Accuracy of the time-dependent Hartree-Fock approximation

TL;DR

This paper analyzes the accuracy of the time-dependent Hartree-Fock approximation for interacting fermions, demonstrating its validity under certain conditions and providing error bounds that vanish in the mean field limit.

Contribution

It provides rigorous error bounds for the TDHF approximation and shows its exactness in the mean field limit for large particle systems.

Findings

TDHF is accurate for large particle numbers and initial Slater or Gibbs states.

Error bounds are established for short times with bounded interactions.

Error vanishes at all times in the mean field limit.

Abstract

This article examines the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find the TDHF approximation to be accurate when there are sufficiently many particles and the initial many-particle state is a Slater determinant, or any Gibbs equilibrium state for noninteracting fermions. Assuming a bounded two-particle interaction, we obtain a bound on the error of the TDHF approximation, valid for short times. We further show that the error of the the TDHF approximation vanishes at all times in the mean field limit.