{"paper":{"title":"On two-temperature problem for harmonic crystals","license":"","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"A.I. Komech, N.J. Mauser, T.V. Dudnikova","submitted_at":"2002-11-11T20:43:52Z","abstract_excerpt":"We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components,$d,n \\ge 1$. The initial date is a random function with finite mean density of the energy which also satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The random function converges to different space-homogeneous processes as $x_d\\to\\pm\\infty$, with the distributions $\\mu_\\pm$. 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 translation-invariant measure as $t\\to\\infty$. The proof is based on the long time asymptoti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0211017","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"}