Coupling of eigenvalues of complex matrices at diabolic and exceptional points

2004/11/30 by A. A. Mailybaev, A P Seyranian, O. N. Kirillov +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Matrix Theory and Algorithms #Numerical methods for differential equations #math-ph #math.MP #msc:15A21

paper · pdf · doi:10.1088/0305-4470/38/8/009

published as J. Phys. A: Math. Gen. 38 (2005) 1723-1740. · 19 pages, 8 figures

arxiv created 2005/01/07 · openalex publication_date 2005/02/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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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