Emergence of fluctuating hydrodynamics in chaotic quantum systems

A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. The corresponding timescales increase with subsystem size as equilibration is limited by the hydrodynamic build-up of fluctuations on extended length scales. We perform large-scale quantum simulations that monitor particle-number fluctuations in tunable ladders of hard-core bosons and explore how the build-up of fluctuations changes as the system crosses over from integrable to fully chaotic dynamics. Our results indicate that the growth of large-scale fluctuations in chaotic, far-from-equilibrium systems is quantitatively determined by equilibrium transport coefficients, in agreement with the predictions of fluctuating hydrodynamics. This emergent hydrodynamic behaviour of subsystem fluctuations provides a test of fluctuation–dissipation relations far from equilibrium and allows the accurate determination of equilibrium transport coefficients using far-from-equilibrium quantum dynamics. Fluctuating hydrodynamics posits that thermalization in non-equilibrium systems depends on equilibrium transport coefficients. This hypothesis is now tested by exploring the emergence of fluctuations in non-equilibrium dynamics of ultracold atoms.