by Wah-chung Wong. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 155-162.

An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.

Thermal and quantum fluctuations of the electromagnetic near field of atoms and macroscopic bodies play a key role in quantum electrodynamics (QED), as in the Lamb shift. They lead, e.g., to atomic level shifts, dispersion interactions (Van der Waals-Casimir-Polder interactions), and state broadening (Purcell effect) because the field is subject to boundary conditions. Such effects can be observed with high precision on the mesoscopic scale which can be accessed in micro-electro-mechanical systems (MEMS) and solid-state-based magnetic microtraps for cold atoms (‘atom chips’). A quantum field theory of atoms (molecules) and photons is adapted to nonequilibrium situations. Atoms and photons are described as fully quantized while macroscopic bodies can be included in terms of classical reflection amplitudes, similar to the scattering approach of cavity QED. The formalism is applied to the study of nonequilibrium two-body potentials. We then investigate the impact of the material properties of metals on the electromagnetic surface noise, with applications to atomic trapping in atom-chip setups and quantum computing, and on the magnetic dipole contribution to the Van der Waals-Casimir-Polder potential in and out of thermal equilibrium. In both cases, the particular properties of superconductors are of high interest. Surface-mode contributions, which dominate the near-field fluctuations, are discussed in the context of the (partial) dynamic atomic dressing after a rapid change of a system parameter and in the Casimir interaction between two conducting plates, where nonequilibrium configurations can give rise to repulsion. / Thermische und Quantenfluktuationen des elektromagnetischen Nahfelds von Atomen und makroskopischen Körpern spielen eine Schlüsselrolle in der Quantenelektrodynamik (QED), wie etwa beim Lamb-Shift. Sie führen z.B. zur Verschiebung atomarer Energieniveaus, Dispersionswechselwirkungen (Van der Waals-Casimir-Polder-Wechselwirkungen) und Zustandsverbreiterungen (Purcell-Effekt), da das Feld Randbedingungen unterliegt. Mikroelektromechanische Systeme (MEMS) und festkörperbasierte magnetische Fallen für kalte Atome (‘Atom-Chips’) ermöglichen den Zugang zu mesoskopischen Skalen, auf denen solche Effekte mit hoher Genauigkeit beobachtet werden können. Eine Quantenfeldtheorie für Atome (Moleküle) und Photonen wird an Nichtgleichgewichtssituationen angepasst. Atome und Photonen werden durch vollständig quantisierte Felder beschrieben, während die Beschreibung makroskopischer Körper, ähnlich wie im Streuformalismus (scattering approach) der Resonator-QED, durch klassische Streuamplituden erfolgt. In diesem Formalismus wird das Nichtgleich- gewichts-Zweiteilchenpotential diskutiert. Anschließend wird der Einfluss der Materialeigenschaften von normalen Metallen auf das elektromagnetische Oberflächenrauschen, das für magnetische Fallen für kalte Atome auf Atom-Chips und für Quantencomputer-Anwendungen von Bedeutung ist, sowie auf den Beitrag des magnetischen Dipolmoments zum Van der Waals-Casimir-Polder-Potential im thermisch- en Gleichgewicht und in Nichtgleichgewichtssituationen untersucht. In beiden Fällen sind die speziellen Eigenschaften von Supraleitern von besonderem Interesse. Beiträge von Oberflächenmoden, die die Feldfluktuationen im Nahfeld dominieren, werden im Kontext des (partiellen) dynamischen Dressing nach einer raschen Änderung eines Systemparameters sowie für die Casimir-Wechselwirkung zweier metallischer Platten diskutiert, zwischen denen in Nichtgleichgewichtssituationen Abstoßung auftreten kann.

Due to the fast increasing capabilities of modern computers it is now feasible to calculate spectra of small atom and molecules with the greater level of accuracy than high-resolution measurements. The mathematical algorithms developed and implemented on high performance supercomputers for the quantum mechanical calculations are directly derived from the first principles of quantum mechanics. The codes developed are primarily used to verify, refine, and predict the energies associated within a given system and given angular momentum state of interest. The Hamiltonian operator used to determine the total energy in the approach presented is called the internal Hamiltonian and is obtained by rigorously separating out the center-of-mass motion (or the elimination of translational motion) from the laboratory-frame Hamiltonian. The methods utilized in the articles presented in this dissertation do not include relativistic corrections and quantum electrodynamic effects, nor do these articles assume the Born-Oppenheimer (BO) approximation with the exception of one publication. There is one major review article included herein which describes the major differences between the non-BO method and the BO approximation using explicitly correlated Gaussian (ECG) basis functions. The physical systems studied in this dissertation are the atomic elements with Z < 7 (although the discussion is not limited to these) and diatomic molecules such as H₂⁺ and H₂ including nuclear isotopic substitution studies with deuterium and tritium, as well as electronic substitutions with the muon particle. Preliminary testing for triatomic molecular functionals using a model potential is also included in this dissertation. It has been concluded that using all-particle ECGs with including the addition of nonzero angular momentum functions to describe nonzero angular momentum states is sufficient in determining the energies of these states for both the atomic and molecular case.

