Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n - 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n - r)-dimensional DFV.

The vector fields admitting one-parameter spatial symmetry group and their reduction

For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.

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

Field emission enhancement by the quantum structure in an ultrathin multilayer planar cold cathode

Field electron emission (FE) from an ultrathin multilayer planar cold cathode (UMPC) including a quantum well structure has been both experimentally and theoretically investigated. We found that by tuning the energy levels of UMPC, the FE characteristic can be evidently improved, which is unexplained by conventional FE mechanism. FE emission mechanism, dependent on the quantum structure effect, which supplies a favorable location of electron emission and enhances tunneling ability, has been presented to expound the notable amelioration. An approximate formula, brought forward, can predict the quantum FE enhancement, in which the theoretical prediction is close to the experimental result. (C) 2008 American Institute of Physics.

State Vector: A New Approach to Prediction of the Failure of Brittle Heterogeneous Media and Large Earthquakes

The concept of state vector stems from statistical physics, where it is usually used to describe activity patterns of a physical field in its manner of coarsegrain. In this paper, we propose an approach by which the state vector was applied to describe quantitatively the damage evolution of the brittle heterogeneous systems, and some interesting results are presented, i.e., prior to the macro-fracture of rock specimens and occurrence of a strong earthquake, evolutions of the four relevant scalars time series derived from the state vectors changed anomalously. As retrospective studies, some prominent large earthquakes occurred in the Chinese Mainland (e.g., the M 7.4 Haicheng earthquake on February 4, 1975, and the M 7.8 Tangshan earthquake on July 28, 1976, etc) were investigated. Results show considerable promise that the time-dependent state vectors could serve as a kind of precursor to predict earthquakes.

Modification of Bertrand's theorem and extended Runge-Lenz vector

It is shown that for a particle with suitable angular moments in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O-3. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

Attosecond pulse extreme-ultraviolet photoionization in a two-color laser field

Attosecond-pulse extreme-ultraviolet (XUV) photoionization in a two-color laser field is investigated. Attosecond pulse trains with different numbers of pulses are examined, and their strong dependence on photoelectronic spectra is found. Single-color driving-laser-field-assisted attosecond XUV photoionization cannot determine the number of attosecond pulses from the photoelectronic energy spectrum that are detected orthogonally to the beam direction and the electric field vector of the linearly polarized laser field. A two-color-field-assisted XUV photoionization scheme is proposed for directly determining the number of attosecond pulses from a spectrum detected orthogonally. (C) 2005 Optical Society of America.

Surface planar ion chip for linear radio-frequency Paul traps

We propose a surface planar ion chip which forms a linear radio frequency Paul ion trap. The electrodes reside in the two planes of a chip, and the trap axis is located above the chip surface. Its electric field and potential distribution are similar to the standard linear radio frequency Paul ion trap. This ion trap geometry may be greatly meaningful for quantum information processing.

TWO-DIMENSIONAL ARRAY OF ION TRAPS ON A PLANAR CHIP

We investigate a planar ion chip design with a two-dimensional array of linear ion traps for the scalable quantum information processor. The segmented electrodes reside in a single plane on a substrate and a grounded metal plate, a combination of appropriate rf and DC potentials are applied to them for stable ion confinement, and the trap axes are located above the surface at a distance controlled by the electrodes' lateral extent and the substrate's height as discussed. The potential distributions are calculated using static electric field qualitatively. This architecture is conceptually simple and many current microfabrication techniques are feasible for the basic structure. It may provide a promising route for scalable quantum computers.

Analytical vectorial structure of hollow Gaussian beams in the far field

The analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HGB in the far-field, which is composed of TE term and TM term, are demonstrated. The physics pictures of HGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HGB propagation. (c) 2008 Optical Society of America.

