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A new technique for the interferometric measurement of an atomic wavefunction is introduced theoretically, which is able to extract phase and amplitude information in a single measurement. I focus on the application of this technique to the single-particle wavefunction of a Bose condensed cloud of rubidium atoms. The technique differs from existing techniques mainly in its simplicity, as it requires only a single laser beam to be added to a typical Bose-Einstein condensation apparatus. A second novel aspect is the consideration of condensate collisions with an optical potential in the low-intensity limit where the potential barrier may be viewed as a phase mask. The technique is then demonstrated experimentally. A related effect, the transient enhancement of momentum during a collision, first predicted by JG Muga et al., has also been demonstrated. Finally, significant redesign and construction of an apparatus to produce condensates of 87Rb is documented. The main result of this work is the production of pure condensates of up to 150k atoms which can be repeated every 45s. A calibration technique is devised and demonstrated, whereby copies of the condensate are made, and the copies are used to reduce the centre-of-mass momentum uncertainty of the interacting cloud by a factor of five.

A new technique for the interferometric measurement of an atomic wavefunction is introduced theoretically, which is able to extract phase and amplitude information in a single measurement. I focus on the application of this technique to the single-particle wavefunction of a Bose condensed cloud of rubidium atoms. The technique differs from existing techniques mainly in its simplicity, as it requires only a single laser beam to be added to a typical Bose-Einstein condensation apparatus. A second novel aspect is the consideration of condensate collisions with an optical potential in the low-intensity limit where the potential barrier may be viewed as a phase mask. The technique is then demonstrated experimentally. A related effect, the transient enhancement of momentum during a collision, first predicted by JG Muga et al., has also been demonstrated. Finally, significant redesign and construction of an apparatus to produce condensates of 87Rb is documented. The main result of this work is the production of pure condensates of up to 150k atoms which can be repeated every 45s. A calibration technique is devised and demonstrated, whereby copies of the condensate are made, and the copies are used to reduce the centre-of-mass momentum uncertainty of the interacting cloud by a factor of five.

<P> Solving the electronic Schrodinger equation for the molecular wavefunction is the central problem in theoretical chemistry. From these wavefunctions (possibly with relativistic corrections), one may completely characterise the chemical reactivity and physical properties of atoms, molecules, and materials. Unfortunately, there are very few systematic approaches for obtaining highly-accurate molecular wavefunctions. The approaches that do exist suffer from the so-called curse of dimensionality: their computational cost grows exponentially as the number of particles increases. Furthermore, even after obtaining an accurate wavefunction, partitioning the molecule into atoms is not straightforward. This is because the kinetic energy operator is a differential operator in spatial coordinates. This is a source of ambiguity in the definition of an atom-in-a-molecule and the associated atomic properties. Even after selecting an appropriate definition of an atom and obtaining the atoms from the wavefunction, the atom's intrinsic reactivity cannot be completely characterised without considering every possible reaction partner. This is because each set of two molecules produces a new wavefunction that is more complicated than the products of the wavefunctions of the separate molecules. </p> <P> This thesis presents methods for addressing the three challenges raised in the previous paragraph: computing atomic properties (e.g. chemical reactivity), partitioning molecules into atoms, and computing accurate molecular wavefunctions. The first challenge is addressed by developing a general-purpose reactivity indicator to quantify the reactivity of an atom within a molecule. This indicator quantifies the reactivity of any point of the molecule using only the electrostatic potential and Fukui potential at that point. The key idea is to include only a vague description of an incoming molecule and compute an approximate interaction with the incoming object; this ensures that the general-purpose reactivity indicator is simple enough to be useful. Practically, this indicator is most useful when it is used to compute the reactivity of the atomic sites in the molecule of interest. </p> <P> Partitioning a molecule into atoms is not straightforward because of the inherent nonlocality of quantum mechanics. In the context of molecular electronic structure, this nonlocality arises from the nature of the kinetic energy operator. The quantum theory of atoms in molecules (QTAIM) is a popular method that partitions molecules into atoms. QT AIM resolves the problem of ambiguity for all permissible forms of the kinetic energy operator. In this thesis the characterisation of an atom provided by QT AIM is extended to include relativistic contributions in the zero-order regular approximation (ZORA). The intrinsic ambiguity arising from the kinetic energy operator is also examined in detail. </p> <P> Computing atomic or molecular properties (including computing the general-purpose reactivity indicator) almost always requires a wavefunction. For this reason, obtaining accurate wavefunctions is the central hurdle of quantum chemistry. This thesis proposes algorithms for finding high-accuracy molecular wavefunctions without exponentially exploding computational cost. To do this, tools for exploiting the smoothness of electronic wavefunctions are crafted. Computational methods that use these tools can break the curse of exponential scaling without sacrificing accuracy. Specifically, the computation cost of these new methods grows only as some polynomial of the electron number. The wavefunctions obtained from these methods are much simpler than those from conventional approaches of similar accuracy, and are therefore ideal for computing the electron density and atomic properties. </p> / Thesis / Doctor of Philosophy (PhD)

