Effective quantum dynamics for magnetic fermions

TL;DR

This paper derives an effective nonlinear Hartree-Fock dynamics for magnetic fermions in two dimensions, validating its accuracy against many-body quantum dynamics under certain conditions.

Contribution

It introduces a derivation of the Hartree-Fock equations for magnetic fermions using the Dirac-Frenkel principle, extending understanding of effective quantum models.

Findings

Effective Hartree-Fock equations accurately describe fermionic dynamics for small times and weak interactions.

The derivation is valid for a large number of particles in a two-dimensional magnetic setting.

The approach bridges many-body quantum mechanics and mean-field approximations.

Abstract

We show how to derive an effective nonlinear dynamics, described by the Hartree-Fock equations, for fermionic quantum particles confined to a two-dimensional box and in presence of an external, uniform magnetic field. The derivation invokes the Dirac-Frenkel principle. We discuss the validity of this effective description with respect to the many-body Schr\"odinger dynamics for small times and for weak interactions, and also in regards to the number of particles.