A one-dimensional lattice model for a quantum mechanical free particle

Two types of particles, A and B with their corresponding antiparticles, are defined in a onedimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field of the other type of particle with nonlocal action but with an effect decreasing with the distance: . It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.     

Charge exchange collisions of H<Superscript>+</Superscript>/D<Superscript>+</Superscript> ions with alkaline Earth atoms (Ca,Mg)

The Classical Trajectory Monte Carlo (CTMC) Method has been used to calculate the differential, partial and total single electron capture cross sections for the collision of H⁺/D⁺ with Ca and Mg atoms in the energy range of 1–100 keV. The differential cross sections at angles near the diffraction limit (<0.1^○) in both systems show a forward peak followed by an asymptotic fall at higher angles. Total and partial capture cross sections are found to be in good agreement with the experimental observations. Oscillations in the partial capture cross sections have been explained due to the swapping of the field electron. Isotope effect in the electron transfer is reported to be negligible.     

Magnetohydrodynamic properties of incompressible Meissner fluids

We consider a superconducting material that exists in the liquid state, more precisely, in which the Meissner-Ochsenfeld effect persists in the liquid state. First, we investigate how the shape of such a hypothetical Meissner liquid will adapt to accomodate for an applied external field. In particular, we analyse the case of a droplet of Meissner fluid, and compute the elongation of the droplet and its quadrupole frequency as a function of the applied field. Next, the influence of an applied field on the flow of the liquid is studied for the case of a surface wave. We derive the dispersion relation for surface waves on an incompressible Meissner fluid. We discuss some candidate realizations of the Meissner fluids and for the case of a superconducting colloid discuss which regime of wave lengths would be most affected by the Meissner effect.     

Low Dimension Dynamics in the EPRB Experiment with Random Variable Analyzers

The Einstein–Podolsky–Rosen–Bohm (EPRB) experiment performed with random variable and spatially separated analyzers is a milestone test in the controversy between Objective Local Theories (OLT) and Quantum Mechanics (QM). Only a few OLT are still possible. Some of the surviving OLT (specifically, the so called non-ergodic theories) would be undetectable in the averaged statistical values, but they may leave their trace in the time dynamics. For, while QM predicts random processes, the OLT of this kind predict the existence of regularities that may be revealed as a low dimensional object in the phase space. We perform a numerical analysis of the time-resolved data recorded in that experiment to unveil any hypothetical low dimensional dynamics that may be present. We find no consistent indication of such dynamics except for one data file, the longest of all in the real time. The possible causes of these dynamics are discussed.      

Klein,Einstein, and Five-Dimensional Unification

I examine the changing attitudes of Oskar Klein (1894–1977) and Albert Einstein (1879–1955) toward the notion of extending general relativity by an extra dimension with the aim of encompassing electromagnetism and gravitation in a unified field theory. I show how Klein developed his model of five-dimensional unification with the goal of explaining the discreteness of atomic energy levels, and how Einstein later embraced that goal. By examining the correspondence between Klein and Einstein, some of which was relayed through Paul Ehrenfest (1880–1933), I speculate that Klein’s work helped motivate Einstein to explore deterministic five-dimensional theories as a potential alternative to probabilistic quantum mechanics. Finally, I consider the contributions of Wolfgang Pauli (1900–1958) to the subject and elucidate his role in convincing Klein and Einstein that their models were not viable. Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. He currently is a member of the Executive Committee of the Forum on the History of Physics of the American Physical Society.     

Many body effects in the electronic and optical properties of the (1 1 1) surface of diamond

The (1 1 1) face is the cleavage surface of diamond. Understanding its properties is very important for the growing technological interest on the chemistry of diamond surfaces. Within DFT the most stable reconstruction is the Pandey chain model, the atoms on the chain being neither buckled nor dimerised. However this geometry gives rise to a semi metallic band structure in contrast with experimental findings that show the presence of a gap ranging from 0.5 to 2 eV. Here we show that the same equilibrium geometry and thus the same metallic band structure is found relaxing the surface using screened exchange (sX) or Hartree-Fock (HF) functionals. We will discuss in detail how breaking the equivalence of the atoms on the chain affects the band structure and we will show that a buckling would yield a semiconducting surface, but is energetically unfavorable. A semiconducting character can be restored, within the equilibrium geometry, if quasiparticle corrections are carefully included within an iterative GW scheme. The result of the theoretical reflectance anisotropy spectra (RAS) at a DFT-RPA level are also presented and discussed. As expected, a strong anisotropy signal is found at low energies due to transitions between surface states inside the fundamental gap.     

Theoretical analysis of optical coupling properties of the waveguide grating with novel rectangular structure

For the waveguide grating photocoupler with novel structure [Yu XQ, Zhang X, Wong KS, Xu GB, Xu XG, Ren Y, et al. A fabrication of coupling grating in the polymeric waveguide by using two-photon initiated photopolymerization. Mater Lett 2004;58:3879–83. [1]; Yu XQ, Zhang X, Xu GB, Zhao HP, He W, Shao ZS, et al. Fabrication of grating waveguide and coupling grating using two-photon initiated photopolymerization. Chem J Chin Univ 2004;25(10):1931–3 (in Chinese). [2]], the electric fields of the TE guided wave and the TE radiating wave are obtained by solving the Helmholtz equation in the spatial rectangular coordinates. And then the relations between the loss coefficient and the different structure parameters of the waveguide and grating are analyzed by using the mode coupling theories, and their corresponding numerical simulation results are given. In the end the result obtained for this novel structure and that for conventional rectangle structure are compared, and the difference and the sameness are obtained.     

Fast sensitivity analysis of defective system

Sensitivity analysis of linear vibration system is of wide interest. In this paper, sensitivity analysis based on non-defective system and defective system is summarized in all cases. Specially, for the defective systems, a fast method for the perturbation problem of state vectors is constructed in terms of the theories of generalized eigenvectors and adjoint matrices. By this method, the state vector derivatives can be expressed by a linear combination of generalized eigenvectors. The expansion coefficients can be obtained without solving large-scale equations based on eigensolutions of original system. Numerical results demonstrate the effectiveness and the stability of the method.     

Twofold-broken rational tori and the uniform semiclassical approximation

We investigate broken rational tori consisting of a chain of four (rather than two) periodic orbits. The normal form that describes this configuration is identified and used to construct a uniform semiclassical approximation, which can be utilized to improve trace formulae. An accuracy gain can be achieved even for the situation when two of the four orbits are ghosts. This is illustrated for a model system, the kicked top. Received 3 August 1999     

Solutions to the reflection equation and integrable systems for N = 2 SQCD with classical groups

Integrable systems underlying the Seiberg-Witten solutions for the N = 2 SQCD with gauge groups SO(n) and Sp(n) are proposed. They are described by the inhomogeneous XXX spin chain with specific boundary conditions given by reflection matrices. We attribute reflection matrices to orientifold planes in the brane construction and briefly discuss its possible deformations.