The Magnetic Laplacian in Shrinking Tubular Neighborhoods of Hypersurfaces
Result description
The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the hypersurfaces tends to zero. We show that the Laplacian convergesin a norm-resolvent sense to a Schrodinger operator on the limiting hypersurface whose electromagnetic potential is expressed in terms of principal curvatures and the projection of the ambient vector potential to the hypersurface. As an application, weobtain an effective approximation of bound-state energies and eigenfunctions in thin quantum layers.
Keywords
curvature of hypersurfaceseffective potentialEigenvalue asymptotics
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/15:00222326
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
The Magnetic Laplacian in Shrinking Tubular Neighborhoods of Hypersurfaces
Original language description
The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the hypersurfaces tends to zero. We show that the Laplacian convergesin a norm-resolvent sense to a Schrodinger operator on the limiting hypersurface whose electromagnetic potential is expressed in terms of principal curvatures and the projection of the ambient vector potential to the hypersurface. As an application, weobtain an effective approximation of bound-state energies and eigenfunctions in thin quantum layers.
Czech name
—
Czech description
—
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
—
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Geometric Analysis
ISSN
1050-6926
e-ISSN
—
Volume of the periodical
25
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
2546-2564
UT code for WoS article
000365472700020
EID of the result in the Scopus database
2-s2.0-84948138228
Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2015