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arXiv · 2506.24049

Geometric condition for the observability of electromagnetic Schr\"odinger operators on $\mathbb{T}^2$

Kévin Le Balc'h·Jingrui Niu·Chenmin Sun
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Abstract

In this article we revisit the observability of the Schr\"odinger equation on the two-dimensional torus. In contrast to the Schr\"odinger operator with a purely electric potential, for which any non-empty open set guarantees observability, the presence of a magnetic potential introduces an additional obstruction. We establish a sufficient and almost necessary geometric condition for the observability of electromagnetic Schr\"odinger operators. This condition incorporates the magnetic potential, which can also be characterized by a geometric control condition for the corresponding magnetic field.

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Kévin Le Balc'h, Jingrui Niu, Chenmin Sun. 2025-06-30. Geometric condition for the observability of electromagnetic Schr\"odinger operators on $\mathbb{T}^2$. https://arxiv.org/abs/2506.24049

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