On the Reduced Hartree-Fock Equations with a Small Anderson Type Background Charge Distribution

Abstract

We demonstrate that the reduced Hartree-Fock equation (REHF) with an Anderson type background charge distribution has an unique stationary solution by explicitly computing a screening mass at positive temperature.

On a Novel Effective Equation of the Reduced Hartree-Fock Theory

“…However, we were unable to prove the smallness assumption (36) in general. Though, we believe this condition should hold in many cases if κ H 2 (Ω) δ (for related results, see [34,23,13]). Nevertheless, we provide an existence result to the simplest case, the LSC equations, via variational principle for completeness sake.…”

“…where the square root is taken via the Borel functional calculus under periodic boundary condition on Ω. The following lemma is crucial to our linear analysis and is based on unpublished notes of Chenn and I. M. Sigal, and proved in Lemma 6 of [13] with ε = 1 .…”

“…where W = 1/u, (12) (−ε 2 ∆ + V − φ)u = 1. (13) This equation was proposed and studied in [17,33]. Together with (3), they bear the name Poisson-Landscape (PL) equation.…”