Tuesday, November 13, 2012

1211.2541 (David Krejcirik et al.)

Location of the essential spectrum in curved quantum layers    [PDF]

David Krejcirik, Zhiqin Lu
We consider the Dirichlet Laplacian in tubular neighbourhoods of complete non-compact Riemannian manifolds immersed in the Euclidean space. We show that the essential spectrum coincides with the spectrum of a planar tube provided that the second fundamental form of the manifold vanishes at infinity and the transport of the cross-section along the manifold is asymptotically parallel. For low dimensions and codimensions, the result applies to the location of propagating states in nanostructures under physically natural conditions.
View original: http://arxiv.org/abs/1211.2541

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