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Derivation of effective evolution equations from many-body quantum mechanics


Schlein, Benjamin (2017). Derivation of effective evolution equations from many-body quantum mechanics. Universita degli Studi di Parma. Rivista di Matematica, 8(1):83-108.

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.

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.

Additional indexing

Item Type:Journal Article, refereed, further contribution
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2017
Deposited On:28 Mar 2018 09:03
Last Modified:30 Jun 2018 07:27
Publisher:Universita degli Studi di Parma
ISSN:0035-6298
OA Status:Closed
Free access at:Official URL. An embargo period may apply.
Official URL:http://rivista.math.unipr.it/vols.html

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