Current Search: Beetle, Christopher (x)
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 Title
 Quantum isotropy and dynamical quantum symmetry reduction.
 Creator
 Hogan, Matthew, Beetle, Christopher, Engle, Jonathan S., Graduate College, Mendonca, P.
 Abstract/Description

We give a diffeomorphism and gauge covariant condition equivalent to homogeneity and isotropy which can be quantized, yielding a definition of a diffeomorphisminvariant, homogeneous isotropic sector of loop quantum gravity without fixing a graph. We then specialize this condition to Bianchi I cosmologies, in which case it becomes a condition for isotropy. We show how, by quantizing and imposing this condition in Bianchi I loop quantum cosmology, one exactly recovers isotropic loop quantum...
Show moreWe give a diffeomorphism and gauge covariant condition equivalent to homogeneity and isotropy which can be quantized, yielding a definition of a diffeomorphisminvariant, homogeneous isotropic sector of loop quantum gravity without fixing a graph. We then specialize this condition to Bianchi I cosmologies, in which case it becomes a condition for isotropy. We show how, by quantizing and imposing this condition in Bianchi I loop quantum cosmology, one exactly recovers isotropic loop quantum cosmology, including the usual ‘improved dynamics.’ We will also discuss how this reduction sheds light on which operator ordering to use when defining operators corresponding to directional Hubble rates, expansion, and shear quantities relevant for discussing the resolution of the initial singularity.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00005821
 Format
 Document (PDF)
 Title
 Exploring the stability of an eigenvalue problem approximation technique used to define the angular momentum of almost spherical black holes.
 Creator
 Wilder, Shawn M., Beetle, Christopher, Graduate College
 Date Issued
 20110408
 PURL
 http://purl.flvc.org/fcla/dt/3164804
 Subject Headings
 Eigenvalues, Black holes (Astronomy), Deformations (Mechanics)
 Format
 Document (PDF)
 Title
 Approximate Isometries as an Eigenvalue Problem and Angular Momentum.
 Creator
 Wilder, Shawn M., Beetle, Christopher, Graduate College
 Date Issued
 20130412
 PURL
 http://purl.flvc.org/fcla/dt/3361373
 Subject Headings
 Black holes (Astronomy), Eigenvalues
 Format
 Document (PDF)
 Title
 Periodic standingwave approximation: Eigenspectral computations for linear gravity and nonlinear toy models.
 Creator
 Beetle, Christopher, Bromley, Benjamin, Price, Richard H.
 Date Issued
 20060713
 PURL
 http://purl.flvc.org/fau/flvc_fau_islandoraimporter_10.1103_PhysRevD.74.024013_1632234668
 Format
 Citation
 Title
 Generic isolated horizons in loop quantum gravity.
 Creator
 Beetle, Christopher, Engle, Jonathan
 Date Issued
 20101115
 PURL
 http://purl.flvc.org/fau/flvc_fau_islandoraimporter_10.1088_02649381_27_23_235024_1632236016
 Format
 Citation
 Title
 General relativistic quasilocal angular momentum continuity and the stability of strongly elliptic eigenvalue problems.
 Creator
 Wilder, Shawn M., Beetle, Christopher, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
 Abstract/Description

