For the rectangular distribution for N = 1 in Fig. , we find that the UP and LP spectral peaks converge with increasing energetic disorder as expected, but the collapse is much slower than for the Gaussian disorder. In fact, the UP and LP states do not fully collapse within 16 σ / Ã0 . Most likely, the peaks converge asymptotically as σ / Ã0 increases. We note again that at weak disorder 0 < σ / Ã0 < 2, the UP and LP spectral features exhibit a broadening due to the presence of disorder . Furthermore, compared to the Gaussian-disordered case, the initial broadening of the UP and LP spectral bands appears to be slower, as more clearly shown in Fig. , maximizing the Rabi splitting near σ / Ã0 ≈ 3.