Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation

TL;DR

This paper reviews the derivation of effective equations for high-density interacting Fermi gases, covering semiclassical, mean-field, and random phase approximation theories, with a focus on initial data and quantum quenches.

Contribution

It systematically compares three levels of effective theories for Fermi gas dynamics, highlighting their precision and applicability.

Findings

Semiclassical Vlasov equation describes initial dynamics.

Hartree-Fock provides a mean-field approximation.

Random phase approximation captures entanglement effects.

Abstract

I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective theories, increasing in precision, can be distinguished: the semiclassical theory given by the Vlasov equation, the mean-field theory given by the Hartree-Fock equation, and the description of the dominant effects of non-trivial entanglement by the random phase approximation. Particular attention is given to the discussion of admissible initial data, and I present an example of a realistic quantum quench that can be approximated by Hartree-Fock dynamics.