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 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.

19 pages, 8 figures

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• Exceptional Points of Non-hermitian Operators
• Repulsion of Resonance States and Exceptional Points
• Observation of a Chiral State in a Microwave Cavity
• Observation of Exceptional Points in Electronic Circuits

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