{"paper":{"title":"Estimating complex eigenvalues of non-self-adjoint Schr\\\"odinger operators via complex dilations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jeffrey Schenker","submitted_at":"2010-07-21T02:31:59Z","abstract_excerpt":"The phenomenon \"hypo-coercivity,\" i.e., the increased rate of contraction for a semi-group upon adding a large skew-adjoint part to the generator, is considered for 1D semigroups generated by the Schr\\\"odinger operators $-\\partial^2_x + x^2 + i{\\gamma} f (x)$ with a complex potential. For $f$ of the special form$ f (x) = 1/(1 + |x|^\\kappa)$, it is shown using complex dilations that the real part of eigenvalues of the operator are larger than a constant times $|\\gamma|^{2/(\\kappa+2)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3552","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"}