Coupling of eigenvalues of complex matrices at diabolic and exceptional points

Alexander Seyranian; Oleg Kirillov; Alexei Mailybaev

doi:10.1088/0305-4470/38/8/009

Coupling of eigenvalues of complex matrices at diabolic and exceptional points

Alexander Seyranian, Oleg Kirillov, Alexei Mailybaev

Research output: Contribution to journal › Article › peer-review

135 Citations (Scopus)

Abstract

The paper presents a general theory of coupling of eigenvalues of complex matrices of an arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossing and avoided crossing scenarios. Two physical examples illustrate effectiveness and accuracy of the presented theory.

Original language	English
Pages (from-to)	1723-1740
Journal	Journal of Physics A: Mathematical and General
Volume	38
Issue number	8
DOIs	https://doi.org/10.1088/0305-4470/38/8/009
Publication status	Published - 9 Feb 2005

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title = "Coupling of eigenvalues of complex matrices at diabolic and exceptional points",

abstract = "The paper presents a general theory of coupling of eigenvalues of complex matrices of an arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossing and avoided crossing scenarios. Two physical examples illustrate effectiveness and accuracy of the presented theory.",

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T1 - Coupling of eigenvalues of complex matrices at diabolic and exceptional points

AU - Seyranian, Alexander

AU - Kirillov, Oleg

AU - Mailybaev, Alexei

PY - 2005/2/9

Y1 - 2005/2/9

N2 - The paper presents a general theory of coupling of eigenvalues of complex matrices of an arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossing and avoided crossing scenarios. Two physical examples illustrate effectiveness and accuracy of the presented theory.

AB - The paper presents a general theory of coupling of eigenvalues of complex matrices of an arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossing and avoided crossing scenarios. Two physical examples illustrate effectiveness and accuracy of the presented theory.

UR - https://www.scopus.com/pages/publications/14544298830

U2 - 10.1088/0305-4470/38/8/009

DO - 10.1088/0305-4470/38/8/009

M3 - Article

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VL - 38

SP - 1723

EP - 1740

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 8

ER -

Coupling of eigenvalues of complex matrices at diabolic and exceptional points

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