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

Area of Science:

• Soft Matter Physics
• Materials Science
• Spectroscopy

Background:

• X-ray photon correlation spectroscopy (XPCS) is vital for studying dynamics across various timescales and length scales.
• Two-time correlation functions (TTCs) are standard for tracking non-equilibrium dynamics in XPCS, enabling one-time correlation extraction.
• Existing theoretical frameworks for TTC analysis are largely based on equilibrium systems with constant parameters.

Purpose of the Study:

• To explore widely used approaches for calculating TTCs in XPCS.
• To investigate common methods for extracting information from correlation functions.
• To address the challenges of analyzing TTCs in non-equilibrium systems compared to equilibrium systems.

Main Methods:

• Analysis of two-time correlation function (TTC) calculations.
• Exploration of projection ('cut') methods for TTC analysis.
• Comparison of dynamic information extraction from equilibrium and non-equilibrium systems.

Main Results:

• Non-equilibrium systems present unique challenges for TTC analysis due to temporal variations in fundamental parameters.
• Different TTC projections can yield divergent results in non-equilibrium scenarios.
• Established methods for equilibrium systems may require adaptation for accurate non-equilibrium dynamics characterization.

Conclusions:

• Accurate analysis of XPCS data in non-equilibrium systems necessitates careful consideration of temporal parameter variations.
• The study provides insights into comparing dynamics between equilibrium and non-equilibrium states using TTCs.
• Further development of theoretical and analytical tools is needed for robust XPCS studies of complex dynamics.