Spectral Gaps for Periodic Elliptic Operators with High Contrast: an Overview

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dc.creatorHempel, Rainer
dc.creatorPost, Olaf
dc.date2002-07-16
dc.date.accessioned2026-07-07T04:29:18Z
dc.date.available2026-07-07T04:29:18Z
dc.descriptionWe discuss the band-gap structure and the integrated density of states for periodic elliptic operators in the Hilbert space $L_2(\R^m)$, for $m \ge 2$. We specifically consider situations where high contrast in the coefficients leads to weak coupling between the period cells. Weak coupling of periodic systems frequently produces spectral gaps or spectral concentration. Our examples include Schrödinger operators, elliptic operators in divergence form, Laplace-Beltrami-operators, Schrödinger and Pauli operators with periodic magnetic fields. There are corresponding applications in heat and wave propagation, quantum mechanics, and photonic crystals.
dc.description12 pages, 1 eps-figure, LaTeX
dc.identifierhttps://arxiv.org/abs/math-ph/0207020
dc.identifierhttp://arxiv.org/abs/math-ph/0207020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57105
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.titleSpectral Gaps for Periodic Elliptic Operators with High Contrast: an Overview
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