Fluctuating hydrodynamics and mesoscopic effects of spatial correlations in dissipative systems with conserved momentum

TL;DR

This paper develops a fluctuating hydrodynamics model for a 1D lattice system with momentum conservation but energy dissipation, revealing novel long-range correlations and instabilities relevant to granular media.

Contribution

It introduces a new fluctuating hydrodynamics framework for dissipative systems with conserved momentum, capturing key granular fluid behaviors and predicting long-range correlations.

Findings

Derived non-linear fluctuating hydrodynamics equations for velocity and temperature.

Predicted and characterized long-range spatial correlations affecting cooling rates.

Identified instability of homogeneous cooling state at large sizes or inelasticities.

Abstract

We introduce a model described in terms of a scalar velocity field on a 1d lattice, evolving through collisions that conserve momentum but do not conserve energy. Such a system posseses some of the main ingredients of fluidized granular media and naturally models them. We deduce non-linear fluctuating hydrodynamics equations for the macroscopic velocity and temperature fields, which replicate the hydrody- namics of shear modes in a granular fluid. Moreover, this Landau-like fluctuating hydrodynamics predicts an essential part of the peculiar behaviour of granular flu- ids, like the instability of homogeneous cooling state at large size or inelasticity. We compute also the exact shape of long range spatial correlations which, even far from the instability, have the physical consequence of noticeably modifying the cooling rate. This effect, which stems from momentum conservation, has not been previously reported in the realm of granular fluids.