{
  "id": "2309.03155",
  "version": "v1",
  "published": "2023-09-06T16:52:04.000Z",
  "updated": "2023-09-06T16:52:04.000Z",
  "title": "Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity",
  "authors": [
    "Harukuni Ikeda"
  ],
  "comment": "17 pages, 7figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "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).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-06T16:52:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic chain far",
      "long-range order",
      "driving force",
      "equilibrium",
      "hyperuniformity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}