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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band gap, Bloch waves, perturbation of periodic operators

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