标题： 威格纳延迟时间的矩 显示英文标题

标题： Moments of the Wigner delay times

摘要： 威格纳时间延迟是开放系统中粒子在散射区域内部停留时间的度量。 对于混沌系统，单个时间延迟的统计（其平均值为威格纳时间延迟）被认为可以用随机矩阵理论很好地描述。 在这里，我们提出一种半经典推导，证明了随机矩阵结果的有效性。 为了简化半经典处理，我们将时间延迟的矩表示为不同能量下散射矩阵的相关函数。 在半经典近似中，散射矩阵的元素用经典散射轨迹来表示，这就需要研究这些轨迹集之间的相关性。 我们描述了相关轨迹集的结构，并制定了它们在逆通道数中的主要阶次的评估规则。 这使我们能够推导出矩生成函数满足的多项式方程。 除了展示我们的半经典结果与随机矩阵理论预测的矩相一致外，我们还推断出在半经典近似中，散射矩阵在所有阶次上都是幺正的。 显示英文摘要

摘要： The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be well described by random matrix theory. Here we present a semiclassical derivation showing the validity of random matrix results. In order to simplify the semiclassical treatment, we express the moments of the delay times in terms of correlation functions of scattering matrices at different energies. In the semiclassical approximation, the elements of the scattering matrix are given in terms of the classical scattering trajectories, requiring one to study correlations between sets of such trajectories. We describe the structure of correlated sets of trajectories and formulate the rules for their evaluation to the leading order in inverse channel number. This allows us to derive a polynomial equation satisfied by the generating function of the moments. Along with showing the agreement of our semiclassical results with the moments predicted by random matrix theory, we infer that the scattering matrix is unitary to all orders in the semiclassical approximation.