Fixed-Point Bifurcations and Path-Information Bounds in Nonlinear Exceptional-Point Sensing
Abstract
Nonlinear exceptional points (NEPs) were proposed to circumvent the noise--responsivity cancellation that limits linear exceptional-point sensors. At an NEP, the stationary frequency response can be singular while the Hamiltonian Petermann factor remains finite, suggesting a genuine signal-to-noise ratio (SNR) enhancement. Yet recent model-specific analyses of nonlinear fluctuations have reached conflicting conclusions. We prove that any singular stationary frequency response requires a fixed-point bifurcation of the nonlinear dynamics. In local fluctuation regimes, the singularities in responsivity and long-time frequency uncertainty are both set by the critical relaxation rate, leading to exact cancellation in the SNR and precluding any divergent enhancement. Furthermore, we derive a path-information bound that applies across both local and nonlinear fluctuation regimes and places a finite ceiling on the long-time SNR enhancement. Notably, this upper bound is attainable in the local fluctuation regime, implying that frequency readout under such parameter settings is information-optimal.
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BibTeX
@misc{yu2026fixedpoint,
title = {{Fixed-Point Bifurcations and Path-Information Bounds in Nonlinear Exceptional-Point Sensing}},
author = {Xue-Hao Yu and Cong-Feng Qiao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39046},
eprint = {2609.39046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39046},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fixed-Point Bifurcations and Path-Information Bounds in Nonlinear Exceptional-Point Sensing
AU - Xue-Hao Yu
AU - Cong-Feng Qiao
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39046
UR - https://arxiv.org/abs/2609.39046
AB - Nonlinear exceptional points (NEPs) were proposed to circumvent the noise--responsivity cancellation that limits linear exceptional-point sensors. At an NEP, the stationary frequency response can be singular while the Hamiltonian Petermann factor remains finite, suggesting a genuine signal-to-noise ratio (SNR) enhancement. Yet recent model-specific analyses of nonlinear fluctuations have reached conflicting conclusions. We prove that any singular stationary frequency response requires a fixed-point bifurcation of the nonlinear dynamics. In local fluctuation regimes, the singularities in responsivity and long-time frequency uncertainty are both set by the critical relaxation rate, leading to exact cancellation in the SNR and precluding any divergent enhancement. Furthermore, we derive a path-information bound that applies across both local and nonlinear fluctuation regimes and places a finite ceiling on the long-time SNR enhancement. Notably, this upper bound is attainable in the local fluctuation regime, implying that frequency readout under such parameter settings is information-optimal.
ER -