Vortices in (Abelian) Chern-Simons gauge theory

The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term. Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory, with both topological and non-topological self-dual vortices, as found by Hong-Kim-Pac, and by Jackiw-Lee-Weinberg. The non-relativistic limit of the latter leads to non-topological Jackiw-Pi vortices with a pure fourth-order potential. Explicit solutions are found by solving the Liouville equation. The scalar matter field can be replaced by spinors, leading to fermionic vortices. Alternatively, topological vortices in external field are constructed in the phenomenological model proposed by Zhang-Hansson-Kivelson. Non-relativistic Maxwell-Chern-Simons vortices are also studied. The Schrodinger symmetry of Jackiw-Pi vortices, as well as the construction of some time-dependent vortices, can be explained by the conformal properties of non-relativistic space-time, derived in a Kaluza-Klein-type framework. (c) 2009 Elsevier B.V. All rights reserved.

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential (A) over cap (i), and find that it has inner structure, namely, (A) over cap (i) can he decomposed in two parts, (b) over cap (i) and (a) over cap (i), where (b) over cap (i) satisfies gauge transformations while (a) over cap (i) satisfies adjoint transformations, so close the Seiberg-Witten mapping of noncommutative, U(1) gauge potential. By, means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor

Knotted wave dislocation with the hopf invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the phi-mapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.

Influence of Coulomb potential for photoionization of H atoms in an elliptically polarized laser field: Velocity gauge versus length gauge

We theoretically study the influence of Coulomb potential for photoionization of hydrogen atoms in an intense laser field with elliptical polarization. The total ionization rates, photoelectron energy spectra, and photoelectron angular distributions are calculated with the Coulomb-Volkov wave functions in the velocity gauge and compared with those calculated in the length gauge as well as those calculated with the Volkov wave functions. By comparing the results obtained by the Coulomb-Volkov and Volkov wave functions, we find that for linear polarization the influence of Coulomb potential is obvious for low-energy photoelectrons, and as the photoelectron energy and/or the laser intensity increase, its influence becomes smaller. This trend, however, is not so clear for the case of elliptical polarization. We also find that the twofold symmetry in the photoelectron angular distributions for elliptical polarization is caused by the cooperation of Coulomb potential and interference of multiple transition channels. About the gauge issue, we show that the difference in the photoelectron angular distributions obtained by the velocity and length gauges becomes rather obvious for elliptical polarization, while the difference is generally smaller for linear polarization.

Implication of scaling hierarchy associated with nonequilibrium: field and particulate

The advent of nanotechnology has necessitated a better understanding of how material microstructure changes at the atomic level would affect the macroscopic properties that control the performance. Such a challenge has uncovered many phenomena that were not previously understood and taken for granted. Among them are the basic foundation of dislocation theories which are now known to be inadequate. Simplifying assumptions invoked at the macroscale may not be applicable at the micro- and/or nanoscale. There are implications of scaling hierrachy associated with in-homegeneity and nonequilibrium. of physical systems. What is taken to be homogeneous and equilibrium at the macroscale may not be so when the physical size of the material is reduced to microns. These fundamental issues cannot be dispensed at will for the sake of convenience because they could alter the outcome of predictions. Even more unsatisfying is the lack of consistency in modeling physical systems. This could translate to the inability for identifying the relevant manufacturing parameters and rendering the end product unpractical because of high cost. Advanced composite and ceramic materials are cases in point. Discussed are potential pitfalls for applying models at both the atomic and continuum levels. No encouragement is made to unravel the truth of nature. Let it be partiuclates, a smooth continuum or a combination of both. The present trend of development in scaling tends to seek for different characteristic lengths of material microstructures with or without the influence of time effects. Much will be learned from atomistic simulation models to show how results could differ as boundary conditions and scales are changed. Quantum mechanics, continuum and cosmological models provide evidence that no general approach is in sight. Of immediate interest is perhaps the establishment of greater precision in terminology so as to better communicate results involving multiscale physical events.

Green's function of a two-dimensional interacting electron gas in a perpendicular magnetic field

It is rigorously proved that the Green's function of a uniform two-dimensional interacting electron gas in a perpendicular magnetic field is diagonal with respect to single-particle states in the Landau gauge. The implication of this theorem is briefly discussed.

