Landau model for superfluid films and interfaces at T = 0: Local interactions

We use a Landau theory appropriate to an inhomogeneous superfluid at temperature T = 0 to describe structural and dynamical effects at a gas-superfluid interface and for a superfluid film on an inert attractive substrate. The parameters of the theory are determined phenomenologically by fitting measured bulk properties of the homogeneous superfluid. The theory then predicts in a consistent way both static properties (density profile, interface or surface tension) and excitations (ripplons, phonons, and their associated wave functions). The simplicity of the theory makes the connection between the symmetries of the system and the form of the excitation spectra particularly transparent. In this paper, we take the Landau free-energy functional to be local. This restriction precludes description of roton effects. Numerical results are, as a consequence, not quantitative; however, calculations are easy enough so that generic features of the spectra and wave functions can be illustrated conveniently. In a companion paper, we allow nonlocality in the free-energy functional, making it possible to incorporate roton effects. Hard-core structure then appears in the film profiles and numerical results are much improved