Small-time local control of a Schrödinger equation: a negative and a positive quadratic result
Karine Beauchard; Frédéric Marbach; Thomas Perrin · 2025 · arXiv
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Abstract (excerpt)
We study the small-time local controllability (STLC) of a bilinear Schrödinger equation with Neumann boundary conditions near its ground state. We focus on the degenerate case where the linearized system is not controllable, necessitating a second-order analysis. We prove two complementary results. The negative result provides a new PDE instance of Sussmann's classical quadratic obstruction, corresponding to a non-vanishing Lie bracket. The positive result appears to be the first to establish STLC at the quadratic order for a physical PDE with a single scalar control. Both proofs rely on a Fou
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Metadata source: arXiv