Spectral Theory for Schrodinger Operators with delta-Interactions Supported on Curves in R-3
Result description
The main objective of this paper is to systematically develop a spectral and scattering theory for self-adjoint Schrodinger operators with delta-interactions supported on closed curves in R-3. We provide bounds for the number of negative eigenvalues depending on the geometry of the curve, prove an isoperimetric inequality for the principal eigenvalue, derive Schatten-von Neumann properties for the resolvent difference with the free Laplacian, and establish an explicit representation for the scattering matrix.
Keywords
spectral theoryscattering theoryself-adjoint Schrodinger operators
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Spectral Theory for Schrodinger Operators with delta-Interactions Supported on Curves in R-3
Original language description
The main objective of this paper is to systematically develop a spectral and scattering theory for self-adjoint Schrodinger operators with delta-interactions supported on closed curves in R-3. We provide bounds for the number of negative eigenvalues depending on the geometry of the curve, prove an isoperimetric inequality for the principal eigenvalue, derive Schatten-von Neumann properties for the resolvent difference with the free Laplacian, and establish an explicit representation for the scattering matrix.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Result continuities
Project
GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annales Henri Poincare
ISSN
1424-0637
e-ISSN
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Volume of the periodical
18
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
43
Pages from-to
1305-1347
UT code for WoS article
000398314900007
EID of the result in the Scopus database
2-s2.0-84996548653
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Year of implementation
2017