Rigorous Density Functional Theory for Inhomogeneous Bose-Condensed Fluids

Abstract

The density functional theory originally developed by Hohenberg, Kohn and Sham provides a rigorous conceptual framework for dealing with inhomogeneous interacting Fermi systems. We extend this approach to deal with inhomogeneous interacting Bose-condensed systems, limiting this presentation to setting up the formalism to deal with ground state $(T=0)$ properties. The key new feature is that one must deal with energy functionals of both the local density $n(\mathbf{r})$ and the local complex macroscopic wavefunction $\Phi (\mathbf{r})$ associated with the Bose broken-symmetry (the local condensate density is $n_c(\mathbf{r})=|\Phi (\mathbf{r}){|}^2$). Implementing the Kohn-Sham scheme, we reduce the problem to a gas of weakly-interacting Bosons moving in self-consistent diagonal and off-diagonal one-body potentials. Our formalism should provide the basis for studies of the surface properties of liquid ${}^4$He as well as the properties of Bose-condensed atomic gases trapped in external potentials.

20 pages

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