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.
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.
Keywords: mode conversion, polarization, Born-Oppenheimer approximation, Maxwell equations, eigenvalue crossing, pseudo-differential systems, semi-classical analysis, lagrangian manifold, propagation of singularities, coherent states, symplectic spinors
Mot 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
Colin de Verdière, Yves 1
@article{AIF_2003__53_4_1023_0, 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}, pages = {1023--1054}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {4}, year = {2003}, doi = {10.5802/aif.1973}, zbl = {02014671}, mrnumber = {2033509}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1973/} }
TY - JOUR AU - Colin de Verdière, Yves TI - The level crossing problem in semi-classical analysis I. The symmetric case JO - Annales de l'Institut Fourier PY - 2003 SP - 1023 EP - 1054 VL - 53 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1973/ DO - 10.5802/aif.1973 LA - en ID - AIF_2003__53_4_1023_0 ER -
%0 Journal Article %A Colin de Verdière, Yves %T The level crossing problem in semi-classical analysis I. The symmetric case %J Annales de l'Institut Fourier %D 2003 %P 1023-1054 %V 53 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1973/ %R 10.5802/aif.1973 %G en %F AIF_2003__53_4_1023_0
Colin de Verdière, Yves. The level crossing problem in semi-classical analysis I. The symmetric case. Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 1023-1054. doi : 10.5802/aif.1973. https://aif.centre-mersenne.org/articles/10.5802/aif.1973/
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