Wigner Measure Propagation and Conical Singularity for General Initial Data

TL;DR

This paper investigates how Wigner measures evolve in Schrödinger equations with conical singularities, proving their propagation along classical trajectories for general initial data under certain conditions.

Contribution

It establishes the propagation of Wigner measures in the presence of conical singularities for broad initial data, extending previous results to more general scenarios.

Findings

Wigner measures propagate along classical trajectories.

Propagation holds for general initial data.

Classical trajectories are well-defined under genericity assumptions.

Abstract

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.