A major focus in condensed matter physics is to study the origin of exotic quantum phases such as coexistent and inhomogeneous phases, quantum criticality, and secondary ordered phases close to quantum critical points. Exotic phenomena in strongly correlated systems occur due to competing complex interactions of spin, charge, lattice, and orbital degrees of freedom. Complex quantum phases in strongly correlated systems are challenging, but they might be very useful due to their possible functionality to make advance devices. In order to understand, utilize, and optimize such behaviors, we need to improve our understanding of these systems. Studies in cold atom systems are of interest since cold atom experiments provide a control on model parameters. In this thesis, we use novel analytical and computational techniques to treat strongly interacting bosonic systems. Taking advantage of the very versatile quantum Monte Carlo Stochastic Green Function algorithm, we studied several interesting problems. First, we explore a recently developed new confining method for cold atoms on optical lattices. Atoms are confined via a hopping integral that decreases as a function of the distance from the center of the lattice. This method might lead to lower temperatures than existing diagonal confinement methods. Next, we study the ground state phase diagram of interacting bosons on a ring-shape lattice with a region of weak hopping integrals. The model, an extension of the well known Bose-Hubbard model, develops a novel local Mott phase in addition to the usual Mott and superfluid phases in the homogeneous system. This might provide a new insight to the description of atomtronics applications. Finally, we study the two species Bose Hubbard model in a two-dimensional lattice. This model presents novel phases due to the complexity associated with multiple species. Its phase diagram shows ordered and coexistence phases including a ferromagnetic phase separated phase with high entropy. This phase might be accessible experimentally. The novel phases found from our studies are linked to experiments on ultra-cold atoms trapped by laser beams.

In highly excited Rydberg atoms, the excited electron is in a large, loosely bound orbit. Hence, in contrast with the ground states, the Rydberg states are very sensitive to external electric field and can be ionized in rather weak fields. The low ionization threshold of Rydberg states results in effective state-specific detection by the selective field ionization technique. In this thesis, high-resolution spectroscopy of Rydberg states of Rubidium using millimeter wave transitions and selective field ionization has been used as a probe of external electric and magnetic fields. Laser cooling and trapping techniques in a magneto-optical trap (MOT) are employed to have a high density and narrow velocity distribution for the atomic sample. In this work the magnetic field inhomogeneity inherent in a MOT is minimized and the stray electric field present at the trap region is compensated in order to have resolved spectra. The Stark line broadening of the spectra obtained in this work may be used to determine the electric field distribution in an expanding ultra-cold neutral plasma.

T2K (Tokai to Kamioka) is the first off-axis long baseline neutrino oscillation experiment, and its primary goal is to measure the neutrino mixing parameter θ₁₃. A beam of muon type neutrinos with mean energy 600 MeV will be directed from the proton synchrotron at JPARC toward the Super-Kamiokande detector 295 km away. A near detector will be located 280 m from the proton beam target and instrumented with sub-detectors for measuring neutrino interactions prior to oscillation. One of these sub-detectors, the side muon range detector (SMRD), will help in measuring the neutrino energy spectrum and identifying backgrounds and also will serve as a cosmic ray muon trigger for calibrations of other sub-detectors. The SMRD will consist of approximately 2000 scintillator slabs distributed inside the iron return yokes for the magnetic field which surrounds the other sub-detectors. The scintillators will be read out via Si-based solid state photosensors. A number of relevant parameters for the photosensors have been measured and the results are presented here. The gain and dark rate have been determined as a function of threshold, bias voltage, and operating temperature. The Si-based photosensors are a new technology that has not been used on previous experiments, and their longevity has been in question especially since T2K will run for approximately ten years. So we have also heated the photosensors to 80 °C for a number of months to accelerate their aging and present the long term variation in dark rate and gain. We find no significant degradation over time. The scintillators have also been characterized; we have performed tests using atmospheric muons and radioactive sources to develop a testing procedure to determine scintillator quality and to reject inferior modules prior to installation. The effect on total light yield of fiber alignment, fiber polishing, gluing the fiber into the scintillator, and fiber damage have been measured. We find that triggering on muons under optimal conditions, the light yield is about 40 photoelectrons. We also conclude that major damage will be detectable using gammas from a source although minor damage may be more difficult to detect.

Our understanding of nuclear structure is built upon mean-field theories such as Hartree-Fock and time-dependent Hartree-Fock. The small-amplitude limit of the latter is the random phase approximation (RPA), which is widely used to model giant resonances in nuclei. Despite this popularity, RPA has been mostly validated against toy models; tests against complex models are scarce in the literature. We perform a thorough test of the RPA against full 0h</font><FONT FACE="Symbol" SIZE=4>w</font> shell model (SM) calculations, including in our investigation binding energies, scalar ground-state observables, for which we develop a new method, and transition strengths. We allow deformed Hartree-Fock solutions and compare results for spherical and deformed nuclei. We obtain reasonable agreement between RPA and SM, albeit with some significant failures. Particularly, we found that the low-lying collectivity is poorly described for deformed mean-field solutions, which we interpret as incomplete symmetry restoration in RPA. Results for observables, and in particular for <I>J</i><SUP>2</sup>, also point out toward the same conclusion regarding the symmetries of the ground state. We also prove, both analytically and numerically, that a long-standing theorem regarding RPA is violated in the case of deformation. The worse violation appears for low-lying transitions, such as isoscalar <I>E</i>2, which we consider as a third argument for an incomplete symmetry restoration.

