{"paper":{"title":"A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C.W. Gardiner","submitted_at":"1997-03-05T03:37:58Z","abstract_excerpt":"The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is generalized to apply to a gas with an exact large number $ N$ of particles. This generalization yields a description of the Schr\\\"odinger picture field operators as the product of an annihilation operator $A$ for the total number of particles and the sum of a ``condensate wavefunction'' $\\xi(x)$ and a phonon field operator $\\chi(x)$ in the form $\\psi(x) \\approx A\\{\\xi(x) + \\chi(x)/\\sqrt{N}\\}$ when the field operator acts on the N particle subspace. It is then possible to expand the Hamiltonian in decreasing powers of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9703005","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"}