Quantum simulations of the ballistic motion of a surface adsorbate

In thermal equilibrium, a surface adsorbate moves ballistically for short timescales and diffusively over longer timescales. The distinction between these regimes depends on the rate of energy transfer between the adsorbate and substrate, which is conventionally described in terms of friction. Motion in the ballistic regime is determined by the local adiabatic potential, independent of the friction, and measurements of ballistic motion should therefore reveal information about those local interactions. Here, we present a method for simulating ballistic motion by calculating the intermediate scattering function (ISF), which is directly accessible through experiment. We show, using a simple tight-binding argument, that the motion can be treated as that of an adsorbate with an effective mass, distinct from its actual mass. Furthermore, the effective mass is expected to be energy, and hence temperature, dependent. A more detailed quantum simulation demonstrates that the experimental ISF also depends on the initial state before scattering, a result that suggests it should be possible to identify the degree of localisation within the adsorbate site. These results establish a direct link between the quantum nature of the system and experiment, opening the door to future measurements.