On the analysis of two-time correlation functions: equilibrium vs non-equilibrium systems

TL;DR

This paper examines the analysis of two-time correlation functions in X-ray photon correlation spectroscopy, highlighting differences between equilibrium and non-equilibrium systems and evaluating methods for extracting dynamical information.

Contribution

It provides a comparative analysis of TTC calculation approaches for equilibrium and non-equilibrium systems, addressing challenges in interpreting non-stationary dynamics.

Findings

Divergent results can arise from different TTC projections in non-equilibrium systems.

Common methods may need adaptation for accurate analysis of non-stationary dynamics.

Theoretical foundations are more established for equilibrium than non-equilibrium systems.

Abstract

X-ray photon correlation spectroscopy (XPCS) is a powerful tool for the investigation of dynamics covering a broad range of time and length scales. The two-time correlation function (TTC) is commonly used to track non-equilibrium dynamical evolution in XPCS measurements, followed by the extraction of one-time correlations. While the theoretical foundation for the quantitative analysis of TTCs is primarily established for equilibrium systems, where key parameters such as diffusion remain constant, non-equilibrium systems pose a unique challenge. In such systems, different projections ("cuts") of the TTC may lead to divergent results if the underlying fundamental parameters themselves are subject to temporal variations. This article explores widely used approaches for TTC calculations and common methods for extracting relevant information from correlation functions on case studies, particularly in the light of comparing dynamics in equilibrium and non-equilibrium systems.