Development of external electron-beam enhancement of the Penning ionization gauge ion source

To study the injection of additional electrons from an external electron gun into the plasma of a Penning ionization gauge (PIG) ion source, a test bench for the external electron-beam enhancement of the PIG (E-PIG) ion source was set up. A source magnet assembly was built to satisfy the request for magnetic field configuration of the E-PIG ion source. Numerical calculations have been done to optimize the magnetic field configuration so as to fit the primary electrons to be fed into the PIG discharge chamber along the spreading magnetic field lines. Many possible methods for improving the performance and stability of the PIG ion source have been used in the E-PIG ion source, including the use of multicrystal LaB6 cathode and optimized axial magnetic field. This article presents a detailed design of the E-PIG ion source. Substantial enhancement of ion charge state is expected to be observed which demonstrates that the E-PIG is a viable alternative to other much more costly and difficult to operate devices for the production of intense ion beams of higher charge state.

Inner structure of Spin(c)(4) gauge potential on 4-dimensional manifolds

The decomposition of Spin(c)(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Delta A(mu) = -lambda A(mu) has been discovered. Here, lambda is the vacuum expectation value of the spinor field, lambda = parallel to Phi parallel to(2), and A(mu) the twisting U(1) potential. It is found that when), takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

The generalized second law of thermodynamics in generalized gravity theories

We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In f ( R) gravity and scalar-tensor gravity, the condition to protect the GSL can also hold because the temperature should be positive, gravity is always attractive and the effective Newton constant should be an approximate constant satisfying the experimental bounds.

Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories

We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of a dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasilocal gravitational energy found recently for f(R) gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the Friedmann-Robertson-Walker spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for f(R) gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.

岩石类材料静态、动态拉伸弹性模量测试方法研究——以巴西圆盘试验和霍普金森压杆、效应为手段

As we all know, rock-like materials will absolutely show very different mechanical properties under the compressive stress and tensile stress respectively. Similarly, under the dynamic compressive stress or dynamic tensile stress, the characteristics of the dynamics showed by the rock-like materials also have great differences from the mechanical behavior under static force. Studying their similarities and differences in rock mechanics theory and practical engineering will be of great significance. Generally, there are compression modulus of elasticity and tensile modulus of elasticity corresponding to compressive stress state and the tensile stress state in the rock. Both the two kinds of elastic modulus play an extremely important role in calculation of engineering mechanics. Their reliability directly affects the accuracy and reliability of the calculation results of internal stress field and displacement field of engineering rock mass. At present, it is easy to obtain the compression modulus of elasticity in laboratory; but it is very difficult to determine the tensile modulus of elasticity with direct tensile test due to that direct tensile test is difficult to perform in laboratory in general. In order to solve this problem, this thesis invents and develops several indirect test methods to determine the static or dynamic tensile modulus of elasticity of rock-type materials with high reliability and good interoperability. For the static tensile modulus of elasticity, the analytical stress field solution has been given out for the Brazilian disc under the radial and linear concentration load with Airy stress function method. At the same time, the stress field has been modeled for the Brazilian disc test by using the finite element software of ANSYS and ADINA. The analytical stress field solution is verified to be right by comparatively researching the analytical stress field solution and the numerical stress field solution. Based on the analytical stress field solution, this thesis proposes that a strain gauge is pasted at the Brazilian disc center along the direction perpendicular to the applied force to indirectly determine the static tensile modulus of elasticity, and related measurement theory also has been developed. The method proposed here has good feasibility and high accuracy verified by the experimental results. For the dynamic tensile modulus of elasticity, two measuring methods and theories are invented here. The first one is that the Split Hopkinson Pressure Bar is used to attract the Brazilian disc to generate the dynamic load, make the dynamic tensile stress is formed at the Brazilian disc center; and also a strain gauge is pasted at the Brazilian disc center to record the deformation. The second is that, in the Hopkinson effect phenomenon, the reflection tensile stress wave is formed when the shock wave propagates to the free end of cylindrical rock bar and reflect, which can make the rock bar is under dynamic tensile stress state; and some strain gauges are pasted at the appropriate place on the rock bar to record the strain coursed by the tensile or compressive stress wave. At last, the dynamic tensile modulus of elasticity can be determined by the recorded strain and the dynamic tensile stress which can be determined by related theories developed in this thesis.