Non-Hermitian Rayleigh-Schrödinger-like perturbation theory at exceptional point
- 1National Sun Yat-sen University
Abstract
We develop a Rayleigh-Schrödinger-like perturbation theory for non-Hermitian quantum systems at an exceptional point of order N. Working in the Jordan basis of the unperturbed Hamiltonian and employing a Puiseux expansion of the perturbed eigenvalues and eigenstates, we derive explicit recursion relations for the expansion coefficients. The corrections to the unperturbed eigenvalue in the Puiseux expansion govern the splitting near the exceptional point; the first two are obtained iteratively in two equivalent forms. One is given in terms of the perturbation Hamiltonian in the Jordan basis, and the other in terms of the generator that drives the eigenvalue evolution with respect to the perturbation. The latter constitutes the exceptional-point counterpart of a geometric perturbation method recently developed for the non-exceptional-point regime. Both representations are verified explicitly for the N = 2 and N = 3 cases. We then apply the theory to an order-3 exceptional point realized in a dissipative three-level trapped-ion system.
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BibTeX
@article{chen2026nonhermitian,
title = {{Non-Hermitian Rayleigh-Schrödinger-like perturbation theory at exceptional point}},
author = {Wei-Ming Chen and Chia-Yi Ju},
journal = {New Journal of Physics},
year = {2026},
month = oct,
doi = {10.1088/1367-2630/aeba0b},
url = {https://iopscience.iop.org/article/10.1088/1367-2630/aeba0b},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Non-Hermitian Rayleigh-Schrödinger-like perturbation theory at exceptional point
AU - Wei-Ming Chen
AU - Chia-Yi Ju
PY - 2026
DA - 2026/10/27
JO - New Journal of Physics
DO - 10.1088/1367-2630/aeba0b
UR - https://iopscience.iop.org/article/10.1088/1367-2630/aeba0b
AB - We develop a Rayleigh-Schrödinger-like perturbation theory for non-Hermitian quantum systems at an exceptional point of order N. Working in the Jordan basis of the unperturbed Hamiltonian and employing a Puiseux expansion of the perturbed eigenvalues and eigenstates, we derive explicit recursion relations for the expansion coefficients. The corrections to the unperturbed eigenvalue in the Puiseux expansion govern the splitting near the exceptional point; the first two are obtained iteratively in two equivalent forms. One is given in terms of the perturbation Hamiltonian in the Jordan basis, and the other in terms of the generator that drives the eigenvalue evolution with respect to the perturbation. The latter constitutes the exceptional-point counterpart of a geometric perturbation method recently developed for the non-exceptional-point regime. Both representations are verified explicitly for the N = 2 and N = 3 cases. We then apply the theory to an order-3 exceptional point realized in a dissipative three-level trapped-ion system.
SN - 1367-2630
ER -