Physics Theses and Dissertations
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Item Partially Covariant Quantum Theory of Gravitation(1972) Moncrief, Vincent E.; Nutku, Yavuz; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, MD)In this thesis it is argued that a strict law of conservation of probability is necessary for the unambiguous interpretation of any proposed quantum theory of gravitation. After a brief review of the current canonicnl methods for quantizing the gravitational field we conclude that they do not guarantee conservation of probability owing to the difficulty of finding a suitable intrinsic time coordinate. In an attempt to circumvent this problem we have proposed an alternative method of quantization which has a conventional Schrodinger equation and therefore a law of probability conservation. This result is achieved by imposing a weaker form of the quantum constraint equations than that of the conventional theory. In order to justify this approach it is necessary to show that, in spite of the weak form of the constraint equations, the Einstein theory is recovered in the classical limit . A partial proof of the desired result is given. The proposed quantum theory is developed somewhat by considering the interaction of matter and gravitational fields. Quantum analogs of the covariant conservation laws are derived for the special case of a massive spin-zero field. Charge conservation is also considered and an invariant scheme for defining the number of particles and anti-particles is developed.Item Investigation of Vanishing of a Horizon for Bianchi Type IX (the Mixmaster) Universe(1972) Chitre, D.M.; Misner, Charles W.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)In this dissertation, the generic, non-rotating, homogeneous closed model universe ( the "Mixmaster Universe", Bianchi Type IX) is studied to gain some insight into how the broad-scale homogeneity of the universe may have been produced at very early times. We begin our discussion by sketching the development of relativistic cosmology until the last decade. In the second chapter we discuss particle horizons in the Robertson-Walker models. These standard models of the universe possess particle horizons. Thus, only a finite part of such a universe could have been causally connected; while the isotropy of 2.7°K microwave radiation implies the universe to be homogeneous on a much larger scale than the size of the horizon. The third chapter discusses in detail the evolution of the Mixmaster Universe near the singularity using the Hamiltonian techniques developed by Misner for these models . At a fixed time (or volume) epoch Ω0, a Mixmaster Universe is specified by initial conditions' β+, β- (shape anisotropy) and p+ , p- (expansion rate anisotropy). In the fourth chapter we derive the equations for rays of high-frequency sound waves and light waves. When these equations are applied in the Mixmaster Universe, we find that for certain subsets of initial conditions, some of these sound rays and light rays would circumnavigate the corresponding universes in certain directions. Our results for light rays parallel those of Doroshkevich and Novikov, however we use entirely different methods (Hamiltonian methods) for treating the Einstein equations. In the last chapter the evolution of the Mixmaster Universe is shown equivalent to a geodesic flow within a bounded region of the Lobatchewsky plane. The boundary shape makes this flow Ergodic. The ergodicity is proved by invoking a certain group of conformal transformations, G, which makes this flow of broken geodesics on the Lobatchewsky plane, D, into a continuous one on D/G. The Einstein equations in this problem lead to a natural measure on initial conditions related to β+, p+. The measure of the circumnavigation sets depends upon the epoch and it goes to zero as the volume of the universe shrinks to zero. Finally, we compute the probability for circumnavigation along any one axis of the universe, It turns out to be roughly 1% for an empty universe and it decreases to 0.02% for realistic models containing radiation and matter in them.Item Continuous Imaginary Time Histories Representing Black Hold Nucleation in Desitter Spacetime(2000) Branoff, Paul M.; Brill, Dieter R.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)We address the issues involved in finding and constructing continuous imaginary time histories (CITHs) representing black hold nucleation in a background de Sitter spacetime. Such rates are often calculated by adopting the instanton methods used to calculate ordinary particle-antiparticle production rates in background fields. Unlike the particle production case, there are certain instances of black hole nucleation described by two separate and distinct solution to the Euclidean Einstein's equations, i.e., the instanton is disconnected. Hence, one must justify including such histories in a path integral. We first discuss the existence of continuous imaginary time histories for black hole nucleation in theories consisting of modifications to Einstein's equations. First, we consider adding powers of the Ricci scalar to Einstein-Hilbert gravity with a cosmological constant. When the higher curvature coupling constants are negative, we find continuous instantons describing a background de Sitter to de Sitter transition characterized by a periodic, non-singular scale factor α (τ). Negative coupling constants imply an equivalent theory of Einstein gravity coupled to a negative energy density scalar field. This motivates our exploration of Einstein