Wigner Measure Propagation and Conical Singularity for General Initial Data

Abstract

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.

24 pages, 1 figure

References in corpus (2)

• Energy transport by acoustic modes of harmonic lattices
• Strong and weak semiclassical limits for some rough Hamiltonians

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