How Slow Is Slow Enough? Critical Timescales and Irreversibility in Non-Hermitian Dynamics

Slowly driven non-Hermitian systems exhibit remarkable dynamical phenomena, including the breakdown of adiabatic following, non-adiabatic state transitions, and chiral state conversion. Although these effects have been extensively studied, a fundamental question remains: how slow must the driving be for a non-adiabatic transition to fully develop?

In this talk, I will present an analytical framework for determining the critical timescale governing these transitions in non-Hermitian two-level systems driven along closed parameter loops. We derive a general expression for the critical timescale and investigate its dependence on the geometry of the driving trajectory, including loops that encircle exceptional points. Particular attention is given to the mechanisms initiating non-adiabatic transitions, highlighting the competing roles of the Stokes phenomenon and finite precision. We show how finite information resolution can determine the onset of state conversion and establish a connection between non-adiabatic dynamics, chirality, and precision-induced irreversibility.