gravity coupled to Narlikar's negative energy density C-field. We again find a continuous background instanton, but such a solution exists only when small violations of the Hamiltonian constraint are allowed. Because of the unattractive features of the above solutions, we explore how one can construct CITHs by surgically altering the disconnected instanton. In the spirit of the path integral, we claim that one should sum over all possible geometries which can connect the instanton. We limit attention to connections with topology S^3 and S^1 x S^2. We find that the S^3 connection is preferred in the context of "no-boundary" quantum cosmology. However, we believe that the S^1 x S^2 connection may be more preferred for two reasons. First, the S^1 x S^2 connection allows two of its dimensions to-be large, implying via holography, that information from the initial state can "survive" the near-annihilation, recreation process. Second, Planck sized perturbations on the S^2 portion of the connection give rise to more histories over which to sum in the path integral.Item A Direct Measurement of the Relativistic Effect of the Gravitational Potential on the Rats of Atomic Clocks Flown in an Aircraft(1976) Williams, Ralph Emerson; Alley, C . O.; Physics and Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)General relativity predicts that standard clocks placed at differing gravitational potentials will run at different rates. Although experiments confirming the gravitational redshift have been done, they involve frequency and not time, and need not appeal to general relativity for explanation. Therefore, considerable interest exists as to the result of an accurate experiment in which real macroscopic clocks are brought together for comparison before and after separation to differing potentials. This experiment consists of flying an ensemble of atomic clocks in a military aircraft and comparing them before and after flight to another clock ensemble remaining on the ground. The ground ensemble included several Hewlett-Packard Cesium Beam clocks, three Efratom optically pumped Rubidium clocks, and two hydrogen masers. The flying ensemble included at least three Hewlett-Packard Cesium clocks and three Efratom Rubidium clocks. Five of the Cesium clocks were new models delivered with a high beam current option resulting in higher stability than standard models. The clocks were maintained under stringent environmental controls to protect against vibration, magnetic fields, and changes in temperature, pressure, and power supply voltage. Five main flights were ma de, each at approximately 30,000 feet altitude for fifteen hours. The aircraft was continuously tracked by a theodolite calibrated radar which obtained position and velocity measurements for every second of flight. This allowed an accurate calculation of a theoretical prediction to compare to experiment. The flying clocks gained approximately 45 nanoseconds (45 x 10-9 s) with respect to the ground clocks. The normalized results (measured effect divided by predicted effect) and the experimental standard deviations of the mean for each of the five flights were as follows: .999 + .016 .977 + .026 .963 + .013 1.002 + .026 .991 + .037 The result for the entire experiment, with standard deviation of the mean, was .987 ±. .011. The statistically expected standard deviation of the mean based on knowledge of clock quality was approximately .015. Considering this result as well as systematic errors, a final result is established of Measured value/ Predicted value = 0.987 ± .016Item Energy Dependence of the Effective Interaction for Nucleon-Nucleus Scattering(1990) Seifert, Helmut; Kelly, James J.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)We have measured cross sections and analyzing powers for 40, 42, 44, 48Ca and 16O at IUCF using the new high-resolution K600 spectrometer for 100 and 200 MeV protons. Measurements at 318 MeV for 40, 42, 44 ,48Ca and 32 ,34S were done at LAMPF using the HRS spectrometer. In this work, we obtain empirical effective interactions by fitting inelastic scattering data for many low-lying normal-parity isoscalar excitations of the self-conjugate nuclei 16O and 40Ca, assuming a local tp folding model. One-nucleon transition densities are from (e, e') . The fitted interactions are iterated to generate optical potentials self-consistently. We find that the fitted parameters are essentially target independent, which supports the validity of the local density hypothesis. Elastic scattering is predicted by extracting the rearrangement factor (1 + pd/dp) from the fitted in elastic interactions. Below 300 MeV the strength of the empirical interaction is reduced at zero density and the general density dependence is weaker compared to the theoretical interaction. Above 300 MeV we find the density dependence is stronger than expected. The empirical interactions provide better descriptions of elastic and inelastic data than IA calculations or LDA calculations using theoretical G-matrices, and can be used for nuclear structure studies of other nuclei . Fitted optical potentials above 300 MeV are comparable to equivalent Schrödinger potentials from the relativistic IA2 model.Item LOCAL MOLECULAR FIELD THEORY FOR NON-EQUILIBRIUM SYSTEMS(2019) Baker III, Edward Bigelow; Weeks, John D; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Local Molecular Field (LMF) theory is a framework for modeling the long range forces of a statistical system using a mimic system with a modified Hamiltonian that includes a self consistent molecular