{"id":"W2964251094","doi":"10.4153/cmb-2005-001-3","title":"Quantum Ergodicity of Boundary Values of Eigenfunctions: A Control Theory Approach","year":2005,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Stability and Controllability of Differential Equations","field":"Engineering","cited_by":30,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Boundary (topology); Mathematical analysis; Manifold (fluid mechanics); Boundary value problem; Geodesic; Bounded function; Neumann boundary condition; Dynamical billiards; Boundary conformal field theory; Eigenfunction; Pure mathematics; Robin boundary condition; Eigenvalues and eigenvectors; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008232433,0.0003119227,0.0004752424,0.001237026,0.0008284375,0.001485715,0.0007687441,0.0005366609,0.002829318],"category_scores_gemma":[0.002271904,0.0002096381,0.0005058465,0.0003179838,0.003408267,0.001351017,0.001267573,0.0008865403,0.0001446057],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001455248,"about_ca_system_score_gemma":0.0005278913,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002430753,"about_ca_topic_score_gemma":0.001207586,"domain_scores_codex":[0.9997492,0.0000669876,0.000008413317,0.00005170298,0.00006666862,0.00005699561],"domain_scores_gemma":[0.9990721,0.0003838346,0.0001441484,0.00007575312,0.0001942263,0.0001299166],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002098123,0.00002578904,0.0005104755,0.00001826256,0.00001168944,0.00009197915,0.0001369874,0.03323295,0.003747925,0.9589363,0.0002903831,0.002976226],"study_design_scores_gemma":[0.00001681466,0.00003341731,0.000655821,0.00001633268,0.000007981424,0.00005095419,0.0001181099,0.5399383,0.001808217,0.4565835,0.0007460294,0.00002452651],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4512255,0.000540927,0.5132335,0.001171351,0.0001042341,0.0000343094,0.0000581791,0.000148849,0.0334832],"genre_scores_gemma":[0.9917747,0.000115255,0.005715114,0.00004784423,0.00004374798,0.00002059581,0.00001303013,0.00002173232,0.002247883],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002829318,"threshold_uncertainty_score":0.01055861,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00903866130334826,"score_gpt":0.1921323513673183,"score_spread":0.18309369006397,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}