{"paper":{"title":"Semiclassical limits, Lagrangian states and coboundary equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Joana Mohr","submitted_at":"2015-12-25T11:06:23Z","abstract_excerpt":"Assume that $f$ is a continuous transformation $f:S^1 \\to S^1$. We consider here the cases where $f$ is either the transformation $f(z)=z^2$ or $f$ is a smooth diffeomorphism of the circle $S^1$. Consider a fixed continuous potential $\\tau:S^1=[0,1) \\to \\mathbb{R}$, $\\nu\\in \\mathbb{R}$ and $\\varphi:S^1 \\to \\mathbb{C}$ (a quantum state). The transformation $\\hat F_{\\nu}$ acting on $\\varphi:S^1 \\to \\mathbb{C}$, $\\hat F_{\\nu}(\\varphi) = \\phi$, defined by $\\displaystyle \\phi(z) = \\hat F_{\\nu} (\\varphi(z)) = \\varphi(f(z))e^{i\\nu\\tau(z)}$ describes a discrete time dynamical evolution of the quantum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07985","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"}