{
  "annotation_id": "e7631355-ec18-4fd8-bde1-dc95f3f1f2db",
  "date_created": "2026-03-02T18:01:21.795000Z",
  "date_modified": "2026-03-02T18:01:21.795000Z",
  "file_hash": "9f961e2c00b4dd33d767549b59fc6b93bc0346e5772b0af3264a28f714307943",
  "private": false,
  "record": {
    "abstract": "We determine the class of damped modes \\tilde{y} which are related to the\ncommon free damping modes y by supersymmetry. They are obtained by employing\nthe factorization of Newton\u0027s differential equation of motion for the free\ndamped oscillator by means of the general solution of the corresponding Riccati\nequation together with Witten\u0027s method of constructing the supersymmetric\npartner operator. This procedure leads to one-parameter families of (transient)\nmodes for each of the three types of free damping, corresponding to a\nparticular type of %time-dependent angular frequency. %time-dependent,\nantirestoring acceleration (adding up to the usual Hooke restoring\nacceleration) of the form a(t)=\\frac{2\\gamma ^2}{(\\gamma t+1)^{2}}\\tilde{y},\nwhere \\gamma is the family parameter that has been chosen as the inverse of the\nRiccati integration constant. In supersymmetric terms, they represent all those\none Riccati parameter damping modes having the same Newtonian free damping\npartner mode",
    "arxiv_id": "physics/9707019",
    "authors": [
      "H. C. Rosu",
      "M. A. Reyes"
    ],
    "categories": [
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevE.57.4850",
    "journal_ref": "Phys. Rev. E 57 (April 1998) 4850-4852",
    "title": "Riccati parameter modes from Newtonian free damping motion by   supersymmetry",
    "url": "https://arxiv.org/abs/physics/9707019"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f0236f03-d3d9-47bf-a073-e95c6975ffa8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}