My dissertation focuses on the design and incentives of survey techniques. As many institutions use surveys to allocate funding or determine policy, ensuring surveys provide accurate information is essential. Though incentives certainly play a role in whether survey participants report information truthfully, economists have largely overlooked the issue while statisticians tend to focus on estimators without directly modeling incentive constraints. One of the chapters models and analyzes the incentives of a commonly used survey technique, randomized response, while the other two chapters of my dissertation design two response techniques which improve upon others found in the literature by obtaining more precise estimates and/or incentivizing participants better. In Chapter One "A Game Theoretic Analysis of the Randomized Response Technique," I explicitly model the decision of participants to truthfully respond in the randomized response survey as a game. Randomized response techniques are used to determine the proportion of a population that belongs to a stigmatized group and introduce noise so the surveyor cannot perfectly infer whether a participant belongs to a stigmatized group, regardless of how a participant responds. The interviewer wants to reduce noise as much as possible while maintaining enough noise to ensure participants respond truthfully. Unlike prior literature, I find that the incentives of a participant depend on the number of participants; therefore, the amount of noise required under randomized response decreases when the number of participants increases as adding respondents relaxes truth-telling constraints. However, adding respondents only relaxes incentive constraints to a limit, so some noise remains even when there are a large number of participants. I improve upon the original randomized response technique in two ways in Chapter 2: "Eliciting Private Information using Correlation: A Modification of Randomized Response." In standard randomized response techniques, participants receive questions independently by using a randomization device such as a die. With my technique, participants receive perfectly correlated questions which reduces the variance of the surveyor's estimator while still protecting the privacy of the subjects. Unlike with the randomized response technique, adding correlation allows the surveyor to use a dominant strategy mechanism though it provides limited information. In addition to correlation, my technique provides the surveyor with private information on the distribution of questions asked. Because of the private information, participants become more uncertain of which question is more associated with the stigmatizing characteristic giving them a stronger incentive to respond truthfully. My final chapter, Chapter 3 "A Response Technique with Dominant Strategies in Forced Responses," improves upon a randomized response technique commonly used in practice. In the forced response technique, a fraction of survey participants are directly asked whether they belong to the stigmatizing group while the remaining participants either simply state "yes" or "no" according to a privately observed command. Unlike the original randomized response technique, the surveyor must worry whether participants obey the command in addition to answering truthfully. Psychologically, participants may feel more inclined to disobey than to lie. Therefore, I design a technique where obeying the command is a dominant strategy by providing the surveyor with private information. The paper then discusses a more general response technique with private information and suggests restrictions on the mechanisms to ensure the surveyor does not have an incentive to try to "trick" respondents into believing they have more privacy protection than they actually do. The chapter concludes with a discussion on privacy measures.

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High-quality platelet single crystals of Tl₂Ba₂CuO₆±δ (Tl-2201) have been grown using a novel time-varying encapsulation scheme, minimizing the thallium oxide loss that has plagued other attempts and reducing cation substitution. This encapsulation scheme allows the melt to be decanted from the crystals, a step previously impossible, and the remaining cation substitution is homogenized via a high-temperature anneal. Oxygen annealing schemes were developed to produce sharp superconducting transitions from 5 to 85 K without damaging the crystals. The crystals' high homogeneity and high degree of crystalline perfection are further evidenced by narrow rocking curves; the crystals are comparable to YSZ-grown YBa₂Cu₃O₆₊δ by both metrics. Electron probe microanalysis (EPMA) ascertained the crystals' composition to be Tl₁.₉₂₀₍₂₎Ba₁.₉₆₍₂₎Cu₁.₀₈₀₍₂₎O₆₊δ; X-ray diffraction found the composition of a Tc = 75 K crystal to be Tl₁.₉₁₄₍₁₄₎Ba₂Cu₁.₀₈₆₍₁₄₎O₆.₀₇₍₅₎, in excellent agreement. X-ray refinement of the crystal structure found the crystals orthorhombic at most dopings, and their structure to be in general agreement with previous powder data. Cation-substituted Tl-2201 can be orthorhombic, orthorhombic crystals can be prepared, and these superconduct, all new results. X-ray diffraction also found evidence of an as yet unidentified commensurate superlattice modulation. The Tl-2201 crystals' electronic structure were studied by X-ray absorption and emission spectroscopies (XAS/XES). The Zhang-Rice singlet band gains less intensity on overdoping than expected, suggesting a breakdown of the Zhang-Rice singlet approximation, and one thallium oxide band does not disperse as expected. The spectra correspond very closely with LDA band structure calculations, and do not exhibit the upper Hubbard bands arising from strong correlations seen in other cuprates. The spectra are noteworthy for their unprecedented (in the high-Tc cuprates) simplicity. The startling degree to which the electronic structure can be explained bodes well for future research in the cuprates. The overdoped cuprates, and Tl-2201 in particular, may offer a unique opportunity for understanding in an otherwise highly confusing family of materials.

