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For some time now, first-principles calculation methods have proven to be an effective tool for investigating the physics of condensed matter systems. The additional use of density functional theory (DFT) and the local density approximation (LDA) has permitted even complex materials to be studied on desktop workstations with remarkable success. The incorporation of linear response theory into these methods has extended their power, allowing investigation of important dynamical properties.;Contained within the following pages are the results of a first-principles study of SrTiO3. This transition metal oxide is often grouped with ferroelectric materials, due to its similar composition and perovskite structure. Although it behaves as if it were to become ferroelectric, it fails to do so, even at the lowest temperatures.;Using the LAPW method for bulk materials, the ground-state equilibrium properties for the cubic phase were found. Additional linear response calculations produced the phonon frequencies throughout the Brillouin zone. Imaginary values for these frequencies revealed two distinct regions of reciprocal space corresponding to structural instabilities of the ferroelectric (FE) and antiferrodistortive (AFD) types. A cell-doubling AFD transition to tetragonal structure is observed experimentally, so subsequent calculations were continued in this phase. Total energy calculations were performed for both FE and AFD distortions in this new phase, and it was found that the AFD instability is enhanced with decreasing lattice parameter, while the FE instability is diminished. Furthermore, these calculations suggest that this material is marginally stable against FE distortions, even at the 105 K volume.

Positive muons implanted in metal distort the surrounding lattice; therefore, in addition to electronic interactions, the elastic forces have to be considered in determining the muon state. to explore the elastic and electronic diffusion and trapping mechanisms, we studied AlCu(,420ppm), AlMg(,1000ppm) and AlAg(,1000ppm) alloys. These alloys were selected for the different effects on the host lattice of these impurities; Cu contracts the Al lattice, Mg expands it and Ag has nearly no effect. On the other hand Cu and Ag are monovalent while Mg is divalent. For AlCu between 5K and 14K the temperature exponent (beta) of the two-state-model trapping rate ((nu)(alpha)T('(beta))) was 0.93 (+OR-) .26 for zero field and 1.16 (+OR-) .14 for a 14.2G longitudinal field. A (beta) of 1 implies a one phonon induced diffusion process. For AlMg the transverse field (150G) second moment of the static random fields was 0.317 (+OR-) .007 (mu)s('-1) between 10K and 60K, 0.221 (+OR-) .013 (mu)s('-1) between 60K and 150K and 0.150 (+OR-) .013 (mu)s('-1) between 150K and 300K. The changing value of the second moment indicates a change in the muon trapping site from tetrahedral to octahedral to vacancy as the temperature is increased, this was confirmed at appropriate temperatures by zero and longitudinal field studies. Comparing the AlMg results with earlier work on AlCu two types of trapping sites can be identified, those dependent on the magnitude but not sign of deformation, and thought to be a few atomic distances away from the defect, and those which are possibly close to Mg. For AlAg, since Ag has almost no elastic effect the weaker depolarization structure suggests a different trapping mechanism, possibly due to the electronic interaction. to study the muon interaction with a uniform strain field, uniaxial stress was applied to an Fe (3 wt. % Si) single crystal. We measured the temperature dependence of the frequency shift versus strain to be -0.348 (+OR-) .007 MHz/100(mu)(epsilon) (25.7 (+OR-) .5 G.100(mu)(epsilon)) at 300K and -0.279 (+OR-) .010 MHz/100(mu)(epsilon) (20.6 (+OR-) .7 G/100(mu)(epsilon)) at 360K. The agreement of the room temperautre result with earlier work on pure Fe shows that these shifts are inherent to Fe and not impurity dependent. That the shifts are proportional to (1/T) confirms that these effects are dominated by a strain-induced-muon-population shifts between crystallographically equivalent but magnetically inequivalent sites.

This thesis is a theoretical, numerical study of the magnetic fields which exist in the anisotropic, high temperature superconductors like $YBa\sb2Cu\sb3O\sb{7-\delta}$, or YBCO for short, using both the anisotropic London theory and simulations based on existing muon spin rotation techniques. The thesis first describes the muon spin rotation ($\mu$SR) techniques, and then gives a brief discussion of superconductivity with regard to the London theory of anisotropic, type II superconductors. Next, numerical results of the application of this theory to YBCO are presented. Three dimensional surface plots of the magnetic field components within the flux line lattice (FLL) are shown, as well as the corresponding contour plots of the fields. Field distributions are calculated from these surfaces, and the graphs are presented. These distributions correspond to the real part of the Fourier transform of the muon histogram, and a comparison between data taken on a polycrystalline sample and the theoretical prediction is made. In addition, variation of the field distributions with parameters such as penetration depth, angle of the average field, and the magnitude of the average field is discussed. The last part of the thesis is a theoretical study of the behavior of muons which have stopped within a superconductor. The muons are assumed to stop uniformly throughout the FLL area, and the precession of each about its local field is recorded as the projection of its polarization along each of three mutually perpendicular "detectors." The depolarization of these signals as a function of time is an indication of the existence of transverse field components which exist within the FLL due solely to the anisotropy of the material. In order to further investigate these off axis fields, we have developed an extension of the usual $\mu$SR techniques, coupled with Fourier analysis, which yields new information. For example, with the proper analysis procedure, one may determine to good precision the direction of the average internal field B with respect to the applied field H$\sb{a}$. Other quantities, which we call moments of the field distribution, may also be determined.

