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

Details MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator

2005-01-27

arxiv.org/abs/math-ph/0501069v2

J.Math.Phys. 46 (2005) 063504

Physics

Mathematical Physics

21 pages, LaTeX2e, 10 figures, minor improvements, references added, to appear in J. Math. Phys

Scientific paper

10.1063/1.1915293

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 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.

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