Small-time approximate controllability of bilinear Schrödinger equations on compact normal homogeneous spaces

Hugo Parada

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arXiv · 2610.29940

Small-time approximate controllability of bilinear Schrödinger equations on compact normal homogeneous spaces

Hugo Parada

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Abstract

We prove small-time global approximate controllability in $L^2$ for bilinear Schrödinger equations on compact connected normal homogeneous spaces. The controls act through finitely many smooth real-valued potentials. We first construct finite saturating families on compact connected Lie groups endowed with bi-invariant metrics, using Peter-Weyl theory and the Casimir operator. Their phase saturation contains the representative algebra and is therefore dense in $L^2$. We extend this construction to normal homogeneous quotients using finite generation of the algebra of highest-weight functions. Global controllability follows by combining the phase-to-gradient transport argument of [8] with the gradient generation theorem of [23] and Moser's transport of positive densities.

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BibTeX RIS

Hugo Parada. 2026-10-21. Small-time approximate controllability of bilinear Schrödinger equations on compact normal homogeneous spaces. https://arxiv.org/abs/2610.29940

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