{"paper":{"title":"Fractal Weyl Law for Open Chaotic Maps","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"St\\'ephane Nonnenmacher (SPhT)","submitted_at":"2005-06-21T11:55:25Z","abstract_excerpt":"This contribution summarizes our work with M.Zworski on open quantum open chaoticmaps (math-ph/0505034). For a simple chaotic scattering system (the open quantum baker's map), we compute the \"long-living resonances\" in the semiclassical r\\'{e}gime, and show that they satisfy a fractal Weyl law. We can prove this fractal law in the case of a modified model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0506056","kind":"arxiv","version":2},"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"}