Improved Spectral Calculations for Discrete Schroedinger Operators

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dc.contributor.advisorEmbree, Marken_US
dc.contributor.committeeMemberSorensen, Danny C.en_US
dc.contributor.committeeMemberDamanik, Daviden_US
dc.creatorPuelz, Charlesen_US
dc.date.accessioned2013-09-16T16:09:17Zen_US
dc.date.accessioned2013-09-16T16:09:21Zen_US
dc.date.available2013-09-16T16:09:17Zen_US
dc.date.available2013-09-16T16:09:21Zen_US
dc.date.created2013-05en_US
dc.date.issued2013-09-16en_US
dc.date.submittedMay 2013en_US
dc.date.updated2013-09-16T16:09:21Zen_US
dc.description.abstractThis work details an O(n^2) algorithm for computing the spectra of discrete Schroedinger operators with periodic potentials. Spectra of these objects enhance our understanding of fundamental aperiodic physical systems and contain rich theoretical structure of interest to the mathematical community. Previous work on the Harper model led to an O(n^2) algorithm relying on properties not satisfied by other aperiodic operators. Physicists working with the Fibonacci Hamiltonian, a popular quasicrystal model, have instead used a problematic dynamical map approach or a sluggish O(n^3) procedure for their calculations. The algorithm presented in this work, a blend of well-established eigenvalue/vector algorithms, provides researchers with a more robust computational tool of general utility. Application to the Fibonacci Hamiltonian in the sparsely studied intermediate coupling regime reveals structure in canonical coverings of the spectrum that will prove useful in motivating conjectures regarding band combinatorics and fractal dimensions.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationPuelz, Charles. "Improved Spectral Calculations for Discrete Schroedinger Operators." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/72024">https://hdl.handle.net/1911/72024</a>.en_US
dc.identifier.slug123456789/ETD-2013-05-444en_US
dc.identifier.urihttps://hdl.handle.net/1911/72024en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectQuasicrystalen_US
dc.subjectSchrödinger operatorsen_US
dc.subjectDiscrete Schroedinger operatoren_US
dc.subjectJacobi operatoren_US
dc.subjectCantor spectrumen_US
dc.subjectFractal dimentionen_US
dc.subjectLarge scale eigenvalue computationsen_US
dc.titleImproved Spectral Calculations for Discrete Schroedinger Operatorsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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