{
  "id": "2310.00802",
  "version": "v1",
  "published": "2023-10-01T21:56:56.000Z",
  "updated": "2023-10-01T21:56:56.000Z",
  "title": "Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles",
  "authors": [
    "Manish Patel",
    "Debasish Chaudhuri"
  ],
  "comment": "21 pages, single column, 6 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft",
    "physics.bio-ph"
  ],
  "abstract": "In this study, we investigate the behavior of free inertial Active Brownian Particles (ABP) in the presence of thermal noise. While finding a closed-form solution for the joint distribution of positions, orientations, and velocities using the Fokker-Planck equation is generally challenging, we utilize a Laplace transform method to obtain the exact temporal evolution of all dynamical moments in arbitrary dimensions. Our expressions in $d$ dimensions reveal that inertia significantly impacts steady-state kinetic temperature and swim pressure while leaving the late-time diffusivity unchanged. Notably, the velocity distribution exhibits a remarkable re-entrant transition from passive Gaussian to active non-Gaussian behaviors. We construct a phase diagram using the exact expression of the $d$-dimensional kurtosis as a function of activity and inertia. Our analytic expressions describe steady states and offer insights into time-dependent crossovers observed in various velocity and displacement moments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-01T21:56:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "re-entrant transition",
      "inertial dynamics",
      "exact moments",
      "impacts steady-state kinetic temperature",
      "significantly impacts steady-state kinetic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}