Nonlinear response of diffusive systems

We use the effective field theory of diffusion to study nonlinear response in thermalizing systems. Focusing on the three and four-point functions of the diffusing density (e.g., energy, spin, or charge density), we identify all transport parameters contributing to these observables, find Kubo formulas for each and establish protocols for their measurement in experiments and numerics on non-integrable lattice or continuum systems. We also discuss out-of-time-ordered correlators, and aspects of quantum chaos that are captured by the hydrodynamic effective field theory.