{"paper":{"title":"Matrix Operator Approach to the Quantum Evolution Operator and the Geometric Phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Jewan Kim, Kwang Sup Soh, Sang Pyo Kim","submitted_at":"2012-12-12T00:30:56Z","abstract_excerpt":"The Moody-Shapere-Wilczek's adiabatic effective Hamiltonian and Lagrangian method is developed further into the matrix effective Hamiltonian (MEH) and Lagrangian (MEL) approach to a parameter-dependent quantum system. The matrix-operator approach formulated in the product integral (PI) provides not only a method to find the wave function efficiently in the MEH approach but also higher order corrections to the effective action systematically in the MEL approach, a la the Magnus expansion and the Kubo cumulant expansion. A coupled quantum system of a light particle of a harmonic oscillator is wo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2680","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"}