Spectral Analysis of a Quantum System with a Double Line Singular Interaction
Result description
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically approaches a constant value, and find conditions which guarantee either the existence of discrete eigenvalues or Hardy-type inequalities. For a class of our models admitting mirror symmetry, we also establish the existence of embedded eigenvalues and show that they turn into resonances after introducing a small perturbation.
Keywords
Schrödinger operatorsingular perturbationspectral analysisHardy inequalityresonance
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 Analysis of a Quantum System with a Double Line Singular Interaction
Original language description
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically approaches a constant value, and find conditions which guarantee either the existence of discrete eigenvalues or Hardy-type inequalities. For a class of our models admitting mirror symmetry, we also establish the existence of embedded eigenvalues and show that they turn into resonances after introducing a small perturbation.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Publications of the Research Institute for Mathematical Sciences
ISSN
0034-5318
e-ISSN
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Volume of the periodical
49
Issue of the periodical within the volume
4
Country of publishing house
JP - JAPAN
Number of pages
29
Pages from-to
831-859
UT code for WoS article
000333547100007
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2013