Observation of nanoscale hydrodynamics in a strongly interacting dipolar spin ensemble in diamond --- Theory

Establishing a quantitative connection between the microscopic description of a quantum many-body system and its emergent macroscopic phenomena remains an important open problem. In this talk, we introduce a novel method that combines analytical, numerical, and experimental approaches to address this challenge. Strongly motivated by recent experiments that utilize strongly interacting dipolar spin ensembles in diamond, we present a framework to efficiently describe the spin dynamics. More specifically, starting from a microscopic Hamiltonian description of the spin ensemble, we construct an effective classical description of the spin polarization dynamics that accurately captures the experimental observations. Our method highlights a hybrid approach to study emergent hydrodynamics in strongly interacting quantum systems.