  We develop a density functional treatment of non-interacting abelian anyons,
which is capable, in principle, of dealing with a system of a large number of
anyons in an external potential. Comparison with exact results for few
particles shows that the model captures the behavior qualitatively and
semi-quantitatively, especially in the vicinity of the fermionic statistics. We
then study anyons with statistics parameter $1+1/n$, which are thought to
condense into a superconducting state. An indication of the superconducting
behavior is the mean-field result that, for uniform density systems, the ground
state energy increases under the application of an external magnetic field
independent of its direction. Our density-functional-theory based analysis does
not find that to be the case for finite systems of anyons, which can
accommodate a weak external magnetic field through density transfer between the
bulk and the boundary rather than through transitions across effective Landau
levels, but the "Meissner repulsion" of the external magnetic field is
recovered in the thermodynamic limit as the effect of the boundary becomes
negligible. We also consider the quantum Hall effect of anyons, and show that
its topological properties, such as the charge and statistics of the
excitations and the quantized Hall conductance, arise in a self-consistent
fashion.
