Ballistic space-time correlators of the classical Toda lattice

TL;DR

This paper derives exact space-time correlation functions for the classical Toda lattice using generalized hydrodynamics, revealing ballistic scaling behavior in conserved field correlations.

Contribution

It provides an exact solution for the linearized generalized hydrodynamic equations of the Toda lattice, yielding explicit scaling functions for correlations.

Findings

Correlations scale ballistically at leading order.

Derived concise formulas for the family of scaling functions.

Enhanced understanding of space-time correlations in integrable systems.

Abstract

The Toda lattice is an integrable system and its natural space-time stationary states are the generalized Gibbs ensembles (GGE). Of particular physical interest are then the space-time correlations of the conserved fields. To leading order they scale ballistically. We report on the exact solution of the respective generalized hydrodynamic equations linearized around a GGE as background state. Thereby we obtain a concise formula for the family of scaling functions.