Observation of a long-time tail in Brownian motion

By photon correlation dynamic laser light scattering the authors have measured the time dependence of the mean-square displacement ( Delta x 2 (t)) of spherical particles (radius approximately 1.7 mu m) in Brownian motion. Clear evidence was found for the existence of a t 1/2 term in ( Delta x 2 (t)) which corresponds to the expected t -3/2 'long-time tail' in the particle velocity autocorrelation function. The experimentally determined amplitude of the t 1/2 term was about 74+or-3% of the value predicted theoretically. Despite detailed consideration of possible systematic errors the authors were unable to explain the magnitude of this disagreement.