SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 156-184, January 2021.
In this paper we study the controllability problem for a symmetric-top molecule, for both its classical and quantum rotational dynamics. The molecule is controlled through three orthogonal electric fields interacting with its electric dipole. We characterize the controllability in terms of the dipole position: when it lies along the symmetry axis of the molecule neither the classical nor the quantum dynamics are controllable due to the presence of a conserved quantity, the third component of the total angular momentum; when it lies in the orthogonal plane to the symmetry axis, a quantum symmetry arises due to the superposition of symmetric states, which has no classical counterpart. If the dipole is neither along the symmetry axis nor orthogonal to it, controllability for the classical dynamics and approximate controllability for the quantum dynamics are proved to hold. The approximate controllability of the symmetric-top Schrödinger equation is established by using a Lie--Galerkin method based on blockwise approximations of the infinite-dimensional systems.

中文翻译：

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旋转对称分子的经典和量子可控性

SIAM控制与优化杂志，第59卷，第1期，第156-184页，2021年1月。
在本文中，我们研究了对称顶部分子的可控性问题，包括经典旋转动力学和量子旋转动力学。分子通过与其电偶极子相互作用的三个正交电场进行控制。我们用偶极位置来描述可控性：当它沿着分子的对称轴放置时，由于存在守恒量，即总角动量的第三部分，经典动力学和量子动力学都无法控制。当它位于与对称轴正交的平面中时，由于对称态的叠加而产生了量子对称，而量子对称没有经典的对应关系。如果偶极子既不沿着对称轴也不正交 证明了经典动力学的可控制性和量子动力学的近似可控制性成立。基于无限维系统的逐块逼近，使用Lie-Galerkin方法建立了对称顶部Schrödinger方程的近似可控性。