{"paper":{"title":"Convergence to equilibrium distribution. The Klein-Gordon equation coupled to a particle","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"T.V. Dudnikova","submitted_at":"2007-11-07T14:11:58Z","abstract_excerpt":"We consider the Hamiltonian system consisting of a Klein-Gordon vector field and a particle in $\\R^3$. The initial date of the system is a random function with a finite mean density of energy which also satisfies a Rosenblatt- or Ibragimov-type mixing condition. Moreover, initial correlation functions are translation-invariant. We study the distribution $\\mu_t$ of the solution at time $t\\in\\R$. The main result is the convergence of $\\mu_t$ to a Gaussian measure as $t\\to\\infty$, where $\\mu_\\infty$ is translation-invariant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1091","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}