Multiplicative noise and the diffusion of conserved densities

TL;DR

This paper investigates how multiplicative noise, arising from variable-dependent transport coefficients, affects long-time correlations and relaxation in stochastic fluid dynamics, especially near critical points.

Contribution

It provides a detailed analysis of multiplicative noise effects in models of conserved densities, highlighting their significance relative to nonlinear interactions.

Findings

Multiplicative noise impacts long-time tails similarly to nonlinear interactions in model B.

In model H, multiplicative noise is a higher order correction to relaxation phenomena.

Fluctuation-dissipation relations are carefully examined in the context of multiplicative noise.

Abstract

Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of multiplicative noise in stochastic fluid dynamics. Multiplicative noise arises from the dependence of transport coefficients, such as the diffusion constants for charge and momentum, on fluctuating hydrodynamic variables. We study long time tails and relaxation in the diffusion of a conserved density (model B), and a conserved density coupled to the transverse momentum density (model H). Careful attention is paid to fluctuation-dissipation relations. We observe that multiplicative noise contributes at the same order as non-linear interactions in model B, but is a higher order correction to the relaxation of a scalar density and the tail of the stress tensor correlation function in model H.