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Towards reading line profiles of Bardeen-Petterson accretion disks
Title
Towards reading line profiles of Bardeen-Petterson accretion disks.
Creator
Vandernoot, Eric P., Florida Atlantic University, Miller, Warner A.
Abstract/Description
Images of highly idealized Bardeen-Petterson accretion disks around Kerr black holes and their generated energy spectra line profiles are created via computer simulations in this work. The line profiles are examined in the relation to the original disk parameters to demonstrate that Bardeen-Petterson disks can be the source of the spectra we observe, even of actual systems. The challenges in computer programming the simulations and methods to overcome the challenges are discussed in the paper...
Show moreImages of highly idealized Bardeen-Petterson accretion disks around Kerr black holes and their generated energy spectra line profiles are created via computer simulations in this work. The line profiles are examined in the relation to the original disk parameters to demonstrate that Bardeen-Petterson disks can be the source of the spectra we observe, even of actual systems. The challenges in computer programming the simulations and methods to overcome the challenges are discussed in the paper. Also discussed are the future work, improvements and intentions for the simulations. Finally, the discussion turns to the usage of indicators in these line profiles to predict parameters of the original disk systems.
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Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/13287
Subject Headings
Black holes (Astronomy), Accretion (Astrophysics), General relativity (Physics), Gravitation, Petterson, Jacobus Antonius,--1946-
Format
Document (PDF)
Quasi-local energy of rotating black hole spacetimes and isometric embeddings of 2-surfaces in Euclidean 3-space
Title
Quasi-local energy of rotating black hole spacetimes and isometric embeddings of 2-surfaces in Euclidean 3-space.
Creator
Ray, Shannon, Miller, Warner A., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
One of the most fundamental problems in classical general relativity is the measure of e↵ective mass of a pure gravitational field. The principle of equivalence prohibits a purely local measure of this mass. This thesis critically examines the most recent quasi-local measure by Wang and Yau for a maximally rotating black hole spacetime. In particular, it examines a family of spacelike 2-surfaces with constant radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which,...
Show moreOne of the most fundamental problems in classical general relativity is the measure of e↵ective mass of a pure gravitational field. The principle of equivalence prohibits a purely local measure of this mass. This thesis critically examines the most recent quasi-local measure by Wang and Yau for a maximally rotating black hole spacetime. In particular, it examines a family of spacelike 2-surfaces with constant radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which, the Wang and Yau quasi-local energy has yet to be explored. In this region, the results of this thesis indicate that the Wang and Yau quasi-local energy yields complex values and is essentially equivalent to the previously defined Brown and York quasi-local energy. However, an application of their quasi-local mass is suggested in a dynamical setting, which can potentially give new and meaningful measures. In supporting this thesis, the development of a novel adiabatic isometric mapping algorithm is included. Its purpose is to provide the isometric embedding of convex 2-surfaces with spherical topology into Euclidean 3-space necessary for completing the calculation of quasilocal energy in numerical relativity codes. The innovation of this algorithm is the guided adiabatic pull- back routine. This uses Ricci flow and Newtons method to give isometric embeddings of piecewise simplicial 2-manifolds, which allows the algorithm to provide accuracy of the edge lengths up to a user set tolerance.
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Date Issued
2017
PURL
http://purl.flvc.org/fau/fd/FA00004865, http://purl.flvc.org/fau/fd/FA00004865
Subject Headings
Gravitational fields., General relativity (Physics), Newton-Raphson method., Ricci flow.
Format
Document (PDF)
Hamiltonian Methods in the Quantization of Gauge Systems
Title
Hamiltonian Methods in the Quantization of Gauge Systems.
Creator
Vaulin, Ruslan, Florida Atlantic University, Miller, Warner A., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
The new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework...
Show moreThe new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework of either of the approaches are equivalent. The central to the proof of equivalence was the fact that the gauge symmetries resuIt in the constraints of the first class in Dirac's terminology that Iead to redundancy of equations of motion for some of the canonica variables. Nevertheless, analysis of the quantum theories showed that in general, the quantum theory of the dynamical Hamiltonian is inequivalent to those of the extended Hamiltonian and the Hamiltonian reduction. The new method of quantization was applied to a number of gauge systems, including the theory of relativistic particle, the Bianchi type IX cosmological model and spinor electrodynamics along side with the traditional methods of quantization. In all of the cases considered the quantum theory of the dynamical Hamiltonian was found to be well-defined and to possess the appropriate classical limit. In particular, the quantization procedure for the Bianchi type IX cosmological spacetime did not run into any of the known problems with quantizing the theory of General Relativity. On the other hand, in the case of the quantum electrodynamics the dynamical Hamiltonian approach led to the quantum theory with the modified self-interaction in the matter sector. The possible consequence of this for the quantization of the full theory of General Relativity including the matter fields are discussed.
