<p>This work introduces a new technique for the determination of quantum phase transitions known as the Conjugate Field Fidelity Susceptibility (CFFS) approach. The CFFS method draws highly on the Quantum Information concept of quantum fidelity susceptibility. An initial introduction to the computational tricks needed to feasibly calculate quantum fidelities will be given. Following this will be a discussion of the nature, derivation and applications of the quantum fidelity and fidelity susceptibilities. Then the CFFS technique will be described before applying it to identify a BKT(Berezinsky-Kosterlitz-Thouless) transition in the Next-Nearest Neighbour Heisenberg Spin Chain. Finally, the method will be applied to confirm the more robust phase diagram of the Next-Nearest Neighbour Heisenberg model on an anisotropic triangular lattice.</p> / Master of Science (MS)

<p>Gravitational lensing can be used as a direct probe of the distribution of dark matter around galaxies , groups, and clusters, making it a powerful tool in astrophysics. In this thesis, we introduce the basics of gravitational lensing and weak gravitational lensing. Using weak lensing to study the ensemble-averaged properties of a population of objects, we present a study of galaxy-galaxy lensing of galaxy-sized dark matter halos using data from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) Deep.</p> <p>We calculated the average velocity dispersion for an L_* galaxy at a redshift of 0.54 to be 113 ± 9 kms^-1, with a mass of 1.7 ± 0.3 x 10¹² h^{- 1}M_⊙. We present the first conclusive evidence for non-spherical galaxy dark matter halos. Our results favour a dark matter halo with an ellipt icity of 0.70 ± 0.18 at > 5σ when averaged over all galaxies. If the sample of foreground lens galaxies is selected by colour , we detect non-spherical halos for all 4 samples except a green subsample. We also consider samples of galaxies divided by colour , redshift and luminosity. Our luminosity samples allowed us to calculate a B-band Tully-Fisher relation which is consistent with theoretical predictions.<br />From our data, we do not detect any evolut ion in galaxy dark matter halos from a redshift of 0. 78 to 0.39, corresponding to no evolut ion from when the Universe was 6.6 Gyr to 9.1 Gyr old in a ACDM cosmology.</p> / Master of Science (MS)

<p>We derive structural parameters for ~2000 globular clusters in the giant Virgo elliptical M87 using extremely deep Hubble Space Telescope images in F606W (V) and F814W (I) taken with the ACS/WFC. The cluster scale sizes (half-light radii r_h) and ellipticities are determined from PSF-convolved King-model profile fitting. We find that the r_h distribution closely resembles the inner Milky Way clusters, peaking at r_h ≃ 2.5 pc and with virtually no clusters more compact than r_h ≃ 1 pc. The metal-poor clusters average 24% larger in r_h than the metal-rich ones. The cluster scale size shows a gradual and noticeable increase with galactocentric distance. Clusters are very slightly larger in the bluer waveband V, a possible hint that we may be beginning to see the effects of mass segregation within the clusters. We derive a color magnitude diagram for the M87 globular cluster system which show a clear bimodal distribution. We analyzed in the detail the sub-structure of the CMD by applying statistical fits to the color distribution. We obtain a Globular Cluster Luminosity Function for all M87 clusters and for its red and blue subpopulations. The best statistical fits describing the Luminosity Functions were also calculated. The metal-poor subpopulation has a brighter peak (mean) than the metal-rich subpopulation.</p> / Master of Science (MS)

<p>We study a two-atom system interacting via a short-range potential, and trapped by an optical lattice, in higher partial waves. These atoms may be made to interact strongly near a Feshbach resonance. Our main purpose is to find the relation between energy levels of the system and the scattering parameters in higher partial waves. We check our analytical results by numerical calculations and find the conditions under which this method is applicable for the d-wave.</p> / Master of Science (MS)

<p>The dynamical state of galaxy groups at intermediate redshifts can provide information about the growth of structure in the universe. We examine three goodness-of-fit tests, the Anderson-Darling (A-D), Kolmogorov and X² tests, in order to determine which statistical tool is best able to distinguish between groups that are relaxed and those that are dynamically complex. We perform Monte Carlo simulations of these three tests and show that the X² test is profoundly unreliable for groups with fewer than 30 members. Power studies of the Kolmogorov and A-D tests are conducted to test their robustness for various sample sizes. We then apply these tests to a sample of the second Canadian Network for Observational Cosmology Redshift Survey (CNOC2) galaxy groups and find that the A-D test is more reliable and powerful at detecting real departures from an underlying Gaussian distribution than the more commonly used X² and Kolmogorov tests. We use this statistic to classify a sample of the CNOC2 groups and find that 34 of 106 groups are inconsistent with an underlying Gaussian velocity distribution, and thus do not appear relaxed. In addition, we compute velocity dispersion profiles (VDPs) for all groups with more than 20 members and compare the overall features of the Gaussian and non-Gaussian groups, finding that the VDPs of the non-Gaussian groups are distinct from those classified as Gaussian. We also compare group properties of both rich individual groups and stacked groups to determine if any there are any trends amongst the classified Gaussian and non-Gaussian groups.</p> / Master of Science (MS)

