The classical limit of the time dependent Hartree-Fock equation. I. The Weyl symbol of the solution

Abstract

We study the time evolution of the Weyl symbol of a solution of the time dependent Hartree Fock equation, assuming that for t=0, it has a Weyl symbol which is integrable in the phase space, such as all its derivatives. We prove that the solution has the same property for all t, and we give an asymptotic expansion, in L1 sense, of this Weyl symbol.

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• Quantum Dynamics with Mean Field Interactions: a New Approach
• Mean field limit for bosons and propagation of Wigner measures
• Mean-field limit and Semiclassical Expansion of a Quantum Particle System

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