{
  "id": "cond-mat/0411195",
  "version": "v1",
  "published": "2004-11-08T16:04:26.000Z",
  "updated": "2004-11-08T16:04:26.000Z",
  "title": "Localization of Polymers in Random Media: Analogy with Quantum Particles in Disorder",
  "authors": [
    "Yadin Y. Goldschmidt",
    "Yohannes Shiferaw"
  ],
  "comment": "To be published as a book chapter in \"Statistics of Linear Polymers in Disordered Media\", edited by B.K. Chakrabarti, Elsevier 2005",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "In this chapter we review the rich behavior of polymer chains embedded in a quenched random environment. We first consider the problem of a Gaussian chain free to move in a random potential with short-ranged correlations. We derive the equilibrium conformation of the chain using a replica variational ansatz, and highlight the crucial role of the system's volume. A mapping is established to that of a quantum particle in a random potential, and the phenomenon of localization is explained in terms of the dominance of localized tail states of the Schr\\\"odinger equation. We also give a physical interpretation of the 1-step replica-symmetry-breaking solution, and elucidate the connection with the statistics of localized tail states. We proceeded to discuss the more realistic case of a chain embedded in a sea of hard obstacles. Here, we show that the chain size exhibits a rich scaling behavior, which depends critically on the volume of the system. In particular, we show that a medium of hard obstacles can be approximated as a Gaussian random potential only for small system sizes. For larger sizes a completely different scaling behavior emerges. Finally we consider the case of a polymer with self-avoiding (excluded volume) interactions. In this case it is found that when disorder is present, the polymer attains a conformation consisting of blobs connected by straight segments. Using Flory type free energy arguments we analyze the statistics of these conformational shapes, and show the existence of a localization-delocalization transition as a function of the strength of the self-avoiding interaction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-08T16:04:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum particle",
      "random media",
      "flory type free energy arguments",
      "localization",
      "localized tail states"
    ],
    "tags": [
      "book chapter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004cond.mat.11195G"
    }
  }
}