It has been well documented that the surfaces of solids may differ from their bulk counterpart. The symmetry that a bulk possesses is broken at the surface. Due to this broken symmetry in the reduced dimension of the surface, the energetic of the surface also differs from the bulk counterpart. Reconstruction, charge redistribution, and surface alloying are phenomena that minimize the surface free energy. Surface properties of scientifically and technologically important bimetallic systems are the main focus of this dissertation. Specifically, surfaces of bulk alloy or heteroepitaxially grown metal-on-metal systems have been investigated primarily with two indispensable surface techniques, scanning tunneling microscopy and angle-resolved photoemission spectroscopy, which reveal the atomic and electronic structure of bimetallic systems, respectively. In the first system detailed herein, the surfaces of the ordered intermetallic alloy FeAl(110) exhibit surface segregation , which changes the Al concentration in the near surface region. The segregation and corresponding concentration change of Al induces a reconstruction on the surface as a function of annealing temperatures. The increased Al concentration gives rise to stronger Al and Fe interaction and results in hybridization of the Al-sp and Fe-d. Moreover, the oxide that forms on this surface is a homogeneous ultrathin alumina film. Because of the nanometer thickness, this thin film displays a two dimensional electronic structure. It is concluded that an even mix of octahedrally and tetrahedrally coordinated Al ions in the zigzag-stripe thin-film alumina structure is formed, which has been under scientific debate for many years. The atomic and electronic structure of Ag on Cu(110) and on Cu(100) systems has also been studied. These bimetallic systems form a surface confined alloying at the initial stages of growth and an overlayer phase as the Ag concentration increases in order to relieve the strain caused by Ag atoms, which have larger atomic size than Cu atoms. Electronically, bulk like energy distribution of the states indicates stronger interaction of Ag and Cu in the surface alloy phases than the overlayer phase, which displays only a two dimensional structure.

LaSb₂ has recently been found to have unusual magnetoresistive properties despite the fact that neither La nor Sb are magnetic. The resistance is anisotropic, and at high magnetic fields presents an anomaly that might be a result of a charge density transition. The magnetoresistance is anisotropic and linear, and the resistivity presents high relative changes when a magnetic field is applied. Discovered in 1954, LaSb₂, as the rest of the light rare-earth diantimonides, was poorly studied. The anisotropic magnetic properties reported in 1998 by Bud'ko, Canfield and their collaborators make the series very interesting. A description of the electronic structure and Fermi surface topology would be of great help in understanding the properties exhibited by LaSb₂, and the rest of the diantimonides. Single-crystals of LaSb₂ were grown by metallic flux method using high-purity La and Sb. Single-crystal X-ray diffraction measurements confirmed the SmSb₂ orthorhombic structure with a=6.38 b=6.23 and c=18.75Å. LaSb₂ presents a micaceous structure, with layers of Sb separated by bi-layers of La-Sb chains. X-ray measurements revealed a mosaic spread of ~0.5-1° and it is likely that the material is highly twinned. After the material is cleaved in vacuo, STM measurements give flat terraces separated by half unit-cell step edges. High-resolution angle-resolved photoemission spectroscopy has been performed on LaSb₂ to study the electronic band structure near the Fermi level and provide information to the Fermi surface topology. Photoemission studies show that the electronic structure is highly two-dimensional, and the locations of the critical points Γ and Z in band dispersion are identified. Neutron diffraction reveals doublet structures as a result of the crystal twinning. At low temperature, new spots are identified, indicating two new substructures that are incommensurate with the main lattice. The reduced dimensionality of the system, the nested Fermi surfaces, and the new periodicities that develop at low temperature can be reconciled in a model characterized by strong electron-phonon coupling that result in a charge-density wave due to an associated Peierls instability and a lattice distortion.

