# The GGE averaged currents of the classical Toda chain

## TL;DR

This paper investigates the averaged currents in the classical Toda chain with random initial data, providing numerical evidence supporting the collision-rate assumption and suggesting a universal structure for integrable systems.

## Contribution

The study offers the first numerical validation of the collision-rate assumption for the Toda chain's averaged currents, reinforcing the generalized Euler equations framework.

## Key findings

- Numerical evidence supports the collision-rate assumption in the Toda chain.
- Averaged currents align with predictions from generalized Euler-type equations.
- Supports the universality of integrable systems' hydrodynamic descriptions.

## Abstract

The Toda chain with random initial data is studied. Of particular interest are generalized Gibbs ensembles, their averaged conserved fields, and the averages of the corresponding currents. While averaged fields are well-understood, the description of averaged currents has hitherto relied on the collision-rate assumption. For the Toda chain, the rate assumption can be investigated numerically. Here, we provide convincing evidence for the validity of the rate assumption. This lends further support to the idea that generalized Euler-type equations have a structure common to all integrable extensive systems.