Spectral gap properties of perturbed periodic media
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Date
2025-05-15
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Abstract
We analyze periodic operators on Rn and small perturbations
of these operators. The perturbation is periodic in n − 1 directions and
has bounded support in the remaining direction. We show that, when the
perturbation has a sign, every spectral gap for the unperturbed operator
is reduced by the perturbation. We develop a general theory that can be
applied to elliptic operators, to systems such as that of linear elasticity, and
to Maxwell’s equations.
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Keywords
band gap, Bloch waves, perturbation of periodic operators