This research comprises a comprehensive spectroscopic study of the characteristics of the solid state crystal YAG (Yttrium Aluminum Garnet) singly doped with Ho (Holmium) ions. An important area of solid state laser crystal research is the determination and optimization of the processes within these laser crystals which lead to efficient laser action. In most laser crystals, there is a donor ion such as Tm (Thulium) and an acceptor ion such as Ho. The donor ion generally has greater absorption than that of the acceptor at the wavelength of the pump source. The donor ion can transfer this absorbed energy to the lasing manifold, {dollar}\rm\sp5 I\sb7{dollar}, of the Ho acceptor ion. A loss process to the 2.1{dollar}\mu{dollar}m laser emission from the {dollar}\rm\sp5 I\sb7{dollar} manifold is the radiative energy transfer of this emission to a neighboring Ho ion. The purpose of this research is to determine the dependence of this radiative energy transfer process on various macroscopic parameters of the YAG:Ho crystals.;Spectral and kinetic data were acquired over a wide range of temperatures and excitation points of the four samples available: YAG:Ho (8.5%), (3%), (1%), and (0.32%). The spectral data include absorption and luminescence. The kinetic data consist of the temporal responses to pulsed excitation.;Models for the spectral and kinetic data were developed and found to agree closely with experimental results. Moreover, these models successfully correlated the Ho-Ho radiative energy transfer with the concentration, temperature, and excitation position parameters of the YAG:Ho crystals. Using these models, one can minimize this loss process by choosing the appropriate crystal parameters and thereby, increase the efficiency of laser action.

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Strongly interacting many-body systems remain a central challenge of modern physics. Recent developments in the field of ultra-cold atomic physics have opened a new window onto this enduring problem. Experimental progress has revolutionized the approach to studying many-body systems and the exotic behaviors that emerge in these systems. It is now possible to engineer and directly measure a variety of models that can capture the essential features of real materials without the added complexity of disorder, impurities, or complicated or irregular geometries. The parameters of these models can be freely tuned with tremendous precision. These experimental realizations are an ideal setting in which to test and calibrate computational many-body methods that can provide insight and quantitative understanding to many of the open questions in condensed matter and many-body physics. in this thesis we study several models of strongly interacting many-fermion systems using cutting-edge numerical techniques including Hartree-Fock-Bogoliubov (HFB) mean-field theory and auxiliary-field quantum Monte Carlo (AFQMC). We explore the exotic phases and behaviors that emerge in these systems, beginning with finite-momentum pairing states in attractive spin-polarized fermions. We next demonstrate the unique capability of AFQMC to treat systems with spin-orbit coupling (SOC). We obtain high-precision, and in many cases numerically exact, results on SOC systems that can eventually be compared directly to experiment. The first system we highlight is the attractive Fermi gas with Rashba SOC, which displays unconventional pairing, charge, and spin properties. We then study the coexistence of charge and superfluid order, as well as topological signatures, in attractive lattice fermions with Rashba SOC. Our results provide a new, high-accuracy understanding of a strongly interacting many-body system and its exotic behaviors. These techniques can serve as a general framework for the treatment of strong interactions and SOC in many-body systems, and provide a foundation for future work on exotic phases in models and real materials.

There is a need for efficient ultraviolet (UV) detectors in many fields, such as aerospace, automotive manufacturing, biology, environmental science, and defense, due to photomultiplier tubes (the currently available technology) often not meeting application constraints in weight, robustness, and power consumption. In my thesis, I demonstrate that high quality vanadium dioxide (VO2) thin films, epitaxially grown on niobium doped titanium dioxide substrates (TiO2:Nb), display a strong photoconductive response in the UV spectral range, making them promising candidates for photomultiplier-free UV photodetection. By adjusting the characteristics of the substrate and VO2 film, the samples achieve external quantum efficiency exceeding 100% (reaching beyond 1,000% for optimized samples) superior to that of current wide band gap UV detectors at room temperature. The mechanism for photocurrent production in VO2/TiO2:Nb heterostructure is a space-charge region, engineered in the heterojunction, yielding favorable conditions for hole tunneling from TiO2:Nb into VO2. Improving upon the heterostructure, I demonstrate up to an order of magnitude improvement in parameters such as responsivity, external quantum efficiency, detectivity, and dark current density by applying Au films to the VO2/TiO2:Nb heterostructure. Ultimately, my work proved that the VO2/TiO2:Nb heterostructure is a promising alternative technology for UV detection in high demand fields, with great potential for scalable device production.