Figure 3. Probability that the exciton started on chromophore 1 is on chromophore 13 .

Below the transition () coherence dies out quickly and the probability reaches its asymptotic value . The beats at times and at reflect interference from clock and anti-clockwise traveling waves interfering after taking half and 1.5 rounds. In the transition point and above we can see that due to the localization it takes much longer time for the excitation to arrive at the opposite end. If we are just slightly above the transition coherent beats smear out by the time they arrive. The reason is that propagation becomes mostly classical as localization stops quantum diffusion. In the critical point however quantum propagation and coherence is possible at the same time.