No description available.

In this work, optical pump – near-infrared probe and near-infrared pump – mid-infrared probe spectroscopy are used for the investigation of pressure-induced insulator-tometal transitions in transition metal oxide compounds. The materials under study are a-Fe₂O₃, also known as hematite, and VO₂. Both materials undergo pressureinduced metallization. However, the physical mechanisms of this phase transition are very different for these systems and have not been fully understood up to now. Using ultrafast pump-probe spectroscopy we obtain an insight into the evolution of the band structure and electron dynamics across the insulator-to-metal transition. In the case of VO₂, our near-infrared pump – mid-infrared probe experiments reveal a non-vanishing pumping threshold for photo-induced metallization even at our highest pressures around 20 GPa. This demonstrates the existence of localized charge carriers and the corresponding persistence of a band gap. Besides the threshold behaviour for photo-induced metallization, the carrier relaxation time scale, and the linear reflectivity and transmissivity have been studied under pressure increase. An anomaly in the threshold behaviour as well as the linear reflectivity and transmissivity at a critical pressure around 7 GPa indicates band gap filling under pressure. This is further supported by results obtained under decompression, where the changes of the linear reflectivity turned out to be almost fully reversible. The observations on VO₂ are highly reproducible and can be explained in terms of a pressure-induced bandwidth-driven insulator-to-metal transition. Fe₂O₃ has been studied via optical pump – near-infrared probe spectroscopy up to pressures of 60 GPa. In the pressure range up to 40 GPa, the changes of the response can be explained by photo-induced absorption and bleaching. The pressure-dependent study of the relaxation dynamics allows to identify cooling of the electron system as origin of the picosecond relaxation process.

Due essentially to the difficulties associated with obtaining explicit forms of stationary marginal distributions of non-linear stationary processes, appropriate characterizations of such processes are worked upon little. After discussing an elaborate motivation behind this thesis and presenting preliminaries in Chapter 1, we characterize, in Chapter 2, the stationary marginal distributions of certain non-linear multivariate stationary processes. To do so, we show that the stationary marginal distributions of these processes belong to specific skew-distribution families, and for a given skew-distribution from the corresponding family, a process, with stationary marginal distribution identical to that given skew-distribution, can be found. While conventional time series analysis greatly depends on the assumption of stationarity, measurements taken from many physical systems, which consist of both periodicity and randomness, often exhibit cyclostationarity (i.e., a periodic structure in their first- and second-order moments). Identifying the hourly global horizontal irradiances (GHIs), collected at a solar monitoring station of Saudi Arabia, as a cyclostationary process and considering the significant impact of that on the energy production in Saudi Arabia, Chapter 3 provides a temporal model of GHIs. Chapter 4 extends the analysis to a spatio-temporal cyclostationary modeling of 45 different solar monitoring stations of the Kingdom. Both the proposed models are shown to produce better forecasts, more realistic simulations, and reliable photovoltaic power estimates in comparison to a classical model that fails to recognize the GHI data as cyclostationary. Chapter 5 extends the notion of cyclostationarity to a novel and flexible class of processes, coined evolving period and amplitude cyclostationary (EPACS) processes, that allows periods and amplitudes of the mean and covariance functions to evolve and, therefore, accommodates a much larger class of processes than the cyclostationary processes. Thereafter, we investigate its properties, provide methodologies for statistical inference, and illustrate the presented methods using a simulation study and a real data example, from the heavens, of the magnitudes of the light emitted from the variable star R Hydrae. Finally, Chapter 6 summarizes the findings of the thesis and discusses its significance and possible future extensions.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18772号 / 理博第4030号 / 新制||理||1581(附属図書館) / 31723 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 田中 耕一郎, 教授 松田 祐司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Recently, Bayesian methods have become the essence of modern statistics, specifically, the ability to incorporate hierarchical models. In particular, correlated data, such as the data found in spatial and temporal applications, have benefited greatly from the development and application of Bayesian statistics. One particular application of Bayesian modeling is Gaussian Markov Random Fields. These methods have proven to be very useful in providing a framework for correlated data. I will demonstrate the power of GMRFs by applying this method to two sets of data; a set of temporal data involving car accidents in the UK and a set of spatial data involving Provo area apartment complexes. For the first set of data, I will examine how including a seatbelt covariate effects our estimates for the number of car accidents. In the second set of data, we will scrutinize the effect of BYU approval on apartment complexes. In both applications we will investigate Laplacian approximations when normal distribution assumptions do not hold.

