Quasiparticle dynamics and hydrodynamics of 1d hard rod gas on diffusion scale

TL;DR

This paper studies the quasiparticle dynamics in a one-dimensional hard rod gas, deriving analytical results for different initial states and revealing how long-range correlations modify hydrodynamic equations at diffusive scales.

Contribution

It provides analytical expressions for quasiparticle correlations and shows how long-range correlations affect hydrodynamic equations in 1D hard rod gases.

Findings

Long-range correlations introduce diffusive corrections to hydrodynamics.

Derived analytical phase space density correlations.

Modified Euler GHD equations depend on initial correlations.

Abstract

We investigate the stochastic dynamics of a quasiparticle within a gas of hard rods, focusing on the evolution of its mean, variance, and autocorrelation for two choices of initial states: (i) one with long-range (LR) correlations and (ii) the other without it. We derive analytical results for the phase space density correlations in the former case to complement the known results for the latter case. These results enable us to obtain expressions for the mean, variance, and autocorrelation of a quasiparticle, which are applicable to both initial states. The LR correlations introduce a diffusive-scale correction to the mean Euler generalized hydrodynamic (GHD) equations, modifying the standard local equilibrium form, and our findings reveal that the form of the correction term depends on the LR correlations present in the initial state.