Subdiffusive motion in kinetically constrained models

TL;DR

This paper investigates a kinetically constrained model with fluctuating densities, demonstrating subdiffusive behavior of excitations and particles, with exponents depending on model parameters, through an effective theory approach.

Contribution

It introduces an effective theory capturing subdiffusive dynamics in a kinetically constrained model with fluctuating densities, linking phenomenology to parameter-dependent exponents.

Findings

Both excitations and probe particles exhibit subdiffusive motion.

Exponents of subdiffusion depend continuously on model parameters.

Effective theory successfully reproduces the phenomenology of the model.

Abstract

We discuss a kinetically constrained model in which real-valued local densities fluctuate in time, as introduced recently by Bertin, Bouchaud and Lequeux. We show how the phenomenology of this model can be reproduced by an effective theory of mobility excitations propagating in a disordered environment. Both excitations and probe particles have subdiffusive motion, characterised by different exponents and operating on different time scales. We derive these exponents, showing that they depend continuously on one of the parameters of the model.