We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like stochastic variables, whose variance satisfies the celebrated Einstein relation for Brownian diffusion. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system. We show numerically the validity of the random matrix approach in quantum chain models.

中文翻译：

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拍摄量子热化过程的快照：量子跳跃轨迹中新兴的古典性

我们从理论上研究经典统计物理学在有限量子系统中的出现，该系统要么完全孤立，要么经过量子测量过程。我们通过对不可积量子系统的随机矩阵理论方法表明，宏观可观测量的测量结果集随时间像随机变量一样演化，其方差满足著名的布朗扩散的爱因斯坦关系。我们的结果表明，如何将本征态热化的框架扩展到在其他情况下封闭的量子系统上的量子测量性质的预测。我们从数字上显示了量子链模型中随机矩阵方法的有效性。