Capillary Wave Theory of Adsorbed Liquid Films and the Structure of the Liquid-Vapor Interface

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Our study provides interface Hamiltonians for adsorbed films in a variety of systems, and shows that the corrections to the classical capillary wave spectrum are of the same order as the surface tension. This implies that it is possible, at least in principle, to measure them in x-ray surface scattering experiments. Interestingly, our study also sheds some light on the nature of the liquid-vapor interface in the absence of external fields and allows us to reconcile the Fisk-Widom scaling hypothesis with capillary wave theory.