Tracking Adiabaticity in Non-Equilibrium Many-Body Systems: The Hard Case of the X-ray Photoemission in Metals

TL;DR

This paper evaluates metrics-based techniques to reliably track adiabaticity in complex many-body quantum systems, specifically analyzing x-ray photoemission in metals, and finds the local density distance to be effective and experimentally accessible.

Contribution

It demonstrates that the local density distance can effectively track adiabaticity in out-of-equilibrium many-body systems, surpassing traditional quantum adiabatic criteria.

Findings

Metrics-based methods remain valid for complex systems.

Local density distance provides additional insights into system dynamics.

Quantum adiabatic criterion often fails in out-of-equilibrium scenarios.

Abstract

The level of adiabaticity determines many properties of time-dependent quantum systems. However, a reliable and easy-to-apply criterion to check and track it remains an open question, especially for complex many-body systems. Here we test techniques based on metrics which have been recently proposed to quantitatively characterize and track adiabaticity. We investigate the time evolution of x-ray photoemission in metals, which displays a strongly out-of-equilibrium character, continuum energy spectrum, and experiences the Anderson orthogonality catastrophe: a nightmarish scenario for this type of test. Our results show that the metrics-based methods remains valid. In particular, we demonstrate that the natural local density distance is able not only to track adiabaticity, but also to provide information not captured by the corresponding Bures' or trace distances about the system's dynamics. In the process, we establish an explicit upper limit for this local density distance in terms of the trace distance, and derive a simple analytical solution that accurately describes the time evolution of a Fermi gas with a localized scattering potential for a large range of parameters. We also demonstrate that, for x-ray photoemission, the quantum adiabatic criterion, as commonly used, fails to predict and track adiabaticity. The local particle density is typically much simpler to compute than the corresponding quantum state and it is experimentally measurable: this makes the method tested extremely appealing.