Faculty Publications

Title

Periodic operators in high-contrast media and the integrated density of states function

Document Type

Article

Keywords

Integrated density of states function, Large coupling limit, Periodic media

Journal/Book/Conference Title

Communications in Partial Differential Equations

Volume

30

Issue

7-9

First Page

1021

Last Page

1037

Abstract

This paper 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 χτ which takes the value 1 in Ω+ and the value τ in [0, 2π)n\Ω+. We extend this setup periodically to ℝn and define the operator L τ = -∇χτ∇. As τ goes to infinity, it is known that the spectrum of Lτ 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 resettled integrated density of states function in the large coupling limit which describes the non-trivial asymptotic behavior of this spectral accumulation. Copyright © Taylor & Francis, Inc.

Original Publication Date

11-23-2005

DOI of published version

10.1081/PDE-200064440

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