For the rectangular-disordered case and N = 2 (Fig. ) the emergence of the MP feature (near 3 σ / Ã0 ) is more evident than in the Gaussian-disordered case (Fig. ) and retains its identity for a larger range of disorder (3 < σ / Ã0 < 9) than the Gaussian case. Further, the collapse of the UP and LP occurs earlier than for the N = 1 case, now at σ / Ã0 ∼ 14. The Lorentzian-disordered case, however, shows none of the spectral changes, compared to the Gaussian and rectangular cases, moving from one to two molecules. As we will see, the Lorentzian case has negligible changes for any number of Fig. presents the data with N = 100. For the Gaussian case (Fig. ), we observe the clearest evidence that at weak disorder, the UP and LP spectral peaks increase their Rabi splitting slightly before contracting . Of course, as A 0 = 0.01 a.u., ω c = 1.00 a.u., N r = 50, 000, N cheb = 2500, γ = 0.001 a.u. Note that the data shown here is identical to Fig. except that the intensity is on a log scale. noted before, the eigenstates of the Hamiltonian still increase their overall splitting with increased disorder, but the photonic character becomes energetically localized to the resonance energy once the molecules have become sufficiently dispersed √ 100 compared to the N = 1 case (Fig. ).