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Title: Location of the essential spectrum in curved quantum layers

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 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

Citation Formats

Krejčiřík, David, E-mail: krejcirik@ujf.cas.cz, and Lu, Zhiqin, E-mail: zlu@uci.edu. Location of the essential spectrum in curved quantum layers. United States: N. p., 2014. Web. doi:10.1063/1.4893035.
Krejčiřík, David, E-mail: krejcirik@ujf.cas.cz, & Lu, Zhiqin, E-mail: zlu@uci.edu. Location of the essential spectrum in curved quantum layers. United States. doi:10.1063/1.4893035.
Krejčiřík, David, E-mail: krejcirik@ujf.cas.cz, and Lu, Zhiqin, E-mail: zlu@uci.edu. Fri . "Location of the essential spectrum in curved quantum layers". United States. doi:10.1063/1.4893035.
@article{osti_22306028,
title = {Location of the essential spectrum in curved quantum layers},
author = {Krejčiřík, David, E-mail: krejcirik@ujf.cas.cz and Lu, Zhiqin, E-mail: zlu@uci.edu},
abstractNote = {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.},
doi = {10.1063/1.4893035},
journal = {Journal of Mathematical Physics},
number = 8,
volume = 55,
place = {United States},
year = {Fri Aug 15 00:00:00 EDT 2014},
month = {Fri Aug 15 00:00:00 EDT 2014}
}