The mean-field limit for the dynamics of large particle systems

This short course explains how the usual mean-field evolution PDEs in Statistical Physics — such as the Vlasov-Poisson, Schrodinger-Poisson or time-dependent Hartree-Fock equations — are rigorously derived from first principles, i.e. from the fundamental microscopic models that govern the evolution of large, interacting particle systems. Mon cher Athos, je veux bien, puisque votre sante l’exige absolument, que vous vous reposiez quinze jours. Allez donc prendre les eaux de Forges ou telles autres qui vous conviendront, et retablissez-vous promptement. Votre affectionne Treville Alexandre Dumas Les Trois Mousquetaires 1. A review of physical models The subject matter of these lectures is the relation between “exact” microscopic models that govern the evolution of large particle systems and a certain type of approximate models known in Statistical Mechanics as “mean-field equations”. This notion of mean-field equation is best understood by getting acquainted with the most famous examples of such equations, described below. MSC 2000 : 82C05, 82C10, 82C22, 35A10, 35Q40, 35Q55.