Coupling of eigenvalues of complex matrices at diabolic and exceptional points

Details Coupling of eigenvalues of complex matrices at diabolic and exceptional points Coupling of eigenvalues of complex matrices at diabolic and exceptional points

2004-11-05

arxiv.org/abs/math-ph/0411024v4

J. Phys. A: Math. Gen. 38 (2005) 1723-1740.

Physics

Mathematical Physics

19 pages, 8 figures

Scientific paper

10.1088/0305-4470/38/8/009

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.

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