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 T\"oplitz 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.
Keywords
Cite
@article{arxiv.1707.04161,
title = {Wave Packets and the Quadratic Monge-Kantorovich Distance in Quantum Mechanics},
author = {François Golse and Thierry Paul},
journal= {arXiv preprint arXiv:1707.04161},
year = {2018}
}
Comments
23 pages, no figure