Multiplicative noise and the diffusion of conserved densities

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.

Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media

“…For example, in appendix D, we show explicitly how fluctuations-dissipation theorem and the Ward-Takahashi identity are satisfied at one-loop order. In the traditional method, special care is needed to ensure those relations (see the recent work [45] for the former).…”

Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media

“…For example, in appendix D, we show explicitly how fluctuations-dissipation theorem and the Ward-Takahashi identity are satisfied at one-loop order. In the traditional method, special care is needed to ensure those relations (see the recent work [42] for the former).…”

Holographic Schwinger-Keldysh field theory of SU(2) diffusion

“…Thus, hydrodynamic EFT provides an ideal framework for investigating fluctuation effects in a variety of physical problems, see e.g. [14][15][16][17][18][19][20] for recent progress.…”