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

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.

arXiv comment16 pages, 6 figures

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• Lattice models for granular-like velocity fields: Hydrodynamic limit
• Kovacs-like memory effect in athermal systems: linear response analysis
• Lattice models for granular-like velocity fields: Finite-size effects
• The kinetic exclusion process: a tale of two fields
• Statistics of the dissipated energy in driven diffusive systems
• Global stability and $H$-theorem in lattice models with non-conservative interactions
• Hydrodynamics of granular particles on a line
• Dynamical and structural properties of an absorbing phase transition: a case study from granular systems
• Driven inelastic Maxwell gas in one dimension
• Induced correlations and rupture of molecular chaos by anisotropic dissipative Janus hard disks
• Critical behavior of a programmable time-crystal lattice gas
• Hydrodynamics of simple active liquids: the emergence of velocity correlations