# Soliton gases and generalized hydrodynamics

## TL;DR

This paper reveals a quantum-classical equivalence in generalized hydrodynamics, showing that quantum integrable systems' hydrodynamics can be described by classical gases with soliton-like scattering, enabling efficient numerical simulations.

## Contribution

It introduces a classical gas model with velocity-dependent jumps that exactly reproduces the hydrodynamics of quantum integrable systems, providing a new computational approach.

## Key findings

- Quantum GHD equations are equivalent to classical soliton-like gases.
- Classical gas model allows efficient numerical simulations of quantum dynamics.
- Applicable to cold-atom experiments and inhomogeneous quantum systems.

## Abstract

Dynamical equations in generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, take a rather simple form, even though an infinite number of conserved charges are taken into account. We show a remarkable quantum-classical equivalence: we demonstrate the equivalence between the equations of GHD, and the Euler-scale hydrodynamic equations of a new family of classical gases which generalize the gas of hard rods. In this family, the "quasi-particles", upon colliding, jump forward or backward by a distance that depends on their velocities, generalizing the jump forward by the rods' length of the fixed-velocity tracer upon elastic collision of two hard rods. Such velocity-dependent position shifts are characteristics of classical soliton scattering. The emerging hydrodynamics of a quantum integrable model is therefore that of the classical gas of its solitons. This provides a "molecular dynamics" for GHD which is numerically efficient and flexible. This is directly applicable, for instance, to the study of inhomogeneous dynamics in integrable quantum chains and in the Lieb-Liniger model realized in cold-atom experiments.