For a quantum system in a macroscopically large volume V, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system v≪V is almost surely totally mixed. We show that the fluctuations around this limiting value, evaluated according to the invariant measure of these unitary flows, are captured by the Gaussian unitary ensemble (GUE) of random matrix theory. An extension of this statement, applicable when the unitary transformations conserve the energy but are maximally noisy or ergodic on any energy shell, allows to decipher the fluctuations around canonical typicality. According to typicality, if the large system is prepared in a generic pure state in a given energy shell, the reduced density matrix of the sub-system is almost surely the canonical Gibbs state of that sub-system. We show that the fluctuations around the Gibbs state are encoded in a deformation of the GUE whose covariance is specified by the Gibbs state. Contact with the eigenstate thermalization hypothesis is discussed.

中文翻译：

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围绕量子遍历系统的典型性的普遍波动。

对于在纯态下制备的，具有宏观大体积V的量子系统，该系统具有最大的噪声或遍历单一动力学，几乎可以肯定地完全混合了任何子系统v≪V的密度约简矩阵。我们表明，根据这些unit流的不变度量评估的围绕此极限值的波动被随机矩阵理论的高斯unit合奏（GUE）捕获。该陈述的扩展适用于单位变换节省能量但在任何能量壳上最大程度地嘈杂或遍历的情况，它可以解释规范性周围的波动。根据典型情况，如果大型系统是在给定的能量壳中以一般纯状态制备的，则子系统的密度降低矩阵几乎可以肯定是该子系统的规范吉布斯状态。我们表明，吉布斯状态周围的波动是在GUE的变形中编码的，该变形的协方差由吉布斯状态指定。讨论了与本征态热化假设的联系。