Quantum mean field asymptotics and multiscale analysis

Zied Ammari (1) , Sébastien Breteaux (2) , Francis Nier (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 BCAM - Basque Center for Applied Mathematics
3 LAGA - Laboratoire Analyse, Géométrie et Applications

We study, via multiscale analysis, some defect of compactness phenomena which occur 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: Wigner measure; Reduced density matrix; Second quantization; Multiscale Analysis; Mean field limit; Semiclassical Analysis; Wigner measure

Domains: Mathematical Physics [math-ph]

Zied Ammari, Sébastien Breteaux, Francis Nier. Quantum mean field asymptotics and multiscale analysis. Tunisian Journal of Mathematics, 2019, 1 (2), pp.221-272. ⟨10.2140/tunis.2019.1.221⟩. ⟨hal-01442714⟩