potential. This theory was formulated in the equilibrium context, being an extension of the Weeks Chandler Andersen (WCA) theory to inhomogeneous systems. This thesis extends the framework further into the nonequilibrium regime. It is first shown that the equilibrium derivation can be generalized readily by using a nonequilibrium ensemble average and its relevant equations of motion. Specifically, the equations of interest are fluid dynamics equations which can be generated as moments of the BBGKY hierarchy. Although this approach works well, for the application to simulations it is desirable to approximate the LMF potential dynamically during a single simulation, instead of a nonequilibrium ensemble. This goal was pursued with a variety of techniques, the most promising of which is a nonequilibrium force balance approach to dynamically approximate the relevant ensemble averages. This method views a quantity such as the particle density as a field, and uses the statistical equations of motion to propagate the field, with the forces in the equations computed from simulation. These results should help LMF theory become more useful in practice, in addition to furthering the theoretical understanding of near equilibrium molecular fluids.Item Quantum Compiling Methods for Fault-Tolerant Gate Sets of Dimension Greater than Two(2019) Glaudell, Andrew Noble; Taylor, Jacob M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Fault-tolerant gate sets whose generators belong to the Clifford hierarchy form the basis of many protocols for scalable quantum computing architectures. At the beginning of the decade, number-theoretic techniques were employed to analyze circuits over these gate sets on single qubits, providing the basis for a number of state-of-the-art quantum compiling algorithms. In this dissertation, I further this program by employing number-theoretic techniques for higher-dimensional gate sets on both qudit and multi-qubit circuits. First, I introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. I show that these canonical forms are T-optimal and describe an algorithm which takes as input a Clifford+T circuit and outputs the canonical form for that operator. The algorithm runs in time linear in the number of gates of the circuit. Our results provide a higher-dimensional generalization of prior work by Matsumoto and Amano who introduced similar canonical forms for single-qubit Clifford+T circuits. Finally, we show that a similar extension of these normal forms to higher dimensions exists, but do not establish uniqueness. Moving to multi-qubit circuits, I provide number-theoretic characterizations for certain restricted Clifford+T circuits by considering unitary matrices over subrings of Z[1/√2, i]. We focus on the subrings Z[1/2], Z[1/√2], Z[1/√−2], and Z[1/2, i], and we prove that unitary matrices with entries in these rings correspond to circuits over well-known universal gate sets. In each case, the desired gate set is obtained by extending the set of classical reversible gates {X, CX, CCX} with an analogue of the Hadamard gate and an optional phase gate. I then establish the existence and uniqueness of a normal form for one of these gate sets, the two-qubit gate set of Clifford+Controlled Phase gate CS. This normal form is optimal in the number of CS gates, making it the first normal form that is non-Clifford optimal for a fault tolerant universal multi-qubit gate set. We provide a synthesis algorithm that runs in a time linear in the gate count and outputs the equivalent normal form. In proving the existence and uniqueness of the normal form, we likewise establish the generators and relations for the two-qubit Clifford+CS group. Finally, we demonstrate that a lower bound of 5 log2 (1/ε) + O(1) CS gates are required to ε-approximate any 4 × 4 unitary matrix. Lastly, using the characterization of circuits over the Clifford+CS gate set and the existence of an optimal normal form, I provide an ancilla-free inexact synthesis algorithm for two-qubit unitaries using the Clifford+SC gate set for Pauli-rotations. These operators require 6 log2 (1/ε) + O(1) CS gates to synthesize in the typical case and 8 log2 (1/ε) + O(1) in the worst case.Item STUDIES IN NONEQUILIBRIUM QUANTUM THERMODYNAMICS(2019) Smith, Andrew Maven; Jarzynski, Christopher; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The first part of this thesis focuses on verifying the quantum nonequilibrium work relation in the presence of decoherence. The nonequilibrium work relation is a generalization of the second law of thermodynamics that links nonequilibrium work measurements to equilibrium free energies via an equality. Despite being well established for classical systems, a quantum work relation is conceptually difficult to construct for systems that interact with their environment. We argue that for a quantum system which undergoes decoherence but not dissipation, these conceptual difficulties do not arise and the work relation can be proven similarly to the case of an isolated system. This result is accompanied by an experimental demonstration using trapped ions. The second part of this thesis examines the relationship between quantum work and coherence by constructing analogous quantities in classical physics. It has recently been shown that quantum coherence can function as a resource for work extraction. Furthermore, it has been suggested that this property could be a truly quantum aspect of thermodynamics with no classical analog. We examine this assertion within the framework of classical Hamiltonian mechanics