{
  "id": "1507.02305",
  "version": "v1",
  "published": "2015-07-08T20:44:50.000Z",
  "updated": "2015-07-08T20:44:50.000Z",
  "title": "Topological Constraints in Directed Polymer Melts",
  "authors": [
    "Pablo Serna",
    "Guy Bunin",
    "Adam Nahum"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft",
    "physics.bio-ph"
  ],
  "abstract": "Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be trivial changes the polymer conformations drastically. Polymers of length $L$ wander in the transverse direction only by a distance of order $(\\ln L)^\\zeta$ with $\\zeta \\simeq 1.5$. This is strongly suppressed in comparison with the Brownian scaling $L^{1/2}$ which holds in the absence of the topological constraint. It is also much less than the prediction $L^{1/4}$ of a mean-field-like `array of obstacles' model: thus we rule out such a model in the present setting. Dynamics are also strongly affected by the constraints, and a tagged monomer in an infinite system performs logarithmically slow subdiffusion. To cast light on the suppression of the strands' wandering, we analyse the topological complexity of subregions of the melt: the complexity is also logarithmically small, and is related to the wandering by a power law. We comment on insights the results give for 3D melts, directed and non-directed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-08T20:44:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological constraint",
      "directed polymer melts",
      "infinite system performs logarithmically slow",
      "system performs logarithmically slow subdiffusion",
      "fundamental open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}