The purpose of this dissertation is to investigate the properties of self-assembled monolayers, particularly alkanethiols and Poly (ethylene glycol) terminated alkanethiols. These simulations are based on realistic interatomic potentials and require scalable and portable multiresolution algorithms implemented on parallel computers. Large-scale molecular dynamics simulations of self-assembled alkanethiol monolayer systems have been carried out using an all-atom model involving a million atoms to investigate their structural properties as a function of temperature, lattice spacing and molecular chain-length. Results show that the alkanethiol chains tilt from the surface normal by a collective angle of 25o along next-nearest neighbor direction at 300K. At 350K the system transforms to a disordered phase characterized by small tilt angle, flexible tilt direction, and random distribution of backbone planes. With increasing lattice spacing, a, the tilt angle increases rapidly from a nearly zero value at a = 4.7Å to as high as 34 o at a = 5.3Å at 300K. We also studied the effect of end groups on the tilt structure of SAM films. We characterized the system with respect to temperature, the alkane chain length, lattice spacing, and the length of the end group. We found that the gauche defects were predominant only in the tails, and the gauche defects increased with the temperature and number of EG units. Effect of electric field on the structure of poly (ethylene glycol) (PEG) terminated alkanethiol self assembled monolayer (SAM) on gold has been studied using parallel molecular dynamics method. An applied electric field triggers a conformational transition from all-trans to a mostly gauche conformation. The polarity of the electric field has a significant effect on the surface structure of PEG leading to a profound effect on the hydrophilicity of the surface. The electric field applied anti-parallel to the surface normal causes a reversible transition to an ordered state in which the oxygen atoms are exposed. On the other hand, an electric field applied in a direction parallel to the surface normal introduces considerable disorder in the system and the oxygen atoms are buried inside.

The successful construction of long time convergent finite difference schemes approximating highly gravitating systems in general relativity remains an elusive task. The presence of constraints and the introduction of artificial time-like boundaries contribute significantly to the difficulty of this problem. Whereas in the absence of boundaries the Bianchi identities ensure that the constraints vanish during evolution provided that they are satisfied initially, this is no longer true when time-like boundaries are introduced. In this work we consider the linearization around the Minkowski space-time in Cartesian coordinates of the generalized Einstein-Christoffel system and analyze different kinds of boundary conditions that are designed to ensure that the constraints vanish throughout the computational domain: the Neumann, Dirichlet, and Sommerfeld cases. In addition to the situation in which the boundary is aligned with a coordinate surface, we examine the presence of corners in the computational domain. We find that, at a corner, there are compatibility conditions which the boundary data and its derivatives must satisfy and that, in general, achieving consistency of a finite difference scheme can be troublesome. We present several numerical experiments aimed at establishing or confirming the well-posedness or ill-posedness of a problem and the consistency of the numerical boundary conditions at the corners. In the case of a smooth boundary we are able to find stable discretizations for all three cases. However, when a corner is present no stable discretization was found for the Sommerfeld case. Finally, we propose an alternative implementation of the Sommerfeld boundary conditions that would preserve the constraints, offer a good approximation for absorbing boundary conditions, and eliminate the problem of the corners.

A solid understanding of dust grains and their extinction properties is needed to better remove the effects of extinction from data and to comprehend the nature of the processes which modify grains. This requires a large sample of Galactic sightlines, extending far beyond the solar neighborhood, sampling not only a large volume of space but also a wide variety of environments. To fulfill this requirement, a database of sightlines toward 426 young, reddened stars was constructed using extinction curves based on IUE spectra. The curves were fit and the Fitzpatrick-Massa (FM) parameters were found. FM parameters allow for a quantitative analysis of curve characteristics. IR photometry was also obtained for these sightlines, and thus R(V) (=A(V)/E(B-V)) was found. Links between the environment and various grain populations responsible for different components of the extinction curve were sought, as were relationships between different FM parameters, especially those which describe the 2175 Angstrom absorption feature (the &quotbump&quot). A search for sightlines which cannot be described by the R(V)-dependent extinction law of Cardelli, Clayton, &amp Mathis (1989; hereafter CCM) was also undertaken. The main results are: (1.) The CCM extinction relation is accurate for the vast majority of Galactic sightlines. Thus, processes which lead to a CCM-like extinction curve dominate the ISM and the grain populations responsible for the extinction are modified efficiently and systematically. (2.) The central wavelength of the bump does not shift, and the bump width is environment-dependent, being narrow along diffuse sightlines and broadening with increasing density. These provide constraints on grain mantle materials. (3.) The Galaxy can support environments that lead to Magellanic Cloud-like extinction; this emphasizes the importance of local environment in determining extinction properties. (4.) Reddened Galactic sightlines which do not adhere to the standard extinction relation tend to be dense and molecule-rich.

The principal goal in this project is to determine if a one-dimensional diode array, the Profiler (Sun Nuclear Corporation), can be used as a tool for intensity modulated radiation therapy quality assurance (QA). A one-dimensional diode array can be used to measure dose and dose profiles for IMRT fields. IMRT fields for real cases at Mary Bird Perkins Cancer Center were used to test the Profiler model 1170 (Sun Nuclear Corporation). The main concern with the Profiler is that there is not central diode in the array. The absorbed dose displayed in the Profiler window is the average of the absorbed dose measured by the two central diodes. Absorbed dose measured using the Profiler was compared with absorbed dose measured using an ion chamber. The dose profiles obtained with the Profiler were also compared to those obtained by film dosimetry. The dose measured with the Profiler was within 5% regard to the dose measured using ion chamber. The quality of the profiles obtained with the Profiler was similar to those obtained using film dosimetry. The Profiler demonstrated to be feasible as a QA instrument for IMRT cases. Therefore, one-dimensional diode array can definitely be used as a tool for IMRT QA.