AuthorSelden, Jeffrey Lee
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PublisherThe University of Arizona.
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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.
Degree ProgramGraduate College