Rigidity in Condensed Matter and its Origin in Configurational Constraint

TL;DR

This paper demonstrates that the shear modulus in condensed matter systems can be universally expressed as a function of mean squared displacement, linking rigidity to configurational constraints across different phases.

Contribution

It establishes a universal relationship between shear modulus and mean squared displacement, connecting rigidity to configurational constraints in both glasses and crystals.

Findings

Shear modulus relates to mean squared displacement across phases

The relationship holds over various temperatures and timescales

Universal behavior observed in glass and crystal systems

Abstract

Motivated by the formal argument that a non-zero shear modulus is the result of averaging over a constrained configurations space, we demonstrate that the shear modulus calculated over a range of temperatures and averaging times can be expressed (relative to its infinite frequency value) as a single function of the mean squared displacement. This result is shown to hold for both a glass-liquid and a crystal-liquid system.