{
  "id": "2209.07739",
  "version": "v1",
  "published": "2022-09-16T06:49:21.000Z",
  "updated": "2022-09-16T06:49:21.000Z",
  "title": "Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system",
  "authors": [
    "Anupam Kundu"
  ],
  "comment": "24 pages",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study transport in a one-dimensional lattice system with two conserved quantities -- `volume' and energy. Considering a slowly evolving local equilibrium that is slightly deviated from an underlying global equilibrium, we estimate the correction to the local equilibrium distribution. This correction arises mainly through the space-time correlations of the local currents. In the continuum limit, we show that the local equilibrium distribution along with the correction yields drift-diffusion equation for the `volume' and super-diffusion equation for the energy in the linear response regime as macroscopic hydrodynamics. We find explicit expression of the super-diffusion equation. Further, we find diffusive correction to the super-diffusive evolution. Such a correction allows us to study a crossover from diffusive to anomalous transport. We demonstrate this crossover numerically through the system size scaling of the stationary current in non-equilibrium steady state prepared by two reservoirs of different temperatures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-16T06:49:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anomalous transport",
      "one-dimensional system",
      "local equilibrium distribution",
      "correction yields drift-diffusion equation",
      "super-diffusion equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}