  We consider the atom-optical delta-kicked accelerator when the initial
momentum distribution is symmetric. We demonstrate the existence of
quantum-resonant dynamics, and derive analytic expressions for the system
evolution. In particular, we consider the dynamical evolution of the momentum
moments and find that all even-ordered momentum moments exhibit a power law
growth. In the ultracold (zero-temperature) limit the exponent is determined by
the order of the moment, whereas for a broad, thermal initial momentum
distribution the exponent is reduced by one. To demonstrate the power law
behavior explicitly we consider the evolutions of the second- and fourth-order
momentum moments, and cumulants, for an initially Gaussian momentum
distribution corresponding to the Maxwell-Boltzmann distribution of an ideal
gas at thermal equilibrium.