Aquest treball presenta l’estudi teòric de l’anisotropia magnètica en complexos de metalls de transició, combinant esquemes de càlcul multiconfiguracionals relativistes amb derivacions analítiques basades en la teoria del camp del lligand, el que permet racionalitzar a través de conceptes senzills els resultats quantitatius obtinguts i interpretar les propietats estudiades. Es desenvolupa primer una metodologia per extreure els paràmetres d’anisotropia en complexos mononuclears de metalls de transició. El mètode es basa en assignar els resultats d’un càlcul ab initio d’alt nivell a un Hamiltonià model mitjançant la teoria d’Hamiltonians efectius. Aquesta metodologia s’aplica a complexos de Ni(II), Co(II) i Mn(III) i es comprova que és aplicable de forma general a complexos mononuclears. S’estén després la metodologia a complexos binuclears, pels quals l’Hamiltonià model usualment utilitzat té una base menys rigorosa. L’Hamiltonià efectiu obtingut per un complex binuclear de Ni(II) introdueix una nova parametrització amb termes addicionals de les interaccions anisotròpiques en sistemes polinuclears. Es tracta d’un procediment universal que proporciona valors precisos i a més és capaç de contrastar la consistència interna dels Hamiltonians models existents. Per racionalitzar les correlacions magnetoestructurals dels paràmetres d’anisotropia en complexos de Ni(II) i Mn(III), es descriuen els mecanismes electrònics bàsics en base a consideracions de la teoria del camp del lligand. Aquest procediment proporciona regles senzilles per augmentar l’anisotropia, que poden ser aplicades en el disseny de nous materials. Finalment, s’estudien les interaccions anisotròpiques simètriques i antisimètriques en compostos binuclears de Cu(II), interaccions de gran importància per explicar les propietats d’alguns materials d’interès tecnològic. Les interaccions antisimètriques s’extreuen a partir de càlculs ab initio d’estructura electrònica per primer cop en aquest treball. Es concentra l’atenció d’aquesta part en dos sistemes: el conegut complex binuclear de Cu(II) amb quatre ponts acetat, i l’òxid de coure en el que recentment s’ha evidenciat una fase ferroelèctrica.

This thesis is devoted to a study of the effect of disorder on strongly correlated electrons. For non-interacting electrons, Anderson localization occurs if the amount of disorder is sufficient. For disorder-free systems, a Mott metal-insulator transition may occur if the electron-electron interactions are strong enough. The question we ask in this thesis is what happens when both disorder and interactions are present. We study the Anderson-Hubbard model, which is the simplest model to include both interactions and disorder, using a Gutzwiller variational wave function approach. We then study Anderson localization of electrons from the response of the Anderson-Hubbard Hamiltonian to an external magnetic field. An Aharonov-Bohm flux induces a persistent current in mesoscopic rings. Strong interactions result in two competing tendencies: they tend to suppress the current because of strong correlations, and they also screen the disorder potential and making the system more homogenous. We find that, for strongly interacting electrons, the localization length may be large, even though the current is suppressed by strong correlations. This unexpected result highlights how strongly correlated materials can be quiet di erent from weakly correlated ones. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2011-08-31 09:51:47.155

The design and construction of a state-of-the-art ultra-high vacuum spectrometer for the performance of angle-resolved inverse photoemission spectroscopy is presented. Detailed descriptions of its most important components are included, especially the Geiger-Muller ultraviolet photodetectors. By building on recent developments in the literature, we expect our spectrometer to achieve resolution comparable or superior to that of other prominent groups, and in general be one of the foremost apparatus for studying the momentum dependence of the unoccupied states in strongly correlated materials. Summaries of the theory of angle-resolved inverse photoemission spectroscopy and the basics of ultra-high vacuum science are also included.

Measures of data quality are important for the evaluation and improvement of survey design and procedures. A detailed investigation of the sources, magnitude and impact of errors is necessary to identify how survey design and procedures may be improved and how resources allocated more efficiently among various aspects of the survey operation. A major part of this thesis is devoted to the overview of statistical theory and methods for measuring the contribution of response variability to the overall error of a survey. A very common practice in surveys is to select groups (clusters) of elements together instead of independent selection of elements. In practice cluster samples tend to produce higher sampling variance for statistics than element samples of the same size. Their frequent use stems from the desirable cost features that they have. Most data collection and sample designs involve some overlapping between interviewer workload and the sampling units (clusters). For those cases, a proportion of the measurement variance, which is due to interviewers, is reflected to some degree in the sampling variance calculations. The prime purpose in this thesis is to determine a variance formula that decomposes the total variance into sampling and measurement variance components for two commonly used data collection and sample designs. Once such a decomposition is obtained, determining an optimum allocation in existence of measurement errors would be possible.

