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.
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Pré-publication, Document de travail
23 pages, no figure. 2017
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https://hal-polytechnique.archives-ouvertes.fr/hal-01562203
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Soumis le : jeudi 13 juillet 2017 - 16:53:26
Dernière modification le : jeudi 11 janvier 2018 - 06:12:13

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  • HAL Id : hal-01562203, version 1

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François Golse, Thierry Paul. WAVE PACKETS AND THE QUADRATIC MONGE-KANTOROVICH DISTANCE IN QUANTUM MECHANICS. 23 pages, no figure. 2017. 〈hal-01562203〉

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