Non-minimal pp-wave Einstein–Yang–Mills–Higgs model: color cross-effects induced by curvature

Non-minimal interactions in the pp-wave Einstein–Yang–Mills–Higgs (EYMH) model are shown to give rise to color cross-effects analogous to the magneto-electricity in the Maxwell theory. In order to illustrate the significance of these color cross-effects, we reconstruct the effective (associated, color, and color-acoustic) metrics for the pp-wave non-minimal seven-parameter EYMH model with parallel gauge and scalar background fields. Then these metrics are used as hints for obtaining explicit exact solutions of the non-minimally extended Yang–Mills and Higgs equations for the test fields propagating in the vacuum interacting with curvature. The influence of the non-minimal coupling on the test particle motion is interpreted in terms of the so-called trapped surfaces, introduced in the Analog Gravity theory.     

A modification of Einstein–Schrödinger theory that contains Einstein–Maxwell–Yang–Mills theory

The Lambda-renormalized Einstein–Schrödinger theory is a modification of the original Einstein–Schrödinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein– Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of d × d Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein–Maxwell–Yang–Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity matrix closely approximates Einstein–Maxwell–Yang–Mills theory in that the extra terms in the field equations are < 10^?13 of the usual terms for worst-case fields accessible to measurement. The theory contains a symmetric metric and Hermitian vector potential, and is easily coupled to the additional fields of Weinberg–Salam theory or flipped SU(5) GUT theory. We also consider the case where symmetric fields have small traceless parts, and show how this suggests a possible dark matter candidate.     

Particle motion and electromagnetic fields of rotating compact gravitating objects with gravitomagnetic charge

The exact solution for the electromagnetic field occuring when the Kerr–Taub–NUT compact object is immersed (i) in an originally uniform magnetic field aligned along the axis of axial symmetry (ii) in dipolar magnetic field generated by current loop has been investigated. Effective potential of motion of charged test particle around Kerr–Taub–NUT gravitational source immersed in magnetic field with different values of external magnetic field and NUT parameter has been also investigated. In both cases presence of NUT parameter and magnetic field shifts stable circular orbits in the direction of the central gravitating object. Finally we find analytical solutions of Maxwell equations in the external background spacetime of a slowly rotating magnetized NUT star. The star is considered isolated and in vacuum, with monopolar configuration model for the stellar magnetic field.     

磁单极子进展概述

自磁单极子概念被狄拉克提出以来,不管是理论还是实验物理学家都一直在努力寻找,但迄今仍然没能找到它们存在的确凿证据.最近,一些凝聚态物理学家声称在动量空间以及自旋冰材料中找到了磁单极子存在的有力证据,并通过磁单极子的集体激发行为解释了一些新颖的物理现象.这使得磁单极子艰难的探索之路出现了一丝新的曙光.作为电动力学教学内容的补充,本文拟把磁单极子的最新进展做一个概述,让大学生对此有一个全面的认识,从而激发他们学习和科研的兴趣.     

On geometric quantization of the Dirac magnetic monopole

We give a simple derivation of the spectrum of the Dirac magnetic monopole on a unit sphere S² based on geometric quantization and the Frobenius reciprocity formula. The starting point is the calculation by Novikov and Schmelzer of the canonical symplectic structure on the coadjoint orbits of the isometry group of 3-dimensional Euclidean space E(3), which showed the appearance of the Dirac magnetic term.     

The interaction of electricity and magnetism in Einstein–Maxwell theory

I consider stationary axially symmetric solutions of the Einstein–Maxwell equations. These show that, in general, time-independent electric and magnetic fields acting together cause rotational effects in the spacetime. An electric charge placed on the axis of a magnetic dipole induces a region of closed timelike curves.     

Some New Solutions Derived From the 5-Dimensional Theory—The New Methods of Creating Solutions

Application of the 5-dimensional coordinate transformations in the 5-dimensional theory lead us to some new solutions for the 4-dimensional Einstein–Maxwell equations and the relevant scaler equation. From the Kerr solution we derive the corresponding solution. And we propose a new method to solve the usual 4-dimensional Einstein–Maxwell equations and the scalar equation, illustrating by three examples.     

整体单极子黑洞引力场中的加速效应

给出了含有整体单极子的黑洞的引力场中试验粒子加速度的表达式, 讨论了整体单极子对加速效应的贡献. 结果表明, 由于整体单极子的存在, 产生了斥力效应; 当速度趋近于光速时, 中性粒子在引力场中受到了斥力作用. 这是牛顿力学中所没有的.     

Trapping energy of a magnetic monopole in magnetic materials

Analytical methods to investigate the interaction of magnetic monopoles with known magnetic media have been developed. Trapping energies of monopoles inside ferro-magnetic or super onducting materials of size greater than about 10⁻⁶ cm are found to be of the order of several kiloelectron volts. These are two to three orders of magnitude higher than in paramagnetic materials. Thus if stable magnetic monopoles exist at all in the universe, they are perhaps trapped in these magnetic materials. The effect of the finite size of the magnetic bodies is taken into account explicitly in our calculations of the trapping energy.     

