# Generalized hydrodynamics with space-time inhomogeneous interactions

## TL;DR

This paper introduces a new hydrodynamic framework extending Generalized Hydrodynamics to handle systems with space-time varying interactions, enabling analytical descriptions of complex out-of-equilibrium dynamics.

## Contribution

It develops a novel analytical approach for inhomogeneous interactions in integrable systems, applicable to both quantum and classical models, advancing the understanding of non-equilibrium phenomena.

## Key findings

- Successfully describes interaction quenches in trapped Bose gases
- Benchmarks results in XXZ spin chain and Sinh-Gordon model
- Enables analytical treatment of space-time dependent interaction modulations

## Abstract

We provide a new hydrodynamic framework to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions. Our result builds up on the recently-introduced Generalized Hydrodynamics (GHD). The method allows to analytically describe the dynamics during generic space-time-dependent smooth modulations of the interactions. As a proof of concept, we study experimentally-motivated interaction quenches in the trapped interacting Bose gas, which cannot be treated with current analytical or numerical methods. We also benchmark our results in the XXZ spin chain and in the classical Sinh-Gordon model.