Influence of diffraction on the spectrum and wavefunctions of an open system

In this paper, we demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge of the system are found to have a strong influence on the transmission spectrum of the system, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.Comment: 27 pages, 29 figures, and 3 tables. Submitted to Physical Review E. A copy with higher resolution figures is available at http://monsoon.harvard.edu/~hersch/papers.htm

Scattering Theory of Kondo Mirages and Observation of Single Kondo Atom Phase Shift

We explain the origin of the Kondo mirage seen in recent quantum corral Scanning Tunneling Microscope (STM) experiments with a scattering theory of electrons on the surfaces of metals. Our theory combined with experimental data provides the first direct observation of a single Kondo atom phase shift. The Kondo mirage at the empty focus of an elliptical quantum corral is shown to arise from multiple electron bounces off the walls of the corral in a manner analagous to the formation of a real image in optics. We demonstrate our theory with direct quantitive comparision to experimental data.Comment: 13 pages; significant clarifications of metho

Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page

An Isoperimetric Inequality for Fundamental Tones of Free Plates

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given $\tau>0$, the free plate eigenvalues $\omega$ and eigenfunctions $u$ are determined by the equation $\Delta\Delta u-\tau\Delta u = \omega u$ together with certain natural boundary conditions. The boundary conditions are complicated but arise naturally from the plate Rayleigh quotient, which contains a Hessian squared term $|D^2u|^2$. We adapt Weinberger's method from the corresponding free membrane problem, taking the fundamental modes of the unit ball as trial functions. These solutions are a linear combination of Bessel and modified Bessel functions.Comment: PhD thesis. Papers are in preparatio

Negative length orbits in normal-superconductor billiard systems

The Path-Length Spectra of mesoscopic systems including diffractive scatterers and connected to superconductor is studied theoretically. We show that the spectra differs fundamentally from that of normal systems due to the presence of Andreev reflection. It is shown that negative path-lengths should arise in the spectra as opposed to normal system. To highlight this effect we carried out both quantum mechanical and semiclassical calculations for the simplest possible diffractive scatterer. The most pronounced peaks in the Path-Length Spectra of the reflection amplitude are identified by the routes that the electron and/or hole travels.Comment: 4 pages, 4 figures include

Evidence for distinct coastal and offshore communities of bottlenose dolphins in the north east Atlantic.

Bottlenose dolphin stock structure in the northeast Atlantic remains poorly understood. However, fine scale photo-id data have shown that populations can comprise multiple overlapping social communities. These social communities form structural elements of bottlenose dolphin (Tursiops truncatus) [corrected] populations, reflecting specific ecological and behavioural adaptations to local habitats. We investigated the social structure of bottlenose dolphins in the waters of northwest Ireland and present evidence for distinct inshore and offshore social communities. Individuals of the inshore community had a coastal distribution restricted to waters within 3 km from shore. These animals exhibited a cohesive, fission-fusion social organisation, with repeated resightings within the research area, within a larger coastal home range. The offshore community comprised one or more distinct groups, found significantly further offshore (>4 km) than the inshore animals. In addition, dorsal fin scarring patterns differed significantly between inshore and offshore communities with individuals of the offshore community having more distinctly marked dorsal fins. Specifically, almost half of the individuals in the offshore community (48%) had characteristic stereotyped damage to the tip of the dorsal fin, rarely recorded in the inshore community (7%). We propose that this characteristic is likely due to interactions with pelagic fisheries. Social segregation and scarring differences found here indicate that the distinct communities are likely to be spatially and behaviourally segregated. Together with recent genetic evidence of distinct offshore and coastal population structures, this provides evidence for bottlenose dolphin inshore/offshore community differentiation in the northeast Atlantic. We recommend that social communities should be considered as fundamental units for the management and conservation of bottlenose dolphins and their habitat specialisations

Unexplained Gaps and Oaxaca-Blinder Decompositions

We analyze four methods to measure unexplained gaps in mean outcomes: three decompositions based on the seminal work of Oaxaca (1973) and Blinder (1973) and an approach involving a seemingly naive regression that includes a group indicator variable. Our analysis yields two principal findings. We show that the coefficient on a group indicator variable from an OLS regression is an attractive approach for obtaining a single measure of the unexplained gap. We also show that a commonly-used pooling decomposition systematically overstates the contribution of observable characteristics to mean outcome differences when compared to OLS regression, therefore understating unexplained differences. We then provide three empirical examples that explore the practical importance of our analytic results

Time Discounting and Smoking Behavior Under Tax Hikes

By combining our broad panel survey of Japanese adults from 2005 to 2008 and actual cigarette tax data, we investigate how smoking behavior including responses to tax hikes depends on time discounting and its biases, such as hyperbolic discounting and the sign effect. Cigarette consumption displays significantly positive correlations with discount rates and the procrastinating tendency, and negative correlations with the sign effect. Hyperbolic, procrastinating, and naïve respondents decrease their after-tax-hike cigarette consumption more than the others, implying that, irrespective of the preannouncement of a future tax hike, they postpone smoking moderation until the tax hike actually takes place. Finally, the government's revenue from cigarette tax peaks at a JPY 29.92 (around USD 0.28 using the conversion rate [107.16] in February 2008) higher tax per cigarette than the present actual level

Interaction effects of region-level GDP per capita and age on labour market transition rates in Italy

Abstract The aim of this paper is to measure the effect of the interaction between age for the population of males and females aged 18 to 74 and region-level GDP per capita on labour market transition probabilities in Italy. We compare different occupational states in a sample of males and females who remained in their region of residence at two points in time (12 months apart). We estimate the transition probabilities using a flexible hierarchical logit model with interaction effects between worker age and region-level GDP per capita. We apply this model using longitudinal data from the Italian Labour Force Survey that cover the 2004–2013 period. We find empirical support for the assumption that people in the same age cohort have different labour market opportunities based on the level of GDP per capita in their region of residence. These differences are particularly relevant among younger workers