Mean-field Evolution of Fermionic Systems

Understand

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 $\omega_N$ 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 $\omega_N$.