Long range correlations and slow time scales in a boundary driven granular model

TL;DR

This paper analyzes a one-dimensional granular model with boundary-driven dynamics, revealing how boundary conditions influence long-range correlations and slow time scales, with implications for granular and active matter systems.

Contribution

It provides analytical insights into how boundary driving induces long-range correlations and slow dynamics in a granular model, connecting these phenomena to active matter physics.

Findings

Spatial correlations are scale-free under boundary driving.

Time scales become very long when driven only at boundaries.

Correlation length grows diffusively in free cooling regime.

Abstract

We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial and temporal correlations are provided by analytical diagonalisation of the system's equations in the infinite size limit. We demonstrate that spatial correlations are scale-free and time-scales become exceedingly long when the system is driven only at the boundaries. On the contrary, in the case a bath is coupled to the bulk sites too, an exponential correlation decay is found with a finite characteristic length. This is also true in the free cooling regime, but in this case the correlation length grows diffusively in time. We discuss the crucial role of boundary driving for long-range correlations and slow time-scales, proposing an analogy between this simplified dynamical model and dense vibro-fluidized granular materials. Several generalizations and connections with the statistical physics of active matter are also suggested.