A Microscopic Derivation Of Coupled Spde's With A Kpz Flavor

TL;DR

This paper derives coupled stochastic partial differential equations with KPZ characteristics from a microscopic particle system conserving energy and volume, combining Hamiltonian dynamics with stochastic noise.

Contribution

It provides a microscopic derivation of coupled SPDEs with KPZ flavor from a particle system with conservation laws and stochastic perturbations.

Findings

Derivation of coupled SPDEs with KPZ features from microscopic models.

Identification of fluctuation behavior of conserved quantities at equilibrium.

Analysis of the impact of stochastic noise on Hamiltonian systems.

Abstract

We consider an interacting particles system composed of a Hamiltonian part and perturbed by a conservative stochastic noise so that the full system conserves two quantities: energy and volume. The Hamiltonian part is regulated by a scaling parameter vanishing in the limit. We study the form of the fluctuations of these quantities at equilibrium and derive coupled stochastic partial differential equations with a KPZ flavor.