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Rigorous Density Functional Theory for Inhomogeneous Bose-Condensed Fluids
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 properties. The key new feature
is that one must deal with energy functionals of both the local density and the local complex macroscopic wavefunction associated
with the Bose broken-symmetry (the local condensate density is ). 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 He
as well as the properties of Bose-condensed atomic gases trapped in external
potentials.Comment: 20 page
The Surface Region of Superfluid He as a Dilute Bose-Condensed Gas
In the low-density surface region of superfluid He, the atoms are far
apart and collisions can be ignored. The only effect of the interactions is
from the long-range attractive Hartree potential produced by the distant
high-density bulk liquid. As a result, at , all the atoms occupy the same
single-particle state in the low-density tail. Striking numerical evidence for
this 100\% surface BEC was given by Pandharipande and coworkers in 1988. We
derive a generalized Gross-Pitaevskii equation for the inhomogeneous condensate
wave function in the low-density region valid at all temperatures.
The overall amplitude of is fixed by the bulk liquid, which ensures
that it vanishes everywhere at the bulk transition temperature.Comment: 6 pages, paper submitted to Low Temperature Conference (LT21),
Prague, Aug., 1996; to appear in proceeding
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