The self-averaging behavior of interacting many-body quantum systems has been mostly studied at equilibrium. The present paper addresses what happens out of equilibrium, as the increase of the strength of on-site disorder takes the system to the localized phase. We consider two local and two nonlocal quantities of great experimental and theoretical interest. In the delocalized phase, self-averaging depends on the observable and on the timescale, but the picture simplifies substantially when localization is reached. In the localized phase, the local observables become self-averaging at all times while the nonlocal quantities are throughout non-self-averaging. These behaviors are explained and scaling analysis is provided using the $\ell$-bit model and a toy model.

中文翻译：

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不平衡多体量子系统中的自平均：接近局域相

相互作用的多体量子系统的自平均行为主要是在平衡状态下进行的。随着现场无序强度的增加，系统将系统推向局部阶段，因此本论文解决了不平衡情况。我们考虑两个具有实验和理论意义的局部和两个非局部量。在非本地化阶段，自平均取决于可观察的时间和时间尺度，但是当达到本地化时，图片将大大简化。在局部化阶段，局部可观测值始终变为自我平均，而非局部量始终处于非自我平均状态。解释了这些行为，并使用$\ell$位模型和玩具模型。