{"paper":{"title":"Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"M. Brack, M. \\\"Ogren, S. M. Reimann, Y. Yu","submitted_at":"2005-05-30T11:35:44Z","abstract_excerpt":"We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term $\\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbits over the manifold $\\mathbb{C}$P$^2$ which characterizes their 4-fold degeneracy. Then we obtain an analytical uniform trace formula which in the limit of strong perturbations (or high energy) asy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0505060","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"}