{"paper":{"title":"Spectral deformation for two-body dispersive systems with e.g. the Yukawa potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Matthias Engelmann, Morten Grud Rasmussen","submitted_at":"2015-09-07T14:52:25Z","abstract_excerpt":"We find an explicit closed formula for the $k$'th iterated commutator $\\mathrm{ad}_A^k(H_V(\\xi))$ of arbitrary order $k\\ge1$ between a Hamiltonian $H_V(\\xi)=M_{\\omega_\\xi}+S_{\\check V}$ and a conjugate operator $A=\\frac{\\mathfrak{i}}{2}(v_\\xi\\cdot\\nabla+\\nabla\\cdot v_\\xi)$, where $M_{\\omega_\\xi}$ is the operator of multiplication with the real analytic function $\\omega_\\xi$ which depends real analytically on the parameter $\\xi$, and the operator $S_{\\check V}$ is the operator of convolution with the (sufficiently nice) function $\\check V$, and $v_\\xi$ is some vector field determined by $\\omega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02066","kind":"arxiv","version":3},"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"}