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

Oleg Kirillov; Alexei Mailybaev; Alexander Seyranian

doi:10.1088/0305-4470/38/24/007

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

Oleg Kirillov, Alexei Mailybaev, Alexander Seyranian

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53 Citations (Scopus)

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.

Original language	English
Pages (from-to)	5531-5546
Journal	Journal of Physics A: Mathematical and General
Volume	38
Issue number	24
DOIs	https://doi.org/10.1088/0305-4470/38/24/007
Publication status	Published - 1 Jun 2005

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title = "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.",

author = "Oleg Kirillov and Alexei Mailybaev and Alexander Seyranian",

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AU - Kirillov, Oleg

AU - Mailybaev, Alexei

AU - Seyranian, Alexander

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Y1 - 2005/6/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/19844373251

U2 - 10.1088/0305-4470/38/24/007

DO - 10.1088/0305-4470/38/24/007

M3 - Article

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VL - 38

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EP - 5546

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 24

ER -

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

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