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 ω=-(i/2)Dk^{2}. We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.
Highlights
Introduction.—Diffusion was invented by Fourier to describe the dynamics of heat [1]
Where standard classical hydrodynamic stood on firm symmetry principles [11], the physical principles governing stochastic hydrodynamics—in particular how “noise” fields interact with conserved densities—were less transparent
We find that the thermal dc conductivity and diffusion constant both receive independent nonvanishing radiative corrections, even in the case of a single conserved density, and that the correction is not sign definite
Summary
Introduction.—Diffusion was invented by Fourier to describe the dynamics of heat [1]. Where T is the temperature, D the diffusivity, c the specific heat, and κ 1⁄4 cD the thermal conductivity. The traditional stochastic approach to hydrodynamic fluctuations with Gaussian noise [3,4,5,7] can be recovered from the general effective action (3) when the interactions that are quadratic in auxiliary fields (i.e., the λand λ0 terms) are absent, by performing a Legendre transform and introducing the noise field ξ 1⁄4 ∂L=∂φa [15].
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