We present and discuss a framework for computer-aided multiscale analysis, which enables
models at a fine (microscopic/stochastic) level of description to perform modeling tasks at a …

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 …

We consider a quantum mechanical system of N bosons with relativistic dispersion
interacting through a mean field Coulomb potential (attractive or repulsive). We choose 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 …

This paper is devoted to the study of propagation of chaos and mean-field limits for systems
of indistinguishable particles, undergoing collision processes. The prime examples we will …

We consider the time evolution of N bosonic particles interacting via a mean field Coulomb
potential. Suppose the initial state is a product wavefunction. We show that at any finite time …

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 …

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 …