{"paper":{"title":"Time dependent Schr\\\"odinger equation for harmonic oscillator in the Aharonov-Bohm magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The propagator kernel for a 2D harmonic oscillator in an Aharonov-Bohm field has a leading term given by a modified Mehler formula.","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Ari Laptev, Jiyu Fan","submitted_at":"2026-05-17T11:26:57Z","abstract_excerpt":"We construct an approximation of the kernel of the solution of the time dependent Schr\\\"odinger equation whose Hamiltonian is a 2D harmonic oscillator in Aharonov-Bohm magnetic field. The main tools used here were established in the paper of A. Laptev and I.M. Sigal, where the authors considered a class of Fourier Integral Operators with global complex phases approximating the fundamental solutions (propagators) for time-dependent Schr\\\"odinger equations. For the example considered in this paper we are able to find the main term in the approximation of the kernel that equals a version of the M"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For the example considered in this paper we are able to find the main term in the approximation of the kernel that equals a version of the Mehler formula.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The global complex-phase Fourier integral operator machinery developed in the earlier Laptev-Sigal paper applies directly to the Hamiltonian consisting of the 2D harmonic oscillator plus the Aharonov-Bohm vector potential.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Approximation of the propagator kernel for the 2D harmonic oscillator in Aharonov-Bohm field, with leading term given by a Mehler-type formula, obtained via Fourier integral operators with global complex phases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The propagator kernel for a 2D harmonic oscillator in an Aharonov-Bohm field has a leading term given by a modified Mehler formula.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"80069c979fe2bdc165f2ba59f28e8e1aed02909d535ddffed14dcefbdc7d5e0a"},"source":{"id":"2605.17395","kind":"arxiv","version":1},"verdict":{"id":"af4c6f48-d897-4d84-98a7-15fd425187f9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:57:09.599251Z","strongest_claim":"For the example considered in this paper we are able to find the main term in the approximation of the kernel that equals a version of the Mehler formula.","one_line_summary":"Approximation of the propagator kernel for the 2D harmonic oscillator in Aharonov-Bohm field, with leading term given by a Mehler-type formula, obtained via Fourier integral operators with global complex phases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The global complex-phase Fourier integral operator machinery developed in the earlier Laptev-Sigal paper applies directly to the Hamiltonian consisting of the 2D harmonic oscillator plus the Aharonov-Bohm vector potential.","pith_extraction_headline":"The propagator kernel for a 2D harmonic oscillator in an Aharonov-Bohm field has a leading term given by a modified Mehler formula."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17395/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T23:01:51.294561Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.657819Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.758632Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.700194Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"07e5c178dac0312aa70b8d24b1c2cd0cad148aa4c82200cbb463c4639d6a0217"},"references":{"count":23,"sample":[{"doi":"","year":2014,"title":"El A ¨ıdi, On a new embedding theorem and the CLR-type inequality for Euclidean and hyperbolic spaces,Bull","work_id":"04cf1917-eb68-44e9-981f-518fc682fb01","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1959,"title":"Y . 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