Nonergodic dynamics of force-free granular gases

TL;DR

This paper investigates the nonergodic and aging behaviors of force-free granular gases through analytical methods and simulations, revealing differences from effective stochastic models and the impact of velocity-dependent restitution.

Contribution

It provides a detailed comparison between granular gas dynamics and an effective Langevin model, highlighting nonergodic effects and the influence of velocity-dependent restitution.

Findings

Time-averaged MSD differs from the effective model due to ballistic correlations.

Non-ergodic behavior persists for realistic velocity-dependent restitution.

Weakening of corrections at longer times for velocity-dependent restitution.

Abstract

We study analytically and by event-driven molecular dynamics simulations the nonergodic and aging properties of force-free cooling granular gases with both constant and velocity-dependent (viscoelastic) restitution coefficient $\varepsilon$ for particle pair collisions. We compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behavior of the ensemble mean squared displacement (MSD) and the velocity correlations in the small dissipation limit. However, we reveal that the time averaged MSD of granular gas particles significantly differs from this effective model due to ballistic correlations for systems with constant $\varepsilon$. For velocity-dependent $\varepsilon$ these corrections become weaker at longer times. Qualitatively the reported non-ergodic behavior is generic for granular gases with any realistic dependence of $\varepsilon$ on the impact velocity.