Emergent hydrodynamics in a strongly interacting dipolar spin ensemble.

Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws1-7. However, despite this mantra, building direct connections between these two descriptions has remained an enduring scientific challenge. In particular, it is difficult to quantitatively predict the emergent 'classical' properties of a system (for example, diffusivity, viscosity and compressibility) from a generic microscopic quantum Hamiltonian7-14. Here we introduce a hybrid solid-state spin platform, where the underlying disordered, dipolar quantum Hamiltonian gives rise to the emergence of unconventional spin diffusion at nanometre length scales. In particular, the combination of positional disorder and on-site random fields leads to diffusive dynamics that are Fickian yet non-Gaussian15-20. Finally, by tuning the underlying parameters within the spin Hamiltonian via a combination of static and driven fields, we demonstrate direct control over the emergent spin diffusion coefficient. Our work enables the investigation of hydrodynamics in many-body quantum spin systems.