{"paper":{"title":"The Quantum Josephson Hamiltonian In The Phase Representation","license":"","headline":"","cross_cats":["cond-mat.mes-hall","cond-mat.soft","cond-mat.supr-con"],"primary_cat":"cond-mat.stat-mech","authors_text":"(2) Physics Department, (3) Istituto Nazionale di Fisica della Materia, A. Smerzi (3) ((1)Institute for Theoretical Atomic, Australia, Cambridge, Harvard-Smithsonian Center for Astrophysics, International School for Advanced Studies, Italy), J. R. Anglin (1), Molecular Physics, P. Drummond (2), Trieste, University of Queensland, USA","submitted_at":"2000-11-26T18:15:10Z","abstract_excerpt":"The quantum Josephson Hamiltonian of two weakly linked Bose-Einstein condensates is written in an overcomplete phase representation, thus avoiding the problem of defining a Hermitian phase operator. We discuss the limit of validity of the standard, non-rigorous Mathieu equation, due to the onset of a higher order $\\cos 2 \\phi$ term in the Josephson potential, and also to the overcompleteness of the representation (the phase $\\phi$ being the relative phase between the two condensates). We thereby unify the Boson Hubbard and Quantum Phase models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0011440","kind":"arxiv","version":1},"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"}