CHEM In the literature: contested

Survival of cavity rate effects in the collective coupling limit

In plain words

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 statement

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.

What would settle it

An exact or controlled large-N calculation of the rate in a microscopic cavity-molecule model with disorder and many cavity modes.

Status in the literature

Unverified 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.