Hard Rod Hydrodynamics and the Levy Chentsov Field

TL;DR

This paper analyzes the hydrodynamics of the hard rod model by representing quasiparticle displacements as height differences in a related field, demonstrating convergence to a Levy Chentsov field with variable rod lengths.

Contribution

It introduces a novel height field representation for the hard rod model and proves convergence of fluctuations to a Levy Chentsov field, including cases with negative rod lengths.

Findings

Laws of large numbers for quasiparticle positions and length fields

Joint convergence of fluctuations to Levy Chentsov field

Extension to variable and negative rod lengths

Abstract

We study the hydrodynamics of the hard rod model proposed by Boldrighini, Dobrushin and Soukhov by describing the displacement of each quasiparticle with respect to the corresponding ideal gas particle as a height difference in a related field. Starting with a family of nonhomogeneous Poisson processes contained in the position-velocity-length space $\mathbb{R}^3$, we show laws of large numbers for the quasiparticle positions and the length fields, and the joint convergence of the quasiparticle fluctuations to a Levy Chentsov field. We allow variable rod lengths, including negative lengths.