Emergent hydrodynamics in integrable quantum systems out of equilibrium

TL;DR

This paper introduces a hydrodynamic framework with infinitely many conservation laws to describe transport in integrable quantum systems out of equilibrium, bridging the gap with non-integrable dynamics and enabling detailed analysis of space-time profiles.

Contribution

It develops a novel hydrodynamic approach incorporating infinite conservation laws for integrable systems, advancing understanding of non-equilibrium transport phenomena.

Findings

Accurate description of energy transport between heat baths.

Full characterization of non-equilibrium steady states.

Application to models including the Lieb-Liniger Bose gas.

Abstract

Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments accessing the intricate dynamics of many-body quantum systems, it is paramount to develop powerful methods that encode the emergent physics. Up to now, the strong dichotomy observed between integrable and non-integrable evolutions made an overarching theory difficult to build, especially for transport phenomena where space-time profiles are drastically different. We present a novel framework for studying transport in integrable systems: hydrodynamics with infinitely-many conservation laws. This bridges the conceptual gap between integrable and non-integrable quantum dynamics, and gives powerful tools for accurate studies of space-time profiles. We apply it to the description of energy transport between heat baths, and provide a full description of the current-carrying non-equilibrium steady state and the transition regions in a family of models including the Lieb-Liniger model of interacting Bose gases, realized in experiments.