酉发展的Wei-Norman方程
Wei-Norman equations for a unitary evolution
摘要：
Wei-Norman技巧允许用指数的乘积来表示线性非自治微分方程的解。特别是，它能够找到一个时间顺序的产品的指数，通过解决一组非线性微分方程。该方法具有许多理论和计算上的优点，特别是在最优控制理论中。我们证明了在酉情形下，即当线性系的解由酉演化算子给出时，通过适当选择序，可将非线性系统约化为一族矩阵Riccati方程.我们的发现在量子控制理论中具有特殊的意义，因为纯量子演化是么正的。
英文摘要：
The Wei-Norman technique allows to express the solution of a system of linear non-autonomous differential equations in terms of product of exponentials. In particular it enables to find a time-ordered product of exponentials by solving a set of nonlinear differential equations. The method has numerous theoretical and computational advantages, in particular in optimal control theory. We show that in the unitary case, i.e.\ when the solution of the linear system is given by a unitary evolution operator, the nonlinear system can be by an appropriate choice of ordering reduced to a hierarchy of matrix Riccati equations. Our findings have a particular significance in quantum control theory since pure quantum evolution is unitary.
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