Universal critical timescales in slow non-Hermitian dynamics

Quantum Physics [Submitted on 2 Apr 2026] Universal critical timescales in slow non-Hermitian dynamics Giorgos Pappas, Diego Bautista Avilés, Luis E. F. Foa Torres, Vassos Achilleos Non-Hermitian systems driven along slow parametric loops undergo non-adiabatic transitions whose outcome depends sensitively on the driving speed, yet no explicit formula has been available for the critical timescale T_{\mathrm{cr}} at which these transitions develop. Using a 2\times 2 Hamiltonian with circular parameter trajectories, we derive T_{\mathrm{cr}} = \mathcal{G}\,\ln(1/|\Delta|) in closed form for non-encircling loops, phase-shifted loops, offset loops, and loops encircling exceptional points, where \mathcal{G} is a geometry-dependent growth factor and \Delta is the instability seed. This formula sharply separates the regime where the system remains in the averagely dominant eigenstate (T< T_{\mathrm{cr}}) from the superadiabatic regime where the instantaneous dominant eigenstate takes over (T> T_{\mathrm{cr}}), resolving the apparent tension between the previous literature. We identify two competing seeds: a geometric Stokes multiplier and the finite-precision floor. When the geometric seed vanishes, precision alone governs the transition, yielding T_{\mathrm{cr}} \propto m\ln\beta, linear in the number of precision bits m. This provides a purely forward-evolution manifestation of precision-induced irreversibility (PIR)~\cite{PIR}, demonstrating that the fundamental limit identified through echo protocols also controls the outcome of slow non-Hermitian dynamics without requiring time reversal. For PT-symmetric energy spectra, T_{\mathrm{cr}} additionally determines the onset of chirality: the dynamics is non-chiral for T< T_{\mathrm{cr}} and chiral for T> T_{\mathrm{cr}}. Comments: 11 pages, 6 Figures Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other) Cite as: arXiv:2604.01918 [quant-ph]   (or arXiv:2604.01918v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.01918 Focus to learn more Submission history From: Vassos Achilleos A [view email] [v1] Thu, 2 Apr 2026 11:35:16 UTC (3,444 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.other References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)