Sodium in a strong magnetic field

We investigate the effects of a magnetic field with low to intermediate strength on several spectroscopic properties of the sodium atom. A model potential is used to describe the core of sodium, reducing the study of the system to an effective one-particle problem. All states with principal quantum numbers n = 3, 4, 5, 6 and 7 are studied and analysed. A grid of twenty values for the field strength in the complete regime B = 0 - 0.02 a.u. is employed. Ionisation energies, transition wavelengths and their dipole oscillator strengths are presented. Received 5 November 2002 Published online 4 February 2003     

Magnetic field driven domain-wall propagation in magnetic nanowires

The mechanism of magnetic field induced magnetic domain-wall (DW) propagation in a nanowire is revealed: A static DW cannot exist in a homogeneous magnetic nanowire when an external magnetic field is applied. Thus, a DW must vary with time under a static magnetic field. A moving DW must dissipate energy due to the Gilbert damping. As a result, the wire has to release its Zeeman energy through the DW propagation along the field direction. The DW propagation speed is proportional to the energy dissipation rate that is determined by the DW structure. The negative differential mobility in the intermediate field is due to the transition from high energy dissipation at low field to low energy dissipation at high field. For the field larger than the so-called Walker breakdown field, DW plane precesses around the wire, leading to the propagation speed oscillation.     

Spin tunneling properties in mesoscopic magnets: effects of a magnetic field

The tunneling of a giant spin at excited levels is studied theoretically in mesoscopic magnets with a magnetic field at an arbitrary angle in the easy plane. Different structures of the tunneling barriers can be generated by the magnetocrystalline anisotropy, the magnitude and the orientation of the field. By calculating the nonvacuum instanton solution explicitly, we obtain the tunnel splittings and the tunneling rates for different angle ranges of the external magnetic field ( θ _H = π/2 and π/2 < θ _H < π). The temperature dependences of the decay rates are clearly shown for each case. It is found that the tunneling rate and the crossover temperature depend on the orientation of the external magnetic field. This feature can be tested with the use of existing experimental techniques. Received 12 March 2001 and Received in final form 18 October 2001     

Equilibrium of a gravitating plasma in a dipolar magnetic field

The equilibria of plasma in a dipolar magnetic field under the gravitational influence of a massive body (a star or black hole) and a self gravitating plasma are considered. Analytical solutions are found that can be useful for understanding the physics of plasma flows in accretion disks and star formation.     

Transient ion dynamics, forced by external electric field in electrolytic cell with blocking electrodes

The nonlinear differential equations, describing the migration and diffusion of ions in electrolytic cell with blocking electrodes, driven by external electric field, have been solved with the help of a numerical algorithm. Usually, the dynamical equations are simplified by applying the Einstein–Nernst relation between diffusion and mobility, although this relation is valid for stationary, time-independent variables. In the present work, we have introduced correction terms, to take into account transient ion currents when external stepwise voltage is switched on. The correction terms are defined and numerically evaluated. The transient behavior of the system described without corrections is compared to the transients when corrections are applied. The results are examined for different regimes and parameters of the system.     

Gravitational field of a tachyon in a de Sitter universe

An exact solution of Einstein’s equations is interpreted as describing the gravitational field of a tachyon in a de Sitter universe. Switching off the cosmological constant yields the gravitational field of a tachyon in flat spacetime background.     

Paradoxical magnetic cooling in a structural transition model

In contrast to the experimentally widely used isentropic demagnetization process for cooling to ultra-low temperatures we examine a particular classical model system that does not cool, but rather heats up with isentropic demagnetization. This system consists of several magnetite particles in a colloidal suspension, and shows the uncommon behavior of disordering structurally while ordering magnetically in an increasing magnetic field. For a six-particle system, we report an uncommon structural transition from a ring to a chain as a function of magnetic field and temperature. Received 5 September 2000     

Topological field patterns in the Yang-Mills theory

We present a formalism where the topological configurations of pure Yang-Mills theory are characterised using gauge fields alone. Here, we obtain an expression for the charges of these topologicalSO(3) gauge field configurations in terms of the Abelian vector potentials. In this formalism we analyse the ’t Hooft-Polyakov monopole solution.     

Holographic superconductors in the AdS black-hole spacetime with a global monopole

We study holographic superconductors in the Schwarzschild–AdS black hole with a global monopole through a charged complex scalar field. We calculate the condensates of the charged operators in the dual conformal field theories (CFTs) and discuss the effects of the global monopole on the condensation formation. Moreover, we compute the electric conductive using the probe approximation and find that the properties of the conductive are quite similar to those in the Schwarzschild–AdS black hole. These results can help us know more about holographic superconductors in the asymptotic AdS black holes.     

On the motion of a charged particle in the field of a magnetic monopole

A quantum mechanical treatment of the motion of a charged particle in the field of a fixed magnetic monopole is given, based on a representation of the corresponding vector potential by means of a distribution. The results are closely similar to those obtained in the work of Wu and Yang, which stems from ideas borrowed from mathematical fiber bundle theory. We believe that our method follows more closely the usual quantum mechanical procedures and provides an alternative approach to that of Wu and Yang. Although the present paper deals with non-relativistic problem, it is clear that the extension to the case of a Pauli or Dirac particle can be easily done using spinor monopole harmonics.