论文标题
自旋系统的选择性和稳健的时间旋转
Selective and Robust Time-Optimal Rotations of Spin Systems
论文作者
论文摘要
我们研究了具有不同偏移项的几个自旋1/2颗粒的选择性和稳健的时间旋转控制。为此，将Pontryagin的最大原理应用于两个旋转模型，该模型足以用于分析计算，并且足够复杂，可以描述不均匀性效应。我们发现，选择性和健壮的控制分别通过单数和规则轨迹描述。使用几何分析与数值模拟相结合，我们确定了不同控制问题的最佳解决方案。可以在没有数值优化的情况下在分析上得出选择性和健壮的控件。我们显示了核磁共振中几种标准控制机制的最佳性，但还设计了新的稳健控制。
We study the selective and robust time-optimal rotation control of several spin-1/2 particles with different offset terms. For that purpose, the Pontryagin Maximum Principle is applied to a model of two spins, which is simple enough for analytic computations and sufficiently complex to describe inhomogeneity effects. We find that selective and robust controls are respectively described by singular and regular trajectories. Using a geometric analysis combined with numerical simulations, we determine the optimal solutions of different control problems. Selective and robust controls can be derived analytically without numerical optimization. We show the optimality of several standard control mechanisms in Nuclear Magnetic Resonance, but new robust controls are also designed.
