Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation

Abstract

The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical surface for different kinds of perturbing matrices are derived. As a physical application, singularities of the surfaces of refractive indices in crystal optics are studied.

23 pages, 7 figures

References in corpus (5)

• Exceptional Points of Non-hermitian Operators
• Observation of a Chiral State in a Microwave Cavity
• Observation of Exceptional Points in Electronic Circuits
• Coupling of eigenvalues of complex matrices at diabolic and exceptional points
• Berry Phase of a Resonant State

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