The objective of this research is to devise a procedure to generate random Set Covering Problem (SCP) instances with known optimal solutions and correlated coefficients. The procedure presented in this work can generate a virtually unlimited number of SCP instances with known optimal solutions and realistic characteristics, thereby facilitating testing of the performance of SCP heuristics and algorithms. A four-phase procedure based on the Karush-Kuhn-Tucker (KKT) conditions is proposed to generate SCP instances with known optimal solutions and correlated coefficients. Given randomly generated values for the objective function coefficients and the sum of the binary constraint coefficients for each variable and a randomly selected optimal solution, the procedure: (1) calculates the range for the number of possible constraints, (2) generates constraint coefficients for the variables with value one in the optimal solution, (3) assigns values to the dual variables, and (4) generates constraint coefficients for variables with value 0 in the optimal solution so that the KKT conditions are satisfied. A computational demonstration of the procedure is provided. A total of 525 SCP instances are simulated under seven correlation levels and three levels for the number of constraints. Each of these instances is solved using three simple heuristic procedures. The performance of the heuristics on the SCP instances generated is summarized and analyzed. The performance of the heuristics generally worsens as the expected correlation between the coefficients increases and as the number of constraints increases. The results provide strong evidence of the benefits of the procedure for generating SCP instances with correlated coefficients, and in particular SCP instances with known optimal solutions.

No description available.

In recent decades enormous progress has been made in studying the geometrical structure of the quantum state space. Far from an abstraction, this geometric struc- ture is defined operationally in terms of the distinguishability of states connected by parameterizations that can be controlled in a laboratory. This geometry is manifest in the kinds of response functions that are measured by well established experimen- tal techniques, such as inelastic neutron scattering. In this thesis we explore the properties of the state space geometry in the vicinity of the ground state of two paradigmatic models of low dimensional magnetism. The first model is the spin-1 anti-ferromagnetic Heisenberg chain, which is a central example of symmetry pro- tected topological physics in one dimension, exhibiting a non-local string order, and symmetry protected short range entanglement. The second is the Kitaev honeycomb model, a rare example of an analytically solvable quantum spin liquid, characterized by long range topological order. In Chapter 2 we employ the single mode approximation to estimate the genuine multipartite entanglement in the spin-1 chain as a function of the unaxial anisotropy up to finite temperature. We find that the genuine multipartite entanglement ex- hibits a finite temperature plateau, and recove the universality class of the phase transition induced by negative anisotropy be examining the finite size scaling of the quantum Fisher information. In Chapter 4 we map out the zero temperature phase diagram in terms of the QFI for a patch of the phase space parameterized by the anisotropy and applied magnetic field, establishing that any non-zero anisotropy en- hances that entanglement of the SPT phase, and the robustness of the phase to finite temperatures. We also establish a connection between genuine multipartite entanglement and state space curvature. In Chapter 3 we turn to the Kitaev honeycomb model and demonstrate that, while the QFI associated to local operators remains trivial, the second derivative of such quantities with respect to the driving parameter exhibit divergences. We characterize the critical exponents associated with these divergences. / Thesis / Doctor of Philosophy (PhD) / Systems composed of many bodies tend to order as their energy is reduced. Steam, a state characterized by the complete disorder of the constituent water molecules, condenses to liquid water as the temperature (energy) decreases, wherein the water molecules are organized enough for insects to walk atop them. Water freezes to ice, which is so ordered that it can hold sleds and skaters. Quantum mechanics allows for patterns of organization that go beyond the solid-liquid-gas states. These patterns are manifest in the smallest degrees of freedom in a solid, the electrons, and are responsible for fridge magnets and transistors. While quantum systems still tend to order at lower energies, they are characterized by omni-present fluctuations that can conceal hidden forms of organization. One can imagine that the states of matter live in a vast space, where each point represents a different pattern. In this thesis we show that by probing the geometry of this space, we can detect hidden kinds of order that would be otherwise invisible to us.

No description available.

No description available.