skip to main content

SciTech ConnectSciTech Connect

Title: Location of the essential spectrum in curved quantum layers

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 codimension, the result applies to the location of propagating states in nanostructures under physically natural conditions.
Authors:
 [1] ;  [2]
  1. Department of Theoretical Physics, Nuclear Physics Institute ASCR, 25068 Řež (Czech Republic)
  2. Department of Mathematics, University of California, Irvine, California 92697 (United States)
Publication Date:
OSTI Identifier:
22306028
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CROSS SECTIONS; EUCLIDEAN SPACE; LAPLACIAN; MATHEMATICAL MANIFOLDS; NANOSTRUCTURES; SPECTRA