Semiclassical analysis of the Schrödinger equation with conical potentials
In this talk we will study the behaviour of the Wigner measures of solutions to the Schrödinger equation with potentials presenting conical singularities. These measures are related to the concentration of the solutions in the limit where a parameter in the equation (e.g. the Planck's constant) goes sufficiently small, and represent a mass density over the phase space, which may be a classical particle or a continuum of mass. The situation becomes particularly interesting with conical singularities, since they give rise to problems of non-unicity in the Hamiltonian flows that ultimately dismiss the existence of any selection principle allowing one to study the measures' time evolution within a pure classical framework.
Local: Sala Jayme Tiomno