MHD {alpha}{sup 2}-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator

Journal Article · Wed Jun 01 00:00:00 EDT 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.1915293· OSTI ID:20699204

Guenther, Uwe; Stefani, Frank; Znojil, Miloslav ^[1]

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1. Research Center Rossendorf, P.O. Box 510119, D-01314 Dresden (Germany)

It is shown that the {alpha}{sup 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}{sup 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.

• OSTI ID: 20699204
• Journal Information: Journal of Mathematical Physics, Vol. 46, Issue 6; Other Information: DOI: 10.1063/1.1915293; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
EQUATIONS
HARMONIC OSCILLATORS
INTERPOLATION
MAGNETOHYDRODYNAMICS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
QUANTUM MECHANICS
SINGULARITY