Emergence of fluctuating hydrodynamics in chaotic quantum systems

Out-of-equilibrium dynamics of isolated quantum many-body systems is generally intractable. In chaotic quantum systems, however, local observables rapidly relax to their equilibrium values. Hence, simple translationally-invariant initial states are expected to quickly reach thermal equilibrium for local expectation values. The equilibration of fluctuations on the other hand goes beyond standard thermalization and is expected to happen on much longer timescales, since their approach to equilibrium is limited by the hydrodynamic build-up of large-scale fluctuations. For classical out-of-equilibrium systems, the framework of macroscopic fluctuation theory (MFT) was recently developed to model the hydrodynamics of fluctuations. Intriguingly, the central thesis of MFT is that the dynamics of fluctuations is completely fixed by the equilibrium diffusion constant. If this extends to quantum many-body systems, however, remains a fundamental open question. Here, I report on recent results, where we have performed large-scale quantum simulations using a 133Cs quantum gas microscope [1] to monitor the full counting statistics of particle-number fluctuations in quasi-1D systems with hard-core bosons at half filling. We prepare ladder systems with up to 100 lattice sites and tunable coupling between the legs and investigate the equilibration of fluctuations starting from a rung charge density wave (CDW). This allows us to study the crossover between ballistic and chaotic dynamics as the coupling between the legs is increased. Indeed, we find a clear separation of equilibration timescales between the relaxation of local expectation values (mean density) and that of non-local quantities (fluctuations) [2]. Moreover, in the chaotic regime we compare the fluctuation dynamics to predictions from MFT and find excellent quantitative agreement with experimental results. This further allows us to accurately determine the linear-response diffusion constant from the observed far-from-equilibrium dynamics of fluctuations and density-density correlations. Our results suggest that large-scale fluctuations of isolated quantum systems display emergent hydrodynamic behavior, which expands the applicability of MFT to the quantum regime.