Intertwiners of Pseudo-Hermitian 2 × 2-Block-Operator Matrices and a No-Go Theorem for Isospectral MHD Dynamo Operators

Pseudo-Hermiticity as a generalization of usual Hermiticity is a rather common feature of (differential) operators emerging in various physical setups. Examples are Hamiltonians of PTand CPT-symmetric quantum mechanical systems [1] as well as the operator of the spherically symmetric α-dynamo [2] in magnetohydrodynamics (MHD). In order to solve the inverse spectral problem for these operators, appropriate uniqueness theorems should be obtained and possibly existing isospectral configurations should be found and classified. As a step toward clarifying the isospectrality problem of dynamo operators, we discuss an intertwining technique for η-pseudo-Hermitian 2 × 2-block-operator matrices with secondorder differential operators as matrix elements. The intertwiners are assumed as first-order matrix differential operators with coefficients which are highly constrained by a system of nonlinear matrix differential equations. We analyze the (hidden) symmetries of this equation system, transforming it into a set of constrained and interlinked matrix Riccati equations. Finally, we test the structure of the spherically symmetric MHD α-dynamo operator on its compatibility with the considered intertwining ansatz and derive a no-go theorem.