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

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.

8 pages, 3 figures, Conf. Proc., 3rd International Workshop "Pseudo-Hermitian Hamiltonians in Quantum Physics", Istanbul, Turkey, June 20-22, 2005

References in corpus (10)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Space of State Vectors in PT Symmetrical Quantum Mechanics
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Asymmetric polarity reversals, bimodal field distribution, and coherence resonance in a spherically symmetric mean-field dynamo model
• Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem
• The MHD alpha^2-dynamo, Z_2-graded pseudo-Hermiticity, level crossings and exceptional points of branching type

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