Using quantum mechanics to simulate ballistic motion of surface adsorbates

When an atom or molecule adsorbed on a surface is thermally excited, it moves in two distinct regimes: ballistic motion at short times, where nothing has yet disturbed its trajectory, and diffusive motion at long times, once collisions with the substrate (friction) randomise its path. Diffusion has been studied extensively, but the short-time ballistic regime, where quantum effects are expected to be most visible, has received far less attention.

In a recently published paper, we develop a full quantum-mechanical simulation of ballistic adsorbate motion and calculate the intermediate scattering function (ISF), the quantity measured directly in helium spin echo (HeSE) experiments. Three main results emerge:

• Effective mass: In a periodic surface potential, an adsorbate’s ballistic motion behaves as though it has a different, band-dependent mass. States below the diffusion barrier are effectively much heavier, while higher-energy states behave like free particles.
• 1D vs 2D corrugation: Comparing sinusoidal (1D) and hexagonal (2D) potentials of the same barrier height shows the same qualitative physics in both cases, so dimensionality changes the details but not the overall trends.
• Sensitivity to coherence and localisation: The ISF depends not just on the surface potential, but on how spatially localised or coherent the adsorbate’s initial quantum state is. This means ballistic HeSE measurements should, in principle, be able to reveal the degree of localisation of an adsorbate within its binding site, which is something not accessible through diffusion measurements alone.

Together, these results establish a direct theoretical link between the quantum nature of adsorbate motion and what is actually measured in scattering experiments, laying the groundwork for a new generation of high-resolution HeSE measurements aimed at probing quantum effects in surface diffusion.