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 PT- and CPT-symmetric quantum mechanical systems [1, 2] as well as the operator of the spherically symmetric a2-dynamo  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 J-pseudo-Hermitian 2×2-block-operator matrices with second-order differential operators as matrix elements. The intertwiners are assumed as first-order matrix differential operators with coefficients which are highly constraint by a system of nonlinear matrix differential equations. We analyze the (hidden) symmetries of this equation system, transforming it into a set of constraint and interlinked matrix Riccati equations.
Finally, we test the structure of the spherically symmetric MHD a2-dynamo operator on its compatibility with the considered intertwining ansatz and derive a no-go theorem.
The talk extends the results of .