On an effective equation of the reduced Hartree-Fock theory

Abstract

We show that there is a 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.

Keywords

• landscape theory
• reduced hartree-fock equation
• semi-conductor model
• 35q40
• 35q81
• 82m36
• 81q10