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

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 $⟨v_i^m(t)v_j^n(0)⟩$ 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.

13 pages, 3 figures

References in corpus (4)

• Generalised hydrodynamics of the classical Toda system
• Non-integrability and the Fourier heat conduction law
• Generalized Gibbs Ensembles of the classical Toda chain
• Equilibrium dynamical correlations in the Toda chain and other integrable models