标题： 从谱系到散射因子 显示英文标题

标题： From spectral to scattering form factor

摘要： 我们提出了一种用于混沌量子散射过程的新指标，即散射形式因子（ScFF）。 它基于将散射振幅峰值的位置映射到随机矩阵的本征值，并计算光谱形式因子（SFF）的类比。 我们计算了几个非混沌系统的光谱和散射形式因子。 我们确定了与漏模环面相移相关的ScFF，这与黎曼zeta函数零点分布密切相关。 我们计算了高度激发弦态衰变为两个快子的衰减振幅的ScFF。 我们展示了它表现出从随机矩阵理论预期的普遍特征——下降、坡段和平坦段——并且总体上与高斯幺正系综一致。 由于弦振幅的特殊结构，它还显示出一些新特征，包括在坡段之前的一个“隆起”，这是由平均本征值密度中的间隙引起的。 对于具有适当状态相关展开的高度激发弦态，“隆起”被消除。 我们还讨论了Gaussian $\beta$- 系综的SFF，写出了高斯正交、幺正和辛系综已知结果之间的插值。 显示英文摘要

摘要： We propose a novel indicator for chaotic quantum scattering processes, the scattering form factor (ScFF). It is based on mapping the locations of peaks in the scattering amplitude to random matrix eigenvalues, and computing the analog of the spectral form factor (SFF). We compute the spectral and scattering form factors of several non-chaotic systems. We determine the ScFF associated with the phase shifts of the leaky torus, closely related to the distribution of the zeros of Riemann zeta function. We compute the ScFF for the decay amplitude of a highly excited string states into two tachyons. We show that it displays the universal features expected from random matrix theory - a decline, a ramp and a plateau - and is in general agreement with the Gaussian unitary ensemble. It also shows some new features, owning to the special structure of the string amplitude, including a "bump" before the ramp associated with gaps in the average eigenvalue density. The "bump" is removed for highly excited string states with an appropriate state dependent unfolding. We also discuss the SFF for the Gaussian $\beta$- ensemble, writing an interpolation between the known results of the Gaussian orthogonal, unitary, and symplectic ensembles.