Measuring adiabaticity in nonequilibrium quantum systems

Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum mechanics naturally characterizes regimes of quantum dynamics and provides an appealingly visual tool for assessing their degree of adiabaticity. Further, the dynamic trajectories of quantum systems in metric space suggest a lack of ergodicity, thus providing a better understanding of the fundamental one-to-one mapping between densities and wave functions.