# Theory of Diffusive Fluctuations

Chen-Lin, Xinyi (Department of Physics, Stanford University, Stanford, California 94305-4060, USA) ; Delacrétaz, Luca V. (Department of Physics, Stanford University, Stanford, California 94305-4060, USA) ; Hartnoll, Sean A. (Department of Physics, Stanford University, Stanford, California 94305-4060, USA)

09 April 2019

Abstract: The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the diffusive pole is shifted in the presence of nonlinear hydrodynamic self-interactions, and that the density-density Green’s function acquires a branch point halfway to the diffusive pole, at frequency $\omega =-\left(i/2\right)D{k}^{2}$. We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.

Published in: Physical Review Letters 122 (2019)