Wigner Measure Propagation and Conical Singularity for General Initial Data

Clotilde Fermanian Kammerer (1) , Patrick Gerard (2) , Caroline Lasser (3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 Zentrum Mathematik-M3

We study the evolution of Wigner measures of a family of solutions of a Schrödinger equation with a scalar potential displaying a conical singularity. Under a genericity assumption, classical trajectories exist and are unique, thus the question of the propagation of Wigner measures along these trajectories becomes relevant. We prove the propagation for general initial data.

Domaines: Equations aux dérivées partielles [math.AP]

Clotilde Fermanian Kammerer, Patrick Gerard, Caroline Lasser. Wigner Measure Propagation and Conical Singularity for General Initial Data. 2012. ⟨hal-00682053⟩