Signatures of three coalescing eigenfunctions

2011/10/31 by Gilles Demange, Eva-Maria Graefe
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/1751-8113/45/2/025303

published as J. Phys. A 45 (2012) 025303 · 14 pages, 4 figures. Typos corrected, slightly extended, to appear in J. Phys. A

arxiv created 2011/12/01 · openalex publication_date 2011/12/08 · arxiv updated 2011/12/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

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 characterization 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.

Citations

• Asymmetric scattering and nonorthogonal mode patterns in optical microspirals
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