Riv. Mat. Univ. Parma, Vol. 8, No. 1, 2017
Benjamin Schlein^{[a]}
Derivation of effective evolution equations from manybody quantum mechanics
Pages: 83108
Received: 31 December 2016
Accepted in revised form: 23 May 2017
Mathematics Subject Classification (2010): 82C10.
Keywords: Quantum dynamics, BoseEinstein condensation, GrossPitaevskii dynamics, HartreeFock equation.
Author address:
[a]: Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
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Abstract:
In these notes, based on a minicourse 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 manybody quantum mechanics.
We discuss the derivation of the Hartree equation in the bosonic meanfield limit,
of the GrossPitaevskii equation describing the dynamics of initially trapped BoseEinstein
condensates and of the HartreeFock equation for fermions in a joint meanfield and semiclassical limit.
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