Publications

2017

• Energy decay for a locally undamped wave equation
  
  • Léautaud Matthieu
  • Lerner Nicolas
  Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc, 2017, 26 (1), pp.157 - 205. (10.5802/afst.1528)
  DOI : 10.5802/afst.1528
• THE SCHRÖDINGER EQUATION IN THE MEAN-FIELD AND SEMICLASSICAL REGIME
  
  • Golse François
  • Paul Thierry
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2017, 223, pp.57-94. In this paper, we establish (1) the classical limit of the Hartree equation leading to the Vlasov equation, (2) the classical limit of the N-body linear Schrödinger equation uniformly in N leading to the N-body Liouville equation of classical mechanics and (3) the simultaneous mean-field and classical limit of the N-body linear Schrödinger equation leading to the Vlasov equation. In all these limits, we assume that the gradient of the interaction potential is Lipschitz continuous. All our results are formulated as estimates involving a quantum analogue of the Monge-Kantorovich distance of exponent 2 adapted to the classical limit, reminiscent of, but different from the one defined in [F. Golse, C. Mouhot, T. Paul, Commun. Math. Phys. 343 (2016), 165-205]. As a by-product, we also provide bounds on the quadratic Monge-Kantorovich distances between the classical densities and the Husimi functions of the quantum density matrices. (10.1007/s00205-016-1031-x)
  DOI : 10.1007/s00205-016-1031-x
• The dynamical Manin–Mumford problem for plane polynomial automorphisms
  
  • Dujardin Romain
  • Favre Charles
  Journal of the European Mathematical Society, European Mathematical Society, 2017, 19 (11), pp.3421-3465. (10.4171/JEMS/743)
  DOI : 10.4171/JEMS/743
• A remark on the irregularity complex
  
  • Sabbah Claude
  Journal of Singularities, Worldwide Center of Mathematics, LLC, 2017. (10.5427/jsing.2017.16d)
  DOI : 10.5427/jsing.2017.16d
• E 1-degeneration of the irregular Hodge filtration
  
  • Sabbah Claude
  • Esnault Hélène
  • Yu Jeng-Daw
  Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2017, 729. (10.1515/crelle-2014-0118)
  DOI : 10.1515/crelle-2014-0118
• Tropical and non-Archimedean limits of degenerating families of volume forms
  
  • Boucksom Sébastien
  • Jonsson Mattias
  Journal de l'École polytechnique — Mathématiques, École polytechnique, 2017, 4, pp.87 - 139. (10.5802/jep.39)
  DOI : 10.5802/jep.39