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

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

2004-11-02

arxiv.org/abs/math-ph/0411006v1

J. Phys. A: Math. Gen. 38 (2005) 5531--5546

Physics

Mathematical Physics

23 pages, 7 figures

Scientific paper

10.1088/0305-4470/38/24/007

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.

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