Derives explicit recursion relations for Puiseux expansion coefficients in non-Hermitian perturbation theory at exceptional points of order N, with two equivalent forms for the first two eigenvalue corrections.
Signatures of three coalescing eigenfunctions
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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 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.
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quant-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Non-Hermitian Rayleigh-Schr\"{o}dinger-like Perturbation Theory at Exceptional Point
Derives explicit recursion relations for Puiseux expansion coefficients in non-Hermitian perturbation theory at exceptional points of order N, with two equivalent forms for the first two eigenvalue corrections.