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

Harukuni Ikeda

Published 2023-09-06Version 1

In one-dimensional many-particle systems, diffusion is strongly suppressed because particles cannot bypass each other. For this reason, the mean-square displacement (MSD) increases in proportion to the square of time, ${\rm MSD}(t)\sim t^{1/2}$ in equilibrium. This phenomenon is called single-file diffusion. Single-file diffusion is observed even in the harmonic lattice, which prevents the existence of long-range order in one dimension. We here study single-file diffusion of the harmonic chain far from equilibrium. We consider the following four types of driving forces that do not satisfy the detailed balance: (i) temporally correlated noise with the power-low Fourier-spectrum $D(\omega)\sim \omega^{-2\alpha}$, (ii) center-of-mass conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $\alpha>-1/4$, we observe ${\rm MSD}(t)\sim t^{1/2+2\alpha}$ for large $t$. On the other hand, for the driving forces (i) with $\alpha<-1/4$ and (ii)-(iv), ${\rm MSD}$ remains finite. As a consequence, the harmonic chain exhibits the long-range order even in one dimension, which is prohibited by the Mermin-Wagner theorem in equilibrium. We also discuss that the model shows hyperuniformity when driven by the driving forces (i) with $\alpha<0$ and (ii)-(iv).