Strong and weak coupling of eigenvalues of complex matrices

Alexei Mailybaev; O. N. Kirillov; A. P. Seyranian

doi:10.1109/PHYCON.2005.1513999

Strong and weak coupling of eigenvalues of complex matrices

Alexei Mailybaev, O. N. Kirillov, A. P. Seyranian

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

Abstract

The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension smoothly 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 numerical examples from crystal optics Illustrate effectiveness and accuracy of the presented theory.

Original language	English
Title of host publication	2005 International Conference on Physics and Control, PhysCon 2005, Proceedings
Editors	A L Fradkov
Place of Publication	St Petersburg
Pages	312-318
Number of pages	7
Volume	2005
DOIs	https://doi.org/10.1109/PHYCON.2005.1513999
Publication status	Published - 2005
Externally published	Yes
Event	2005 International Conference on Physics and Control, PhysCon 2005 - St. Petersburg, Russian Federation Duration: 24 Aug 2005 → 26 Aug 2005

Conference

Conference	2005 International Conference on Physics and Control, PhysCon 2005
Country/Territory	Russian Federation
City	St. Petersburg
Period	24/08/05 → 26/08/05

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10.1109/PHYCON.2005.1513999

Cite this

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title = "Strong and weak coupling of eigenvalues of complex matrices",

abstract = "The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension smoothly 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 numerical examples from crystal optics Illustrate effectiveness and accuracy of the presented theory.",

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note = "2005 International Conference on Physics and Control, PhysCon 2005 ; Conference date: 24-08-2005 Through 26-08-2005",

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Mailybaev, A, Kirillov, ON & Seyranian, AP 2005, Strong and weak coupling of eigenvalues of complex matrices. in AL Fradkov (ed.), 2005 International Conference on Physics and Control, PhysCon 2005, Proceedings. vol. 2005, 1513999, St Petersburg, pp. 312-318, 2005 International Conference on Physics and Control, PhysCon 2005, St. Petersburg, Russian Federation, 24/08/05. https://doi.org/10.1109/PHYCON.2005.1513999

Strong and weak coupling of eigenvalues of complex matrices. / Mailybaev, Alexei; Kirillov, O. N.; Seyranian, A. P.
2005 International Conference on Physics and Control, PhysCon 2005, Proceedings. ed. / A L Fradkov. Vol. 2005 St Petersburg, 2005. p. 312-318 1513999.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Mailybaev, Alexei

AU - Kirillov, O. N.

AU - Seyranian, A. P.

PY - 2005

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N2 - The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension smoothly 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 numerical examples from crystal optics Illustrate effectiveness and accuracy of the presented theory.

AB - The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension smoothly 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 numerical examples from crystal optics Illustrate effectiveness and accuracy of the presented theory.

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DO - 10.1109/PHYCON.2005.1513999

M3 - Conference contribution

AN - SCOPUS:33746699692

SN - 9780780392342

VL - 2005

SP - 312

EP - 318

BT - 2005 International Conference on Physics and Control, PhysCon 2005, Proceedings

A2 - Fradkov, A L

CY - St Petersburg

T2 - 2005 International Conference on Physics and Control, PhysCon 2005

Y2 - 24 August 2005 through 26 August 2005

ER -

Strong and weak coupling of eigenvalues of complex matrices

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