Density functionals for classical fluids

The objective of this project is the further development of overcomplete representations of density functionals, invented by Percus in 1997. The essential idea of an overcomplete description of thermodynamic functionals (or functions) is to introduce a set of additional variables (over the basic local particle density) such that with respect to a direct evaluation the overcomplete format has a simpler formal structure and is physically more transparent.So far, we derived a particular realization of this idea for a class of one-dimensional particle systems. During the second year of the fellowship, the generalization of this representation to higher dimensions should be pursued. A familiar strategy to organize such a first-principles approach is to reduce the geometry of the phase space by going over to the corresponding lattice system. Another possibility when trying to apply mathematical techniques is to construct solvable free energy models thereof. Both programs are to be implemented.