On the Hierarchical Preconditioning of the Combined Field Integral Equation

This paper analyzes how hierarchical bases preconditioners constructed for the Electric Field Integral Equation (EFIE) can be effectively applied to the Combined Field Integral Equation (CFIE). For the case where no hierarchical solenoidal basis is available (e.g., on unstructured meshes), a new scheme is proposed: the CFIE is implicitly preconditioned on the solenoidal Helmholtz subspace by using a Helmholtz projector, while a hierarchical non-solenoidal basis is used for the non-solenoidal Helmholtz subspace. This results in a well-conditioned system. Numerical results corroborate the presented theory

Reforming the NCAA Drug-Testing Program to Withstand State Constitutional Scrutiny: An Analysis and Proposal

Shortly after year-round testing went into effect, the California Court of Appeal held that the NCAA\u27s original drug testing program violated a student-athlete\u27s right of privacy as protected by the California Constitution. This Note examines the impact of that decision and attempts to design a program that will withstand state constitutional scrutiny. Part I describes the current NCAA drug-testing program. Part II looks at the fourth amendment argument against drug testing of student-athletes. Part III assesses the viability of a federal constitutional attack on NCAA testing, while Part IV discusses a state constitutional challenge. Finally, Part V proposes reform of the current NCAA drug-testing program to achieve its goals within the bounds of federal and state constitutional rights of privacy

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the produced photon pairs can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.Comment: 11 pages, 9 figures, v3 with added reference

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Characterization of a Quantum Light Source Based on Spontaneous Parametric Down-Conversion

We have built a quantum light source capable of producing different types of quantum states. The quantum light source is based on entangled state preparation in the process of spontaneous parametric down-conversion. The single-photon detection rate of eight-hundred thousand per second demonstrates that we have created a bright state-of-the-art quantum light source. As a part of the characterization we measured two-photon quantum interference in a Hong-Ou-Mandel interferometer.Comment: 33 page

On the Spinning Motion of the Hovering Magnetic Top

In this paper we analyze the spinning motion of the hovering magnetic top. We have observed that its motion looks different from that of a classical top. A classical top rotates about its own axis which precesses around a vertical fixed external axis. The hovering magnetic top, on the other hand, has its axis slightly tilted and moves rigidly as a whole about the vertical axis. We call this motion synchronous, because in a stroboscopic experiment we see that a point at the rim of the top moves synchronously with the top axis. We show that the synchronous motion may be attributed to a small deviation of the magnetic moment from the symmetry axis of the top. We calculate the minimum angular velocity required for stability in terms of the moments of inertia and magnetic field and show that it is different from that of a classical top. We also give experimental results that were taken with a top whose moment of inertia can be changed. These results show very good agreement with our calculations.Comment: 19 pages (including 3 figures named fig1.eps-fig3.eps), uses amssymb, epsf and amsbsy (AMSLaTeX

Assumptions that imply quantum dynamics is linear

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schrodinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.Comment: 10 pages. Added references. Improved discussion of equations of motion for mean values. Expanded Introductio