Collective Hard Core Interactions Leave Multiscale Signatures in Number Fluctuation Spectra

TL;DR

This paper introduces a trajectory-free method using number fluctuation spectra to analyze multiscale dynamics in dense suspensions, revealing how interactions influence microscopic and collective behaviors across scales.

Contribution

The study presents a novel approach combining experiments and theory to connect spectral features with underlying particle dynamics and interactions in dense suspensions.

Findings

High-frequency scalings relate to self-diffusion.

Low-frequency scalings reveal long-lived correlations.

Interactions produce distinct spectral signatures at different scales.

Abstract

A full understanding of transport in dense, interacting suspensions requires analysis frameworks sensitive to self and collective dynamics across all relevant spatial and temporal scales. Here we introduce a trajectory-free approach to address this problem based on the power spectral density of particle number fluctuations (N-PSD). By combining colloidal experiments and theory we show that the N-PSD naturally probes behaviour across multiple important dynamic regimes and we fully uncover the mechanistic origins of characteristic spectral scalings and timescales. In particular, we demonstrate that while high-frequency scalings link to self-diffusion, low-frequency scalings sensitively capture long-lived correlations and collective dynamics. In this regime, interactions lead to non-trivial spectral signatures, governed by pairwise particle exchange at small length scales and collective rearrangements over large scales. Our findings thus provide important insight into the effect of interactions on microscopic dynamics and fluctuation phenomena and establish a powerful new tool with which to probe dynamics in complex systems.