Visualizing Quantum Reactive Scattering Dynamics

The Born-Oppenheimer approximation, which allows a decoupling of electronic and nuclear motion, underlies the investigation of molecular dynamics. In some cases this decoupling is not possible, so that nuclear motion can induce changes in electronic state. It is then necessary to account for collision-induced transitions between multiple potential energy surfaces. This is an inherently quantum phenomena. In this dissertation we present a new way to visualize these non-adiabatic transitions in chemical reactions of open-shell atoms. Toward this end, we have developed new algorithms and developed a MATLAB-based software suite for simulating non-adiabatic reactions. We have also determined new molecular potential energy surfaces and their couplings required to simulate the reactive dynamics

Ultracold Atom-Atom Scattering with R-Matrix Methods

Novel experimental methods have allowed for the routine production of ultracold (sub-Kelvin) atoms and small molecules. This has facilitated the study of chemical reactions involving only a small number of partial waves, allowing for unprecedented control over ultracold chemical reactions. This thesis describes work towards a new set of theories, based on Wigner's R-matrix methodology, which are adapted for so-called heavy particle scattering, and in particular atom-atom scattering. From these new theories a new set of methods are constructed to accurately simulate scattering observables such as scattering lengths, cross-sections, and resonances for atom-atom scattering events at ultracold temperatures by producing high resolution plots of these observables. The methods utilise software built for high-accuracy diatomic spectra, such as Duo, to provide molecular eigenenergies and wavefunctions of the bound system at short internuclear distances (in a region known as the inner region), only requiring as input a matrix of diatomic internuclear potential energy curves and couplings. These methods then act as 'harnesses', allowing this information to be used to perform an R-matrix propagation at long internuclear distances (in a region known as the outer region) using R-matrix propagation codes such as PFARM. The result of this propagation is then used to produce the aforementioned scattering observables. In this work these new R-matrix methods are applied to the case of a particle scattering off a Morse potential, to elastic argon-argon collisions, and to the intramultiplet mixing of oxygen when impacted by helium. This work also serves as a basis for the future simulation of more complex scattering events, such as atom-diatom collisions and higher polyatomic collisions

Quantum Theory of Complex Ultracold Collisions

This thesis reports on a variety of calculations on cold and ultracold scattering, with a broad theme of how best to consider and understand complex systems in simple ways. Firstly, we investigate quantum defect theory. We demonstrate that it is not only an excellent model for simple systems, but can also provide simple predictions of the \emph{range} of possible behaviours for complex systems, in particular for a model of collisional losses. These predictions agree well with expensive coupled-channels calculations in cases where the full calculations also predict only the range of possible behaviours. Secondly, we consider effects relating to thermalisation of cold and ultracold gases. We show that considering the correct transport cross section, $\sigma_\eta^{(1)}$, is important for determination of scattering lengths and their signs by interspecies thermalisation. This cross section is also important to the understanding of high-quality simulations of sympathetic cooling in a microwave trap, which suggest Rb is likely to be a good coolant for CaF. We also correct an error in the interpretation of previous results for sympathetic cooling in a magnetic trap, showing this may work from over 100 mK for Li+CaF and many Kelvin when using atomic hydrogen as a coolant. Thirdly, we study quantum chaos in ultracold collisions. We find very clear and strong signs of chaos in Li+CaH. We also show that a more strongly coupled system, Li+CaF, is \emph{not} fully chaotic and that there is unexpected structure in the levels of chaos as the CaF rotational constant is varied. We also show that signatures of chaos can emerge in a very simple atom-atom system, Yb(${}^1S_0$)+Yb(${}^3P_2$), which interacts on only two Born-Oppenheimer potentials. Finally, we examine the idea that metastable states in 2-body scattering greatly enhance 3-body recombination at ultracold temperatures. We attempt to put it on a more rigorous theoretical grounding by considering Smith's collision lifetime and related quantities, but those are shown to lack clear interpretations in the ultracold regime. We therefore consider 3-body scattering theory and arrive at some general conclusions about how we expect such 2-body features to appear in 3-body scattering and suggest possible ways forward

New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time's Arrow of Dynamical Systems

