Photon number variance in isolated cavities

We consider a strictly isolated single-mode optical cavity resonating at an gular frequency, omega, containing atoms whose one-electron level energies are supposed to be h omega, 2h omega... Bh omega, and m photons. If the ato ms are initially in their highest energy state and m = 0, we find that at e quilibrium: variance (m)/mean(m) = (B + 1)/6, indicating that the internal field statistics is sub-Poissonian if the number of atomic levels B does no t exceed 4. Remarkably, this result does not depend on the number of atoms, nor on the number of electrons that each atom incorporates. Our result has application to the statistics of the light emitted by pulsed lasers and nu clear magnetic resonance. On the mathematical side, the result is based on the restricted partitions of integers.