The level crossing problem in semi-classical analysis I. The symmetric case

Yves Colin de Verdière[1]

  • [1] Université Joseph Fourier, Institut Fourier (unité mixte CNRS-UJF 5582), BP 74, 38402 Saint-Martin d'Hères Cedex (France)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 4, page 1023-1054
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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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 53.4 (2003): 1023-1054. <http://eudml.org/doc/116061>.

@article{ColindeVerdière2003,
abstract = {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.},
affiliation = {Université Joseph Fourier, Institut Fourier (unité mixte CNRS-UJF 5582), BP 74, 38402 Saint-Martin d'Hères Cedex (France)},
author = {Colin de Verdière, Yves},
journal = {Annales de l’institut Fourier},
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},
language = {eng},
number = {4},
pages = {1023-1054},
publisher = {Association des Annales de l'Institut Fourier},
title = {The level crossing problem in semi-classical analysis I. The symmetric case},
url = {http://eudml.org/doc/116061},
volume = {53},
year = {2003},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 4
SP - 1023
EP - 1054
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/116061
ER -

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