Coupling of eigenvalues of complex matrices at diabolic and exceptional points

Alexander Seyranian, Oleg Kirillov, Alexei Mailybaev

Research output: Contribution to journalArticlepeer-review

90 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 languageEnglish
Pages (from-to)1723-1740
JournalJournal of Physics A: Mathematical and General
Volume38
Issue number8
DOIs
Publication statusPublished - 9 Feb 2005

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