We consider the dynamics of a large number N of nonrelativistic bosons in the mean field
limit for a class of interaction potentials that includes Coulomb interaction. In order to …

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 …

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 …

We consider the many-body quantum dynamics of systems of bosons interacting through a
two-body potential N^ 3 β-1 V (N^ β x) N 3 β-1 V (N β x), scaling with the number of particles …

We consider a system of N bosons interacting through a singular two-body potential scaling
with N and having the form N 3 β− 1 V (N β x), for an arbitrary parameter β∈(0, 1). We …

We prove that Gibbs measures of nonlinear Schrödinger equations arise as high-
temperature limits of thermal states in many-body quantum mechanics. Our results hold for …

We present microscopic derivations of the defocusing two-dimensional cubic nonlinear
Schrödinger equation and the Gross–Pitaevskii equation starting from an interacting N …

This paper studies the derivation of the nonlinear system of Schrödinger--Klein--Gordon (S-
KG) equations, coupled by a Yukawa-type interaction, from a microscopic quantum field …