and canonical quantization. For classical states we define a so called non-uniformity measure and show that it is a resource for work extraction similar to quantum coherence. Additionally, we show that work extracted from non-uniformity and coherence agree in the classical limit. This calls into question the idea that coherence qualitatively separates classical and quantum thermodynamics. The final part of this thesis explores the connection between decoherence and adiabatic (quasistatic) driving. This topic is inspired by an experiment where it was seen that strong dephasing suppressed energy level transitions. Using a perturbative method we investigate this mechanism in the regime of small to moderate decoherence rate and ask if decoherence can help suppress energy transitions when compared with an adiabatic process without decoherence. We find that strategies that include decoherence are inferior to those where decoherence is absent.Item Topological dispersion relations in spin-orbit coupled Bose gases(2019) Valdes Curiel, Ana; Spielman, Ian; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum degenerate gases have proven to be an ideal platform for the simulation of complex quantum systems. Due to their high level of control it is possible to readily design and implement systems with effective Hamiltonians in the laboratory. This thesis presents new tools for the characterization and control of engineered quantum systems and describes their application in the realization of a topological system with Rashba-type spin-orbit coupling. The underlying properties of these engineered systems depend on their underlying energies. I describe a Fourier transform spectroscopy technique for characterizing the single particle spectrum of a quantum system. We tested Fourier spectroscopy by measuring the dispersion relation of a spin-1 spin-orbit coupled Bose-Einstein condensate (BEC) and found good agreement with our predictions. Decoherence due to uncontrolled fluctuations of the environment presents fundamental obstacles in quantum science. I describe an implementation of continuous dynamical decoupling (CDD) in a spin-1 BEC. We applied a strong radio-frequency (RF) magnetic field to the ground state hyperfine manifold of Rubidium-87 atoms, generating a dynamically protected dressed system that was first-order insensitive to changes in magnetic field. The CDD states constitute effective clock states and we observed a reduction in sensitivity to magnetic field of up to four orders of magnitude. We additionally show that the CDD states can be coupled in a fully connected geometry and thus enable the implementation of new models not possible using the bare atomic states. Finally, I describe a new realization of Rashba-type SOC using Raman coupled CDD states. Our system had non-trivial topology but no underlying crystalline structure that yields integer valued Chern numbers in conventional materials. We validated our procedure using Fourier transform spectroscopy to measure the full dispersion relation containing only a single Dirac point. We measured the quantum geometry underlying the dispersion relation and obtained the topological index using matter-wave interferometry. In contrast to crystalline materials, where topological indices take on integer values, our continuum system reveals an unconventional half-integer Chern number.Item QUANTUM ALGORITHMS FOR DIFFERENTIAL EQUATIONS(2019) Ostrander, Aaron Jacob; Childs, Andrew; Monroe, Chris; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis describes quantum algorithms for Hamiltonian simulation, ordinary differential equations (ODEs), and partial differential equations (PDEs). Product formulas are used to simulate Hamiltonians which can be expressed as a sum of terms which can each be simulated individually. By simulating each of these terms in sequence, the net effect approximately simulates the total Hamiltonian. We find that the error of product formulas can be improved by randomizing over the order in which the Hamiltonian terms are simulated. We prove that this approach is asymptotically better than ordinary product formulas and present numerical comparisons for small numbers of qubits. The ODE algorithm applies to the initial value problem for time-independent first order linear ODEs. We approximate the propagator of the ODE by a truncated Taylor series, and we encode the initial value problem in a large linear system. We solve this linear system with a quantum linear system algorithm (QLSA) whose output we perform a post-selective measurement on. The resulting state encodes the solution to the initial value problem. We prove that our algorithm is asymptotically optimal with respect to several system parameters. The PDE algorithms apply the finite difference method (FDM) to Poisson's equation, the wave equation, and the Klein-Gordon equation. We use high order FDM approximations of the Laplacian operator to develop linear systems for Poisson's equation in cubic volumes under periodic, Neumann, and Dirichlet boundary conditions. Using QLSAs, we output states encoding solutions to Poisson's equation. We prove that our algorithm is exponentially faster with respect to the spatial dimension than analogous classical algorithms. We also consider how high order Laplacian approximations can be used for simulating the wave and Klein-Gordon equations. We consider under what conditions it suffices to use Hamiltonian simulation for time evolution, and we propose an algorithm for these cases that uses QLSAs for state preparation and post-processing.