The aim of this book is to provide an introduction to some representative nonrelativistic
quantum control problems and to their theoretical analysis and solution by modern …

We prove the superposition principle for probability measure-valued solutions to non-local
Fokker–Planck–Kolmogorov equations, which in turn yields the equivalence between …

In this paper, we prove a quantitative version of the semiclassical limit from the Hartree to the
Vlasov equation with singular interaction, including the Coulomb potential. To reach this …

We consider the quantum dynamics of many bosons systems in the mean field limit with a
singular pair-interaction potential, including the attractive or repulsive Coulombic case in …

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 …

This paper provides an overview of the theory of flows associated to nonsmooth vector
fields, describing the main developments from the seminal paper (DiPerna and Lions in …

We prove a quantitative and global in time semiclassical limit from the Hartree to the Vlasov
equation in the case of a singular interaction potential in dimension d≥ 3, including the case …

The purpose of this article is twofold. On one hand, we rigorously derive the Newton--
Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in …

We prove semiclassical estimates for the Schrödinger-von Neumann evolution with C 1, 1
potentials and density matrices whose square root have either Wigner functions with low …

In this article, we describe the propagation properties of the one-dimensional wave and
transport equations with variable coefficients semi-discretized in space by finite difference …