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 The Li6(a,2a)d Reaction at 50 to 80 MeV(1970) Watson, John W.; Pugh, Howel G.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)The Li6(a,2a)d reaction was studied at 50.4, 59.0, 60.5, 70.3 and 79.6 MeV bombarding energy. For each bombarding energy, several coincident energy spectra of the two emitted a-particles were measured. Special emphasis was placed on measuring spectra at pairs of angles where zero momentum (in the laboratory frame of reference) was possible for the residual deuteron. Using the constraints on three body kinematics, events corresponding to an a+ a+ d final state were selected from the coincident energy spectra. The cross section for these events was projected onto the E1 energy axis of the coincident spectra. The projected energy spectra were analyzed with the Plane Wave Impulse Approximation. From those points in the projected spectra which corresponded to zero deuteron recoil momentum, off-mass-shell a-a scattering cross sections were extracted. These were found to be in excellent agreement with free a-a scattering cross sections, if free cross sections for the final state center of mass energy of the two a's in the Li6 (a,2a)d reaction were chosen for the comparison. Off- mass-shell a-a cross sections were also extracted for data where the residual deuteron had a momentum of 30 MeV/c. These cross sections were also found to agree with free a-a scattering, but it was necessary to introduce an ad hoc shift in the a-a scattering angle to produce this agreement. Predictions of off-mass-shell a-a cross sections were made using a potential model. These indicate that the off-mass-shell cross section should indeed be very similar to the on-mass-shell cross section at the final state energy. Using the Plane Wave Impulse Approximation a momentum distribution for a's in Li6 was extracted from the experimental data. A cluster model for Li6 was devised to fit the binding energy and r.m.s. charge radius of Li6, as well as the 3s1 a-d scattering phase shift. For comparison with the experimental data, the momentum wave function of the a-particle in Li6 was calculated by taking the Fourier transform of the a-d relative motion. The theoretical and experimental momentum distributions were found to be in serious disagreement, both in magnitude and width at half maximum. By introducing a cut-off radius into the theoretical wave function, the discrepancies between theory and experiment were accounted for. It was also found, that if the cut-off radius is used as an adjustable parameter, then this Li6 wave function and reaction model explains the magnitudes and widths of the a-d relative momentum distributions determined from a wide variety of other reactions.Item A Field Theory of Extended Particles Based on Covariant Harmonic Oscillator Wavefunctions(1976) Karr, Thomas John; Kim, Young Suh; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)We attempt to combine the covariant harmonic oscillator (CHO) quark model with second quantized field theory. We review the CHO formalism for a system of two quarks (meson). We introduce a mesonic field Φ(x1 ,x2) that depends on the position of both quarks, and then derive the field equations from a covariant lagrangian L(x1, x2). The CHO equation allows a complete separation of the average meson coordinate X from the relative quark coordinate ξ. The CHO wavefunction in the field expresses the extended size and internal structure of the meson. Φ, describes mesons in the ground state and any excited state , with angular momentum ∞ mass^2. From Φ we construct conserved tensors like P^μ the meson momentum. We second quantize Φ in the X variable only and discuss the extended particle commutation relations. We investigate a Φ^3-type meson interaction where the vertex function is an overlap integral of the wavefunctions entering the interaction region. We derive a nonlinear integrodifferential equation for the U matrix , linearize and solve it by perturbation theory. The result is simple diagramatic rules for the S matrix. The S matrix is covariant and unitary. We do not find any contradiction between the principles of QFT and the CHO quark model. The Φ field theory includes scalar meson(point particle)theory as a special case, while its greater generality illuminates the difference between point and extended particles.Item Lie Algebraic Methods for Treating Lattice Parameter Errors in Particle Accelerators(1986) Healy, Liam Michael; Dragt, Alex J.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Orbital dynamics in particle accelerators, and ray tracing in light optics, are examples of Hamiltonian systems. The transformation from initial to final phase space coordinates in such systems is a symplectic map. Lie algebraic techniques have been used with great success in the case of idealized systems to represent symplectic maps by Lie transformations. These techniques allow rapid computation in tracking particles while maintaining complete symplecticity, and easy extraction of analytical quantities such as chromaticities and aberrations. Real accelerators differ from ideal ones in a number of ways. Magnetic or electric devices, designed to guide and focus the beam, may be in the wrong place or have the wrong orientation, and they may not have the intended field strengths. The purpose of this dissertation is to extend the Lie algebraic techniques to treat these misplacement, misalignment and mispowering errors. Symplectic maps describing accelerators with errors typically have first-order terms. There are two major aspects to creating a Lie algebraic theory of accelerator errors: creation of appropriate maps and their subsequent manipulation and use. There are several aspects to the manipulation and use of symplectic maps. A first aspect is particle tracking. That is, one must find how particle positions are transformed by a map. A second is concatenation, the combining of several maps into a single map including nonlinear feed-down effects from high-order elements. A third aspect is the computation of the fixed point of a map, and the expansion of a map about its fixed point. For the case of a map representing a full turn in a circular accelerator, the fixed point corresponds to the closed orbit. The creation of a map for an element with errors requires the integration of a Hamiltonian with first-order terms to obtain the corresponding Lie transformation. It also involves a procedure for the complete specification of errors, and the generation of the map for an element with errors from the map of an ideal element. The methods described are expected to be applicable to other electromagnetic systems such as electron microscopes, and also to light optics systems.Item Vapor Pressures of Saturated Aqueous Salt Solutions of Selected Inorganic Salts(1965) Acheson, Donald Theodore; Mason, Edward A.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)The vapor pressure of saturated aqueous salt solutions as functions of temperature have been measured for lithium bromide, lithium iodide, sodium bromide, potassium hydroxide, cesium fluoride, and zinc bromide. The temperature range is about plus s 0 c. to 70°c., with this range extended from minus 10°c. to plus 105°c. for lithium bromide and restricted to plus s 0 c. to 35°c. for sodium bromide. Vapor pressures, water 0 activities, and heats of vaporization and solution are tabulated at 5 C. intervals except in the vicinities of changes of hydration of the solid phase, where pressures and activities are plotted with sufficient frequency to show details. The experimental uncertainty in pressure is + 10 x 10-3 millibars and that in the heat of solution is+ 2 percent.Item Topics in Nonlinear Wave Theory With Applications(1984) Tracy, Eugene Raymond; Chen, Hsing Hen; Physics; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Selected topics in nonlinear wave theory are discussed and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasiperiodic solutions to several nonlinear wave equations which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schrodinger equation, an equation with general applicability in one dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in our numerical studies, and the numerical work of other authors. The method of solution (related to the Inverse Scattering Method) is then analyzed within te context of Hamiltonian dynamics where we show that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation which appears here and in the work of other authors is shown to be a special form of Liouville's Transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's Inversion Problem, is surveyed briefly.