Solvent-free peroxide-initiated polymer modifications are widely used to improve the physical and/or chemical properties of commodity plastics and elastomers. Although the reactions that underlie polymer grafting are known, our understanding of H-atom transfer reactions in this context is incomplete. Fundamental questions remain unanswered, such as the difference in reactivity between different polymers (polyethylene versus polypropylene and polyisobutylene) and differences in the regiochemical outcomes of grafting reactions upon them. Herein, experimental data pertaining to the H-atom transfers involved in polyolefin graft modifications were obtained to improve our fundamental understanding of these reactions by using radical-trapping techniques and quantum chemical calculations. In this project, experimental measurements of the efficiency of H-atom abstraction by t-butoxyl radicals from polyolefins, and suitable model compounds such as pentane, 2,4-dimethylpentane and 2,2,4,4-tetramethylpentane were determined. Insight is gained from alkyl-trapping experiments to quantify the relative reactivities of the primary, secondary and tertiary positions of the model compounds. Experimental data were compared to quantum chemical calculations, which revealed that entropic effects dictate the regioselectivity and preclude abstraction at the secondary position in favour of the less enthalpically-favourable primary abstraction site. MP2 and CBS-QB3 level calculations were able to reproduce experimental trends in model compound reactivity, while the highly common B3LYP density functional, used in other investigations on the subject, could not. / Thesis (Master, Chemical Engineering) -- Queen's University, 2011-10-20 16:48:38.083

No description available.

This thesis discusses the theory and presents the numerical solution of the S-wave models of electron-hydrogen and electron-helium scattering. The Convergent Close-Coupling (CCC) method is used to obtain the numerical results. The focus within the electron-hydrogen S-wave model is to investigate cross section results for scattering from excited states; in particular, the elastic free-free transitions. These contain a divergent potential matrix element as the first term. The investigation of the electron-helium S-wave model is split into two sections, firstly applying the Frozen-Core approximation and then relaxing this approximation. This includes the first accurate ab initio calculation of double-excitation of helium.

In the last twenty years, electron-atom scattering theory has witnessed significant theoretical developments. One of these advances is the use of the momentum-space convergent closecoupling approach to fully incorporate target atom continua. This theoretical framework is based on the momentum-space Lippmann-Schwinger equation, an integral form of the Schrodinger equation. Although the approach has been highly successful in its application to atomic scattering theory, computing numerical solutions is inherently difficult because the momentum-space LS equation is a singular integral equation. Standard numerical integration techniques are normally employed to solve the problem and as computing power has increased, calculations have improved. However, there remains the problem of the integral's singular nature, which demands complicated methods for selecting integration points, particularly near the energy-dependant singularity. The rotated-contour method uses a conlplex-variable approach that solves the momentum-space LS equation by integrating along a deformed contour in the complex momentum plane away from the singularities. This method has the potential for simplifying the numerical integrations associated with the close-coupling equations. A rotated-contour method is first applied to a simple scattering model - electron scattering from the Yukawa potential. This gives some insight into the difficulties that arise when calculating potential matrix elements for complex momenta. The method is then applied to the s-wave model of the electron-hydrogen scattering problem and finally, the full problem. Existing FORTRAN software written to solve the momentum-space LS equations for electron-hydrogen scattering using standard techniques has been converted to C++. Extensive modification of the code has resulted in a flexible Windows-based program with a graphical user interface that runs on any modern computer using PC architecture. The program can calculate results using either a conventional method (no rotation) or a rotatedcontour method. Using a rotated-contour method to solve the momentum-space LS equations necessitates detailed knowledge of the analytic nature and singularity structure of the coupled channels potentials. This is achieved through the extensive use of the computer symbolic algebra system Maple to compute closed-form solutions for the direct potentials and for a range of partial-wave direct and exchange potentials. It is found that logarithmic branch point singularities are present on the real momentum axis for an extensive class of partial-wave direct-potential matrix elements. The analysis reveals that arotated contour method cannot be applied to the full atomic scattering problem due to these analytic problems which are associated with the long-range nature of the Coulomb potential.

Zugl.: Berlin, Freie Univ., Diss., 2005

München, Techn. University, Diss., 2007.