{"paper":{"title":"Minimal velocity estimates and soft mode bounds for the massless spin-boson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Kupiainen, W. De Roeck","submitted_at":"2013-01-10T23:42:47Z","abstract_excerpt":"We consider generalised versions of the spin-boson model at small coupling. We assume the spin (or atom) to sit at the origin $0 \\in \\mathbb{R}^d$ and the propagation speed $v_p$ of free bosons to be constant, i.e.\\ independent of momentum. In particular, the bosons are massless. We prove detailed bounds on the mean number of bosons contained in the ball $\\{|x| \\leq v_p t \\}$. In particular, we prove that, as $t \\to \\infty$, this number tends to an asymptotic value that can be naturally identified as the mean number of bosons bound to the atom in the ground state. Physically, this means that b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2358","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"}