Title: The strictly-correlated electron functional for spherically symmetric systems revisited,
Abstract: The strong-interaction limit of the Hohenberg-Kohn functional defines a
multimarginal optimal transport problem with Coulomb cost. From physical
arguments, the solution of this limit is expected to yield strictly-correlated
particle positions, related to each other by co-motion functions (or optimal
maps), but the existence of such a deterministic solution in the general
three-dimensional case is still an open question. A conjecture for the
co-motion functions for radially symmetric densities was presented in
Phys.~Rev.~A {\bf 75}, 042511 (2007), and later used to build approximate
exchange-correlation functionals for electrons confined in low-density quantum
dots. Colombo and Stra [Math.~Models Methods Appl.~Sci., {\bf 26} 1025 (2016)]
have recently shown that these conjectured maps are not always optimal. Here we
revisit the whole issue both from the formal and numerical point of view,
finding that even if the conjectured maps are not always optimal, they still
yield an interaction energy (cost) that is numerically very close to the true
minimum. We also prove that the functional built from the conjectured maps has
the expected functional derivative also when they are not optimal.