The level crossing problem in semi-classical analysis I. The symmetric case
[Le problème du croisement générique en analyse semi-classique I. Le cas symétrique]
Colin de Verdière, Yves
Annales de l'Institut Fourier, Tome 53 (2003), p. 1023-1054 / Harvested from Numdam
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Nous décrivons une forme normale microlocale pour un système symétrique d'équations pseudo-différentielles dont le symbole principal est à valeurs matrices symétriques réelles ayant un croisement générique de valeurs propres. Nous utilisons cette forme normale pour décrire de façon précise les solutions mucrolocales.

We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.

Publié le : 2003-01-01
DOI : https://doi.org/10.5802/aif.1973
Classification:  35C20,  35Q40,  35S30
Mots clés: conversion de modes, polarisation, approximation de Born-Oppenheimer, équations de Maxwell, croisements de valeurs propres, systèmes d'opérateurs pseudo-différentiels, analyse semi-classique, variétés lagrangiennes, propagation des singularités, états coh 
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     author = {Colin de Verdi\`ere, Yves},
     title = {The level crossing problem in semi-classical analysis I. The symmetric case},
     journal = {Annales de l'Institut Fourier},
     volume = {53},
     year = {2003},
     pages = {1023-1054},
     doi = {10.5802/aif.1973},
     mrnumber = {2033509},
     zbl = {02014671},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2003__53_4_1023_0}
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Colin de Verdière, Yves. The level crossing problem in semi-classical analysis I. The symmetric case. Annales de l'Institut Fourier, Tome 53 (2003) pp. 1023-1054. doi : 10.5802/aif.1973. http://gdmltest.u-ga.fr/item/AIF_2003__53_4_1023_0/

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