{
  "id": "cond-mat/0007112",
  "version": "v1",
  "published": "2000-07-06T21:21:45.000Z",
  "updated": "2000-07-06T21:21:45.000Z",
  "title": "On the approximation of Feynman-Kac path integrals for quantum statistical mechanics",
  "authors": [
    "Stephen D. Bond",
    "Brian B. Laird",
    "Benedict J. Leimkuhler"
  ],
  "comment": "4 pages, 2 figures, submitted to Physical Review Letters",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function space, by restricting the integration to a subspace of all admissible paths. Using this process, a wide class of methods can be derived, with each method corresponding to a different choice for the approximating subspace. The traditional ``short-time'' approximation and ``Fourier discretization'' can be recovered from this approach, using linear and spectral basis functions respectively. As an illustration, a novel method is formulated using cubic elements and is shown to have improved convergence properties when applied to a simple model problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-07-06T21:21:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum statistical mechanics",
      "approximation",
      "feynman-kac path integral representation",
      "quantum mechanical density matrix",
      "infinite-dimensional path integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000cond.mat..7112B"
    }
  }
}