{
  "id": "cond-mat/0408316",
  "version": "v1",
  "published": "2004-08-13T09:49:42.000Z",
  "updated": "2004-08-13T09:49:42.000Z",
  "title": "The quantum measurement process in an exactly solvable model",
  "authors": [
    "Armen E. Allahverdyan",
    "Roger Balian",
    "Theo M. Nieuwenhuizen"
  ],
  "comment": "7 pages revtex, 2 figures",
  "doi": "10.1063/1.1874554",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.other",
    "quant-ph"
  ],
  "abstract": "An exactly solvable model for a quantum measurement is discussed which is governed by hamiltonian quantum dynamics. The $z$-component $\\hat s_z$ of a spin-1/2 is measured with an apparatus, which itself consists of magnet coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state according to the sign of $s_z$ of the tested spin. The quantum measurement goes in two steps. On a timescale $1/\\sqrt{N}$ the off-diagonal elements of the spin's density matrix vanish due to a unitary evolution of the tested spin and the $N$ apparatus spins; on a larger but still short timescale this is made definite by the bath. Then the system is in a `classical' state, having a diagonal density matrix. The registration of that state is a quantum process which can already be understood from classical statistical mechanics. The von Neumann collapse and the Born rule are derived rather than postulated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-13T09:49:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ta",
      "02.50.Cw"
    ],
    "keywords": [
      "exactly solvable model",
      "quantum measurement process",
      "spins density matrix",
      "hamiltonian quantum dynamics",
      "von neumann collapse"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005AIPC..750...26A"
    }
  }
}