Title :
On eigenvalue surfaces near a diabolic point
Author :
Kirillov, O.N. ; Mailybaev, A.A. ; Seyranian, A.P.
Author_Institution :
Inst. of Mech., Moscow State Lomonosov Univ., Russia
Abstract :
The paper presents a 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.
Keywords :
Hermitian matrices; eigenvalues and eigenfunctions; refractive index; Hermitian matrix; arbitrary complex perturbation; asymptotic formulae; conical surface deformation; crystal optics; diabolic point; eigenvalue surfaces; real symmetric matrix; refractive indices; Bifurcation; Chemistry; Eigenvalues and eigenfunctions; Optical filters; Optical refraction; Optical variables control; Physics; Quantum mechanics; Surface treatment; Symmetric matrices;
Conference_Titel :
Physics and Control, 2005. Proceedings. 2005 International Conference
Print_ISBN :
0-7803-9235-3
DOI :
10.1109/PHYCON.2005.1514000
