Riv. Mat. Univ. Parma, Vol. 8, No. 1, 2017

Benjamin Schlein[a]

Derivation of effective evolution equations from many-body quantum mechanics

Pages: ( in press )
Accepted in revised form: 23 May 2017
Mathematics Subject Classification (2010): 82C10.
Keywords: Quantum dynamics, Bose-Einstein condensation, Gross-Pitaevskii dynamics, Hartree-Fock equation.
[a]: Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

Abstract: In these notes, based on a mini-course held at the summer school ''Methods and Models of Kinetic Theory'' that took place in Porto Ercole in June 2016, we review some of the recent developments in the derivation of effective evolution equations starting from many-body quantum mechanics. We discuss the derivation of the Hartree equation in the bosonic mean-field limit, of the Gross-Pitaevskii equation describing the dynamics of initially trapped Bose-Einstein condensates and of the Hartree-Fock equation for fermions in a joint mean-field and semiclassical limit.

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