Resonances of a matrix Schrödinger operator created by crossings of classical trajectories

Thời gian: 14:00 đến 15:00 Ngày 20/10/2022

Địa điểm: C101, VIASM

Báo cáo viên: Kenta Higuchi (Ehime University, Japan)

Tóm tắt:

It is well-known that scalar Schrödinger operators do not have resonances near a non-trapping energy of the underlying classical mechanics. However, we found that systems of Schödinger operators create resonances near a non-trapping energy when a directed cycle is composed by a couple of non-trapping trajectories. We give an example of such resonances for a system appearing in the Born-Oppenheimer approximation of polyatomic molecules, and describe their precise asymptotic distribution in the semiclassical limit in terms of the geometry of such directed cycles.

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