Classical observable coalescence as a discriminating diagnostic for spectral degeneracies in non-Hermitian systems
Abstract
Exceptional points (EPs) are conventionally identified through eigenvector coalescence, inaccessible in classical platforms lacking a Hamiltonian spectrum. We introduce classical observable coalescence as a diagnostic identifying EPs directly from physical configurations, and demonstrate it in a known non-Hermitian Ising chain with coupling J and staggered imaginary field γ, chosen for verifiability against established quantum results. A mean-field reduction of the Heisenberg dynamics yields equilibrium branches organising into two symmetry-related families whose fusion at the boundary of the EP supersurface |γ|=|J| exhibits the characteristic √(J2−γ2) branch-point structure and two-sheeted Riemann topology. Crucially, the degeneracy at $γ=0,η=0 $ is shown to be a diabolic point, producing no observable coalescence, establishing the diagnostic as discriminating rather than merely suggestive. An exact Jordan-Wigner and Bogoliubov-de Gennes treatment confirms eigenvector coalescence at the same threshold, and a coupled gain-loss circuit realisation is proposed, establishing classical observables as experimentally accessible signatures of non-Hermitian criticality.
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BibTeX
@misc{nkaimbi2026classical,
title = {{Classical observable coalescence as a discriminating diagnostic for spectral degeneracies in non-Hermitian systems}},
author = {P. K. Nkaimbi and C. A. Mba and A. B. Moubissi and M. R. Kamsap and L. C. Fai and M. E. Ateuafack and M. N. Jipdi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05877},
eprint = {2610.05877},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05877},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical observable coalescence as a discriminating diagnostic for spectral degeneracies in non-Hermitian systems
AU - P. K. Nkaimbi
AU - C. A. Mba
AU - A. B. Moubissi
AU - M. R. Kamsap
AU - L. C. Fai
AU - M. E. Ateuafack
AU - M. N. Jipdi
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05877
UR - https://arxiv.org/abs/2610.05877
AB - Exceptional points (EPs) are conventionally identified through eigenvector coalescence, inaccessible in classical platforms lacking a Hamiltonian spectrum. We introduce classical observable coalescence as a diagnostic identifying EPs directly from physical configurations, and demonstrate it in a known non-Hermitian Ising chain with coupling J and staggered imaginary field γ, chosen for verifiability against established quantum results. A mean-field reduction of the Heisenberg dynamics yields equilibrium branches organising into two symmetry-related families whose fusion at the boundary of the EP supersurface |γ|=|J| exhibits the characteristic √(J^2−γ^2) branch-point structure and two-sheeted Riemann topology. Crucially, the degeneracy at $γ=0,η=0 $ is shown to be a diabolic point, producing no observable coalescence, establishing the diagnostic as discriminating rather than merely suggestive. An exact Jordan-Wigner and Bogoliubov-de Gennes treatment confirms eigenvector coalescence at the same threshold, and a coupled gain-loss circuit realisation is proposed, establishing classical observables as experimentally accessible signatures of non-Hermitian criticality.
ER -