{"paper":{"title":"Resonance widths in a case of multidimensional phase space tunneling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Alain Grigis, Andr\\'e Martinez","submitted_at":"2012-05-31T14:22:58Z","abstract_excerpt":"We consider a semiclassical $2\\times 2$ matrix Schr\\\"odinger operator of the form $P=-h^2\\Delta {\\bf I}_2 + {\\rm diag}(x_n-\\mu, \\tau V_2(x)) +hR(x,hD_x)$, where $\\mu$ and $\\tau$ are two small positive constants, $V_2$ is real-analytic and admits a non degenerate minimum at 0, and $R=(r_{j,k}(x,hD_x))_{1\\leq j,k\\leq 2}$ is a symmetric off-diagonal $2\\times 2$ matrix of first-order differential operators with analytic coefficients. Then, denoting by $e_1$ the first eigenvalue of $-\\Delta + \\la \\tau V_2\"(0)x,x\\ra /2$, and under some ellipticity condition on $r_{1,2}=r_{2,1}^*$, we show that, for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.7004","kind":"arxiv","version":1},"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"}