{"id":"W2927289114","doi":"10.1103/physreve.99.042101","title":"Diffusion in a bistable system: The eigenvalue spectrum of the Fokker-Planck operator and Kramers' reaction rate theory","year":2019,"lang":"en","type":"article","venue":"Physical review. E","topic":"stochastic dynamics and bifurcation","field":"Physics and Astronomy","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Fokker–Planck equation; Eigenfunction; Eigenvalues and eigenvectors; Operator (biology); Physics; Diffusion; Mathematical analysis; Bistability; Spectrum (functional analysis); Quantum mechanics; Mathematics; Differential equation","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003353798,0.00009874094,0.0002229316,0.00001257783,0.00005410438,0.00001620308,0.000117162,0.0000116309,0.000011109],"category_scores_gemma":[0.00001398743,0.00005026826,0.00007733056,0.0001719597,0.0000360765,0.00005137535,0.00005949991,0.0001269302,0.00002625153],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000224034,"about_ca_system_score_gemma":0.00002771243,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002109891,"about_ca_topic_score_gemma":0.000004499042,"domain_scores_codex":[0.9992959,0.0001428435,0.0001747691,0.0001560534,0.0001111714,0.0001192837],"domain_scores_gemma":[0.999437,0.000139359,0.000130895,0.0002478806,0.0000227684,0.00002203444],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"observational","study_design_scores_codex":[0.00004025099,0.0002269444,0.02196414,0.0007698537,0.00004964408,1.393917e-7,0.0003305284,0.00004868717,0.04826685,0.9187326,0.0001299486,0.009440423],"study_design_scores_gemma":[0.004911582,0.0006244218,0.3756554,0.02195593,0.001189838,0.0000101576,0.003974522,0.2132058,0.01657668,0.3458506,0.01418317,0.001861896],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9915686,0.000592387,0.0005297711,0.0002954705,0.0001693471,0.0007083769,0.00001288688,0.000005702115,0.006117476],"genre_scores_gemma":[0.9995226,0.00008771518,0.000004271596,0.00006704264,0.0001352359,0.00003270063,0.000007509237,0.000008313826,0.0001345796],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5728819,"threshold_uncertainty_score":0.204988,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.003510015713807886,"score_gpt":0.241597486634477,"score_spread":0.2380874709206691,"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."}}