Elastic fluctuations as observed in a confocal slice

TL;DR

This paper investigates how three-dimensional elastic fluctuations in colloidal solids manifest in two-dimensional confocal slices, revealing unique dispersion features and providing formulas to infer 3D properties from 2D observations.

Contribution

It develops an effective theory for projected crystals, showing non-standard dispersion exponents and deriving formulas to extract 3D elastic constants from 2D experimental data.

Findings

Effective 2D elastic properties with analytic expressions

Non-standard dispersion exponents in projected crystals

Method to infer 3D elastic constants from 2D slices

Abstract

Recent confocal experiments on colloidal solids motivate a fuller study of the projection of three-dimensional fluctuations onto a two-dimensional confocal slice. We show that the effective theory of a projected crystal displays several exceptional features, such as non-standard exponents in the dispersion relations. We provide analytic expressions for the effective two-dimensional elastic properties which allow one to work back from sliced experimental observations to three-dimensional elastic constants.