{"paper":{"title":"Asymptotics of the ground state energy of heavy molecules in self-generated magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Victor Ivrii","submitted_at":"2013-03-19T08:06:13Z","abstract_excerpt":"We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$ H=((D-A)\\cdot\\boldsymbol{\\sigma})^2-V $$ with $$V=\\sum_{1\\le m\\le M} \\frac{Z_m}{|x-y_m|}$$ and a corresponding Multiparticle Quantum Hamiltonian $$ \\mathsf{H}=\\sum_{1\\le n\\le N} H_{x_n} +\\sum_{1\\le n < n'\\le N}|x_n-x_{n'}|^{-1} $$ on the Fock space $\\wedge _{1\\le n\\le N} L^2(\\mathbb{R}^3, \\mathbb{C}^2)$. Here $A$ is a self-generated magnetic fiels. Then the ground state energy is given by $$ \\mathsf{E}(A)=\\inf \\operatorname{Spec}(\\mathsf{H})+\\frac{1}{\\al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4505","kind":"arxiv","version":4},"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"}