Wigner Measure Propagation and Conical Singularity for General Initial Data

Details Wigner Measure Propagation and Conical Singularity for General Initial Data Wigner Measure Propagation and Conical Singularity for General Initial Data

2012-03-22

arxiv.org/abs/1203.5047v1

Mathematics

Analysis of PDEs

24 pages, 1 figure

Scientific paper

We study the evolution of Wigner measures of a family of solutions of a Schr\"odinger 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.

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