Emergent Non-Biorthogonal Born Rule at Dynamical Quantum Phase Transitions
Abstract
Non-Hermitian dynamics possesses distinct left and right eigenstates, but their normalization freedom obscures a direct probabilistic interpretation. Starting from a globally Hermitian system governed by the standard Born rule, we generalize dynamical quantum phase transitions (DQPTs) from a reference state to a physical subspace. This generalization provides a clear probabilistic interpretation of left and right states: when each state is normalized to itself, their mutual overlap determines a directly accessible dynamical transition rate. We discuss the new phenomena governed by this emergent non-biorthogonal Born rule and further identify a class of exceptional-point DQPTs (EP-DQPTs), at which the eigenstates of the critical propagator coalesce. Our theory places the probabilistic interpretation of non-Hermitian quantum mechanics on the firm footing of Hermitian quantum mechanics.
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BibTeX
@misc{yang2026emergent,
title = {{Emergent Non-Biorthogonal Born Rule at Dynamical Quantum Phase Transitions}},
author = {Wei-Wei Yang and Henning Schomerus and Jiangping Hu and Zhesen Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17855},
eprint = {2610.17855},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17855},
}
RIS
TY - UNPB
TI - Emergent Non-Biorthogonal Born Rule at Dynamical Quantum Phase Transitions
AU - Wei-Wei Yang
AU - Henning Schomerus
AU - Jiangping Hu
AU - Zhesen Yang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17855
UR - https://arxiv.org/abs/2610.17855
AB - Non-Hermitian dynamics possesses distinct left and right eigenstates, but their normalization freedom obscures a direct probabilistic interpretation. Starting from a globally Hermitian system governed by the standard Born rule, we generalize dynamical quantum phase transitions (DQPTs) from a reference state to a physical subspace. This generalization provides a clear probabilistic interpretation of left and right states: when each state is normalized to itself, their mutual overlap determines a directly accessible dynamical transition rate. We discuss the new phenomena governed by this emergent non-biorthogonal Born rule and further identify a class of exceptional-point DQPTs (EP-DQPTs), at which the eigenstates of the critical propagator coalesce. Our theory places the probabilistic interpretation of non-Hermitian quantum mechanics on the firm footing of Hermitian quantum mechanics.
ER -