Mean-field limit of Bose systems: rigorous results

2015/10/15 by Mathieu Lewin, Lewin, Mathieu
Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Gases (cond-mat.quant-gas) #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions

paper · pdf · doi:10.48550/arxiv.1510.04407

openalex publication_date 2015/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials

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