Momentum fluctuations in coarse grained systems

TL;DR

This paper investigates how different coarse grained systems like lattice gas and lattice Boltzmann define momentum, revealing discrepancies with fundamental definitions especially in fluctuating properties and at large wavelengths.

Contribution

It demonstrates that common momentum definitions in coarse grained models can differ from fundamental momentum, especially in fluctuations and large wavelength limits.

Findings

Fluctuating properties of momentum definitions differ from fundamental expectations.

Discrepancies persist even at large wavelengths in lattice gases.

Analytical representations of momentum distributions are provided for short times.

Abstract

At first glance the definition of mass and momentum appears to be uniquely defined. We show here, however, that this certainty can be misleading for many coarse grained systems. We show that particularly the fluctuating properties of common definitions of momentum in coarse grained methods like lattice gas and lattice Boltzmann do not agree with a fundamental definition of momentum. In the case of lattice gases, the definition of momentum will even disagree in the limit of large wavelength. For short times we can give analytical representations for the distribution of different momentum measures and thereby give a full account of these differences.