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.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

arXiv:2610.17855 [quant-ph]

(or arXiv:2610.17855v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.17855 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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