6533b829fe1ef96bd128a527
RESEARCH PRODUCT
Small-time bilinear control of Schrödinger equations with application to rotating linear molecules
Thomas ChambrionEugenio Pozzolisubject
FOS: Physical sciencesSchrödinger equation[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Mathematical Physics (math-ph)infinite-dimensional systemsOptimization and Control (math.OC)Control and Systems Engineeringbilinear systemsFOS: Mathematicslinear molecule[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Electrical and Electronic EngineeringQuantum Physics (quant-ph)small-time controllability[PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph]Analysis of PDEs (math.AP)description
In [14] Duca and Nersesyan proved a small-time controllability property of nonlinear Schrödinger equations on a d-dimensional torus $\mathbb{T}^d$. In this paper we study a similar property, in the linear setting, starting from a closed Riemannian manifold. We then focus on the 2-dimensional sphere $S^2$, which models the bilinear control of a rotating linear top: as a corollary, we obtain the approximate controllability in arbitrarily small times among particular eigenfunctions of the Laplacian of $S^2$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2023-07-01 | Automatica |