This thesis is devoted to a study of the effect of disorder on strongly correlated electrons. For non-interacting electrons, Anderson localization occurs if the amount of disorder is sufficient. For disorder-free systems, a Mott metal-insulator transition may occur if the electron-electron interactions are strong enough. The question we ask in this thesis is what happens when both disorder and interactions are present. We study the Anderson-Hubbard model, which is the simplest model to include both interactions and disorder, using a Gutzwiller variational wave function approach. We then study Anderson localization of electrons from the response of the Anderson-Hubbard Hamiltonian to an external magnetic field. An Aharonov-Bohm flux induces a persistent current in mesoscopic rings. Strong interactions result in two competing tendencies: they tend to suppress the current because of strong correlations, and they also screen the disorder potential and making the system more homogenous. We find that, for strongly interacting electrons, the localization length may be large, even though the current is suppressed by strong correlations. This unexpected result highlights how strongly correlated materials can be quiet di erent from weakly correlated ones. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2011-08-31 09:51:47.155

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京都大学 / 新制・課程博士 / 博士(理学) / 甲第24964号 / 理博第4989号 / 新制||理||1712(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)准教授 倉重 佑輝, 教授 渡邊 一也, 教授 林 重彦 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Electronic structure methods aim to accurately describe the behaviour of the electrons in molecules and materials. To be applicable to arbitrary systems, these methods cannot depend on observations of specific chemical phenomena and must be derived solely from the fundamental physical constants and laws that govern all electrons. Such methods are called ab initio methods. Ab initio methods directly solve the electronic Schrödinger equation to obtain the electronic energy and wavefunction. For more than one electron, solving the electronic Schrödinger equation is impossible, so it is imperative to develop approximate methods that cater to the needs of their users, which can vary depending on the chemical systems under study, the available computational resources and time, and the desired level of accuracy. The most accessible ab initio approaches, including Hartree-Fock methods and Kohn-Sham density functional theory methods, assume that only one electronic configuration is needed to describe the system. While these single-reference methods are successful when describing systems where a single electron configuration dominates, like most closed-shell ground-state organic molecules in their equilibrium geometries, single-reference methods are unreliable for molecules in nonequilibrium geometries (e.g., transition states) and molecules containing unpaired electrons (e.g., transition metal complexes and radicals). For these types of multireference systems, accurate results can only be obtained if multiple electronic configurations are accounted for. Wavefunctions that incorporate many electronic configurations are called multideterminant wavefunctions. This thesis presents a systematic approach to developing multideterminant wavefunctions. First, we establish a framework that outlines the structural components of a multideterminant wavefunction and propose several novel wavefunction ansätze. Then, we present a software package that is designed to aid the development of new wavefunctions and algorithms. Using this approach, we develop an algorithm for evaluating the geminal wavefunctions, a class of multideterminant wavefunctions that are expressed with respect to electron pairs. Finally, we explore using machine learning to solve the Schrödinger equation by presenting a neural network wavefunction ansatz and optimizing its parameters using stochastic gradient descent. / Thesis / Doctor of Science (PhD)

In the exploration of chemical systems through quantum mechanics, accurate treatment of the electron wavefunction, and the related electron density, is fundamental to extracting information concerning properties of a system. This work examines challenges in achieving accurate chemical information through manipulation of the one-electron basis set.