<p>Optical spectroscopy is an experimental tool used to probe the intermediate-energy level excitations in solid materials with the ultimate goal of achieving a bosonic spectral function. Reflectance of a sample is measured and then manipulated to yield frequency-dependent conductivity, dielectric functions, scattering rates and self-energies. The technique is particularly useful in probing the underlying electronic mechanisms in high-temperature superconductors.</p> <p>The technique is applied to an Iron pnictide superconductor, namely BaFe_1.8Co_0.2As₂. The reflectance is measured and reported, along with all relevant quantities derived from this result. In particular the bosonic spectral function is uncovered and then interpreted.</p> <p>In addition, a "proof of concept" is included to illustrate the advantages and disadvantages of the Maximum Entropy Inversion method which is used to uncover the boson spectral function. The results reported here make reference to an already published article on the Bi-2212 superconductor and the conclusion will be verified.</p> / Master of Science (MSc)

<p>Bohmian mechanics is an alternative formulation of quantum mechanics that incorporates the familiar and intuitive picture of particles moving along trajectories and yet predicts the same results as the more widely accepted Copenhagen interpretation. In recent years there has been renewed interest in this Bohmian view, in part for the novel approach that it suggests to certain problems, such as decay processes, both from a theoretical and computational stand point. In this thesis we focus on using the concepts introduced by the Bohmian framework as a practical computational tool.</p> <p>I evaluate a number of implementations of the Bohmian method, get a sense of their strengths and weaknesses and attempt to overcome some stability issues that arise. For problems in one-dimension (ID), accurate solutions of the time-dependent Schrodinger equation produce a wave function from which Bohmian trajectories can be computed by integrating along flux lines. For direct integration of the quantum Hamilton-Jacobi equations, the main problems that arise are related to evaluating the quantum potential (QP), especially in regions of low probability density. Sufficient accuracy is required to avoid unphysical trajectory crossings. A number of interpolation schemes were investigated, and smoothed splines with special treatment of edge effects gave the best results.</p> <p>For problems in 2D the alternating direction implicit (ADI) method was employed to produce the wave function. Ways of dealing with unphysical reflections from the boundaries of a finite size domain were studied. The use of cellular automata, especially the lattice-Boltzmann method (LBM) were also considered. Here Bohm trajectories would be propagated by following a small set of rules. The main problem identified is that, unless a scheme can be found in which the quantum potential is self-generating from an equation of continuity, the overhead of computing the QP at each time step, is prohibitive.</p> / Doctor of Philosophy (PhD)

<p>X-ray fluorescence (XRF) has been demonstrated to be a useful technique for measuring trace quantities of heavy metals in various tissues within the body. This thesis investigates a means of improving the measurement of lead in bone, as well as increasing the existing sensitivity of measuring kidney mercury content. The XRF measurement of uranium is also explored. This work assesses the feasibility of a normalisation method for the 57 Co/90° system, in relating detected signal to the lead content of the sample. The feasibility of normalisation has been shown, which reduces subject dose and improves system transportability, as well as removes subjectivity, by eliminating the need for acquiring planar x-ray images of the measurement site. In the measurement of renal mercury concentrations, a gain in sensitivity increasing the x-ray tube operating voltage of the current system is investigated. It found that 250 kV, rather than 175 kV, and a titanium rather than uranium filter, results in a 2.5 ± 0.2 times gain in sensitivity. This potential improvement could have profound clinical implications for the accuracy of occupational monitoring, and for assessing whether there is a quantitative relationship between biological fluid levels and mercury content in this critical organ. The XRF measurement of bone uranium content is also explored. Both source-excited and polarised systems have been developed, however, the sensitivity is currently beyond that which is useful for occupational monitoring of exposure to this toxin. The particular case of measuring uranium in survivors of "Friendly Fire" incidents (from Operation Desert Storm) is investigated, and the first detectable quantity of uranium has been observed in a member of this cohort, with the XRF system designed and built during the course of this work.</p> / Doctor of Philosophy (PhD)

