TY - JOUR
T1 - Coupling of eigenvalues of complex matrices at diabolic and exceptional points
AU - Seyranian, Alexander
AU - Kirillov, Oleg
AU - Mailybaev, Alexei
PY - 2005/2/9
Y1 - 2005/2/9
N2 - 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.
AB - 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.
U2 - 10.1088/0305-4470/38/8/009
DO - 10.1088/0305-4470/38/8/009
M3 - Article
SN - 0305-4470
VL - 38
SP - 1723
EP - 1740
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 8
ER -