Perfect transmission scattering as a PT-symmetric spectral problem
Result description
We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian quantum mechanical framework from the physical viewpoint. One of the most interesting features of the analysis is that the complex eigenvalues of the underlying non-Hermitian problem, associated with a reflectionless scattering system, lead to the loss of perfect-transmission energies as the parameters characterizing the scattering potential are varied. On the other hand, the scattering data can serve to describe the spectrum of a large class of Schrödinger operators with complex Robin boundary conditions.
Keywords
PT-symmetrycomplex Robin boundary conditionsreflectionless scattering
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/61389005:_____/11:00365515
Result on the web
http://www.sciencedirect.com/science/article/B6TVM-52NW5J1-2/2/a0d251c7ab17aac9fd7d68d17f965bcb
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Perfect transmission scattering as a PT-symmetric spectral problem
Original language description
We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian quantum mechanical framework from the physical viewpoint. One of the most interesting features of the analysis is that the complex eigenvalues of the underlying non-Hermitian problem, associated with a reflectionless scattering system, lead to the loss of perfect-transmission energies as the parameters characterizing the scattering potential are varied. On the other hand, the scattering data can serve to describe the spectrum of a large class of Schrödinger operators with complex Robin boundary conditions.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physics Letters A
ISSN
0375-9601
e-ISSN
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Volume of the periodical
375
Issue of the periodical within the volume
22
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
4
Pages from-to
2149-2152
UT code for WoS article
000291192200002
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
2011