On static solutions of the Einstein-Scalar Field equations

In this article we study self-gravitating static solutions of the Einstein-Scalar Field system in arbitrary dimensions. We discuss the existence of geodesically complete solutions depending on the form of the scalar field potential \(V(\phi )\), and provide full global geometric estimates when the solutions exist. The most complete results are obtained for the physically important Klein–Gordon field and are summarised as follows. When \(V(\phi )=m^{2}|\phi |^{2}\), it is proved that geodesically complete solutions have Ricci-flat spatial metric, have constant lapse and are vacuum, (that is \(\phi \) is constant and equal to zero if \(m\ne 0\)). In particular, when the spatial dimension is three, the only such solutions are either Minkowski or a quotient thereof (no nontrivial solutions exist). When \(V(\phi )=m^{2}|\phi |^{2}+2\Lambda \), that is, when a vacuum energy or a cosmological constant is included, it is proved that no geodesically complete solution exists when \(\Lambda >0\), whereas when \(\Lambda <0\) it is proved that no non-vacuum geodesically complete solution exists unless \(m^{2}<-2\Lambda /(n-1)\), (n is the spatial dimension) and the spatial manifold is non-compact. The proofs are based on novel techniques in comparison geometry á la Bakry-Émery that have their own interest.     

Comment on the Roberts Solution for the Spherically-Symmetric Einstein-Scalar Field Equations

We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial case. We generalize this solution and discuss its relations with other known exact solutions.     

光学系统的景深

景深是观察和测量用的光学系统经常要讨论的一个概念．在不同用途的光学仪器中对它的要求不同：有的情况要求景深越大越好，有的则要求越小越好．为此，需要根据影响景深的因素出发，依据观测目的进行光学仪器的设计．本文依据景深的形成原理推导的数学表达式并结合两种典型的光学仪器予以讨论．     

Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint

Journal of Statistical Physics - A correction to this paper has been published: https://doi.org/10.1007/s10955-021-02770-w     

双模压缩真空态与运动原子相互作用系统的场熵演化特性

利用全量子理论,研究了双模压缩真空场与运动原子相互作用系统的场熵演化特性,讨论了不同初始状态态下原子的运动速度、模场结构对场熵的影响。结果表明,场熵通过时间因子sin2(εpgt/2)度与场模结构参数,原子运动和场模结构引起了附加的“熵振荡”。     

比较正反判断正确认识电场

关于静电场特性的判断,学生作业与考试最容易出错。因此,静电特性的教学是教学中的难点。为有效地突破难点,提高教学效果,下面将与部分静电场特性有关的错误判断、反驳举例及正确判断等项列表于下,以便在对照比较错误判断与正确判断的基础上,加深理解,更加正确地认识电场。     

双原子-真空场系统中的纠缠动力学

分别用量子约化熵和量子相对熵研究了双二能级原子与单模真空场相互作用的纠缠动力学.结果表明:通过选择合适的系统参数可以实现双原子纠缠的放大与保持,可以制备出纠缠度为1的双原子纠缠态.     

Gauge Transformation and Constraint Induced Operator Ordering for Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion of a particle is constrained, excess terms exist using hermitian form of Cartesian momentum pi （i=1, 2,3） in usual kinetic energy （1/2/μ）∑ pi^2 , and the correct kinetic energy turns out to be （1/2μ） ∑1/ fipi f ipi, where fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.     

Gauge Transformation and Constraint Induced Operator Ordering for Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion ofa particle is constrained, excess terms exist using hermitian form of Cartesian momentum pi (I=1,2,3) in usual kinetic energ y (1/2μ) ∑ pi2, and the correct kinetic energy turns out to be (1/2μ) ∑ 1/ fipi fipi, where fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.     

Constraint on the Parameter of Group By Two Order Transformation of Field Variable Being Equal to Zero in Non-Abelian

A sufficient and necessary condition that two order transformation of field variable in non-abelian gauge field is equal to zero is derived.Two order transformation of both the parameter of Group and field variable of Fermi fields are necessarily equal to zero.     

