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Semiclassical measure for Schrödinger operators with homogeneous potentials of order zero

Keita Mikami
(University of Tokyo)
Mat/Fys-seminar
Torsdag, 4 oktober, 2018, at 15:15-16:00, in Aud. D2 (1531-119)
Abstrakt:

In 1991, Herbst proved that the time evolution for Schrödinger operators with homogeneous potentials of order zero localizes to the direction of the critical point of the potential(localization in direction).

In this talk, we introduce the analysis of Weyl sequences of the Schrödinger operators with homogeneous potentials of order zero. We employ semiclassical analysis, especially semiclassical measure to obtain several results which can be regarded as a semiclassical analogue of the localization in direction.

As an application, we obtain a necessary condition of the observability for Schrödinger operators with homogeneous potentials of order zero.

Kontaktperson: Erik Skibsted