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Journal of Mathematical Physics / Volume 46 / Issue 6 / METHODS OF MATHEMATICAL PHYSICS

J. Math. Phys. 46, 063504 (2005); http://dx.doi.org/10.1063/1.1915293 (22 pages)

MHD α2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator

Uwe Günther1, Frank Stefani1, and Miloslav Znojil2

1Research Center Rossendorf, P.O. Box 510119, D-01314 Dresden, Germany
2Ústav Jaderné Fyziky AV ČR, 250 68 Řež, Czech Republic

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(Received 28 January 2005; accepted 18 March 2005; published online 17 May 2005)

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 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.

© 2005 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. KREIN SPACE PROPERTIES OF PT -SYMMETRIC QUANTUM MODELS AND OF THE SPHERICALLY SYMMETRIC MHD α2 -DYNAMO
    1. PT -symmetric quantum models
    2. The spherically symmetric MHD α2 -dynamo
    3. Spectral phase transitions
  3. PT -SYMMETRIC INTERPOLATION BETWEEN SQUARE WELL AND HARMONIC OSCILLATOR
    1. Toy model PT -symmetric differential equation
    2. The emergence of mathE ≠ 0 on certain finite subintervals of ν ∊ (−2,0)
  4. THE HERBST LIMIT AND ITS RELATION TO THE SQUIRE EQUATION OF HYDRODYNAMICS
  5. CONLUSIONS

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KEYWORDS and PACS

Keywords

harmonic oscillators, quantum theory, matrix algebra, mathematical operators, interpolation, magnetohydrodynamics

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.1915293

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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