Critical analysis of the density functional theory prediction of enhanced capillary waves

We present a critical analysis of the density functional description for capillary wave fluctuations on free liquid surfaces. The proposal made by Mecke and Dietrich, [Phys. Rev. E 59, 6766 (1999)10.1103/PhysRevE.59.6766], to obtain the effective wave vector dependent surface tension, and their prediction of an enhanced regime of capillary waves at mesoscopic scales, has had a large impact including claims of experimental observation [Fradin, Nature (London) 403, 871 (2000)10.1038/35002533; Mora, Phys. Rev. Lett. 90, 216101 (2003)10.1103/PhysRevLett.90.216101]. Our analysis shows that there is a qualitative problem in the convergence of the low q expansion used for that prediction, and that the assumed link between the equilibrium density functional description of the liquid surface and its capillary wave fluctuations leads always to the unphysical decrease of the surface tension for large wave vectors.