Berlin 2014 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 11: Quantenmechanik
MP 11.1: Vortrag
Donnerstag, 20. März 2014, 16:30–16:50, SPA SR125
First-order asymptotic corrections to the meanfield limit — Matthias Christandl1, •Robert Matjeschk2, Friederike Trimborn2,3, and Reinhard Werner2 — 1Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland — 2Leibniz Universität Hannover — 3Bundesministerium für Bildung und Forschung
We derive a complete algebraic theory for treating permutation invariant problems beyond separability to first order in the asymptotics. Our work builds on a C*-algebraic theory for permutation invariant operators on n-particles, with an algebraic description of the limit n→∞ (the meanfield limit). We use the fluctuation ansatz, a version of a non-commutative central limit, and derive a continuous-variable algebra (the fluctuation algebra) that asymptotically describes the 1/n-corrections to this meanfield limit. Using the fluctuation algebra, we derive a method for estimating the ground-state energy of meanfield models up to first order, and for estimating the time-evolution of correlations between different particles. Moreover, we show that the meanfield ground-state problem is closely related to the finite de Finetti problem and therefore obtain a lower bound, complementing recent results in this direction.