{
  "id": "2303.15157",
  "version": "v1",
  "published": "2023-03-27T12:49:00.000Z",
  "updated": "2023-03-27T12:49:00.000Z",
  "title": "Brownian motion of a particle with higher-derivative dynamics",
  "authors": [
    "Z. C. Tu"
  ],
  "comment": "This manuscript is a translation of a Chinese paper contributing for 100 anniversary of Department of Physics, Beijing Normal University",
  "categories": [
    "cond-mat.stat-mech",
    "physics.class-ph"
  ],
  "abstract": "The Brownian motion of a particle with higher-derivative dynamics (HDD) coupling with a bath consisting of harmonic oscillators is investigated. The Langevin equation and corresponding Fokker-Planck equation for the Brownian motion of the HDD particle are derived. As a case study, we particularly consider a stochastic Pais-Uhlenbeck oscillator. It is found that the Boltzmann distribution is pathological while this distribution is the steady solution to the Fokker-Planck equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-27T12:49:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian motion",
      "higher-derivative dynamics",
      "stochastic pais-uhlenbeck oscillator",
      "case study",
      "langevin equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}