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the three-body problem to the 6\emph{th} order system. A new approach makes the system of geodesic equations with respect to the evolution parameter of a dynamical system (\emph{internal time}) \emph{fundamentally irreversible}. To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of internal time. This allows us to solve the extremely important quantum-classical correspondence problem for dynamical Poincar\'e systems.Comment: 66 pages, 10 figures, 91 reference

Cold and Ultracold Molecules: Science, Technology, and Applications

This article presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the Special Issue of the New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography, and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field.Comment: 82 pages, 9 figures, review article to appear in New Journal of Physics Special Issue on Cold and Ultracold Molecule

Bifunctionate Solutions to the Schrödinger Equation for Reactive, Three-Atom, Colinear Encounters

Two methods for solving the Schrödinger equation for one dimensional, three atom, electronically adiabatic, reactive collisions have been investigated. The first bifunctionate method was proposed by Diestler in 1969. It solves for vibrational excitation probabilities by expanding two parts of the total solution to the scattering problem in eigenfunctions of the unperturbed diatoms. These diatoms are the target and product diatoms in the reactive encounter. This formalism allows the eigenfunction series representation of the total solution to decay to zero in the interaction region of the reaction. Proposition 1 shows that this decay process is indicative of a failure in Diestler's method which renders its solutions invalid. A technique proposed as a means of solving the equations governing nuclear collisions was also investigated. This formalism, called the Method of Subtracted Asymptotics, has been shown to be an application of the general mechanism of eigenfunction expansion to the scattering problem. Because of analysis problems induced by the extensive eigenfunction series demanded by this method, the Method of Subtracted Asymptotics is not an efficient or practical manner of solving the scattering problem. This method is treated in part 2 of this work. Tests used to varify the numerical accuracy of several studies of the Method of Subtracted Asymptotics required the values of several special functions on the complex plane. To meet these needs, algorithms which compute the value of a complex number raised to a complex power, the Gamma function, the Digamma function and the Hyper geometric function were prepared. These algorithms are discussed and presented in part 1 of this thesis.</p

PROGRAM, THE NEBRASKA ACADEMY OF SCIENCES: One Hundred-Thirty-First Annual Meeting, APRIL 23-24, 2021. ONLINE

AFFILIATED SOCIETIES OF THE NEBRASKA ACADEMY OF SCIENCES, INC. 1.American Association of Physics Teachers, Nebraska Section: Web site: http://www.aapt.org/sections/officers.cfm?section=Nebraska 2.Friends of Loren Eiseley: Web site: http://www.eiseley.org/ 3.Lincoln Gem & Mineral Club: Web site: http://www.lincolngemmineralclub.org/ 4.Nebraska Chapter, National Council for Geographic Education 5.Nebraska Geological Society: Web site: http://www.nebraskageologicalsociety.org Sponsors of a $50 award to the outstanding student paper presented at the Nebraska Academy of SciencesAnnual Meeting, Earth Science /Nebraska Chapter, National Council Sections 6.Nebraska Graduate Women in Science 7.Nebraska Junior Academy of Sciences: Web site: http://www.nebraskajunioracademyofsciences.org/ 8.Nebraska Ornithologists’ Union: Web site: http://www.noubirds.org/ 9.Nebraska Psychological Association: http://www.nebpsych.org/ 10.Nebraska-Southeast South Dakota Section Mathematical Association of America: Web site: http://sections.maa.org/nesesd/ 11.Nebraska Space Grant Consortium: Web site: http://www.ne.spacegrant.org/ CONTENTS AERONAUTICS & SPACE SCIENCE ANTHROPOLOGY APPLIED SCIENCE & TECHNOLOGY BIOLOGICAL & MEDICAL SCIENCES COLLEGIATE ACADEMY: BIOLOGY COLLEGIATE ACADEMY: CHEMISTRY & PHYSICS EARTH SCIENCES ENVIRONMENTAL SCIENCES GENERAL CHEMISTRY GENERAL PHYSICS TEACHING OF SCIENCE & MATHEMATICS 2020-2021 PROGRAM COMMITTEE 2020-2021 EXECUTIVE COMMITTEE FRIENDS OF THE ACADEMY NEBRASKA ACADEMY OF SCIENCS FRIEND OF SCIENCE AWARD WINNERS FRIEND OF SCIENCE AWARD TO DR PAUL KAR