{"paper":{"title":"Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Sumiyoshi Abe","submitted_at":"2003-07-14T12:04:39Z","abstract_excerpt":"Based on the canonical formalism, the dilatation symmetry is implemented to the Fokker-Planck equation for the Wigner distribution function that describes atomic motion in an optical lattice. This reveals the symmetry principle underlying the recent result obtained by Lutz [Phys. Rev. A 67, 051402(R) (2003)] on the connection between anomalous transport in the optical lattice and Tsallis statistics in the high-energy regime.Lutz's discussion is generalized to the nonstationary case, and the condition, under which the solution distribution decays as a power law, is derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0307306","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"}