Rafael Benguria (Santiago)
Estimate for the Indirect Coulomb Energy for Two and
Three Dimensional Atoms
Abstract: In this talk I will present a new lower bound on the
indirect Coulomb energy in two dimensional quantum mechanics in terms
of the single particle density of the system. The new universal lower
bound is an alternative to the Lieb--Solovej--Yngvason bound with a
smaller constant, $C=(4/3)^{3/2}\sqrt{5 \pi -1} \approx 5.90 <
C_{LSY}=
192\sqrt{2 \pi} \approx 481.27$, which also involves an additive
gradient energy term of the single particle density.
I will also review the analogous situation in 3-d. In 2-d this is
joint work with P. Gallegos and M. Tusek. In 3-d is a joint
collaboration with G. Bley and M. Loss.