The quantumN-body problem in the mean-field and semiclassical regime | Zendy

François Golse | Zendy

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The quantumN-body problem in the mean-field and semiclassical regime

Author(s) -

François Golse

Publication year - 2018

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2017.0229

Subject(s) - semiclassical physics , planck constant , limit (mathematics) , quantum , planck , mean field theory , mathematical physics , mathematics , constant (computer programming) , convergence (economics) , zero (linguistics) , physics , quantum mechanics , field (mathematics) , mathematical analysis , pure mathematics , computer science , economics , programming language , economic growth , linguistics , philosophy

The present work discusses the mean-field limit for the quantumN -body problem in the semiclassical regime. More precisely, we establish a convergence rate for the mean-field limit which is uniform as the ratio of Planck constant to the action of the typical single particle tends to zero. This convergence rate is formulated in terms of a quantum analogue of the quadratic Monge–Kantorovich or Wasserstein distance. This paper is an account of some recent collaboration with C. Mouhot, T. Paul and M. Pulvirenti.This article is part of the themed issue ‘Hilbert’s sixth problem’.

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