多输入薛定谔方程：可控性、跟踪和对量子角动量的应用
Multi-input Schrödinger equation: controllability, tracking, and application to the quantum angular momentum
摘要：
我们提出了一个充分条件，利用几个控制的双线性离散谱薛定谔方程的近似可控性。可控性的结果扩展到同时可控性，近似可控性在$H^s$，和跟踪模。结果是更一般的比那些存在于文献中，即使在一个控制的情况下，并允许治疗的情况下，其中的频谱不受控制的运营商是非常退化的（例如，它有多个特征值或相等的差距之间的不同对的特征值）。我们将一般结果应用于旋转极性线性分子，由三个正交的外场驱动。这个模型的一个显着的属性是存在无限多的简并和共振的频谱中，防止在文献中的结果的应用。
英文摘要：
We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schrödinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability, approximate controllability in $H^s$, and tracking in modulus. The result is more general than those present in the literature even in the case of one control and permits to treat situations in which the spectrum of the uncontrolled operator is very degenerate (e.g. it has multiple eigenvalues or equal gaps among different pairs of eigenvalues). We apply the general result to a rotating polar linear molecule, driven by three orthogonal external fields. A remarkable property of this model is the presence of infinitely many degeneracies and resonances in the spectrum preventing the application of the results in the literature.
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