Haag’s theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag’s Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues.     

Self-Diffusion Imaging by Spin Echo in Earth's Magnetic Field

The NMR of the Earth's magnetic field is used for diffusion-weighted imaging of phantoms. Due to a weak Larmor field, care needs to be taken regarding the use of the usual high field assumption in calculating the effect of the applied inhomogeneous magnetic field. The usual definition of the magnetic field gradient must be replaced by a generalized formula valid when the strength of a nonuniform magnetic field and a Larmor field are comparable (J. Stepišnik,Z. Phys. Chem.190, 51–62 (1995)). It turns out that the expression for spin echo attenuation is identical to the well-known Torrey formula only when the applied nonuniform field has a proper symmetry. This kind of problem may occur in a strong Larmor field as well as when the slow diffusion rate of particles needs an extremely strong gradient to be applied. The measurements of the geomagnetic field NMR demonstrate the usefulness of the method for diffusion and flow-weighted imaging.     

静电场和稳恒电流磁场诸定律的统一性浅探

从点电荷的场强公式出发，根据狭义相对论中场强张量的变换，推导出了静电场和稳恒电流磁场的诸定律，使学生对电场和磁场的统一性有了更为深刻的认识．     

Kerr效应对双光子Tavis-Cummings模型腔场谱的影响

应用全量子理论,研究了含Kerr介质时,耦合双原子与单模量子化光场双光子跃迁相互作用系统的腔场谱,给出了初始时刻原子处于激发态,光场处于数态时的计算结果。讨论了Kerr介质对双光子Tavis-Cummings模型腔场谱量子特性的影响。结果表明,随Kerr效应的加强,腔场谱的峰高、峰位以及峰的个数均发生明显变化:Rabi峰由4个演化为等高双峰;弱场时由5峰演化为差别较大的不等高双峰;强场时则有两高频峰逐渐减弱而先后消失,低频峰逐渐增强直至饱和,最终演化为经典的单峰结构。     

Coupled dilaton and electromagnetic field in cylindrically symmetric spacetime

An exact solution is obtained for coupled dilaton and electromagnetic field in a cylindrically symmetric spacetime where an axial magnetic field as well as a radial electric field both are present. Depending on the choice of the arbitrary constants our solution reduces either to dilatonic gravity with pure electric field or to that with pure magnetic field. In the first case we have a curvature singularity at a finite distance from the axis indicating the existence of the boundary of a charged cylinder which may represent the source of the electric field. For the second case we have a singularity on the axis. When the dilaton field is absent the electromagnetic field disappears in both the cases. Whereas the contrary is not true. It is further shown that light rays except for those proceeding in the radial direction are either trapped or escape to infinity depending on the magnitudes of certain constant parameters as well as on the nature of the electromagnetic field. Nature of circular geodesics is also studied in the presence of dilaton field in the cylindrically symmetric spacetime.     

Antiferromagnets in a field and ferromagnets in a random field

A new mean field approach for antiferromagnets in a field is shown to be equivalent to a mean field treatment of ferromagnets in a random field. Phase diagrams of the two systems are analogous.     

利用轴向磁化的永磁环制造轴向梯度磁场

首先叙述了由单个轴向磁化环所产生的磁场,并就两个永磁环所产生的纵向磁场进行了分析.对于两个沿同一方向磁化的永磁体环,沿磁环中心线将会产生一个强度较为均匀的轴向磁场.如果两者的磁化方向相反,则在两磁铁间的区域将产生一个纵向的梯度磁场,其磁场强度介于-B₀到+B₀之间.设计制造了一个高梯度的轴向磁场,其磁场梯度为47.2Tm,测量结果与计算结果非常一致.文中还讨论了产生变梯度磁场的方法.由于永磁环所产生的磁场和螺线管的磁场较为相似,磁铁外部空间将有较大的漏场,最后还讨论了屏蔽漏场的问题.