King's College London

Recent significant progress in the hydrodynamic framework, via the study of integrable models, opened up fundamental questions for many-body physics: Can we describe non-equilibrium motion, fluctuations and correlations from hydrodynamic principles? Can these be derived from microscopic models? Do they form a basis for the emergent laws of many-body physics, from large to small scales? This project aims to answer these questions, using integrability as a powerful tool.

The project will use a wealth of methods from the hydrodynamic framework, from integrability, and from many-body theory.

Generalised Hydrodynamics (GHD) is the hydrodynamic theory of integrable systems, developed by the PI and others. It will be used to obtain exact results and it will be further studied and developed, especially towards the higher-dimensional setup and at higher orders.

Quantum Bethe Ansatz is a method for describing and studying integrable models. It will be used to obtain exact results and to prove the large-scale hydrodynamic principles from small-scale model descriptions, and it will be extended to the higher-dimensional setup.

Ballistic (Macroscopic) Fluctuation Theory is a new set of tools developed by the PI and others, within the hydrodynamic framework. It will be used to obtain new results and developed further.

The C-star algebraic formulation is a very general framework in many-body theory which provides mathematical rigour. It will be used to understand the emergence of hydrodynamic principles for large-scale physics from microscopic interactions.

In the first 10 months of the project:

• We developed the hydrodynamic theory for full-counting statistics out of equilibrium, correcting previous results and uncovering the emergent principles for large-scale fluctuations.
• We showed that in integrable systems, there is no emergent hydrodynamic noise, with all fluctuations being transported from the initial fluctuations by the an Euler-like hydrodynamic equation. The PI developed the fluctuating hydrodynamic for this, and for a larger class of systems.
• The PI extended the Ballistic Macroscopic Fluctuation Theory to higher dimensions and obtained the general projection formula from the principle of relaxation of fluctuations.
• We developed the idea of emergent hydrodyamics in classical circuit models, giving a new framework for studying hydrodynamics with potential for exact analytical calculations and large-scale numerics.