Effective Hamiltonian for liquid-vapor interfaces

Starting from a density functional theory for inhomogeneous fluids we derive an effective Hamiltonian for liquid-vapor interfaces of simple fluids which goes beyond the common phenomenological capillary-wave description. In contrast to other approaches we take into account the long-ranged power-law decay of the dispersion forces between the fluid particles which changes the functional form of the wave-vector-dependent surface tension qualitatively. In particular, we find two different forms of the bending rigidity for the capillary waves, a negative one for small wave vectors determined by the long-ranged dispersion forces and a positive rigidity for large wave vectors due to the distortions of the intrinsic density profile in the vicinity of the locally curved interface. The differences to the standard capillary-wave theory and the relevance of these results for the interpretation of scattering experiments are discussed.