In this paper we provide a novel strategy to prove the validity of Hartreeʼs theory for the
ground state energy of bosonic quantum systems in the mean-field regime. For the known …

How and why could an interacting system of many particles be described as if all particles
were independent and identically distributed? This question is at least as old as statistical …

These notes deal with the mean-field approximation for equilibrium states of N-body systems
in classical and quantum statistical mechanics. A general strategy for the justification of …

We prove that nonlinear Gibbs measures can be obtained from the corresponding many-
body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T …

In this paper, we will obtain a rigorous derivation of the defocusing cubic nonlinear
Schrödinger equation on the three-dimensional torus T 3 from the many-body limit of …

We provide a rigorous derivation of nonlinear Gibbs measures in two and three space
dimensions, starting from many-body quantum systems in thermal equilibrium. More …

The quantum de Finetti theorem asserts that the-body density matrices of an-body bosonic
state approach a convex combination of Hartree states (pure tensor powers) when is large …

We study the ground state for many interacting bosons in a double-well potential, in a joint
limit where the particle number and the distance between the potential wells both go to …

The results summarized here are intended as rigorous mathematical statements on various
physical models coming from condensed matter physics, statistical mechanics (classical and …

In a recent paper, in collaboration with Mathieu Lewin and Phan Thanh Nam, we showed
that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived …