Drift of phase fluctuations in the ABC model

TL;DR

This paper analytically confirms the existence of an antisymmetric drift in phase fluctuations of the ABC model, previously conjectured through numerical simulations, by deriving an explicit formula under the fluctuating hydrodynamics framework.

Contribution

It provides the first analytical derivation of the drift in the ABC model's phase fluctuations, validating previous conjectures and revealing its antisymmetric nature.

Findings

Confirmed the presence of a drift in phase fluctuations.

Derived an explicit analytical expression for the drift.

Showed the drift is antisymmetric in the three densities.

Abstract

In a recent work, Bodineau and Derrida analyzed the phase fluctuations in the ABC model. In particular, they computed the asymptotic variance and, on the basis of numerical simulations, they conjectured the presence of a drift, which they guessed to be an antisymmetric function of the three densities. By assuming the validity of the fluctuating hydrodynamic approximation, we prove the presence of such a drift, providing an analytical expression for it. This expression is then shown to be an antisymmetric function of the three densities. The antisymmetry of the drift can also be inferred from a symmetry property of the underlying microscopic dynamics.