In this talk I will discuss the dynamics of interacting fermionic systems in the meanfield regime. Compared to the bosonic case, fermionic meanfield scaling is naturally coupled with a semiclassical scaling, making the analysis more involved. From a physical point of view, as the number of particles grows one expects the quantum evolution of the system to be effectively described by HartreeFock theory. The next degree of approximation is provided by a classical effective dynamics, corresponding to the Vlasov equation. I will consider initial data which are close to quasifree states, both at zero and at positive temperature, with an appropriate semiclassical structure. Under some regularity assumptions on the interaction potential I will show that the time evolution of such initial data stays close to a quasifree state, with reduced oneparticle density matrix given by the solution of the timedependent HartreeFock equation. The result holds for all (semiclassical) times, and gives effective bounds on the rate of convergence towards the HartreeFock dynamics as the number of particles goes to infinity
Marcello Porta
Location
Nantes
Date and time

Conférence  Physique mathématique