Physics – Quantum Physics
Scientific paper
2011-10-07
J. Phys. A 45 (2012) 025303
Physics
Quantum Physics
14 pages, 4 figures. Typos corrected, slightly extended, to appear in J. Phys. A
Scientific paper
10.1088/1751-8113/45/2/025303
Parameter dependent non-Hermitian quantum systems typically not only possess eigenvalue degeneracies, but also degeneracies of the corresponding eigenfunctions at exceptional points. While the effect of two coalescing eigenfunctions on cyclic parameter variation is well investigated, little attention has hitherto been paid to the effect of more than two coalescing eigenfunctions. Here a characterisation of behaviours of symmetric Hamiltonians with three coalescing eigenfunctions is presented, using perturbation theory for non-Hermitian operators. Two main types of parameter perturbations need to be distinguished, which lead to characteristic eigenvalue and eigenvector patterns under cyclic variation. A physical system is introduced for which both behaviours might be experimentally accessible.
Demange Gilles
Graefe Eva-Maria
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