Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation
arXiv:math-ph/0411006 · doi:10.1088/0305-4470/38/24/007
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