{"id":"W4387687158","doi":"10.48550/arxiv.2310.08859","title":"Scattering and Blow-up for threshold even solutions to the nonlinear Schrödinger equation with repulsive delta potential at low frequencies","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Japan Society for the Promotion of Science; Natural Sciences and Engineering Research Council of Canada","keywords":"Scattering; Physics; Nonlinear system; Action (physics); Nonlinear Schrödinger equation; Space (punctuation); Low frequency; Mathematical physics; Work (physics); Schrödinger equation; Supercritical fluid; Standing wave; Classical mechanics; Quantum electrodynamics; Quantum mechanics; Mathematical analysis; Mathematics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003427977,0.0003425298,0.00038733,0.0001387463,0.0005078239,0.00007677444,0.0004891197,0.0001758925,0.00001648779],"category_scores_gemma":[0.0002471691,0.0002911441,0.0001536773,0.0002952754,0.0001933947,0.0001935152,0.001466145,0.0003647297,0.0000433798],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002819957,"about_ca_system_score_gemma":0.00008747877,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003589067,"about_ca_topic_score_gemma":0.0002044122,"domain_scores_codex":[0.9982932,0.0000390715,0.0002732528,0.0007987897,0.0001516919,0.0004439442],"domain_scores_gemma":[0.9979557,0.0004579721,0.0002985295,0.0008647701,0.0002882596,0.0001347385],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0003257881,0.0002418575,0.0001237132,0.001746608,0.0006351452,0.00007138713,0.00240961,0.5397019,0.004146298,0.4484926,0.001919759,0.0001852816],"study_design_scores_gemma":[0.0004996273,0.00008758263,0.0000243501,0.0005038193,0.000356694,0.000005211346,0.0003680954,0.2307888,0.0005754107,0.766325,0.00004308825,0.0004223208],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4426766,0.00001347114,0.5550281,0.0004559411,0.0001721383,0.001272639,0.000146464,0.0001639945,0.00007062362],"genre_scores_gemma":[0.9767523,0.00003308674,0.02072786,0.00006005895,0.0001600244,0.00003700341,0.0000674204,0.00009563776,0.002066607],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5343003,"threshold_uncertainty_score":0.999954,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1670359789200193,"score_gpt":0.2476742777640863,"score_spread":0.08063829884406698,"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."}}