Measuring adiabaticity in non-equilibrium quantum systems

TL;DR

This paper introduces a metric-space approach to quantify adiabaticity in non-equilibrium quantum systems, offering visual tools and insights into quantum dynamics and the density-wavefunction relationship.

Contribution

It presents a novel metric-space framework for characterizing adiabaticity and analyzing quantum dynamics, enhancing understanding of out-of-equilibrium quantum behavior.

Findings

Metric-space approach effectively characterizes adiabaticity regimes

Quantum trajectories in metric space reveal non-ergodic behavior

Provides visual tools for assessing quantum dynamical regimes

Abstract

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 wavefunctions.