Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem
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.
Cite
@article{arxiv.math-ph/0208012,
title = {Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem},
author = {U. Guenther and F. Stefani},
journal= {arXiv preprint arXiv:math-ph/0208012},
year = {2007}
}
Comments
13 pages, LaTeX2e, improved references, to appear in J. Math. Phys