{"paper":{"title":"Optimizing the second hyperpolarizability with minimally-parametrized potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Christopher J. Burke, Joseph Lesnefsky, Rolfe G. Petschek, Timothy J. Atherton","submitted_at":"2012-12-17T17:01:08Z","abstract_excerpt":"The dimensionless zero-frequency intrinsic second hyperpolarizability \\gamma_{int}=\\gamma/4E_{10}^{-5}m^{-2}(e\\hbar)^{4} was optimized for a single electron in a 1D well by adjusting the shape of the potential. Optimized potentials were found to have hyperpolarizabilities in the range -0.15\\lessapprox\\gamma_{int}\\lessapprox0.60 ; potentials optimizing gamma were arbitrarily close to the lower bound and were within \\sim0.5% of the upper bound. All optimal potentials posses parity symmetry. Analysis of the Hessian of \\gamma_{int} around the maximum reveals that effectively only a single paramete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4069","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"}