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

@article{Borisov2013QuantumWW,
  title={Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones},
  author={Denis I. Borisov and Konstantin Pankrashkin},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2013},
  volume={46}
}
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… 

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