We use Langevin molecular dynamics (MD) simulations to improve the picture of the processes that contribute to QHAS broadening, as a function of momentum transfer at the crystal. We use a simulation of realistic damped vibrational motion in a harmonic well to establish the contributions to QHAS measurements due to both vibrational motion and intracell diffusion (usually referred to as vibrational dephasing). We demonstrate the experimental conditions under which such contributions are likely to be important. These results are compared with those from a simulation of thermal diffusion over a sinusoidally corrugated potential. We show that resolution and atom-surface "friction" play an important role in determining the form of QHAS measurements and we demonstrate that there is no simple relationship between the "activation energy" derived from an Arrhenius plot of QHAS data and the adiabatic potential barrier height. MD simulations are therefore necessary to perform a complete analysis of the data. Finally, we discuss the application of our results to more sophisticated potentials, particularly those with multiple adsorption sites. (C) 2004 American Institute of Physics.