  We consider resonant dynamics in a dilute atomic gas falling under gravity
through a periodically pulsed standing-wave laser field. Our numerical
calculations are based on a Monte Carlo method for an incoherent mixture of
noninteracting plane waves, and show that quantum resonances are highly
sensitive to the relative acceleration between the atomic gas and the pulsed
optical standing wave. For particular values of the atomic acceleration, we
observe fractional resonances. We investigate the effect of the initial atomic
momentum width on the fractional resonances, and quantify the sensitivity of
fractional resonances to thermal effects.
