Quantum Particles Constrained on Cylindrical Surfaces with Non-constant Diameter

We present a theoretical formulation of the one-electron problem constrained on the surface of a cylindrical tubule with varying diameter. Because of the cylindrical symmetry, we may reduce the problem to a one-dimensional equation for each angular momentum quantum number $m$ along the cylindrical axis. The geometrical properties of the surface determine the electronic structures through the geometry dependent term in the equation. Magnetic fields parallel to the axis can readily be incorporated. Our formulation is applied to simple examples such as the catenoid and the sinusoidal tubules. The existence of bound states as well as the band structures, which are induced geometrically, for these surfaces are shown. To show that the electronic structures can be altered significantly by applying a magnetic field, Aharonov-Bohm effects in these examples are demonstrated.Comment: 7 pages, 7 figures, submitted to J. Phys. Soc. Jp

Scattering From a Two Dimensional Array of Flux Tubes: A Study of The Validity of Mean Field Theory

Mean Field Theory has been extensively used in the study of systems of anyons in two spatial dimensions. In this paper we study the physical grounds for the validity of this approximation by considering the Quantum Mechanical scattering of a charged particle from a two dimensional array of magnetic flux tubes. The flux tubes are arranged on a regular lattice which is infinitely long in the ``$y$'' direction but which has a (small) finite number of columns in the ``$x$'' direction. Their physical size is assumed to be infinitesimally small. We develop a method for computing the scattering angle as well as the reflection and transmission coefficients to lowest order in the Aharonov--Bohm interaction. The results of our calculation are compared to the scattering of the same particle from a region of constant magnetic field whose magnitude is equal to the mean field of all the flux tubes. For an incident plane wave, the Mean Field approximation is shown to be valid provided the flux in each tube is much less than a single flux quantum. This is precisely the regime in which Mean Field Theory for anyons is expected to be valid. When the flux per tube becomes of order 1, Mean Field Theory is no longer valid.Comment: 23 pages, University of British Columbia Preprint UBCTP93-01

Theory and Applications of X-ray Standing Waves in Real Crystals

Theoretical aspects of x-ray standing wave method for investigation of the real structure of crystals are considered in this review paper. Starting from the general approach of the secondary radiation yield from deformed crystals this theory is applied to different concreat cases. Various models of deformed crystals like: bicrystal model, multilayer model, crystals with extended deformation field are considered in detailes. Peculiarities of x-ray standing wave behavior in different scattering geometries (Bragg, Laue) are analysed in detailes. New possibilities to solve the phase problem with x-ray standing wave method are discussed in the review. General theoretical approaches are illustrated with a big number of experimental results.Comment: 101 pages, 43 figures, 3 table

Coupled Simulation of Transient Heat Flow and Electric Currents in Thin Wires: Application to Bond Wires in Microelectronic Chip Packaging

This work addresses the simulation of heat flow and electric currents in thin wires. An important application is the use of bond wires in microelectronic chip packaging. The heat distribution is modeled by an electrothermal coupled problem, which poses numerical challenges due to the presence of different geometric scales. The necessity of very fine grids is relaxed by solving and embedding a 1D sub-problem along the wire into the surrounding 3D geometry. The arising singularities are described using de Rham currents. It is shown that the problem is related to fluid flow in porous 3D media with 1D fractures [C. D'Angelo, SIAM Journal on Numerical Analysis 50.1, pp. 194-215, 2012]. A careful formulation of the 1D-3D coupling condition is essential to obtain a stable scheme that yields a physical solution. Elliptic model problems are used to investigate the numerical errors and the corresponding convergence rates. Additionally, the transient electrothermal simulation of a simplified microelectronic chip package as used in industrial applications is presented.Comment: all numerical results can be reproduced by the Matlab code openly available at https://github.com/tc88/ETwireSi

SPS pilot signal design and power transponder analysis, volume 2, phase 3

The problem of pilot signal parameter optimization and the related problem of power transponder performance analysis for the Solar Power Satellite reference phase control system are addressed. Signal and interference models were established to enable specifications of the front end filters including both the notch filter and the antenna frequency response. A simulation program package was developed to be included in SOLARSIM to perform tradeoffs of system parameters based on minimizing the phase error for the pilot phase extraction. An analytical model that characterizes the overall power transponder operation was developed. From this model, the effects of different phase noise disturbance sources that contribute to phase variations at the output of the power transponders were studied and quantified. Results indicate that it is feasible to hold the antenna array phase error to less than one degree per power module for the type of disturbances modeled

Two-dimensional conformal field theory and the butterfly effect

We study chaotic dynamics in two-dimensional conformal field theory through out-of-time order thermal correlators of the form $\langle W(t)VW(t)V\rangle$. We reproduce bulk calculations similar to those of [1], by studying the large $c$ Virasoro identity block. The contribution of this block to the above correlation function begins to decrease exponentially after a delay of $\sim t_* - \frac{\beta}{2\pi}\log \beta^2E_w E_v$, where $t_*$ is the scrambling time $\frac{\beta}{2\pi}\log c$, and $E_w,E_v$ are the energy scales of the $W,V$ operators.Comment: v1: 14 pages plus appendices, 2 figures. v2: references updated and minor changes to the text. v3: minor error corrected in Appendix B, but the conclusion is unchange