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Mathematics  2006 

Spectral gap of segments of periodic waveguides

DOI: 10.1007/s11005-006-0111-5

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Abstract:

We consider a periodic strip in the plane and the associated quantum waveguide with Dirichlet boundary conditions. We analyse finite segments of the waveguide consisting of $L$ periodicity cells, equipped with periodic boundary conditions at the ``new'' boundaries. Our main result is that the distance between the first and second eigenvalue of such a finite segment behaves like $L^{-2}$.

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