共振解析场在一般多态系统中的应用
Resonant Analytic Fields Applied to Generic Multi-state Systems
摘要：
用解析方法研究了旋波近似及其在多态量子系统中的有效性。它们的适用性也验证了从一般状态的观点，通过使用直接的数值积分的薛定谔方程。首先，我们介绍了一个扩展的多状态系统的行波近似。在最优域诱导光滑过渡的假设下，我们得到了三种解析控制域，并证明了它们对于随机矩阵表示的一般系统的有效性和不足.通过比较，我们得出结论，基于我们的粗粒度方法的分析场优于其他的一般量子系统具有大量的状态。最后，对实际混沌系统的分析域进行了进一步的扩展，并在带状随机矩阵系统中证明了其有效性。
英文摘要：
Rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approach. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the Schroedinger equation. First, we introduce an extension of the rotating-wave approximation for multi-state systems. Under an assumption that a smooth transition is induced by the optimal field, we obtain three types of analytic control fields and demonstrate their validity and deficiency for generic systems represented by random matrices. Through the comparison, we conclude that the analytic field based on our coarse-grained approach outperforms the other ones for generic quantum systems with a large number of states. Finally, the further extension of the analytic field is introduced for realistic chaotic systems and its validity is shown in banded random matrix systems.
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