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arXiv · 1211.5786

Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones

Denis Borisov·Konstantin Pankrashkin
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Abstract

We consider small perturbations of the Laplace operator in a multi-dimensional cylindrical domain by second order differential operators with periodic coefficients. We show that under certain non-degeneracy conditions such perturbations can open a gap in the continuous spectrum and give the leading asymptotic terms for the gap edges. We also estimate the values of quasi-momentum at which the spectrum edges are attained. The general machinery is illustrated by several new examples in two- and three-dimensional structures.

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Denis Borisov, Konstantin Pankrashkin. 2013-04-08. Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. https://doi.org/10.1088/1751-8113/46/23/235203

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