Signatures of three coalescing eigenfunctions

By G. Demange, Eva-Maria Graefe. 2011

183 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/87ceefe7036910eb575192b47c86e03cb0ef9d18

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In Atomic and Molecular Physics, and Optics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system (2018, background): “Around the n-th order EP [27, 28], where the coalescence of n levels occurs, the eigenenergy shows an 1/n dependence on the perturbative parameter .”
Biorthogonal quantum mechanics (2013, unknown): “, in [21, 39, 40].”
Exceptional points in optics and photonics (2019, background): “In principle, when more than two eigenvalue surfaces are involved, it is also possible thatmore than two surfaces simultaneously collapse at one point, creating a higher-order exceptional point (40, 41).”
Exceptional topology of non-Hermitian systems (2019, unknown): “Demange and Graefe (2012) showed, however, that not all higher-order EPs scale in this fashion.”