We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest model of a 1D disordered chain and we analyse both the dynamics of an initially localized state and the dynamics of quantum states drawn at random from the ensemble corresponding to the minimum knowledge about the initial state. While in the former case the site distribution remains confined in a limited portion of the chain, the site distribution of random pure state fluctuates around an equilibrium average that is delocalized over the entire chain. A clear connection between the equilibration observed when the system is initialized in a fully localized state and the amplitude of dynamical fluctuations of a typical random pure state is established.

我们考虑了显示安德森定位的孤立量子系统的平衡概念。假定该系统处于纯状态，即由经历单一动力学的波函数描述。我们集中于一维无序链的最简单模型，我们分析了初始局域态的动力学和从与初始状态的最低知识相对应的集合中随机抽取的量子态的动力学。在前一种情况下，位点分布仍局限在链的有限部分中，而随机纯态的位点分布则围绕平衡平均值波动，该平衡平均值在整个链上都是局部分布的。