Revision 1

Accepted · first revision · record

Title: Survival of cavity rate effects in the collective coupling limit
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.
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.
Settled by: An exact or controlled large-N calculation of the rate in a microscopic cavity-molecule model with disorder and many cavity modes.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: contested
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.
Posed since: (empty)