Effects of varying curvature and width on the electronic states of GaAs quantum rings

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability density shows peaks: (i) where the curvature is larger in a constant-with ring, and (ii) in thicker parts of a circular ring. For rings of typical dimensions, it is shown that the effects of a varying width may be stronger than those of the varying curvature. Also, a width profile which compensates the main localization effects of the varying curvature is obtained.

NONLINEAR SCALAR COUPLING MODELS AND PROTON-NUCLEUS SCATTERING OBSERVABLES

The effects of nonlinear scalar field couplings on elastic proton-nucleus scattering observables are investigated using a relativistic impulse approximation. Nonlinear couplings affect in a nontrivial way the effective nucleon mass and the nuclear scalar and vector densities. Modifications on the densities might have observable consequences on scattering observables. Our investigation indicates that the description of the observables for the reactions p-O-16 and p-Ca-40 at 200 MeV are not greatly modified with the use of nonlinear models in comparison with the description using linear models.

Casimir effect for the scalar field under Robin boundary conditions: a functional integral approach

In this work we show how to define the action of a scalar field such that the Robin boundary condition is implemented dynamically, i.e. as a consequence of the stationary action principle. We discuss the quantization of that system via functional integration. Using this formalism, we derive an expression for the Casimir energy of a massless scalar field under Robin boundary conditions on a pair of parallel plates, characterized by constants c(1) and c(2). Some special cases are discussed; in particular, we show that for some values of cl and c(2) the Casimir energy as a function of the distance between the plates presents a minimum. We also discuss the renormalization at one-loop order of the two-point Green function in the philambda(4) theory subject to the Robin boundary condition on a plate.

Static potential in scalar QED(3) with non-minimal coupling

Here we compute the static potential in scalar QED(3) at leading order in 1/Nf. We show that the addition of a non-minimal coupling of Pauli-type (is an element of(mu nu alpha)j(mu)partial derivative(nu)A(alpha)), although it breaks parity, it does not change the analytic structure of the photon propagator and consequently the static potential remains logarithmic ( confining) at large distances. The non-minimal coupling modifies the potential, however, at small charge separations giving rise to a repulsive force of short range between opposite sign charges, which is relevant for the existence of bound states. This effect is in agreement with a previous calculation based on Moller scattering, but differently from such calculation we show here that the repulsion appears independently of the presence of a tree level Chern-Simons term which rather affects the large distance behaviour of the potential turning it into a constant.

SMALLEST UNIVERSE OF NEGATIVE CURVATURE

The smallest known three-dimensional closed manifold of curvature k = -1 was discovered a few years ago by Weeks. This kind of manifold is constructed from a hyperbolic polyhedron with faces pair-wise identified. Here it is used as the comoving spatial section of a Friedmann cosmological model, in the spirit of Ellis and Schreiber's idea of small universes. Its nontrivial global topology has the effect of producing multiple images of single cosmic sources, and this is the basis of an attempt to solve a famous controversy about the redshifts of quasars.

Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields

The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a self-dual field through a linear and a quadratic term in the self-dual field. Integrating perturbatively over the scalar fields and deriving effective actions for the self-dual and the gauge field we are able to consistently neglect awkward extra terms generated via master action and establish quantum duality up to cubic terms in the coupling constant. The duality holds for the partition function and some correlation functions. The absence of ghosts imposes restrictions on the coupling with the scalar fields.

PATH-ORDERED PHASE-FACTORS IN SCALAR QUANTUM ELECTRODYNAMICS

Starting from linear equations for the complex scalar field, the two- and three-point Green's functions are obtained in the infrared approximation. We show that the infrared singularity factorizes in the vertex function as in spinor QED, reproducing in a simple and straightforward way the result of lengthy perturbative calculations.

Effects of direction and curvature on variable error pattern of reaching movements

A number of studies have analyzed various indices of the final position variability in order to provide insight into different levels of neuromotor processing during reaching movements. Yet the possible effects of movement kinematics on variability have often been neglected. The present study was designed to test the effects of movement direction and curvature on the pattern of movement variable errors. Subjects performed series of reaching movements over the same distance and into the same target. However, due either to changes in starting position or to applied obstacles, the movements were performed in different directions or along the trajectories of different curvatures. The pattern of movement variable errors was assessed by means of the principal component analysis applied on the 2-D scatter of movement final positions. The orientation of these ellipses demonstrated changes associated with changes in both movement direction and curvature. However, neither movement direction nor movement curvature affected movement variable errors assessed by area of the ellipses. Therefore it was concluded that the end-point variability depends partly, but not exclusively, on movement kinematics.

UNRUH-DEWITT DETECTORS IN THE PRESENCE OF SCALAR SOURCES

We analyze the response of Unruh-DeWitt detectors in the presence of inertial scalar sources. We show that, in general, a detector responds to the corresponding Coulomb field. However, in some cases, pure vacuum contributions can overwhelm the influence of the Coulomb field rendering the effect of the external source on the detector's response arbitrarily small. We revisit in this context the celebrated question of whether uniformly accelerated observers can see the radiation coming from an inertial charge, and point out the present impediments to answering this question.

Curvature versus V-bends in a group B titanium T-loop spring

Objective: To compare the system of forces acting on curvature and preactivated V-bends in titanium T-loop springs (TTLSs) made of 0.017- X 0.025-inch TMA (titanium molibdenium alloy) wire.Materials and Methods: Pictures of TTLSs preactivated by curvature and V-bends were inserted in the LOOP software program to design both TTLSs. Symmetry was assured using the program. Both TTLSs used the same amount (length) of wire and had the same angulation between their anterior and posterior extremities when passive. The loops were activated 7 mm, and forces and moments were registered after each 0.5 mm of deactivation. The brackets were at the same height, separated by 23 mm and angulated 0 degrees.Results: The preactivated curvature TTLS delivered horizontal forces ranging from 34 gF to 456 gF, while the TTLS preactivated by V-bends delivered forces ranging from 54 gF to 517 gF. The forces decreased more (30 gF vs 33 gF) with every 0.5 mm of activation on the preactivated V-bend TTLS than on the preactivated curvature TTLS. Vertical forces were low and clinically insignificant for both TTLSs. The moment to force (MF) ratios were systematically higher on the preactivated curvature than on the preactivated V-bend TTLS (from 5.8 mm to 38.8 mm vs 4.7 mm to 28.3 mm).Conclusions: Although both loops show symmetrical moments in their anterior and posterior extremities and can be used for group B anchorage, the curvature preactivated TTLS delivers lower horizontal forces and higher MF ratios than the acute preactivated V-bend TTLS.

Spherically symmetric scalar field in general relativity

We analyze the presence of a scalar field around a spherically symmetric distribution of an ordinary matter, obtaining an exact solution for a given scalar field distribution.

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.