可积系统的谱平均和参数平均
Spectral and Parametric Averaging for Integrable Systems
摘要：
分析了量子混沌中可积系统系综平均的两种理论方法--谱平均和参量平均。对于谱平均，我们引入了一种新的方法--重标谱平均。与传统的谱平均方法不同，它可以描述谱阶梯的关联函数，并产生区间水平数方差的持续振荡。参数平均，虽然不像重新缩放的频谱平均的频谱阶梯和间隔电平数方差的关联函数那样准确，但也可以产生全局电平数方差的持续振荡，并且更好地描述饱和电平刚度作为运行能量的函数。总的来说，它是最可靠的方法，用于广泛的统计。
英文摘要：
We analyze two theoretical approaches to ensemble averaging for integrable systems in quantum chaos - spectral averaging and parametric averaging. For spectral averaging, we introduce a new procedure - rescaled spectral averaging. Unlike traditional spectral averaging, it can describe the correlation function of spectral staircase and produce persistent oscillations of the interval level number variance. Parametric averaging, while not as accurate as rescaled spectral averaging for the correlation function of spectral staircase and interval level number variance, can also produce persistent oscillations of the global level number variance and better describes saturation level rigidity as a function of the running energy. Overall, it is the most reliable method for a wide range of statistics.
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