Dean-Kawasaki fluctuating hydrodynamics for backscattering hard rods

TL;DR

This paper investigates the impact of velocity-flipping on one-dimensional hard rods, showing a transition from ballistic to diffusive density correlations due to integrability-breaking perturbations.

Contribution

It introduces a Dean-Kawasaki fluctuating hydrodynamic framework to analyze how flipping rates alter transport behavior in backscattering hard rods.

Findings

Density correlations are ballistic for short times ($t \,<\, 1/\gamma$).

Density correlations become diffusive for long times ($t \,>\, 1/\gamma$).

Flipping rate $\\gamma$ breaks integrability and changes transport properties.

Abstract

We study a system of backscattering hard rods in one dimension. Contrary to the usual ballistic hard rods, these hard rods flip the sign of their velocities with a rate $\gamma$. This leads to the decay of the odd moments of velocity while preserving the even moments: the number of conserved quantities in the system becomes half. The introduction of the flipping rate, $\gamma$, is a kind of integrability-breaking perturbation. One expects a change in the transport properties in the system due to the integrability breaking. We show using a Dean-Kawasaki fluctuating hydrodynamic formulation that for $t \gg 1/\gamma$, the two-time density density correlation spreads in a diffusive manner, and for $t \ll 1/\gamma$, the correlation spreads ballistically.