Density functional formalism in the canonical ensemble

Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails, work in nanopore systems could certainly benefit from such extension. We show that, if the asymptotic behaviour of the canonical distribution functions is taken into account, the HKSM theorem can be extended to the canonical ensemble. We generate $N$-modified correlation and distribution functions hierarchies and prove that, if they are employed, either a modified external field or the density profiles can be indistinctly used as independent variables. We also write down the $N$% -modified free energy functional and prove that its minimum is reached when the equilibrium values of the new hierarchy are used. This completes the extension of the HKSM theorem.Comment: revtex, to be submitted to Phys. Rev. Let

Microscopic View on Short-Range Wetting at the Free Surface of the Binary Metallic Liquid Gallium-Bismuth: An X-ray Reflectivity and Square Gradient Theory Study

We present an x-ray reflectivity study of wetting at the free surface of the binary liquid metal gallium-bismuth (Ga-Bi) in the region where the bulk phase separates into Bi-rich and Ga-rich liquid phases. The measurements reveal the evolution of the microscopic structure of wetting films of the Bi-rich, low-surface-tension phase along different paths in the bulk phase diagram. A balance between the surface potential preferring the Bi-rich phase and the gravitational potential which favors the Ga-rich phase at the surface pins the interface of the two demixed liquid metallic phases close to the free surface. This enables us to resolve it on an Angstrom level and to apply a mean-field, square gradient model extended by thermally activated capillary waves as dominant thermal fluctuations. The sole free parameter of the gradient model, i.e. the so-called influence parameter, $\kappa$, is determined from our measurements. Relying on a calculation of the liquid/liquid interfacial tension that makes it possible to distinguish between intrinsic and capillary wave contributions to the interfacial structure we estimate that fluctuations affect the observed short-range, complete wetting phenomena only marginally. A critical wetting transition that should be sensitive to thermal fluctuations seems to be absent in this binary metallic alloy.Comment: RevTex4, twocolumn, 15 pages, 10 figure