Three models of Krein-space related physics: PT-symmetric Quantum Mechanics, Squire equation and the MHD α²-dynamo

PT-symmetric Quantum Mechanics, the Squire equation of hydrodynamics and the spherically symmetric α²-dynamo of magnetohydrodynamics (MHD) can be structurally linked and treated in a unified way as spectral problems in Krein spaces. We demonstrate their interrelation explicitly and provide examples for specific parameter dependencies of their spectra. Special emphasis is laid on the physical relevance of transitions between real and complex spectral branches in connection with phase transitions between sectors of exact PT-symmetry and spontaneously broken PT-symmetry in Quantum Mechanics as well as with possible polarity reversals of dynamo maintained magnetic fields of planets. We briefly comment on third order spectral branch points with geometric multiplicity one and algebraic multiplicity three as well as on a dynamo related resonant unfolding of diabolical points (spectral intersection points of geometric and algebraic multiplicity two).

Based on:

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