Ballistic macroscopic fluctuation theory via mapping to point particles

TL;DR

This paper develops a unified framework for ballistic macroscopic fluctuation theory by mapping integrable models to point particles, enabling derivation of fluctuation statistics and correlations from initial noise.

Contribution

It introduces a novel mapping of integrable models to point particles, generalizing the hard sphere analogy, to derive fluctuation and correlation properties in ballistic systems.

Findings

Re-derivation of full-counting statistics

Derivation of long-range correlation functions

Confirmation that fluctuations originate from initial noise

Abstract

Ballistic Macroscopic Fluctuation Theory (BMFT) captures the evolution of fluctuations and correlations in systems where transport is strictly ballistic. We show that, for \emph{generic integrable models}, BMFT can be constructed through a direct mapping onto ensembles of classical or quantum point particles. This mapping generalises the well-known correspondence between hard spheres and point particles: the two-body \emph{scattering shift} now plays the role of an effective rod length for arbitrary interactions. Within this framework, we re-derive both the full-counting statistics and the long-range correlation functions previously obtained by other means, thereby providing a unified derivation. Our results corroborate the general picture that all late-time fluctuations and correlations stem from the initial noise, subsequently convected by Euler-scale hydrodynamics.