This thesis introduces a novel mobility model based on so called &ldquo / 2D correlated diffusion process&rdquo / . In this model, motion components over x and y axes are dependent. Joint density function of the process is derived. The expected exit time from an arbitrary domain is characterized by a boundary value problem. Analytical solution of this problem is given for a specific case. Numerical solution of the problem is presented by several examples. The results obtained in these examples are verified by simulations. The expected exit time computed by this method holds for any given 2D domain and any given starting position inside.

Within condensed matter physics, systems with strong electronic correlations give rise to fascinating phenomena which characteristically require a physical description beyond a one-electron theory, such as high temperature superconductivity, or Mott metal-insulator transitions. In this thesis, a class of strongly correlated electron systems is considered. These systems exhibit fractionally charged excitations with charge +e/2 or -e/2 in two dimensions (2D) and three dimensions (3D), a consequence of both strong correlations and the geometrical frustration of the interactions on the underlying lattices. Such geometrically frustrated systems are typically characterized by a high density of low-lying excitations, leading to various interesting physical effects. This thesis constitutes a study of a model of spinless fermions on the geometrically frustrated kagome lattice. Focus is given in particular to the regime in which nearest-neighbour repulsions V are large in comparison with hopping t between neighbouring sites, the regime in which excitations with fractional charge occur. In the classical limit t = 0, the geometric frustration results in a macroscopically large ground-state degeneracy. This degeneracy is lifted by quantum fluctuations. A low-energy effective Hamiltonian is derived for the spinless fermion model for the case of 1/3 filling in the regime where |t| << V . In this limit, the effective Hamiltonian is given by ring-exchange of order ~ t^3/V^2, lifting the degeneracy. The effective model is shown to be equivalent to a corresponding hard-core bosonic model due to a gauge invariance which removes the fermionic sign problem. The model is furthermore mapped directly to a Quantum Dimer model on the hexagonal lattice. Through the mapping it is determined that the kagome lattice model exhibits plaquette order in the ground state and also that fractional charges within the model are linearly confined. Subsequently a doped version of the effective model is studied, for the case where exactly one spinless fermion is added or subtracted from the system at 1/3 filling. The sign of the newly introduced hopping term is shown to be removable due to a gauge invariance for the case of hole doping. This gauge invariance is a direct result of the bipartite nature of the hole hopping and is confirmed numerically in spectral density calculations. For further understanding of the low-energy physics, a derivation of the model gauge field theory is presented and discussed in relation to the confining quantum electrodynamic in two dimensions. Exact diagonalization calculations illustrate the nature of the fractional charge confinement in terms of the string tension between a bound pair of defects. The calculations employ topological symmetries that exist for the manifold of ground-state configurations. Dynamical calculations of the spectral densities are considered for the full spinless fermion Hamiltonian and compared in the strongly correlated regime with the doped effective Hamiltonian. Calculations for the effective Hamiltonian are then presented for the strongly correlated regime where |t| << V . In the limit g << |t|, the fractional charges are shown to be effectively free in the context of the finite clusters studied. Prominent features of the spectral densities at the Gamma point for the hole and particle contributions are attributed to approximate eigenfunctions of the spinless fermion Hamiltonian in this limit. This is confirmed through an analytical derivation. The case of g ~ t is then considered, as in this case the confinement of the fractional charges is observable in the spectral densities calculated for finite clusters. The bound states for the effectively confined defect pair are qualitatively estimated through the solution of the time-independent Schroedinger equation for a potential which scales linearly with g. The double-peaked feature of spectral density calculations over a range of g values can thus be interpreted as a signature of the confinement of the fractionally charged defect pair. Furthermore, the metal-insulator transition for the effective Hamiltonian is studied for both t > 0 and t < 0. Exact diagonalization calculations are found to be consistent with the predictions of the effective model. Further calculations confirm that the sign of t is rendered inconsequential due to the gauge invariance for g in the regime |t| << V . The charge-order melting metal-insulator transition is studied through density-matrix renormalization group calculations. The opening of the energy gap is found to differ for the two signs of t, reflecting the difference in the band structure at the Fermi level in each case. The qualitative nature of transition in each case is discussed. As a step towards a realization of the model in experiment, density-density correlation functions are introduced and such a calculation is shown for the plaquette phase for the effective model Hamiltonian at 1/3 filling in the absence of defects. Finally, the open problem of statistics of the fractional charges is discussed.