GUILLOT Jean-Claude

Emeritus Professor

Address:

Ecole Polytechnique
Centre de Mathématiques Appliquées
UMR CNRS 7641
91198 PALAISEAU Cedex, FRANCE


Tél: 33 1 69 33 46 00
Fax: 33 1 69 33 46 46
Mail:
jean-claude.guillot@polytechnique.edu

Research topics:

· Partial Differential Equations

· Scattering Theory

· Inverse Problems

· Quantum Field Theory





Recent articles:



· The multipolar Hamiltonian in QED for moving atoms and ions (with J.Robert). J.Phys.A: Math.Gen., vol 35, p 5023-5039, 2002.


· Semiclassical asymptotics in magnetic Bloch bands (with M.Dimassi and J.Ralston). J.Phys.A: Math.Gen., Vol 35, p 7597-7605, 2002.



· The Quantum Electrodynamics of Relativistic Bound States with Cutoffs.I. (with M.Dimassi). Applied Mathematical Letters, vol 16, p 551-555, 2003.



· Quantum electrodynamics of relativistic bound states with cutoffs.II. (with J.M.Barbaroux and M.Dimassi). Contemporary Mathematics, vol 307, p 9-14, 2002.



· Quantum electrodynamics of relativistic bound states with cutoffs (with J.M.Barbaroux and M.Dimassi). Journal of Hyperbolic Differential Equations, vol 1, p 271-314, 2004.



· On Effective Hamiltonians for Adiabatic Perturbations of Magnetic Schrödinger Operators. (with M.Dimassi and J.Ralston). Asymptotic Analysis, vol 40, p 137-146, 2004.



· Hierarchy of Multipolar Terms for Non Relativistic Moving Atoms in QED. (with A.Felhi and J.Robert). Preprint ArXiv: math-ph/0312009 and preprint mp-arc 03-513, 2003.


· On Effective Hamiltonians for Adiabatic Perturbations of Magnetic Schrödinger Operators. (with M.Dimassi and J.Ralston).Mat. Contemp.vol 26, p 31-39, 2004.



· Gaussian Beam Construction for Adiabatic Perturbations of Magnetic Schrödinger Operators. (with M.Dimassi and J.Ralston). Mathematical Physics, Analysis and Geometry, vol 9, p.187-201, 2006.



· L’électron habillé non relativiste dans un champ magnétique (with L.Amour and B.Grébert). C.R.Acad.Sci.Paris, Ser.I 340 p 421-426, 2005.



· The dressed nonrelativistic electron in a magnetic field (with L.Amour and B.Grébert). Math. Meth. Appl. Sci., vol 29, p 1121- 1146, 2006.


· The dressed moving atoms and ions (with L.Amour and B.Grébert ).

J. Math. Pures Appl., vol 86, p 117- 200, 2006.

·A mathematical model for the Fermi weak interactions (with L.Amour and B.Grébert ).

Cubo 9, no 2, p 37-57, 2007.


· Organisation de la Journée Relativiste du Centre de Mathématiques Appliquées de l'Ecole Polytechnique qui s'est tenue le 17 octobre 2007.

Intervenants: S. De Bièvre, C.Gérard, D. Häfner, Ph. LeFloch et M. Lewin.


· Le problème infrarouge pour l’électron habillé non relativiste dans un champ magnétique ( with L.Amour, J.Faupin and B.Grébert ). C.R.Acad. Sci.Paris Ser. I, 346, p 1045-1050, 2008.


· On the infrared problem for the dressed non-relativistic electron in a magnetic field ( with L.Amour, J.Faupin and B.Grébert ). Contemporary Mathematics 500, p 1-23, 2009.


· Limiting absorption principle at low energies for a mathematical model of weak interaction: the decay of a boson ( with J.-M. Barbaroux ). C.R.Acad. Sci.Paris Ser. I, 347, p 1087-1092, 2009.


· Spectral theory for a mathematical model of the weak interaction: the decay of the intermediate vector bosons W+/- ( with J.-M. Barbaroux ). Advances in Mathematical Physics, vol. 2009, Article ID 978903, 52 pages, 2009. See also http: / / ArXiv.org / abs / 0904.3171.


· Spectral theory for a mathematical model of the weak interaction: the decay of the intermediate vector bosons W+/- . II (with W. H. Aschbacher, J.-M. Barbaroux, J. Faupin ).Ann. Henri Poincaré, 12,

p 1539-1570, 2011.


· Corrigendum to "Inverse spectral theory for a singular Sturm- Liouville operator on [0,1]" Journal of Differential. Eq., Volume 250 (2011),1232-1233.


· Organisation avec G. Allaire et J.-M. Barbaroux du colloque”Modèles Mathématiques de la Théorie Quantique des Champs”. Centre de Mathématiques Appliquées de l'Ecole Polytechnique les 7 et 8 décembre 2010. Intervenants: Z.Ammari, V.Bach, L.Bruneau, T.Daudé, J.Faupin. V.Georgescu, M.Griesemer, P.Indelicato, M.Lewin et A.Panati.


. Spectral Theory of a Mathematical Model in Quantum Field Theory for any Spin. Preprint see arXiv:1209.3207v1 [math-ph] (2012).