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

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

Distinguishing between types of data and methods of collecting them

The author examines the role of different data collection methods--including the types of data they produce--in the analysis of social phenomena in developing countries. He points out that one confusing factor in the"quantitative-qualitative"debate is that a distinction is not clearly made between methods of data collection used and types of data generated. He maintains the divide between quantitative and qualitative types of data but analyzes methods according to their"contextuality": the degree to which they try to understand human behavior in the social, cultural, economic, and political environment of a given place. He emphasizes that it is most fruitful to think of both methods and data as lying on a continuum stretching from more to less contextual methodology and from more to less qualitative data output. Using characteristic information needs for health planning derived from data on the use of health services, he shows that each combination of method (more or less contextual) and data (more or less qualitative) is a unique primary source that can fulfill different information requirements. He concludes that: 1) Certain information about health utilization can be obtained only through contextual methods--in which case strict statistical representability must give way to inductive conclusions, assessments of internal validity, and replicability of results. 2) Often contextual methods are needed to design appropriate noncontextual data collection tools. 3) Even where noncontextual data collection methods are needed, contextual methods can play an important role in assessing the validity of the results at the local level. 4) In cases where different data collection methods can be used to probe general results, the methods can--and need to be--formally linked.Early Child and Children's Health,Health Monitoring&Evaluation,Health Systems Development&Reform,Housing&Human Habitats,Public Health Promotion,Health Monitoring&Evaluation,Poverty Assessment,ICT Policy and Strategies,Health Systems Development&Reform,Scientific Research&Science Parks

Using rapid city surveys to inform municipal social policy : an application in Cali, Colombia

Many developing countries assign local governments increasing responsibilities in fighting poverty. This requires local social policy to go beyond the execution of centrally designed and funded education and health programs. Hence, local governments and their partners have both an opportunity and a need to analyze key local bottlenecks for poverty reduction and social development. Drawing on an example from Cali, Colombia, The author describes a tool for such policy formulation at the local level-a rapid city household survey. Although the survey uses pre-coded and closed- ended questions, it is contextual in the sense that it is tailor-made to social and economic conditions in Cali. The survey places particular emphasis on collecting key quantitative information, such as household welfare and service access, as well as qualitative information, such as service evaluations and population priorities. Combining the quantitative and qualitative data allows, for example, the mapping of population budget priorities or service satisfaction levels by welfare group. Rapid city household surveys could provide an important tool for the development of local social policies.Health Economics&Finance,Environmental Economics&Policies,Health Monitoring&Evaluation,Public Health Promotion,Health Systems Development&Reform,Poverty Assessment,Health Economics&Finance,Health Monitoring&Evaluation,Environmental Economics&Policies,Governance Indicators

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

Hermitian modular forms congruent to 1 modulo p

For any natural number $\ell$ and any prime $p\equiv 1 \pmod{4}$ not dividing $\ell$ there is a Hermitian modular form of arbitrary genus $n$ over L:=\Q [\sqrt{-\ell}] that is congruent to 1 modulo $p$ which is a Hermitian theta series of an $O_L$-lattice of rank $p-1$ admitting a fixed point free automorphism of order $p$. It is shown that also for non-free lattices such theta series are modular forms

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

Multiple beam interference in a quadrupolar glass fiber

Motivated by the recent observation of periodic filter characteristics of an oval-shaped micro-cavity, we study the possible interference of multiple beams in the far field of a laser-illuminated quadrupolar glass fiber. From numerical ray-tracing simulations of the experimental situation we obtain the interference-relevant length-difference spectrum and compare it with data extracted from the experimental filter results. Our analysis reveals that different polygonal cavity modes being refractively output-coupled in the high-curvature region of the fiber contribute to the observed far-field interference.Comment: 4 pages, 4 fig