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dc.contributor.advisorFriedlander, Leoniden_US
dc.contributor.authorSelden, Jeffrey Lee
dc.creatorSelden, Jeffrey Leeen_US
dc.date.accessioned2013-05-09T10:57:14Z
dc.date.available2013-05-09T10:57:14Z
dc.date.issued2004en_US
dc.identifier.urihttp://hdl.handle.net/10150/290083
dc.description.abstractThis dissertation studies the asymptotic behavior for the integrated density of states function for operators associated with the propagation of classical waves in a high-contrast, periodic, two-component medium. Consider a domain Ω₊ contained in the hypercube [0, 2π)ⁿ. We define a function χ(τ) which takes the value 1 in Ω₊ and the value τ in [0, 2π)\Ω₊. We extend this setup periodically to Rⁿ and define the operator L(τ) = -∇χ(τ)∇. As τ → ∞, it is known that the spectrum of L(τ) exhibits a band-gap structure and that the spectral density accumulates at the upper endpoints of the bands. We establish the existence and some important properties of a rescaled integrated density of states function in the large coupling limit which describes the non-trivial asymptotic behavior of this spectral accumulation.
dc.language.isoen_USen_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.subjectMathematics.en_US
dc.titleThe density of states in a quasi-gapen_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_US
dc.identifier.proquest3132253en_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.namePh.D.en_US
dc.identifier.bibrecord.b46711570en_US
refterms.dateFOA2018-06-30T01:14:24Z
html.description.abstractThis dissertation studies the asymptotic behavior for the integrated density of states function for operators associated with the propagation of classical waves in a high-contrast, periodic, two-component medium. Consider a domain Ω₊ contained in the hypercube [0, 2π)ⁿ. We define a function χ(τ) which takes the value 1 in Ω₊ and the value τ in [0, 2π)\Ω₊. We extend this setup periodically to Rⁿ and define the operator L(τ) = -∇χ(τ)∇. As τ → ∞, it is known that the spectrum of L(τ) exhibits a band-gap structure and that the spectral density accumulates at the upper endpoints of the bands. We establish the existence and some important properties of a rescaled integrated density of states function in the large coupling limit which describes the non-trivial asymptotic behavior of this spectral accumulation.


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