中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
学术报告
偏微分方程讨论班
Speaker: 牛景瑞 （索邦大学）
Inviter: 范晨捷
Language: Chinese
Title：Geometric condition for the observability of the Schrödinger equations with magnetic potential on two-dimensional tori
Time&Venue：2025年12月9日（星期二）16:00-17:00 & 思源楼S723
Abstract:In this talk, we study the observability for the Schrödinger equation on the two-dimensional torus, subject to a first-order perturbation by a magnetic potential. This situation turns out to be different from the case of the Schrödinger equation with a purely electric potential. More precisely, there is a sufficient and almost necessary geometric control condition for the electromagnetic Schrödinger equation that goes beyond the classical geometric control condition established by Lebeau for the unperturbed case. Under this new geometric condition, the high-frequency observability result holds on the semiclassical timescale O(h^{-3/2}), much shorter than the O(h^{-2}) timescale required for the purely electric Schrödinger operator observed from any nonempty measurable set. This talk is based on joint work with Kévin Le Balc'h and Chenmin Sun.
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