Anomalous Diffusion at Liquid Surfaces

We study the role of bulk-surface exchange in the diffusion of adsorbed molecules at liquid-solid and liquid-fluid interfaces. For ``strong adsorbers'' (readsorption time much less than desorption time) we find anomalous surface diffusion on time scales less than the surface retention time: Displacement moments grow as 〈rq〉~t^ζ(q), where ζ(q)0ex0ex=0ex0exq for $q<1$, ζ(q)0ex0ex=0ex0ex(q+1)/2 for $q>1$, and 〈r〉~tlnt. This superdiffusive behavior arises because molecules execute L\'evy walks on the surface, mediated by the liquid bulk.