On the existence of bound states in asymmetric leaky wires
Result description
We analyze spectral properties of a leaky wire model with a potential bias. It describes a two-dimensional quantum particle exposed to a potential consisting of two parts. One is an attractive delta-interaction supported by a non-straight, piecewise smooth curve L dividing the plane into two regions of which one, the "interior," is convex. The other interaction component is a constant positive potential V-0 in one of the regions. We show that in the critical case, V-0 = alpha(2), the discrete spectrum is non-void if and only if the bias is supported in the interior. We also analyze the non-critical situations, in particular, we show that in the subcritical case, V-0 < alpha(2), the system may have any finite number of bound states provided the angle between the asymptotes of L is small enough.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/16:00307405
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On the existence of bound states in asymmetric leaky wires
Original language description
We analyze spectral properties of a leaky wire model with a potential bias. It describes a two-dimensional quantum particle exposed to a potential consisting of two parts. One is an attractive delta-interaction supported by a non-straight, piecewise smooth curve L dividing the plane into two regions of which one, the "interior," is convex. The other interaction component is a constant positive potential V-0 in one of the regions. We show that in the critical case, V-0 = alpha(2), the discrete spectrum is non-void if and only if the bias is supported in the interior. We also analyze the non-critical situations, in particular, we show that in the subcritical case, V-0 < alpha(2), the system may have any finite number of bound states provided the angle between the asymptotes of L is small enough.
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
GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
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 Mathematical Physics
ISSN
0022-2488
e-ISSN
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Volume of the periodical
57
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
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UT code for WoS article
000371620000030
EID of the result in the Scopus database
2-s2.0-84957991287
Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2016