Persistent Link:
http://hdl.handle.net/10150/290083
Title:
The density of states in a quasi-gap
Author:
Selden, Jeffrey Lee
Issue Date:
2004
Publisher:
The University of Arizona.
Rights:
Copyright © 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.
Abstract:
This 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.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Friedlander, Leonid

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleThe density of states in a quasi-gapen_US
dc.creatorSelden, Jeffrey Leeen_US
dc.contributor.authorSelden, Jeffrey Leeen_US
dc.date.issued2004en_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.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.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorFriedlander, Leoniden_US
dc.identifier.proquest3132253en_US
dc.identifier.bibrecord.b46711570en_US
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