Deterministic soluble model of coarsening

We investigate a three-phase deterministic one-dimensional phase ordering model in which interfaces move ballistically and annihilate upon colliding. We determine analytically the autocorrelation function A(t). This is done by computing generalized first-passage-type probabilities ${\mathrm{P}}_{\mathrm{n}}$(t), which measure the fraction of space crossed by exactly n interfaces during the time interval (0,t), and then expressing the autocorrelation function via ${\mathrm{P}}_{\mathrm{n}}$'s. We further reveal the spatial structure of the system by analyzing the domain size distribution.