Affordable Access

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

Authors
Publication Date
Disciplines
  • Law
  • Mathematics
  • Physics

Abstract

The level crossing problem in semi-classical analysis I. The symmetric case AN N A L E S D E L’INSTI T U T F O U R IE R ANNALES DE L’INSTITUT FOURIER Yves COLIN DE VERDIÈRE The level crossing problem in semi-classical analysis I. The symmetric case Tome 53, no 4 (2003), p. 1023-1054. <http://aif.cedram.org/item?id=AIF_2003__53_4_1023_0> © Association des Annales de l’institut Fourier, 2003, tous droits réservés. L’accès aux articles de la revue « Annales de l’institut Fourier » (http://aif.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://aif.cedram.org/legal/). Toute re- production en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement per- sonnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedram Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.cedram.org/ 1023- THE LEVEL CROSSING PROBLEM IN SEMI-CLASSICAL ANALYSIS I. The symmetric case by Yves COLIN DE VERDIÈRE Introduction. Let us consider a d x d self-adjoint system of semi-classical pseudo- differential operators HU = 0 in R~. Many examples occur in physics: let us mention the Born-Oppenheimer approximation in molecular physics (see [5], [14], [15], [40] and [31]), the Maxwell equations for electromagnetic waves in a non homogeneous and anisotropic medium (see [41]), the propagation of elastic waves in anisotropic media (see [36]), the propagation of waves in oceans (see [35] and [49]), the spin-orbit interaction (see [25] and, for a global and geometrical point of view, [19] and [20]). The principal symbol Hclass of H is a matrix valued function on the phase space T~R~, often called the dispersion matrix by physicists. The ideal generated by det(Hclass) is called the dispersion relation. Near a generic point of the phase space

There are no comments yet on this publication. Be the first to share your thoughts.