{"paper":{"title":"Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th"],"primary_cat":"physics.chem-ph","authors_text":"Joseph E. Lawrence","submitted_at":"2024-09-04T15:38:27Z","abstract_excerpt":"Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface whose period is $\\tau=\\hbar/(k_{\\rm B}T)$. Unfortunately, the standard theory is only applicable below the \"crossover temperature\", where the periodic orbit first appears. This paper presents a rigorous semiclassical ($\\hbar\\to0$) theory for the rate that is valid at any temperature. The theory is derived by combining Bleistein's method for generating uniform asymptotic expansions with a real-time modification of Richardson's flux-correlation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02820","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.02820/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}