Critical timescales for chiral state conversion and irreversibility

Abstract: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 $m$ of digits in base $\beta$ (bits for $\beta=2$). For loops encircling an exceptional point, the Stokes seed only sets an intermediate plateau; the final transition is again seeded by the precision floor, and $T_{\mathrm{cr}}$ remains linear in $m$. 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 $T> T_{\mathrm{cr}}$.

Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other)

arXiv:2604.01918 [quant-ph]

(or arXiv:2604.01918v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.01918 Focus to learn more arXiv-issued DOI via DataCite

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