  We study the Brownian motion of a charged test particle driven by quantum
electromagnetic fluctuations in the vacuum region near a non-dispersive and
non-absorbing dielectric half-space and calculate the mean squared fluctuations
in the velocity of the test particle. Our results show that a nonzero
susceptibility of the dielectrics has its imprints on the velocity dispersions
of the test particles. The most noteworthy feature in sharp contrast to the
case of an idealized perfectly conducting interface is that the velocity
dispersions in the parallel directions are no longer negative and does not die
off in time, suggesting that the potentially problematic negativeness of the
dispersions in those directions in the case of perfect conductors is just a
result of our idealization and does not occur for real material boundaries.
