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 Schrödinger dynamics for small times and for weak interactions, and also in regards to the number of particles.
Effective quantum dynamics for magnetic fermions / Ferrero, Margherita; Monaco, Domenico. - In: OPEN COMMUNICATIONS IN NONLINEAR MATHEMATICAL PHYSICS. - ISSN 2802-9356. - 4:(2024), pp. 157-187. [10.46298/ocnmp.13820]
Effective quantum dynamics for magnetic fermions
Domenico Monaco
2024
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 Schrödinger dynamics for small times and for weak interactions, and also in regards to the number of particles.| File | Dimensione | Formato | |
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