The range and nature of effective interactions in hard-sphere solids

TL;DR

This paper investigates how effective interactions in hard-sphere solids, observed via particle displacement correlations, differ between thermally agitated and non-thermal systems, using numerical data for comparison.

Contribution

It clarifies the distinction between true pair interactions and effective interactions derived from correlation matrices in thermal systems.

Findings

Effective interactions differ from true pair potentials in thermally agitated systems.

Numerical data confirms the differences between thermal and non-thermal effective interactions.

The study provides insights into interpreting correlation-based interaction measurements.

Abstract

Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential between particles. If the system is thermally agitated, however, only an effective interaction is accessible from the correlation matrix. We show how this effective interaction differs from the non-thermal case by comparing with high-statistics numerical data from hard-sphere crystals.