Critical Current of the Ionization Waves and Anomaly of the Positive Column in an Axial Magnetic Field

Influences of an axial magnetic field on the ionization wave and the positive column in rare gas discharges are studied experimentally. The upper critical current I_c for the appearance of ionization waves in the magnetic field B is newly found. As B is gradually increased, the value of I_e slightly increases from the Pupp's value and after passing a prominent maximum, finally become very small. In addition an anomaly takes place in the axial electric field E of the positive column stable for helical instabilities. With increasing the magnetic field the value of E goes through a weak maximum before decreasing. It is concluded that this anomaly, apparently incompatible with classical diffusion theory, is closely related to the appearance of ionization waves in the positive column.     

噪声之间的正负耦合对激光场的影响

从理论上对加性噪声和倍增噪声之间有耦合作用的一维激光模型进行了分析，发现耦合的性质对激光场涨落影响较大，噪声之间的正耦合会延缓强度相关函数的衰减，增强激光系统的统计涨落。噪声之间的负耦合能抑制激光系统的统计涨落，提高激光场的相干性，使激光系统由随机过程向确定过程过渡。     

The Relativistic Dynamics of the Combined Particle–Field System in Renormalized Classical Electrodynamics

This paper develops a general theory for the nonlinear, renormalized interaction between charged particles and electromagnetic fields. For the combined “particle + field” system, a fundamental relativistically invariant dynamical equation is derived from first principles. This theory was first obtained in an alternative way by one of us (J.K.) in an earlier paper. Here, we prove that the initial-value problem for the “particle + field” system is well-posed. The existence and uniqueness result is based on a careful analysis of the singularites of the electromagnetic field along the trajectory of the moving charged particle. Furthermore, the Banach fixed-point principle is used. The theory improves the classical Dirac theory for the motion of electrons. In particular, it is shown how to deal with the Dirac paradox of runaway solutions. Received: 10 December 1997 / Accepted: 21 April 1998     

Imaginary Photon Field Effect in the Interaction System of Multi-atom with Single-mode Photon Field

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in the interaction system of multi-atom with single-mode photon field with imaginary photon process. We find that the geometric phases in a cycle case have nothing to do with the frequency of the photon field, the coupling coefficient between photons and atoms, and the atom transition frequency. If we use the more accuracy device, the geometric phases in the imaginary photon process may be observed, and the geometric phases in this process have the observable physical effect.     

外控弱周期电流约束下电极B-Z反应体系中的时间自组织

以经典BZ化学反应体系的三变量Oregonator模型及电极过程动力学为基础,提出了外控弱周期电极电流约束下电极BZ反应体系与体相BZ反应体系相互耦合的动力学模型.在体相处于稳定定态参数条件下,系统地研究了外控弱周期电流约束下电极BZ反应体系中的动力学行为,定量分析了电流慢变流型上的准定态稳定性及有利于出现极限环振荡区域.研究表明,与以前所报道的外控弱周期电位约束情况类似,在外控弱周期电流约束下电极BZ反应体系中的极限环振荡区域亦发生了蜕变,但体系对外控电流约束中的这种持续性之周期扰动的响应表现在两个方面:有利于出现极限环振荡区域的缩变及原非振荡区胁迫振荡的出现.     

On the Anomaly of the Electrical Field Strength in the Magnetized Positive Column of Glow Discharges at Small Currents

The axial electrical field strength in the positive column of glow discharges at small currents in noble gases passes through a maximum with the increase of an axially directed magnetic field. This maximum is explained of the contrary processes of extension of the radial profiles of the electron energy and the concentration of the metastable atoms on the one hand and the decrease of the ambipolar diffusion losses on the other hand. Using the results of measurements of metastable atom concentrations, the electrical field strength is calculated as a function of magnetical induction with the aid of a set of balance equations. The radial and axial distribution of the electrons is checked by probe measurements. The methods for measuring the concentration of the excited atoms and the electrons are described.