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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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Submitted on : Thursday, July 13, 2017 - 4:53:26 PM
Last modification on : Friday, November 26, 2021 - 6:00:09 PM
Long-term archiving on: : Friday, January 26, 2018 - 6:57:44 PM

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

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