A single mathematical theory now lets physicists predict how thousands of atoms move together, whether they are sloshing inside an ultracold gas trap or rippling through a one-dimensional quantum wire. This matters because the standard rules of hydrodynamics—the equations that describe how water flows or how air moves—were thought to break down in systems that are too orderly or too small. The researcher has already shown that a new framework called generalised hydrodynamics (GHD) works for exactly those systems: one-dimensional chains of atoms that do not behave chaotically. But the theory remains incomplete. It cannot yet describe fluctuations, correlations, or the large-scale oscillations that emerge when many particles move in synchrony. If this project succeeds, it will establish whether a single set of universal hydrodynamic principles governs all many-body systems, from quantum gases to soliton waves in shallow water. That would give physicists a unified language for predicting emergent behaviour at the largest scales of space and time, directly from the microscopic rules. This is fundamental science. There is no immediate practical application. But the same kind of deep theoretical work that produced quantum mechanics and statistical physics later enabled everything from semiconductor electronics to magnetic resonance imaging. A complete theory of emergent behaviour could eventually underpin new materials, quantum technologies, or energy systems that no one has yet imagined.
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Hydrodynamics is a powerful framework for studying the emergent, large-scale behaviours in many-body interacting systems. It is now understood that some of the general principles underlying hydrodynamics can in fact be applied much beyond conventional systems. This includes systems in one dimension of space which possess the property of integrability. These are, by many measures, non-chaotic, and therefore were believed until recently to lie beyond the realm of hydrodynamics. In the last few years I have co-pioneered and developed their hydrodynamic theory, dubbed generalised hydrodynamics. It is one of the most successful non-conventional hydrodynamic theory, and finds many applications, from soliton gas to models of statistical mechanics, quantum chains and cold atomic quantum gases, with stunning experimental verifications. The development of GHD required us to focus on the general structures of hydrodynamics, leading us to propose new general methods to understand physical quantities at the largest scales of space and time, including fluctuations, correlations, and ``structured behaviours" such as many-body oscillations. This calls for a re-think of what the universal principles of hydrodynamics are. Can we describe non-equilibrium motion, fluctuations, correlations and structured behaviours in many-body systems 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? GHD gives partial answers and a clear way forward, but much is still open. This project will attempt to answer these questions, using GHD and integrability as powerful tools for physically relevant systems and exact calculations. This will require varied skills and expertises. My track record of directing successful research teams, combined with my world-leading expertise on generalised hydrodynamics and emergent behaviours, places me perfectly to lead this groundbreaking project.
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