A note on the validity of Bogoliubov correction to mean field dynamics Journal Article


Author(s): Nam, Phan Thanh; Napiórkowski, Marcin
Article Title: A note on the validity of Bogoliubov correction to mean field dynamics
Affiliation IST Austria
Abstract: We study the norm approximation to the Schrödinger dynamics of N bosons in with an interaction potential of the form . Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large N limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all . The range of β is expected to be optimal for this large class of initial states.
Keywords: Mean-field limits; Quantum dynamics; Bogoliubov theory
Journal Title: Journal de Mathématiques Pures et Appliquées
Volume: 108
Issue 5
ISSN: 0021-7824
Publisher: Elsevier  
Date Published: 2017-11-01
Start Page: 662
End Page: 688
URL:
DOI: 10.1016/j.matpur.2017.05.013
Notes: The first author thanks Mathieu Lewin for helpful discussions. We thank David Mitrouskas and Sören Petrat for finding a gap in a previous version of this paper. We thank the referees for useful comments and remarks. The support of the Austrian Science Fund (FWF) project Nr. P 27533-N27 is gratefully acknowledged.
Open access: yes (repository)