Modul:   MAT673  Seminar PDE and Mathematical Physics

First-order corrections to the meanfield limit via non-commutative central limit

Talk by Dr. Robert Matjeschk

Speaker invited by: Prof. Dr. Benjamin Schlein

Date: 05.05.14  Time: 17.15 - 19.00  Room: Y27H25

We derive an algebraic theory for treating permutation invariant problems beyond separability up to first order in the asymptotics. Our work builds on a C*-algebraic description of mean field models, namely many particle algebras, that converge to classical algebras in the limit of infinitely many particles. We use a non-commutative central limit theorem to derive a CCR algebra that describes the first-order corrections to the limit. We analyse the structure of the algebra, and show how to use it in order to estimate the ground-state energy and time evolution of correlations of quantum spin systems, up to first order in the particle number. Moreover, we describe the close relation to finite de Finetti theorems and obtain an inner version of the finite de Finetti bound.