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Date Issued
2006
PURL
http://purl.flvc.org/fau/fd/FA00000882
Subject Headings
Quantum field theory, Mathematical physics, Evolution equations, Nonlinear, Hamiltonian systems
Format
Document (PDF)
Central Moments of Squeezed States: A Coincidence Statistics Analogue
Title
Central Moments of Squeezed States: A Coincidence Statistics Analogue.
Creator
Tison, Christopher C., Miller, Warner A., Alsing, Paul M., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
As a subset of quantum optics, single photons are one of the competing physical resources for quantum information processing. When used as carriers of quantum information, they have no equal. For the processing of quantum information, single photons have proven difficult to scale beyond the order of ⇠ 10 photons. The lack of single-photon-level interaction has led to creative approaches which rely on postselection to filter the possible measured outcomes to those which appear as though...
Show moreAs a subset of quantum optics, single photons are one of the competing physical resources for quantum information processing. When used as carriers of quantum information, they have no equal. For the processing of quantum information, single photons have proven difficult to scale beyond the order of ⇠ 10 photons. The lack of single-photon-level interaction has led to creative approaches which rely on postselection to filter the possible measured outcomes to those which appear as though interaction occurred. This approach of post-selection leans heavily on the ability to not only generate but also detect scores of single photons simultaneously and with near perfect efficiency. Our work relaxes the emphasis which has been placed on single photons for quantum information processing to that of states with, in principle, an arbitrary number of photons. Central moment expectations on two-mode squeezed states are shown to exhibit post-selection behavior which reflects the single-photon counterpart. These measures are proven to be robust to loss and return entangled state statistics on average. With naive estimation of the central moment, states with ~ 20 modes are within reach with current technology, closing the gap between quantum states which can and cannot be classically simulated.
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Date Issued
2018
PURL
http://purl.flvc.org/fau/fd/FA00005951
Subject Headings
Squeezed states (Optics), Quantum optics, Photons, Integrated optics
Format
Document (PDF)
Non-Separable Superpositions of Complex Phase Front and Polarization States in Classical-Singular and Quantum-Entangled Optics
Title
Non-Separable Superpositions of Complex Phase Front and Polarization States in Classical-Singular and Quantum-Entangled Optics.
Creator
Khajavi, Behzad, Miller, Warner A., Galvez, Enrique J., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
The angular momentum of light originates from two sources: one is the spin angular momentum (SAM) of individual photons, which is related to the polarization of light and the other is the orbital angular momentum (OAM) associated with helical wavefront of the light if it is helically phased (complex phase front). A beam of light that is composed of photons possessing both OAM and SAM states can be used in different areas of study such as rotating microscopic particles, interacting with...
Show moreThe angular momentum of light originates from two sources: one is the spin angular momentum (SAM) of individual photons, which is related to the polarization of light and the other is the orbital angular momentum (OAM) associated with helical wavefront of the light if it is helically phased (complex phase front). A beam of light that is composed of photons possessing both OAM and SAM states can be used in different areas of study such as rotating microscopic particles, interacting with nonlinear materials, investigating atom-light interactions, communication and medical imaging technologies, quantum information, quantum entanglement and etc. In this dissertation we study coherent beams that convey photons in superposition states of polarization and complex phase front. Our study includes two fields: (I) classical wave-like behavior with visible light in the field of singular optics. (II) quantum particle-like behavior of photons of light in the field of quantum-entangled optics. The approach is to investigate the state of such photons both mathematically and experimentally in classical-singular and quantum-entangled fields. We discuss seven projects based on this research. In one project we present a new method to encode OAM modes into perpendicular polarization components and making superpositions of polarization and spatial modes mapped by Poincare sphere. In another project using spatial light modulators (SLM) we realized highorder disclination patterns in the polarization map of the cross section of the beam. We also realize new forms of polarization disclination patterns (line patterns where rotational invariance is violated) known as monstars that were not previously seen. We proposed a new definition for characterizing these patterns since they can have zero or negative singularity index. In another project, instead of SLM we used q-plates to generate new forms of monstars. We proposed a robust and easy method for determining the topological charge of a complex phase front beam by inspecting the interference pattern the beam reflected from a wedged optical flat. In another project we encoded OAM modes onto orthogonal polarization components of a photon from an entangled pair and investigated the quantum entanglement. We also prepared a polarization entangled state and calculated some measures of entanglement. We summarize the projects and discuss the future prospects.
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Date Issued
2018
PURL
http://purl.flvc.org/fau/fd/FA00005960
Subject Headings
Optics, Polarization (Light), Quantum entanglement, Photons
Format
Document (PDF)