从混沌腔散射脉冲：从代数衰减到指数衰减的过渡
Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay
摘要：
无损耗混沌腔的系综平均散射功率随时间呈幂律衰减。在具有有限持续时间的脉冲的情况下，从腔的单个实现散射的功率最初紧密地跟踪幂律系综衰减，但最终过渡到指数衰减。在本文中，我们将探讨这种过渡的性质耦合到一个单一的端口的情况下。我们发现，对于一个给定的脉冲形状，过渡的性质是普遍的，如果时间是适当的归一化。我们将交叉时间定义为在各个实现中与反射功率的平均值的偏差变得与平均反射功率相当的时间。我们数值证明，随机选择的腔实现和给定的脉冲形状，反射功率的概率分布函数只取决于时间，归一化到这个交叉时间。
英文摘要：
The ensemble averaged power scattered in and out of lossless chaotic cavities decays as a power law in time for large times. In the case of a pulse with a finite duration, the power scattered from a single realization of a cavity closely tracks the power law ensemble decay initially, but eventually transitions to an exponential decay. In this paper, we explore the nature of this transition in the case of coupling to a single port. We find that for a given pulse shape, the properties of the transition are universal if time is properly normalized. We define the crossover time to be the time at which the deviations from the mean of the reflected power in individual realizations become comparable to the mean reflected power. We demonstrate numerically that, for randomly chosen cavity realizations and given pulse shapes, the probability distribution function of reflected power depends only on time, normalized to this crossover time.
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