The spherically symmetric α²-dynamo, resonant unfolding of diabolical points and third-order exceptional points in Krein space related setups

In the first part of the talk we consider the spectral behavior of the spherically symmetric α²-dynamo with idealized boundary conditions. The corresponding operator is self-adjoint in a Krein space and therefore it shares many features with Hamiltonians of PT-symmetric Quantum Mechanics. The spectrum of a dynamo with constant α-profile contains a countably infinite number of diabolical points which under inhomogeneous perturbations unfold in a very specific and resonant way. We describe this mechanism in detail and discuss its physical implications.

In the second part of the talk we discuss coalescing second-order exceptional points in Krein space related models and the emergence of third-order Jordan structures. We demonstrate the basic mechanism on a most simple PT-symmetric 4x4 matrix model and use the obtained results to identify similar structures in the spectral decomposition of α²-dynamo operators.