Periodic operators in high-contrast media and the integrated density of states function
Integrated density of states function, Large coupling limit, Periodic media
Communications in Partial Differential Equations
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
DOI of published version
Selden, Jeffrey, "Periodic operators in high-contrast media and the integrated density of states function" (2005). Faculty Publications. 2904.