28.06.2018 15:45 Sabine Jansen (LMU):
Rigorous derivation of density functionals for classical systemsMI 03.08.011 (Boltzmannstr. 3, 85748 Garching)

In density functional theory one postulates a free energy functional on a space of functions representing the space/orientation/etc-dependent densities of the system. In this talk we present a rigorous derivation of such functionals starting from a partition function of a system of interacting classical particles. For homogeneous (constant density) systems, this is the standard virial expansion, but the challenge here is to implement it for inhomogeneous densities. These can be realized by considering particles with space dependent activities. The main technical difficulty lies on the need of an inversion formula in an appropriate functional space. We resolve this issue exploiting the combinatorial structure of such inversions. As a byproduct of our method, if we apply it to the homogeneous case, we improve the existing value for the radius of convergence of the virial expansion. Applications include inhomogeneous systems such as multi-species gases (inhomogeneous sizes of the spheres) and liquid crystals (inhomogeneous position and orientation). This is joint work with Tobias Kuna and Dimitrios Tsagkarogiannis.