Light and heavy particles on a fluctuating surface: Bunchwise balance, irreducible sequences and local density-height correlations

TL;DR

This paper introduces the concept of bunchwise balance in non-equilibrium systems, exactly determines steady states in a Light-Heavy particle model, and analyzes coarsening dynamics and correlations through irreducible sequences.

Contribution

It presents a novel bunchwise balance mechanism, introduces irreducible sequences for coarsening analysis, and proposes a local correlation function to distinguish phases.

Findings

Exact steady state determination in a subspace of the phase diagram.

Identification of irreducible sequences as a coarsening length scale.

Observation of power-law decay in correlation functions during coarsening.

Abstract

We study the early time and coarsening dynamics in the Light-Heavy model, a system consisting of two species of particles ($light$ and $heavy$) coupled to a fluctuating surface (described by tilt fields). The dynamics of particles and tilts are coupled through local update rules, and are known to lead to different ordered and disordered steady state phases depending on the microscopic rates. We introduce a generalized balance mechanism in non-equilibrium systems, namely $bunchwise~balance$, in which incoming and outgoing transition currents are balanced between groups of configurations. This allows us to exactly determine the steady state in a subspace of the phase diagram of this model. We introduce the concept of $irreducible~sequences$ of interfaces and bends in this model. These sequences are non-local, and we show that they provide a coarsening length scale in the ordered phases at late times. Finally, we propose a $local$ correlation function ($\mathcal{S}$) that has a direct relation to the number of irreducible sequences, and is able to distinguish between several phases of this system through its coarsening properties. Starting from a totally disordered initial configuration, $\mathcal{S}$ displays an initial linear rise and a broad maximum. As the system evolves towards the ordered steady states, $\mathcal{S}$ further exhibits power law decays at late times that encode coarsening properties of the approach to the ordered phases. Focusing on early time dynamics, we posit coupled mean-field evolution equations governing the particles and tilts, which at short times are well approximated by a set of linearized equations, which we solve analytically. Beyond a timescale set by a lattice cutoff and preceding the onset of coarsening, our linearized theory predicts the existence of an intermediate power-law stretch, which we also find in simulations of the ordered regime of the system.