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Measurement of a reaction-diffusion crossover in exciton-exciton recombination inside carbon nanotubes using femtosecond optical absorption

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.