Using a new method [19], it is possible to derive mean field equations from the microscopic
N body Schrödinger evolution of interacting particles without using BBGKY hierarchies. This …

This course explains how the usual mean field evolution partial differential equations (PDEs)
in Statistical Physics—such as the Vlasov-Poisson system, the vorticity formulation of the two …

We prove rigorously that the one-particle density matrix of three dimensional interacting
Bose systems with a short-scale repulsive pair interaction converges to the solution of the …

Consider a system of $ N $ bosons in three dimensions interacting via a repulsive short
range pair potential $ N^ 2V (N (x_i-x_j)) $, where $\bx=(x_1,>..., x_N) $ denotes the …

The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-
boson states, in the limit of large N. In this paper we provide estimates on the rate of …

In these notes we review the material presented at the summer school on “Mathematical
Physics, Analysis and Stochastics” held at the University of Heidelberg in July 2014. We …

The main result in this paper is a new inequality bearing on solutions of the N-body linear
Schrödinger equation and of the mean field Hartree equation. This inequality implies that the …

We study the time-evolution of initially trapped Bose–Einstein condensates in the Gross–
Pitaevskii regime. We show that condensation is preserved by the many-body evolution and …

Starting from first‐principle many‐body quantum dynamics, we show that the dynamics of
Bose‐Einstein condensates can be approximated by the time‐dependent nonlinear Gross …

We shall present a new strategy for handling mean field limits of quantum mechanical
systems. The new method is simple and effective. It is simple, because it translates the idea …