Dynamical correlations of conserved quantities in the one-dimensional equal mass hard particle gas

TL;DR

This paper analytically computes and verifies the equilibrium spatio-temporal correlations of velocities in a one-dimensional hard particle gas, revealing ballistic scaling characteristic of integrable systems.

Contribution

It provides an exact analytical calculation of velocity correlations in a 1D hard particle gas using a mapping to a non-interacting system, verified by simulations.

Findings

Correlation functions exhibit ballistic scaling.

Analytical results match microscopic simulations.

System behavior consistent with integrable models.

Abstract

We study a gas of point particles with hard-core repulsion in one dimension where the particles move freely in-between elastic collisions. We prepare the system with a uniform density on the infinite line. The velocities $\{v_i; i \in \mathbb{Z} \}$ of the particles are chosen independently from a thermal distribution. Using a mapping to the non-interacting gas, we analytically compute the equilibrium spatio-temporal correlations $\langle v_i^m(t) v_j^n(0)\rangle$ for arbitrary integers $m,n$. The analytical results are verified with microscopic simulations of the Hamiltonian dynamics. The correlation functions have ballistic scaling, as expected in an integrable model.