Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

TL;DR

This paper uses molecular dynamics simulations to study spacetime correlations in the Toda lattice at equilibrium, confirming predictions from generalized hydrodynamics with high precision.

Contribution

It provides the first detailed numerical verification of generalized hydrodynamics predictions for the Toda lattice's spacetime correlations.

Findings

Numerical correlations agree with theory within 3.5%

Ballistic scaling confirmed at large system sizes and times

Simulations cover a wide range of pressure and temperature

Abstract

We report on molecular dynamics simulations of spacetime correlations of the Toda lattice in thermal equilibrium. The correlations of stretch, momentum, and energy are computed numerically over a wide range of pressure and temperature. Our numerical results are compared with the predictions from linearized generalized hydrodynamics on the Euler scale. The system size is N=3000,4000 and time t =600, at which ballistic scaling is well confirmed. With no adjustable parameters, the numerically obtained scaling functions agree with the theory within a precision of less than 3.5%.