量子猫映射的矩阵元：短窗口中的涨落
Matrix elements for the quantum cat map: Fluctuations in short windows
摘要：
我们研究了量子化猫映射的矩阵系数的涨落。我们考虑对应于本征态的矩阵系数之和，本征态的本征相位位于随机选择的窗口中，假设窗口的长度随着普朗克常数而收缩。我们表明，如果窗口的长度是小于的普朗克常数的平方根，但大于不同的本征相位之间的分离，那么这个总和的方差是成比例的窗口的长度，与比例常数相一致的个别矩阵元素对应的赫克本征函数的方差。
英文摘要：
We study fluctuations of the matrix coefficients for the quantized cat map. We consider the sum of matrix coefficients corresponding to eigenstates whose eigenphases lie in a randomly chosen window, assuming that the length of the window shrinks with Planck's constant. We show that if the length of the window is smaller than the square root of Planck's constant, but larger than the separation between distinct eigenphases, then the variance of this sum is proportional to the length of the window, with a proportionality constant which coincides with the variance of the individual matrix elements corresponding to Hecke eigenfunctions.
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