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arXiv · 1211.2541

Location of the essential spectrum in curved quantum layers

David Krejcirik·Zhiqin Lu
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Abstract

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.

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David Krejcirik, Zhiqin Lu. 2012-11-12. Location of the essential spectrum in curved quantum layers. https://doi.org/10.1063/1.4893035

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