{
  "annotation_id": "b49c5160-4367-4306-b75d-ade97b80d672",
  "date_created": "2026-03-02T18:00:32.609000Z",
  "date_modified": "2026-03-02T18:00:32.609000Z",
  "file_hash": "850c65d79d662a2a5bc0250957e3f84ba23d261eb0a39cf7d696344a1dcc7928",
  "private": false,
  "record": {
    "abstract": "Gibbs statistical mechanics is derived for the Hamiltonian system coupling\nself-consistently a wave to N particles. This identifies Landau damping with a\nregime where a second order phase transition occurs. For nonequilibrium initial\ndata with warm particles, a critical initial wave intensity is found: above it,\nthermodynamics predicts a finite wave amplitude in the limit of infinite N;\nbelow it, the equilibrium amplitude vanishes. Simulations support these\npredictions providing new insight on the long-time nonlinear fate of the wave\ndue to Landau damping in plasmas.",
    "arxiv_id": "physics/0012053",
    "authors": [
      "M. -C. Firpo",
      "Y. Elskens"
    ],
    "categories": [
      "physics.plasm-ph",
      "cond-mat.stat-mech",
      "math.DS",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevLett.84.3318",
    "journal_ref": "Phys. Rev. Lett. 84 (2000) 3318-3321",
    "title": "Phase transition in the collisionless regime for wave-particle   interaction",
    "url": "https://arxiv.org/abs/physics/0012053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0a923799-bc1e-47bb-b0fe-3ed82dc0f3c1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}