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Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem

U. Guenther·F. Stefani
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Abstract

The isospectrality problem is studied for the operator of the spherical hydromagnetic alpha^2-dynamo. It is shown that this operator is formally pseudo-Hermitian (J-symmetric) and lives in a Krein space. Based on the J-symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the alpha^2-dynamo operator matrix. An intrinsic structural inconsistency is obtained in the set of associated matrix Riccati equations. This inconsistency is interpreted as a no-go theorem which forbids the construction of isospectral alpha^2-dynamo operator classes with the help of first-order differential intertwining operators.

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U. Guenther, F. Stefani. 2003-03-18. Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem. https://doi.org/10.1063/1.1573741

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