English

Two Comments on the Derivation of the Time-Dependent Hartree-Fock Equation

Mathematical Physics 2022-07-19 v1 math.MP

Abstract

We revisit the derivation of the time-dependent Hartree-Fock equation for interacting fermions in a regime coupling a mean-field and a semiclassical scaling, contributing two comments to the result obtained in 2014 by Benedikter, Porta, and Schlein. First, the derivation holds in arbitrary space dimension. Second, by using an explicit formula for the unitary implementation of particle-hole transformations, we cast the proof in a form similar to the coherent state method of Rodnianski and Schlein for bosons.

Keywords

Cite

@article{arxiv.2207.07939,
  title  = {Two Comments on the Derivation of the Time-Dependent Hartree-Fock Equation},
  author = {Niels Benedikter and Davide Desio},
  journal= {arXiv preprint arXiv:2207.07939},
  year   = {2022}
}

Comments

12 pages, contribution to the Proceedings of the Intensive Period "INdAM Quantum Meetings (IQM22)" at Politecnico di Milano, March - May 2022