Stochastic dynamics of quasiparticles in the hard rod gas

TL;DR

This paper investigates the stochastic behavior of quasiparticles in a one-dimensional hard rod gas, revealing their Brownian motion characteristics and correlations, and develops a fluctuating hydrodynamics framework for the system.

Contribution

It provides an exact analysis of quasiparticle dynamics, introduces a Brownian motion model for quasiparticles, and develops a fluctuating hydrodynamics theory for the hard rod gas.

Findings

Quasiparticles behave as drifting Brownian particles.

Two tagged quasiparticles exhibit strong correlations, moving like a rigid rod.

Developed a Dean-Kawasaki-type fluctuating hydrodynamic theory for the system.

Abstract

We consider a one-dimensional gas of hard rods, one of the simplest examples of an interacting integrable model. It is well known that the hydrodynamics of such integrable models can be understood by viewing the system as a gas of quasiparticles. Here, we explore the dynamics of individual quasiparticles for a variety of initial conditions of the background gas. The mean, variance, and two-time correlations are computed exactly and lead to a picture of quasiparticles as drifting Brownian particles. For the case of a homogeneous background, we show that the motion of two tagged quasiparticles is strongly correlated, and they move like a rigid rod at late times. Apart from a microscopic derivation based on the mapping to point particles, we provide an alternate derivation which emphasizes that quasiparticle fluctuations are related to initial phase-space fluctuations, which are carried over in time by Euler scale dynamics. For the homogeneous state, we use the Brownian motion picture to develop a Dean-Kawasaki-type fluctuating hydrodynamic theory, formally having the same structure as that derived recently by Ferrari and Olla. We discuss differences with existing proposals on the hydrodynamics of hard rods and some puzzles.