Fig. 2.

(A) Burst and rest behavior of the proton is shown for one trajectory. On the y axis, we show the distance that the proton jumps with respect to a reference starting point at the beginning of the trajectory. The motion of the proton goes through periods of bursts where it can jump rather long distances due to correlated proton hopping followed by resting periods. The regions labeled B indicate points where there is a burst in activity and R are regimes where the proton is going through a resting period. (B) Proton history correlation function (44) [, where h is 1 when a tagged species in the system is a proton or 0 if it is not] is shown for individual proton species in the system as well as the ensemble average. The two blue curves, for example, illustrate two limiting cases involving a trapped proton and a very short-lived proton transiently formed during concerted PT events. The red, green, and violet curves shown, interpolate between these two limiting cases. The black curve represents the average over all PT events from different trajectories, whereas the dashed magenta curve is a fit to this average using several exponentials.