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

TL;DR

This paper investigates higher order spectral branch points in Krein space operators, demonstrating their occurrence in PT-symmetric matrix models, MHD dynamos, and extended hydrodynamic equations, revealing complex spectral transition phenomena.

Contribution

It provides a semi-analytical study of coalescing square root branch points and illustrates their presence in physical models like MHD dynamos and hydrodynamic equations.

Findings

Higher order branch points can form from coalescing exceptional points.

Numerical evidence of these points in MHD alpha^2-dynamo spectra.

Semi-analytical methods elucidate spectral transition mechanisms.

Abstract

The spectra of self-adjoint operators in Krein spaces are known to possess real sectors as well as sectors of pair-wise complex conjugate eigenvalues. Transitions from one spectral sector to the other are a rather generic feature and they usually occur at exceptional points of square root branching type. For certain parameter configurations two or more such exceptional points may happen to coalesce and to form a higher order branch point. We study the coalescence of two square root branch points semi-analytically for a PT-symmetric 4x4 matrix toy model and illustrate numerically its occurrence in the spectrum of the 2x2 operator matrix of the magnetohydrodynamic alpha^2-dynamo and of an extended version of the hydrodynamic Squire equation.