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

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

2002-08-07

arxiv.org/abs/math-ph/0208012v3

J. Math. Phys. 44 (2003) 3097-3111

Physics

Mathematical Physics

13 pages, LaTeX2e, improved references, to appear in J. Math. Phys

Scientific paper

10.1063/1.1573741

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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