<p>We develop a model of self-gravitating, pressure truncated, filamentary molecular clouds with a rather general helical magnetic field topology. By comparing with existing observational data, our analysis suggests that the mass per unit length of many filamentary clouds is significantly reduced by the effects of external pressure, and that toroidal fields play a significant role in squeezing clouds. We show that there is an upper limit to the mass per unit length allowed for equilibrium, whose value depends on the strength and character of the magnetic field threading the filament. Clouds that are below this critical mass per unit length are always stable against radial gravitational collapse. Our theoretical models involve 3 parameters; two to describe the mass loading of the poloidal and toroidal fields, and a third to describe the radial concentration of the filament. We find that many of our models with helical fields are in good agreement with the observed ∼r-2 radial density structure of filamentary clouds. Unmagnetized filaments and models with purely poloidal magnetic fields result in steep density gradients that are not allowed by the observations. We consider the stability of our models against axisymmetric modes of fragmentation. Many of our models fragment gravitationally, although some are subject to MHD-driven "sausage" modes of instability. Our main result is that the toroidal magnetic field helps to stabilize long wavelength gravitational instabilities, but short wavelength MHD "sausage" instabilities result when the toroidal field is sufficiently strong. Many of our models lie in a physical regime where the growth rates of gravitational and MHD instabilities are at a minimum. We then go on to develop a model of the helically magnetized cores that might originate from finite segments of our filament models. Only modest toroidal fields are required to produce prolate cores, with mean projected axis ratios in the range 0.3-1. Thus, many of our models are in good agreement with the observed shapes of cores (Myers et al 1991, Ryden 1996), which find axis ratios distributed about a mean value in the range 0.5-0.6. We show that the Bonnor-Ebert critical mass is reduced by about 20%, as a result of the helical field in our models.</p> / Doctor of Philosophy (PhD)

<p>We have used Hα and photometric data for two morphologically distinct Local Group galaxies, the spiral M33 and dwarf irregular NGC 6822, to study the distribution of the luminous blue O and B (OB) stars and HII regions in the galaxies as well as to determine whether individual regions of the galaxies are separately and/or collectively in a state of ionization balance. In the case of M33, we have concentrated on the inner 1 kpc region of the galaxy. Using the Hα data, three distinct ionized gas environments (bright, halo and field) defined by the surface brightness of the Hα emission have been identified. We find that ~50% of OB stars are located in the field, so that 1/2 of the lifetime of OB stars must be spent outside recognizable HII regions. This result suggests that if OB stars escape from bright HII regions by destroying their parent molecular clouds, then molecular cloud lifetimes after forming OB stars could be as low as ~5x10⁶ yrs or 1/2 the typical lifetime of OB stars. We show that a possible origin for the large field OB population is that they were born in and subsequently percolated out of the ~10³ giant molecular clouds with masses ≳10₃M⨀ predicted to exist within the inner kpc of the galaxy. Using UBV photometry and stellar ionization models, we predict Hα fiuxes in the bright, halo and field regions and compare them to those observed to find that predicted fluxes are a factor of ~3-7 greater than observed so that the three ionized gas environments, separately as well as collectively, are not in ionization balance. Furthermore, the most substantial loss of ionizing photons appears to he taking place in the field. We find that observed and predicted Hα luminosities are in best agreement when Case A recombination is assumed in the field. Our findings suggest that star formation rates obtained from Hα luminosities must underestimate the true star formation rate within the inner region of M33. A similar analysis of an individual, isolated region with bright and halo Hα emission has produced results that are comparable to those found on the larger scale: the isolated region, as a whole, is also not in ionization balance.</p> <p>In the case of NGC 6822, four distinct components of the Hα emission (bright, halo, diffuse and field) differentiated by their surface brightnesses have been identified. We find that only 1/4 of the OB stars are found in the combined bright and halo regions, suggesting that OB stars spend roughly 3/4 of their lifetimes outside "classical" HII regions. Molecular cloud lifetimes after forming OB stars could be as low as ~1-3x10⁶ yrs or 1/4 the typical main sequence lifetimes of OB stars if OB stars escape from bright HII regions by destroying their parent clouds. Additionally, the field population of OB stars cannot have originated in and percolated out of existing HII regions. Comparing the observed Hα emission with that predicted from BV photometry and stellar ionizing flux models, we find that although the bright, halo and diffuse regions are probably in a state of ionization balance, the field region, which is producing at least 6 times as much ionizing flux as is observed, is clearly not. The ionization balance results suggest that star formation rates obtained from Hα luminosities must underestimate the true star formation rate in NGC 6822 by about 50%. Comparing the results for NGC 6822 and M33 reveals that the inner kiloparsec region of M33 is in a more serious state of ionization imbalance, perhaps due to its higher surface density of blue stars. Thus the morphological class or surface density of a galaxy may be important factors in how accurately we can determine star formation rates from Hα luminosities.</p> <p>Finally, we have performed optical spectroscopy of luminous blue stars in both NGC 6822 and M33 using respectively, the 4-m CTIO telescope plus ARGUS spectrograph and the 4-m Mayall telescope at KPNO plus HYDRA spectrograph. Due to the limited S/N ratio of the data, we have been able to classify only ~50% of the stars observed in NGC 6822 and ~40% of the stars observed in M33. Out of the 37 NGC 6822 and 15 M33 stars with classifiable spectra respectively 28 and 11 potential OB stars have been identified. We have used the NGC 6822 spectra to gauge the reliability of the principle stellar ionization model used for the ionization balance calculations in both galaxies.</p> / Doctor of Philosophy (PhD)