{"paper":{"title":"Transport and large deviations for Schrodinger operators and Mather measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.PR","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, P. Thieullen","submitted_at":"2016-06-01T14:16:51Z","abstract_excerpt":"In this mainly survey paper we consider the Lagrangian $ L(x,v) = \\frac{1}{2} \\, |v|^2 - V(x) $, and a closed form $w$ on the torus $ \\mathbb{T}^n $. For the associated Hamiltonian we consider the the Schrodinger operator ${\\bf H}_\\beta=\\, -\\,\\frac{1}{2 \\beta^2} \\, \\Delta +V$ where $\\beta$ is large real parameter. Moreover, for the given form $\\beta\\, w$ we consider the associated twist operator ${\\bf H}_\\beta^w$. We denote by $({\\bf H}_\\beta^w)^*$ the corresponding backward operator. We are interested in the positive eigenfunction $ \\psi_\\beta$ associated to the the eigenvalue $ E_\\beta$ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00297","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"}