Relation between structure of blocked clusters and relaxation dynamics in kinetically constrained models

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Materials Science

Background:

• Kinetically constrained models (KCMs) are crucial for understanding glassy dynamics and amorphous materials.
• Previous research has explored relationships between cooperative length and relaxation times in these models.
• The Fredrickson-Andersen (FA), Kob-Andersen (KA), and spiral models represent distinct theoretical frameworks for KCMs.

Purpose of the Study:

• To investigate the quantitative relationship between cooperative length (culling time, τc) and relaxation time (persistence time, τp).
• To analyze this relationship across different KCMs: FA, KA, and spiral models.
• To examine the time-decay behavior of the persistence function and its dependence on particle density.

Main Methods:

• Mapping the dynamics of KCMs to the diffusion of defects.
• Calculating persistence time (τp) as the time until a particle's first movement.
• Calculating culling time (τc) as the minimum number of particle movements required before a target particle can move.
• Analyzing the persistence function P(t) decay, fitting it to a subexponential form P(t)=exp[-(t/τ)^{β}].

Main Results:

• A universal power-law relationship τp = τc^γ was discovered, with γ being model- and dimension-dependent.
• The persistence function in the FA and KA models exhibits subexponential decay.
• The exponent β in the persistence function decay approaches 0 as particle density approaches 1, a novel finding.

Conclusions:

• The study establishes a quantitative link between local cooperative rearrangements (culling time) and global relaxation dynamics (persistence time).
• The observed behavior of the persistence function exponent suggests a significant change in dynamics at high particle densities.
• These findings offer new insights into the fundamental mechanisms governing slow dynamics in glassy systems.