Mean–Field Evolution of Fermionic Systems
By Niels Benedikter, M. Porta, B. Schlein. Communications in Mathematical Physics, 2013
133 citations recorded by the source corpus.
The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b997a72e6b8a0d7ef95ccc78306f23131887d929
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In Atomic and Molecular Physics, and Optics
- Niels Benedikter
- M. Porta
- B. Schlein
- P. Pickl
- Igor Rodnianski
- E. Lenzmann
- Clément Mouhot
- M. Machedon
In Mathematical Physics
Citations in the corpus
- Effective Evolution Equations from Quantum Dynamics (2015, background): “In order to discuss the results of [15] we need to introduce the fermionic Fock space over L2(R3), which is defined as the direct sum F = C⊕ ⊕”