The Hartree equation for infinite quantum systems
We review some recent results obtained with Mathieu Lewin [] concerning the nonlinear Hartree equation for density matrices of infinite trace, describing the time evolution of quantum systems with infinitely many particles. Our main result is the asymptotic stability of a large class of translation-invariant density matrices which are stationary solutions to the Hartree equation. We also mention some related result obtained in collaboration with Rupert Frank [] about Strichartz estimates for orthonormal...