Publikationsrepositorium - Helmholtz-Zentrum Dresden-Rossendorf
1 PublikationMHD α²-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
Günther, U.; Stefani, F.; Znojil, M.
Abstract
It is shown that the α²-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 α²-dynamo and the PT-symmetric model the strong similarities are demonstrated with the help of a 2×2 operator matrix representation, whereas the Squire equation is re-interpreted 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: MHD dynamo; Squire equation; Couette flow; PT-symmetric Quantum Mechanics; Krein space; operator theory; spectral analysis; exceptional points; phase transitions; singularities; Herbst limit
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Journal of Mathematical Physics 46(2005), 063504
DOI: 10.1063/1.1915293
ISSN: 0022-2488
Cited 58 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ-7078
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