Small-time approximate controllability of bilinear Schrödinger equations on compact normal homogeneous spaces
Abstract
We prove small-time global approximate controllability in L2 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 L2. 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 trans- port argument of [8] with the gradient generation theorem of [23] and Moser’s transport of positive densities.
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BibTeX
@misc{parada2026smalltime,
title = {{Small-time approximate controllability of bilinear Schrödinger equations on compact normal homogeneous spaces}},
author = {Hugo Parada},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29940},
eprint = {2610.29940},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05828704v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Small-time approximate controllability of bilinear Schrödinger equations on compact normal homogeneous spaces
AU - Hugo Parada
PY - 2026
DA - 2026/10/21
PB - HAL
DO - 10.48550/arxiv.2610.29940
UR - https://hal.science/hal-05828704v1
AB - We prove small-time global approximate controllability in L2 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 L2. 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 trans- port argument of [8] with the gradient generation theorem of [23] and Moser’s transport of positive densities.
ER -