{
  "id": "1807.06781",
  "version": "v1",
  "published": "2018-07-18T05:43:15.000Z",
  "updated": "2018-07-18T05:43:15.000Z",
  "title": "Mean-field Dynamics for the Nelson Model with Fermions",
  "authors": [
    "Nikolai Leopold",
    "Sören Petrat"
  ],
  "comment": "34 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The Nelson model (with ultraviolet cutoff) describes a quantum system of non-relativistic particles coupled to a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions which is coupled to a semiclassical limit. At time zero, we assume that the bosons of the radiation field are close to a coherent state and that the state of the fermions is close to a Slater determinant with a certain semiclassical structure. We prove that the many-body state approximately retains its Slater determinant and semiclassical structure at later times and that its time evolution can be approximated by the fermionic Schroedinger-Klein-Gordon equations. We prove the convergence for reduced densities with explicit rates and for all semiclassical times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-18T05:43:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "81Q05",
      "81T10",
      "82C10"
    ],
    "keywords": [
      "nelson model",
      "mean-field dynamics",
      "zero mass quantized scalar field",
      "time evolution",
      "non-relativistic particles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}