Mean-field limit of Bose systems: rigorous results
Mathieu Lewin (CEREMADE)
TL;DR
This paper reviews recent rigorous results on deriving the Gross-Pitaevskii equation and Bogoliubov spectrum for Bose systems in the mean-field regime, connecting many-body quantum mechanics to effective equations.
Contribution
It provides a comprehensive review of recent mathematical proofs establishing the mean-field limit for Bose systems, including the derivation of key equations.
Findings
Rigorous derivation of the Gross-Pitaevskii equation
Analysis of the Bogoliubov excitation spectrum
Validation of mean-field approximation in Bose systems
Abstract
We review recent results about the derivation of the Gross-Pitaevskii equation and of the Bogoliubov excitation spectrum, starting from many-body quantum mechanics. We focus on the mean-field regime, where the interaction is multiplied by a coupling constant of order 1/N where N is the number of particles in the system.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Strong Light-Matter Interactions · Quantum, superfluid, helium dynamics