Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 376, Issue 2118, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2017.0229
Keywords
Schrodinger equation; Hartree equation; mean field limit; classical limit; Wasserstein distance
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The present work discusses the mean-field limit for the quantum N-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.
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