Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

1 Publication

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

Günther, U.; Stefani, F.

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.

  • Journal of Mathematical Physics 44 (2003) 3097-3111

Permalink: https://www.hzdr.de/publications/Publ-4577
Publ.-Id: 4577