Coupling of eigenvalues of complex matrices at diabolic and exceptional points
Mathematical Physics
2007-05-23 v4 math.MP
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.
Cite
@article{arxiv.math-ph/0411024,
title = {Coupling of eigenvalues of complex matrices at diabolic and exceptional points},
author = {A. A. Mailybaev and O. N. Kirillov and A. P. Seyranian},
journal= {arXiv preprint arXiv:math-ph/0411024},
year = {2007}
}
Comments
19 pages, 8 figures