%0 Journal Article
%T Spectral gap of segments of periodic waveguides
%A Sylwia Kondej
%A Ivan Veselic'
%J Mathematics
%D 2006
%I arXiv
%R 10.1007/s11005-006-0111-5
%X 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 $L^{-2}$.
%U http://arxiv.org/abs/math-ph/0608005v2