On the spectrum of leaky surfaces with a potential bias
Result description
We discuss operators of the type H = -Delta + V(x) - alpha delta(x - Sigma) with an attractive interaction, alpha > 0, in L-2(R-3), where Sigma is an infinite surface, asymptotically planar and smooth outside a compact, dividing the space into two regions, of which one is supposed to be convex, and V is a potential bias being a positive constant V-0 in one of the regions and zero in the other. We find the essential spectrum and ask about the existence of the discrete one with a particular attention to the critical case, V-0 = alpha(2). We show that sigma(disc)(H) is then empty if the bias is supported in the 'exterior' region, while in the opposite case isolated eigenvalues may exist.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/18:00328100
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On the spectrum of leaky surfaces with a potential bias
Original language description
We discuss operators of the type H = -Delta + V(x) - alpha delta(x - Sigma) with an attractive interaction, alpha > 0, in L-2(R-3), where Sigma is an infinite surface, asymptotically planar and smooth outside a compact, dividing the space into two regions, of which one is supposed to be convex, and V is a potential bias being a positive constant V-0 in one of the regions and zero in the other. We find the essential spectrum and ask about the existence of the discrete one with a particular attention to the critical case, V-0 = alpha(2). We show that sigma(disc)(H) is then empty if the bias is supported in the 'exterior' region, while in the opposite case isolated eigenvalues may exist.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
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
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
EMS Series of Congress Reports
ISBN
978-3-03719-186-6
ISSN
—
e-ISSN
—
Number of pages
12
Pages from-to
169-181
Publisher name
European Mathematical Society
Place of publication
Zurich
Event location
Trondheim
Event date
Jul 4, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000442187600009
Basic information
Result type
D - Article in proceedings
OECD FORD
Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Year of implementation
2018