Dynamical fluctuations close to Jamming versus Vibrational Modes : a pedagogical discussion illustrated on hard spheres simulations, colloidal and granular experiments

TL;DR

This paper reviews the theoretical and experimental analysis of vibrational modes near the jamming transition in disordered systems, emphasizing data analysis techniques and their limitations in colloidal and granular experiments.

Contribution

It provides a comprehensive overview of interpreting eigenmodes in disordered systems and discusses methodological challenges in experimental data analysis near jamming.

Findings

Eigenmodes can be extracted from covariance matrices in experiments.

Experimental resolution and sampling affect the interpretation of vibrational modes.

The harmonic approximation has limitations in describing real disordered systems.

Abstract

Studying the jamming transition of granular and colloidal systems, has lead to a proliferation of theoretical and numerical results formulated in the language of the eigenspectrum of the dynamical matrix for these disordered system. Only recently however, these modes have been accessed experimentally in colloidal and granular media, computing the eigenmodes of the covariance matrix of the particle positions. At the same time new conceptual and methodological questions have appeared, regarding the interpretation of these results. In the present paper, we first give an overview of the theoretical framework which is appropriate to discuss the interpretation of the eigenmodes and eigenvalues of the correlation matrix in terms of the vibrational properties of these systems. We then illustrate several aspects of the statistical and data analysis techniques which are necessary to extract reliable results from experimental data. Concentrating on the case of hard sphere simulations, colloidal and granular experiments, we discuss how to test the existence of a metastable state, the statistical independence of the sampling, the effect of the experimental resolution, and the harmonic hypothesis underlying the approach, highlighting both its promises and limitations.