Nonlinear Response in Diffusive Systems

Abstract

Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved densities. We uncover a simple scaling behavior of correlators at late times, and, focusing on three and four-point functions, derive the asymptotically exact universal scaling functions that characterize nonlinear response in diffusive systems. This allows for precision tests of thermalization beyond linear response in quantum and classical many-body systems. We confirm our predictions in a classical lattice gas.

10+11 pages, 4 figures; v2: references added, published version

References in corpus (10)

• Theory of universal incoherent metallic transport
• Nonlinear light-matter interaction at terahertz frequencies
• Correlation functions and transport coefficients in generalised hydrodynamics
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
• Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems
• A lower bound to the thermal diffusivity of insulators
• Thermal three-point functions from holographic Schwinger-Keldysh contours
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Cited by in corpus (10)

• Many-Body Localization in the Age of Classical Computing
• The Schwinger-Keldysh Coset Construction
• Non-Gaussian diffusive fluctuations in Dirac fluids
• Corrections to diffusion in interacting quantum systems
• A Bound on Thermalization from Diffusive Fluctuations
• Ballistic Modes as a Source of Anomalous Charge Noise
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Effective Description of Ajar Systems with a $U(1)$ Symmetry
• Non-Gaussian statistics of concentration fluctuations in free liquid diffusion
• A complex scalar field theory for charged fluids, superfluids, and fracton fluids