{
  "id": "2109.03854",
  "version": "v1",
  "published": "2021-09-08T18:09:03.000Z",
  "updated": "2021-09-08T18:09:03.000Z",
  "title": "Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations",
  "authors": [
    "Choon-Lin Ho"
  ],
  "comment": "8 pages, no figures",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP",
    "nlin.SI",
    "quant-ph"
  ],
  "abstract": "A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift. It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schr\\\"odinger equation. The formalism of supersymmetric quantum mechanics is extended by applying the Darboux transformation directly to the non-stationary Schr\\\"odinger equation. From a solution of a Fokker-Planck equation a solution of the Darboux partner is obtained. For drift coefficients satisfying the condition of shape invariance, a supersymmetric hierarchy of Fokker-Planck equations with solutions related by the Darboux transformation is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-08T18:09:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fokker-planck equation",
      "time-dependent darboux transformation",
      "supersymmetric hierarchy",
      "supersymmetric quantum mechanics",
      "darboux partner"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}