Low-loss planar and stripe waveguides in Nd3+-doped silicate glass produced by oxygen-ion implantation

We report on the fabrication and characterization of low-loss planar and stripe waveguides in a Nd3+-doped glass by 6 MeV oxygen-ion implantation at a dose of 1x10(15) ions/cm(2). The dark mode spectroscopy of the planar waveguide was measured using a prism coupling arrangement. The refractive index profile of the planar waveguide was reconstructed from a code based on the reflectivity calculation method. The results indicate that a refractive index enhanced region as well as an optical barrier have been created after the ion beam processing. The near-field mode profiles of the stripe waveguide were obtained by an end-fire coupling arrangement, by which three quasitransverse electric modes were observed. After annealing, the propagation losses of the planar and stripe waveguides were reduced to be similar to 0.5 and similar to 1.8 dB/cm, respectively. (c) 2007 American Institute of Physics.

Electric field distribution in resonant reflection filters under normal incidence

Electric field distributions inside resonant reflection filters constructed using planar periodic waveguides are investigated in this paper. The electric fields may be intensified by resonance effects. Although the resonant reflection peaks can be quite narrow using weakly modulated planar periodic waveguides, the strong electric field enhancement limits their use in high-power laser systems. Strongly modulated waveguides may be used to reduce the electric field enhancement and a cover layer may be used to narrow the bandwidth at the same time. Desired results (i.e. almost no electric field enhancement together with narrow bandwidth) can be realized using this simple structure.

Planar refractive microlens arrays in indium phosphide and quartz substrates

Large-area concave refractive microlens arrays, or concave template structures, and then the non-refractive-index-gradient type of planar refractive microlens arrays in InP and quartz substrates, are fabricated utilizing the method consisting of conventional UV photolithography, thermal shaping of concave photoresist microlenses, etching with an argon ion beam of large diameter, and filling or growing optical medium structures onto the curved surfaces of preshaped concave templates. Several key conditions for fabricating concave and also planar microlenses are discussed in detail. The concave structures obtained are characterized by scanning electron microscope and surface profile measurements. The far-field optical characteristics of quartz/ZrO2 planar refractive microlens arrays have been acquired experimentally. (c) 2008 Society of Photo-Optical Instrumentation Engineers.

Rashba spin-orbit coupling in InSb nanowires under transverse electric field

We investigate the Rashba spin-orbit coupling brought by transverse electric field in InSb nanowires. In small k(z) (k(z) is the wave vector along the wire direction) range, the Rashba spin-orbit splitting energy has a linear relationship with k(z), so we can define a Rashba coefficient similarly to the quantum well case. We deduce some empirical formulas of the spin-orbit splitting energy and Rashba coefficient, and compare them with the effective-mass calculating results. It is interesting to find that the Rashba spin-orbit splitting energy decreases as k(z) increases when k(z) is large due to the k(z)-quadratic term in the band energy. The Rashba coefficient increases with increasing electric field, and shows a saturating trend when the electric field is large. As the radius increases, the Rashba coefficient increases at first, then decreases. The effects of magnetic fields along different directions are discussed. The case where the magnetic field is along the wire direction or the electric field direction are similar. The spin state in an energy band changes smoothly as k(z) changes. The case where the magnetic field is perpendicular to the wire direction and the electric field direction is quite different from the above two cases, the k(z)-positive and negative parts of the energy bands are not symmetrical, and the energy bands with different spins cross at a k(z)-nonzero point, where the spin splitting energy and the effective g factor are zero.

Resonant tunneling theory of planar quantum dot structures

The ballistic transport in the semiconductor, planar, circular quantum dot structures is studied theoretically. The transmission probabilities show apparent resonant tunneling peaks, which correspond to energies of bound states in the dot. By use of structures with different angles between the inject and exit channels, the resonant peaks can be identified very effectively. The perpendicular magnetic field has obvious effect on the energies of bound states in the quantum dot, and thus the resonant peaks. The treatment of the boundary conditions simplifies the problem to the solution of a set of linear algebraic equations. The theoretical results in this paper can be used to design planar resonant tunneling devices, whose resonant peaks are adjustable by the angle between the inject and exit channels and the applied magnetic field. The resonant tunneling in the circular dot structures can also be used to study the bound states in the absence and presence of magnetic field.