N-particle irreducible actions for stochastic fluids

TL;DR

This paper develops effective actions for stochastic fluid dynamics, computes loop corrections, and explores the impact of higher-order effects on fluid behavior through numerical solutions of Schwinger-Dyson equations.

Contribution

It introduces 1PI and 2PI effective actions for stochastic fluids and analyzes higher-loop effects and their renormalization impacts.

Findings

Higher-loop effects renormalize the non-linear coupling.

Numerical solutions show the emergence of a diffuson-cascade.

Indications of $n$-loop corrections with decreasing exponential suppression.

Abstract

We construct one- and two-particle irreducible (1PI and 2PI) effective actions for the stochastic fluid dynamics of a conserved density undergoing diffusive motion. We compute the 1PI action at one-loop order, and the 2PI action in two-loop approximation. We derive a set of Schwinger-Dyson equations, and regularize the resulting equations using Pauli-Villars fields. We numerically solve the Schwinger-Dyson equations for a non-critical fluid. We find that higher-loop effects summed by the Schwinger-Dyson renormalize the non-linear coupling. We also find indications of a diffuson-cascade, the appearance $n$-loop corrections with smaller and smaller exponential suppression.