A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space

Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in which to represent the classical groups as subgroups of rotation groups, and similarly their Lie algebras. In this article we show how the geometric algebra of a six-dimensional real Euclidean vector space naturally allows one to construct the special unitary group on a two-qubit (quantum bit) Hilbert space, in a fashion similar to that used in the well-established Bloch sphere model for a single qubit. This is then used to illustrate the Cartan decompositions and subalgebras of the four-dimensional special unitary group, which have recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev. A 67, 042313, 2003] to study the entangling capabilities of two-qubit unitaries.Comment: 14 pages, 2 figures, in press (Proceedings of SPIE Conference on Defense & Security

A Superfield for Every Dash-Chromotopology

The recent classification scheme of so-called adinkraic off-shell supermultiplets of N-extended worldline supersymmetry without central charges finds a combinatorial explosion. Completing our earlier efforts, we now complete the constructive proof that all of these trillions or more of supermultiplets have a superfield representation. While different as superfields and supermultiplets, these are still super-differentially related to a much more modest number of minimal supermultiplets, which we construct herein.Comment: 13 pages, integrated illustration

Self-Assembled Monolayers for Phosphorus Doping of Silicon for Field Effect Devices

Moore\u27s law continues to drive the semiconductor industry to create smaller transistors and improve device performance. Smaller transistors require shallower junctions, especially for the non-planar geometries such as FinFETs and nanowires which are becoming more common. Conventional doping techniques such as ion implantation and spin-on diffusants have difficulty producing shallow junctions, especially for conformal doping of non-planar structures. Molecular monolayer doping (MLD) is presented as an alternative doping method with the capability to produce ultra-shallow junctions with low sheet resistances for planar and non-planar structures. MLD relies on the formation of a self-assembled monolayer of a dopant-containing compound which is annealed to diffuse dopants into the substrate, forming an ultra-shallow junction with a high surface concentration. This work fabricates and characterizes field effect devices using MLD to dope the source and drain regions. To support this goal, a low-cost reaction chamber for MLD is developed using materials that are commonly found in chemistry stockrooms and local home goods stores. The results of the MLD process are quantified using four point probe measurements and SIMS profiles, with diffused layers measured to have sheet resistances on the order of 1000 Ω/□ and surface concentrations on the order of 1020 cm-3. MLD is demonstrated to be patternable using SiO2 as a masking layer, verified with four point probe measurements, electrical testing, and thin oxide growth over a wafer with heavily doped and lightly doped areas to reproduce the original doping pattern. A fabrication process and mask design compatible with the MLD process is created to fabricate NMOSFETs. The NMOSFETs are electrically tested and show field effect behavior with threshold voltages around -0.3 V and subthreshold swing of 150 mV/dec. The devices do show high series resistance, due to an unintended 13.1 Å interfacial layer of SiO2 in the contact cuts, discovered by STEM images. Future work proposes process revisions to mitigate this issue and scale down the size of the FETs to further explore MLD\u27s potential for creating cutting edge field effect devices

The impact of competitive show choir on the enrollment of male singers in choral ensembles in Nebraska and Iowa.

The purpose of this study was to investigate the relationship between competitive show choir and male enrollment in high school choral ensembles. This study was conducted in two parts. Part I involved the completion of a survey by high school choral directors (N=25) to obtain demographic- information, male enrollment information, and ratings of importance of nine elements of their choral program. Part II was a survey of male students (N=57) currently enrolled in high school choral programs to obtain information on the factors that influenced their decision to join choir. Results indicated: 1) Directors placed a higher importance on the traditional established components of a choral program such as All State, contest ratings and the musical. 2) There were no differences in male enrollment in schools with s ow choirs as compared to those without show choirs. 3) There is a moderate correlation between male enrollment and participation in competitive show choir. 4) Male students cite quality of performances and personal enjoyment as main factors influencing them to enroll in a choral ensemble

Matrix Transfer Function Design for Flexible Structures: An Application

The application of matrix transfer function design techniques to the problem of disturbance rejection on a flexible space structure is demonstrated. The design approach is based on parameterizing a class of stabilizing compensators for the plant and formulating the design specifications as a constrained minimization problem in terms of these parameters. The solution yields a matrix transfer function representation of the compensator. A state space realization of the compensator is constructed to investigate performance and stability on the nominal and perturbed models. The application is made to the ACOSSA (Active Control of Space Structures) optical structure

Fermion absorption cross section of a Schwarzschild black hole

We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painleve-Gullstrand coordinates. We calculate the absorption cross section for a range of gravitational couplings Mm/m_P^2 and incident particle energies E. At high couplings, where the Schwarzschild radius R_S is much greater than the wavelength lambda, we find that the cross section approaches the classical result for a point particle. At intermediate couplings we find oscillations around the classical limit whose precise form depends on the particle mass. These oscillations give quantum violations of the equivalence principle. At high energies the cross section converges on the geometric-optics value of 27 \pi R_S^2/4, and at low energies we find agreement with an approximation derived by Unruh. When the hole is much smaller than the particle wavelength we confirm that the minimum possible cross section approaches \pi R_S^2/2.Comment: 11 pages, 3 figure

Hypergeometric decomposition of symmetric K3 quartic pencils

We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite field hypergeometric sums; then we match up each differential equation to a factor of the zeta function, and we write this in terms of global L-functions. This computation gives a complete, explicit description of the motives for these pencils in terms of hypergeometric motives.Comment: 70 pages, minor revision, to appear in Research in the Mathematical Science

Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration

We discuss four off-shell N=4 D=1 supersymmetry transformations, their associated one-dimensional sigma-models and their mutual relations. They are given by I) the (4,4)_{lin} linear supermultiplet (supersymmetric extension of R^4), II) the (3,4,1)_{lin} linear supermultiplet (supersymmetric extension of R^3), III) the (3,4,1)_{nl} non-linear supermultiplet living on S^3 and IV) the (2,4,2)_{nl} non-linear supermultiplet living on S^2. The I -> II map is the supersymmetric extension of the R^4 -> R^3 bilinear map, while the II -> IV map is the supersymmetric extension of the S^3 -> S^2 first Hopf fibration. The restrictions on the S^3, S^2 spheres are expressed in terms of the stereographic projections. The non-linear supermultiplets, whose supertransformations are local differential polynomials, are not equivalent to the linear supermultiplets with the same field content. The sigma-models are determined in terms of an unconstrained prepotential of the target coordinates. The Uniformization Problem requires solving an inverse problem for the prepotential. The basic features of the supersymmetric extension of the second and third Hopf maps are briefly sketched. Finally, the Schur's lemma (i.e. the real, complex or quaternionic property) is extended to all minimal linear supermultiplets up to N<=8.Comment: 24 page