Vol. 1, No. 2, 2019

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ISSN (electronic): 2576-7666
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Quantum mean-field asymptotics and multiscale analysis

Zied Ammari, Sébastien Breteaux and Francis Nier

Vol. 1 (2019), No. 2, 221–272
Abstract

We study, via multiscale analysis, a defect-of-compactness phenomenon which occurs in bosonic and fermionic quantum mean-field problems. The approach relies on a combination of mean-field asymptotics and second microlocalized semiclassical measures. The phase space geometric description is illustrated by various examples.

Keywords
semiclassical measures, multiscale measures, reduced density matrices, second quantization, microlocal analysis
Mathematical Subject Classification 2010
Primary: 81S30, 81Q20, 81V70, 81S05
Milestones
Received: 16 October 2017
Accepted: 27 February 2018
Published: 14 May 2018
Authors
Zied Ammari
IRMAR
Université de Rennes I
UMR-CNRS 6625
Campus de Beaulieu
Rennes
France
Sébastien Breteaux
Institut Elie Cartan de Lorraine
Université de Lorraine
Metz
France
Francis Nier
LAGA
UMR-CNRS 9345
Université de Paris 13
Villetaneuse
France