Third order spectral branch points in Krein space related setups: PT-symmetric matrix toy model, MHD alpha^2-dynamo, and extended Squire equation

摘要

The spectra of self-adjoint operators in Krein spaces are known to possessreal sectors as well as sectors of pair-wise complex conjugate eigenvalues.Transitions from one spectral sector to the other are a rather generic featureand they usually occur at exceptional points of square root branching type. Forcertain parameter configurations two or more such exceptional points may happento coalesce and to form a higher order branch point. We study the coalescenceof two square root branch points semi-analytically for a PT-symmetric 4x4matrix toy model and illustrate numerically its occurrence in the spectrum ofthe 2x2 operator matrix of the magnetohydrodynamic alpha^2-dynamo and of anextended version of the hydrodynamic Squire equation.