In general relativity, angular momentum of the gravitational field in some volume bounded by an axially symmetric sphere is welldefined as a boundary integral. The definition relies on the symmetry generating vector field, a Killing field, of the boundary. When no such symmetry exists, one defines angular momentum using an approximate Killing field. Contained in the literature are various approximations that capture certain properties of metric preserving vector fields. We explore the...
Show moreIn general relativity, angular momentum of the gravitational field in some volume bounded by an axially symmetric sphere is welldefined as a boundary integral. The definition relies on the symmetry generating vector field, a Killing field, of the boundary. When no such symmetry exists, one defines angular momentum using an approximate Killing field. Contained in the literature are various approximations that capture certain properties of metric preserving vector fields. We explore the continuity of an angular momentum definition that employs an approximate Killing field that is an eigenvector of a particular secondorder differential operator. We find that the eigenvector varies continuously in Hilbert space under smooth perturbations of a smooth boundary geometry. Furthermore, we find that not only is the approximate Killing field continuous but that the eigenvalue problem which defines it is stable in the sense that all of its eigenvalues and eigenvectors are continuous in Hilbert space. We conclude that the stability follows because the eigenvalue problem is strongly elliptic. Additionally, we provide a practical introduction to the mathematical theory of strongly elliptic operators and generalize the above stability results for a large class of such operators.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004235
 Subject Headings
 Boundary element methods, Boundary value problems, Differential equations, Elliptic  Numerical solutions, Differential equations, Partial  Numerical solutions, Eigenvalues, Spectral theory (Mathematics)
 Format
 Document (PDF)
 Title
 Improving In Vivo Two Photon Microscopy Without Adaptive Optics.
 Creator
 Estrada, Gerardo, Beetle, Christopher, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
 Abstract/Description

Two photon microscopy is one of the fastest growing methods of invivo imaging of the brain. It has the capability of imaging structures on the scale of 1μm. At this scale the wavelength of the imaging field (usually near infrared), is comparable to the size of the structures being imaged, which makes the use of ray optics invalid. A better understanding is needed to predict the result of introducing different media into the light path. We use Wolf's integral, which is capable of fulfilling...
Show moreTwo photon microscopy is one of the fastest growing methods of invivo imaging of the brain. It has the capability of imaging structures on the scale of 1μm. At this scale the wavelength of the imaging field (usually near infrared), is comparable to the size of the structures being imaged, which makes the use of ray optics invalid. A better understanding is needed to predict the result of introducing different media into the light path. We use Wolf's integral, which is capable of fulfilling these needs without the shortcomings of ray optics. We predict the effects of aberrating media introduced into the light path like glass coverslips and then correct the aberration using the same method. We also create a method to predict aberrations when the interfaces of the media in the lightpath are not aligned with the propagation direction of the wavefront.
Show less  Date Issued
 2015
 PURL
 http://purl.flvc.org/fau/fd/FA00004495
 Subject Headings
 Cellular signal transmission  Measurement, Image analysis, Imaging systems in medicine, Membranes (Biology)  Imaging, Neurons  Imaging, Optics, Adaptive
 Format
 Document (PDF)
 Title
 ON THE PARAXIAL APPROXIMATION IN QUANTUM OPTICS.
 Creator
 Jongewaard, Maria Fernanda de Boer, Beetle, Christopher, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
 Abstract/Description

We examine how best to associate quantum states of a single particle to modes of a narrowly collimated beam of classical radiation modeled in the paraxial approximation, both for scalar particles and for photons. Our analysis stresses the importance of the relationship between the inner product used to define orthogonal modes of the paraxial beam, on the one hand, and the inner product underlying the statistical interpretation of the quantum theory, on the other. While several candidates for...
Show moreWe examine how best to associate quantum states of a single particle to modes of a narrowly collimated beam of classical radiation modeled in the paraxial approximation, both for scalar particles and for photons. Our analysis stresses the importance of the relationship between the inner product used to define orthogonal modes of the paraxial beam, on the one hand, and the inner product underlying the statistical interpretation of the quantum theory, on the other. While several candidates for such an association have been proposed in the literature, we argue that one of them is uniquely well suited to the task. Specifically, the mapping from beam modes to ”henochromatic” fields on spacetime is unique within a large class of similar mappings in that it is unitary in a mathematically precise sense. We also show that the singleparticle quantum states associated to the orthogonal modes of a classical beam in the henochromatic approach are not only orthogonal, but also complete in the quantum Hilbert space.
Show less  Date Issued
 2023
 PURL
 http://purl.flvc.org/fau/fd/FA00014212
 Subject Headings
 Quantum optics, Hilbert space, Quantum theory
 Format
 Document (PDF)