{"paper":{"title":"Multi-mode solitons in the classical Dicke-Jaynes-Cummings-Gaudin Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.MP"],"primary_cat":"math-ph","authors_text":"Beno\\^it Dou\\c{c}ot (LPTHE), Olivier Babelon (LPTHE)","submitted_at":"2012-03-12T13:42:21Z","abstract_excerpt":"We present a detailed analysis of the classical Dicke-Jaynes-Cummings-Gaudin integrable model, which describes a system of $n$ spins coupled to a single harmonic oscillator. We focus on the singularities of the vector-valued moment map whose components are the $n+1$ mutually commuting conserved Hamiltonians. The level sets of the moment map corresponding to singular values may be viewed as degenerate and often singular Arnold-Liouville torii. A particularly interesting example of singularity corresponds to unstable equilibrium points where the rank of the moment map is zero, or singular lines "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2488","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"}