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

2004/11/02 by O. N. Kirillov, Oleg N. Kirillov, Alexei A. Mailybaev +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Elasticity and Wave Propagation #Quantum chaos and dynamical systems #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/38/24/007

published as J. Phys. A: Math. Gen. 38 (2005) 5531--5546 · 23 pages, 7 figures

arxiv created 2004/11/02 · openalex publication_date 2005/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. 1

Citations

• Coupling of eigenvalues of complex matrices at diabolic and exceptional points

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