In this work, patterns in the behavior of different classes and types of thermoelectric materials are observed, and an alchemy that could help engineer a highly efficient thermoelectric is proposed. A method based on cross-correlation of Seebeck waveforms is also presented in order to capture physics of magnetic transition. The method is used to compute Curie temperature of LaCoO3 with an accuracy of 10K. In total, over 26 systems are analyzed, and 19 presented: Chalcogenides (PbSe, PbTe, Sb2Te3, Ag2Se), Skutterudites and Clathrates (CoSb3, SrFe4Sb12, Cd (CN)2, CdC, Ba8Ga16Si30*), Perovskites (SrTiO3, BaTiO3, LaCoO3, CaSiO3, Ce3InN*, YCoO3*), Half-Heuslers (ZrNiSn, NbFeSb, LiAlSi, CoSbTi, ScPtSb*, CaMgSi*), and an assorted class of thermoelectric materials (FeSi, FeSi2, ZnO, Ag QDSL*). Relaxation time is estimated from experimental conductance curve fits. A maximum upper bound of zT is evaluated for systems that have no experimental backing. In general, thermoelectric parameters (power factor, Seebeck coefficient and zT) are estimated for the aforementioned crystal structures. Strongly correlated systems are treated using LDAU and GGAU approximations. LDA/GGA/L(S)DA+U/GGA+U approach specific errors have also been highlighted. Densities of experimental results are estimated.

We consider a gas of indistinguishable bosons, confined to a ring of radius R, and interacting via a pair-wise cosine potential. This may be thought of as the quantized Hamiltonian Mean Field (HMF) model for bosons originally introduced by Chavanis as a generalization of Antoni and Ruffo’s classical model. This thesis contains three parts: In part one, the dynamics of a Bose-condensate are considered by studying a generalized Gross-Pitaevskii equation (GGPE). Quantum effects due to the quantum pressure are found to substantially alter the system’s dynamics, and can serve to inhibit a pathological instability for repulsive interactions. The non-commutativity of the large-N , long-time, and classical limits is discussed. In part two, we consider the GGPE studied above and seek static solutions. Exact solutions are identified by solving a non-linear eigenvalue problem which is closely related to the Mathieu equation. Stationary solutions are identified as solitary waves (or solitons) due to their small spatial extent and the system’s underlying Galilean invariance. Asymptotic series are developed to give an analytic solution to the non- linear eigenvalue problem, and these are then used to study the stability of the solitary wave mentioned above. In part three, the exact solutions outlined above are used to study quantum fluctuations of gapless excitations in the HMF model’s symmetry broken phase. It is found that this phase is destroyed at zero temperature by large quantum fluctuations. This demonstrates that mean-field theory is not exact, and can in fact be qualitatively wrong, for long-range interacting quantum systems, in contrast to conventional wisdom. / Thesis / Doctor of Philosophy (PhD) / The Hamiltonian Mean Field (HMF) model was initially proposed as a simplified description of self-gravitating systems. Its simplicity shortens calculations and makes the underlying physics more transparent. This has made the HMF model a key tool in the study of systems with long-range interactions. In this thesis we study a quantum extension of the HMF model. The goal is to understand how quantum effects can modify the behaviour of a system with long-range interactions. We focus on how the model relaxes to equilibrium, the existence of special “solitary waves”, and whether quantum fluctuations can prevent a second order (quantum) phase transition from occurring at zero temperature.

In 2004 Robert W. Spekkens introduced a toy theory designed to make a case for the epistemic view of quantum mechanics. But how does Spekkens’ toy model differ from quantum theory? While some differences are well-established, we attempt to approach this question from a tomographic point of view. More specifically, we provide experimentally viableprocedureswhichenablesustocompletelycharacterizethestatesandgatesthatare available in the toy model. We show that, in contrast to quantum theory, decompositions of transformations in the toy model must be done in a non-linear fashion.

The aim of this study is to compare the performance of the four interest rate models (Vasicek Model, Cox Ingersoll Ross Model, Ho Lee Model and Black Der- man Toy Model) that are commonly used in pricing zero coupon bond options. In this study, 1{5 years US Treasury Bond daily data between the dates June 1, 1976 and December 31, 2007 are used. By using the four interest rate models, estimated option prices are compared with the real observed prices for the begin- ing work days of each months of the years 2004 and 2005. The models are then evaluated according to the sum of squared errors. Option prices are found by constructing interest rate trees for the binomial models based on Ho Lee Model and Black Derman Toy Model and by estimating the parameters for the Vasicek and the Cox Ingersoll Ross Models.