MHD alpha(2)-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
Result description
It is shown that the alpha(2)-dynamo of magnetohydrodynamics, the hydrodynamic Squire equation as well as an interpolation model of PT-symmetric quantum mechanics are closely related as spectral problems in Krein spaces. For the alpha(2)-dynamo and the PT-symmetric model the strong similarities are demonstrated with the help of a 2x2 operator matrix representation, whereas the Squire equation is reinterpreted as a rescaled and Wick-rotated PT-symmetric problem. Based on recent results on the Squire equation the spectrum of the PT-symmetric interpolation model is analyzed in detail and the Herbst limit is described as spectral singularity.
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
MHD alpha(2)-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
Original language description
It is shown that the alpha(2)-dynamo of magnetohydrodynamics, the hydrodynamic Squire equation as well as an interpolation model of PT-symmetric quantum mechanics are closely related as spectral problems in Krein spaces. For the alpha(2)-dynamo and the PT-symmetric model the strong similarities are demonstrated with the help of a 2x2 operator matrix representation, whereas the Squire equation is reinterpreted as a rescaled and Wick-rotated PT-symmetric problem. Based on recent results on the Squire equation the spectrum of the PT-symmetric interpolation model is analyzed in detail and the Herbst limit is described as spectral singularity.
Czech name
MHD alfa 2 ? dynamo Squireova rovnice a PT-symetrická interpolace mezi pravoúhlou jámou a harmonickým oscilátorem
Czech description
Popsány matematické podobnosti fyzikálně různých modelů.
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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2005
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
46
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
1
Pages from-to
063504
UT code for WoS article
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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
2005