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

TL;DR

This paper reveals deep mathematical connections between magnetohydrodynamic dynamos, hydrodynamic equations, and PT-symmetric quantum models, using spectral analysis in Krein spaces to unify these physical systems.

Contribution

It demonstrates the spectral equivalences and relationships among the alpha^2-dynamo, Squire equation, and PT-symmetric quantum models through operator matrix representations.

Findings

Spectral similarities between dynamo and PT-symmetric models.

Re-interpretation of the Squire equation as a PT-symmetric problem.

Analysis of the spectrum and spectral singularities in the interpolation model.

Abstract

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.