Nonlinear Response in Diffusive Systems

TL;DR

This paper develops an effective field theory approach to analyze nonlinear response in diffusive systems, deriving universal scaling functions for higher-point correlators to test thermalization beyond linear response.

Contribution

It introduces a novel EFT framework for computing higher-point functions and universal scaling behaviors in diffusive systems, advancing understanding of nonlinear thermalization.

Findings

Derived universal scaling functions for three and four-point correlators

Confirmed theoretical predictions with classical lattice gas simulations

Provided a new method for testing thermalization beyond linear response

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.