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

TL;DR

This paper establishes a precise relationship between solutions of the Poisson-Landscape and reduced Hartree-Fock equations in the semi-classical, low-temperature limit, with explicit bounds on their differences.

Contribution

It demonstrates a one-to-one correspondence between solutions of these equations and quantifies their differences with explicit estimates.

Findings

One-to-one correspondence between solutions

Explicit estimates of solution differences

Applicability in semi-classical, low-temperature regime

Abstract

We show that there is an one-to-one correspondence between solutions to the Poisson-Landscape equations and the reduced Hartree-Fock equations in the semi-classical limit at low temperature. Moreover, we prove that the difference between the two corresponding solutions is small by providing explicit estimates.