The density of states in a quasi-gap

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 ri!+ contained in the hypercube [0, 27r)"'. We define a function Xt which takes the value 1 in and the value r in [0, 27r)"' \ Q+. We extend this setup periodically to R" and define the operator = — Vxi-V. As r —»• oo, it is known that the spectrum of Lr exhibits a band-gap structure and that the spectral density accumulates at the upper endpoints of the bands. We estabUsh the existence and some important properties of a rescaled integrated density of states function in the large couphng limit which describes the non-trivial asymptotic behavior of this spectral accumulation.

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