Integrability breaking from backscattering

TL;DR

This paper investigates how stochastic backscattering affects transport in a one-dimensional hard-rod gas, revealing a crossover from ballistic to diffusive behavior while preserving certain conserved quantities.

Contribution

It provides exact expressions for diffusion and structure factors under stochastic backscattering, highlighting the persistence of conserved quantities and non-Gaussian features.

Findings

Diffusive hydrodynamics emerges due to backscattering

Exact formulas for diffusion and structure factors derived

Particle density structure factor is non-Gaussian and singular

Abstract

We analyze the onset of diffusive hydrodynamics in the one-dimensional hard-rod gas subject to stochastic backscattering. While this perturbation breaks integrability and leads to a crossover from ballistic to diffusive transport, it preserves infinitely many conserved quantities corresponding to even moments of the velocity distribution of the gas. In the limit of small noise, we derive the exact expressions for the diffusion and structure factor matrices, and show that they generically have off-diagonal components in the presence of interactions. We find that the particle density structure factor is non-Gaussian and singular near the origin, with a return probability showing logarithmic deviations from diffusion.