Optical microcavities as quantum-chaotic model systems: Openness makes the difference!

Optical microcavities are open billiards for light in which electromagnetic waves can, however, be confined by total internal reflection at dielectric boundaries. These resonators enrich the class of model systems in the field of quantum chaos and are an ideal testing ground for the correspondence of ray and wave dynamics that, typically, is taken for granted. Using phase-space methods we show that this assumption has to be corrected towards the long-wavelength limit. Generalizing the concept of Husimi functions to dielectric interfaces, we find that curved interfaces require a semiclassical correction of Fresnel's law due to an interference effect called Goos-Haenchen shift. It is accompanied by the so-called Fresnel filtering which, in turn, corrects Snell's law. These two contributions are especially important near the critical angle. They are of similar magnitude and correspond to ray displacements in independent phase-space directions that can be incorporated in an adjusted reflection law. We show that deviations from ray-wave correspondence can be straightforwardly understood with the resulting adjusted reflection law and discuss its consequences for the phase-space dynamics in optical billiards.Comment: 12 pages, 5 figures, to appear in Adv. Sol. St. Phys. 4

The optical M\"{o}bius strip cavity: Tailoring geometric phases and far fields

The M\"{o}bius strip, a long sheet of paper whose ends are glued together after a $180^{\circ}$ twist, has remarkable geometric and topological properties. Here, we consider dielectric M\"{o}bius strips of finite width and investigate the interplay between geometric properties and resonant light propagation. We show how the polarization dynamics of the electromagnetic wave depends on the topological properties, and demonstrate how the geometric phase can be manipulated between $0$ and $\pi$ through the system geometry. The loss of the M\"{o}bius character in thick cavities and for small twist segment lengths allows one to manipulate the polarization dynamics and the far-field emission, and opens the venue for applications.Comment: 6 pages, 5 figure

Anderson orthogonality catastrophe in realistic quantum dots

We study Anderson orthogonality catastrophe (AOC) for an parabolic quantum dot (PQD), one of the experimentally realizable few-electron systems. The finite number of electrons in PQD causes AOC to be incomplete, with a broad distribution of many-body overlaps. This is a signature of mesoscopic fluctuations and is in agreement with earlier results obtained for chaotic quantum dots. Here, we focus on the effects of degeneracies in PQDs, realized through their inherent shell structures, on AOC. We find rich and interesting behaviours as a function of the strength and position of the perturbation, the system size, and the applied magnetic field. In particular, even for weak perturbations, we observe a pronounced AOC which is related to the degeneracy of energy levels. Most importantly, the power law decay of the many-body overlap as a function of increasing number of particles is modified in comparison to the metallic case due to rearrangements of energy levels in different shells.Comment: 14 pages, 15 figure

Classical Phase Space Revealed by Coherent Light

We study the far field characteristics of oval-resonator laser diodes made of an AlGaAs/GaAs quantum well. The resonator shapes are various oval geometries, thereby probing chaotic and mixed classical dynamics. The far field pattern shows a pronounced fine structure that strongly depends on the cavity shape. Comparing the experimental data with ray-model simulations for a Fresnel billiard yields convincing agreement for all geometries and reveals the importance of the underlying classical phase space for the lasing characteristics.Comment: 4 pages, 5 figures (reduced quality), accepted for publication in Physical Review Letter

Many-body effects in the mesoscopic x-ray edge problem

Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray excitation of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case.Comment: 9 pages, 3 figures, Proceedings ``Quantum Mechanics and Chaos'' (Osaka 2006

Actors: The Ideal Abstraction for Programming Kernel-Based Concurrency

GPU and multicore hardware architectures are commonly used in many different application areas to accelerate problem solutions relative to single CPU architectures. The typical approach to accessing these hardware architectures requires embedding logic into the programming language used to construct the application; the two primary forms of embedding are: calls to API routines to access the concurrent functionality, or pragmas providing concurrency hints to a language compiler such that particular blocks of code are targeted to the concurrent functionality. The former approach is verbose and semantically bankrupt, while the success of the latter approach is restricted to simple, static uses of the functionality. Actor-based applications are constructed from independent, encapsulated actors that interact through strongly-typed channels. This paper presents a first attempt at using actors to program kernels targeted at such concurrent hardware. Besides the glove-like fit of a kernel to the actor abstraction, quantitative code analysis shows that actor-based kernels are always significantly simpler than API-based coding, and generally simpler than pragma-based coding. Additionally, performance measurements show that the overheads of actor-based kernels are commensurate to API-based kernels, and range from equivalent to vastly improved for pragma-based annotations, both for sample and real-world applications

Trade and growth in Ecuador : a partial equilibrium view

When the outbreak of the debt crisis in 1982 halted private international capital flows to most developing countries, it was not easy for Ecuador to cope with the changed international circumstances. Investments were largely in imported machinery as domestic capital goods production was in its infancy. Exports were concentrated in petroleum and several agricultural products and could not be counted on to increase foreign exchange in the short run. The trade balance was improved in the first half of the 1980s by reducing imports. The author examines the behavior of the Ecuadoran economy in a period of scarce foreign exchange. He uses a small, econometrically specified"trade and growth"model of the Ecuadoran economy to illustrate the importance of trade elasticities. He estimates trade elasticities for Ecuador and integrates them into a small simulation model of Ecuador's supply side. He uses a nested constant-elasticity-of-substitution production function to derive factor input demands for two types of imported goods important in Ecuador: imported intermediate goods and imported machinery. Elasticity estimates of imported factor of production are very low. They characterize both types of imports as complements to domestic factors. The author uses the econometrically specified model to examine the connection between imported factors of production and output capacity. He analyzed trade balance responses to a terms-of-trade shock, a devaluation, and an increase in world demand. Low trade elasticities on the import side make the economy vulnerable to external shocks. The low elasticities necessitate large relative price shifts (through devaluation) to improve the trade balance if growth-reducing policies are to be avoided in times of scarce foreign exchange. A deterioration in terms of trade has a pronounced negative impact on the trade balance. To the extent that trade elasticities remain low in the 1990s, events such as a commodity price decline, a renewed credit squeeze, or increased protectionism against Ecuadoran exports - like the recent European Union quotas on banana imports - can translate into renewed domestic supply disturbances. Policies that lead to diversification of exports and higher price responsiveness for both imports and exports would reduce the vulnerability of Ecuador's economy to external shocks.Economic Theory&Research,Environmental Economics&Policies,TF054105-DONOR FUNDED OPERATION ADMINISTRATION FEE INCOME AND EXPENSE ACCOUNT,Markets and Market Access,Access to Markets