WAVE PACKETS AND THE QUADRATIC MONGE-KANTOROVICH DISTANCE IN QUANTUM MECHANICS

Abstract : In this paper, we extend the upper and lower bounds for the " pseudo-distance " on quantum densities analogous to the quadratic Monge-Kantorovich(-Vasershtein) distance introduced in [F. Golse, C. Mouhot, T. Paul, Commun. Math. Phys. 343 (2016) 165–205] to positive quantizations defined in terms of the family of phase space translates of a density operator, not necessarily of rank one as in the case of the Töplitz quantization. As a corollary , we prove that the uniform (for vanishing h) convergence rate for the mean-field limit of the N-particle Heisenberg equation holds for a much wider class of initial data than in [F. Golse, C. Mouhot, T. Paul, loc. cit.]. We also discuss the relevance of the pseudo-distance compared to the Schatten norms for the purpose of metrizing the set of quantum density operators in the semiclassical regime.
Document type :
Journal articles
Complete list of metadatas

Cited literature [16 references]  Display  Hide  Download

https://hal-polytechnique.archives-ouvertes.fr/hal-01562203
Contributor : François Golse <>
Submitted on : Thursday, July 13, 2017 - 4:53:26 PM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM
Long-term archiving on : Friday, January 26, 2018 - 6:57:44 PM

Files

CohStaGenFin.pdf
Files produced by the author(s)

Identifiers

Citation

François Golse, Thierry Paul. WAVE PACKETS AND THE QUADRATIC MONGE-KANTOROVICH DISTANCE IN QUANTUM MECHANICS. Comptes Rendus Mathématique, Elsevier Masson, 2018, 356, pp.177-197. ⟨10.1016/j.crma.2017.12.007⟩. ⟨hal-01562203⟩

Share

Metrics

Record views

225

Files downloads

334