  Exciton-exciton recombination in isolated semiconducting single-walled carbon
nanotubes was studied using femtosecond transient absorption. Under sufficient
excitation to saturate the optical absorption, we observed an abrupt transition
between reaction- and diffusion- limited kinetics, arising from reactions
between incoherent localized excitons with a finite probability of ~ 0.2 per
encounter. This represents the first experimental observation of a crossover
between classical and critical kinetics in a 1D coalescing random walk, which
is a paradigm for the study of non- equilibrium systems.
