Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity

TL;DR

This paper explores how non-equilibrium driving forces can induce long-range order and hyperuniformity in a one-dimensional harmonic chain, overcoming equilibrium limitations like the Mermin-Wagner theorem.

Contribution

It demonstrates that specific non-equilibrium forces can suppress diffusion and stabilize crystalline order and hyperuniformity in 1D systems, which are impossible at equilibrium.

Findings

MSD scales as t^{1/2+2θ} for certain noise spectra

Crystalline order and hyperuniformity are achieved in 1D under non-equilibrium driving

Hyperuniformity of noise fluctuations stabilizes long-range order

Abstract

In one dimension, particles can not bypass each other. As a consequence, the mean-squared displacement (MSD) in equilibrium shows sub-diffusion ${\rm MSD}(t)\sim t^{1/2}$, instead of normal diffusion ${\rm MSD}(t)\sim t$. This phenomenon is the so-called single-file diffusion. Here, we investigate how the above equilibrium behaviors are modified far from equilibrium. In particular, we want to uncover what kind of non-equilibrium driving force can suppress diffusion and achieve the long-range crystalline order in one dimension, which is prohibited by the Mermin-Wagner theorem in equilibrium. For that purpose, we investigate the harmonic chain driven by the following four types of driving forces that do not satisfy the detailed balance: (i) temporally correlated noise with the noise spectrum $D(\omega)\sim \omega^{-2\theta}$, (ii) conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $\theta>-1/4$, we observe ${\rm MSD}(t)\sim t^{1/2+2\theta}$ for large $t$. On the other hand, for the driving forces (i) with $\theta<-1/4$ and (ii)-(iv), MSD remains finite. As a consequence, the harmonic chain exhibits the crystalline order even in one dimension. Furthermore, the density fluctuations of the model are highly suppressed in a large scale in the crystal phase. This phenomenon is known as hyperuniformity. We discuss that hyperuniformity of the noise fluctuations themselves is the relevant mechanism to stabilize the long-range crystalline order in one dimension and yield hyperuniformity of the density fluctuations.