  We present a study of the collisional relaxation of ion velocities in a
strongly coupled, ultracold neutral plasma on short timescales compared to the
inverse collision rate. Non-exponential decay towards equilibrium for the
average velocity of a tagged population of ions heralds non-Markovian dynamics
and a breakdown of assumptions underlying standard kinetic theory. We prove the
equivalence of the average-velocity curve to the velocity autocorrelation
function, a fundamental statistical quantity that provides access to
equilibrium transport coefficients and aspects of individual particle
trajectories in a regime where experimental measurements have been lacking.
From our data, we calculate the ion self-diffusion constant. This demonstrates
the utility of ultracold neutral plasmas for isolating the effects of strong
coupling on collisional processes, which is of interest for dense laboratory
and astrophysical plasmas.
