Semiclassical analysis of generic codimension 3 crossings. (English) Zbl 1098.81038

Fermanian Kammerer, Clotilde

Int. Math. Res. Not. 2004, No. 45, 2391-2435 (2004).

In this paper the mechanism of Landau-Zehner transitions for codimension 3 crossings and the reduction to normal forms is considered using Wigner measures. The author studies e.g. two-scale Wigner measures for symplectic submanifolds, the geometry of crossings, Colin de Verdiere’s normal form, the propagation of the two-scale Wigner measures for solutions of a model problem, and the energy transfer at finite distances. Also, a result is proved on the measures considered as traces on the crossing set in a set of certain specific distributions.

Reviewer: Horst Lange (Freiburg)

MSC:

81Q20	Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35S05	Pseudodifferential operators as generalizations of partial differential operators
81S30	Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics

Keywords:

Semiclassical crossings; Landau-Zehner transitions