{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b8ba26fadaac96ac38459f24b3eb08c4884c5965af66ca4f42d766928ad04a1c","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","8883d21a923f0f2fc5804c7ed99683b74bb6717102f5b0726f25e7f03972a589"],"salt":"a8e26546dc8957a12ead833b1b68fd49868ef89c52620bbbcc6ab1d81ebf7d4e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"chem.polaritonic-chemistry.collective-limit","kind":"well-posed","literature_status":"contested","n":"1","parents":[{"note":"","parent_revision":"8883d21a923f0f2fc5804c7ed99683b74bb6717102f5b0726f25e7f03972a589","relation":"special_case"}],"plain":"In experiments a huge number of molecules share one light mode, so each molecule feels only a tiny part of the coupling. Theory must decide whether any effect on a single molecule's reaction survives this sharing.","posed_since":"","precise":"For $N$ molecules each with a reactive coordinate and a bright vibration coupled with strength $g/\\sqrt{N}$ to one or many cavity modes, at fixed collective Rabi splitting $2 g$ and temperature $T$, determine whether the thermal reaction rate per molecule differs from its free value by an amount that stays finite as $N\\ \\text{goes to}\\ \\infty$ ($N$ of about $10^{6}\\ \\text{to}\\ 10^{10}$ in experiments), including disorder, multimode cavities and dark states. An answer is a proof or exact calculation in a defined model.","problem_ref":null,"references":"","settled_by":"An exact or controlled large-N calculation of the rate in a microscopic cavity-molecule model with disorder and many cavity modes.","status_note":"Most equilibrium rate theories through 2024 find the per-molecule effect vanishes as 1/N at fixed Rabi splitting; proposed exceptions rely on nonequilibrium or disorder effects.","title":"Survival of cavity rate effects in the collective coupling 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