Efficient Spatial Redistribution of Quantum Dot Spontaneous Emission from 2D Photonic Crystals

We investigate the modification of the spontaneous emission dynamics and external quantum efficiency for self-assembled InGaAs quantum dots coupled to extended and localised photonic states in GaAs 2D-photonic crystals. The 2D-photonic bandgap is shown to give rise to a 5-10 times enhancement of the external quantum efficiency whilst the spontaneous emission rate is simultaneously reduced by a comparable factor. Our findings are quantitatively explained by a modal redistribution of spontaneous emission due to the modified local density of photonic states. The results suggest that quantum dots embedded within 2D-photonic crystals are suitable for practical single photon sources with high external efficiency

Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform

This paper is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. Here we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different spaces. Through the use of this tool we derive and classify for the first time all two-dimensional (2D) superintegrable systems. The underlying spaces are exactly those derived by Koenigs in his remarkable paper giving all 2D manifolds (with zero potential) that admit at least three second order symmetries. Our derivation is very simple and quite distinct. We also show that every superintegrable system is the Stäckel transform of a superintegrable system on a constant curvature space

Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems

This paper is the conclusion of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in conformally flat spaces. For two-dimensional and for conformally flat three-dimensional spaces with nondegenerate potentials we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension. We also correct an error in an earlier paper in the series (that does not alter the structure results) and we elucidate the distinction between superintegrable systems with bases of functionally linearly independent and functionally linearly dependent symmetries

Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory

This paper is part of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in real or complex conformally flat spaces. Here we consider classical superintegrable systems with nondegenerate potentials in three dimensions. We show that there exists a standard structure for such systems, based on the algebra of 3×3 symmetric matrices, and that the quadratic algebra always closes at order 6. We show that the spaces of truly second-, third-, fourth-, and sixth-order constants of the motion are of dimension 6, 4, 21, and 56, respectively, and we construct explicit bases for the fourth- and sixth order constants in terms of products of the second order constants

Tools for Verifying Classical and Quantum Superintegrability

Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n-1 symmetries polynomial in the canonical momenta, so that they are in fact superintegrable. These newly discovered systems are all separable in some coordinate system and, typically, they depend on one or more parameters in such a way that the system is superintegrable exactly when some of the parameters are rational numbers. Most of the constructions to date are for n=2 but cases where n>2 are multiplying rapidly. In this article we organize a large class of such systems, many new, and emphasize the underlying mechanisms which enable this phenomena to occur and to prove superintegrability. In addition to proofs of classical superintegrability we show that the 2D caged anisotropic oscillator and a Stackel transformed version on the 2-sheet hyperboloid are quantum superintegrable for all rational relative frequencies, and that a deformed 2D Kepler-Coulomb system is quantum superintegrable for all rational values of a parameter k in the potential

The effects of lunar dust accumulation on the performance of photovoltaic arrays

Lunar base activity, particularly rocket launch and landing, will suspend and transport lunar dust. From preliminary models, the resulting dust accumulation can be significant, even as far as 2 km from the source. For example, at 2 km approximately 0.28 mg/sq cm of dust is anticipated to accumulate after only 10 surface missions with a 26,800 N excursion vehicle. The possible associated penalties in photovoltaic array performance were therefore the subject of experimental as well as theoretical investigation. To evaluate effects of dust accumulation on relative power output, current-voltage characteristics of dust-covered silicon cells were determined under the illumination of a Spectrolab X-25L solar simulator. The dust material used in these experiments was a terrestrial basalt which approximated lunar soil in particle size and composition. Cell short circuit current, an indicator of the penetrating light intensity, was found to decrease exponentially with dust accumulation. This was predicted independently by modeling the light occlusion caused by a growing layer of dust particles. Moreover, the maximum power output of dust-covered cells, derived from the I-V curves, was also found to degrade exponentially. Experimental results are presented and potential implications discussed

Superintegrable Systems in Darboux spaces

Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Staeckel multiplier transformations). We present tables of the results

A social studies/science technology project manual for upper elementary educators in the Dubuque Community School District

In the last five years, the Dubuque Community School District\u27s technology infrastructure has grown tenfold. With the implementation of a district-wide networked computer system also came growing expectations for classroom teachers to provide technological opportunities for students (Dubuque Community School District, 2001). With the administration\u27s eagerness to bring Dubuque\u27s students into the information world, teachers have not been provided with any technology curriculum or manuals on how to incorporate computer projects into their lessons. This graduate research project was developed to give the classroom teacher a means to provide these technological opportunities in a very systematic and step-by-step manner. The step-by-step manual allows teachers to include technology in their instructional program by providing the means to do it. An easy to follow technology project manual was created for fifth and sixth grade teachers. The manual provides actual instructions for technology projects that coincide with the Dubuque Community School District\u27s (DCSD) science and social studies curriculum. The manual has project ideas for use with Microsoft PowerPoint (1996), Microsoft Classroom Tools (1997), HyperStudio (1996), Adobe PhotoShop (2000), word processing using Microsoft Word (1997). The manual includes a section on the safe use of the Internet