标题： 安德森局域化：一种由无序引起的量子束缚态 显示英文标题

标题： Anderson localization: A disorder-induced quantum bound state

摘要： 费米能级的电子在经历安德森局域化转变时，在无序介质中失去长距离传播的能力。 我们使用格林函数在一个解析可解的模型中来描述该转变过程中扩散的消失。 我们发现电子-空穴关联函数的低能渐进行为会随着一个与无序相关的的时间尺度发生跃迁，该时间尺度分隔了两个不同的区域。 这个尺度决定了传播粒子在有限体积内被束缚的时间长短。 它具有临界性，并在局域化转变时发散。 根据我们的分析，无扩散相由无法用布洛赫波空间和扩散方程描述的量子束缚态组成。 我们确定了现有方法所需的必要修正，以获得安德森局域化出现的一致微观图像。 显示英文摘要

摘要： Electrons at the Fermi energy lose their ability to propagate to long distances in disordered media when undergoing the Anderson localization transition. We use Green functions in an analytically solvable model to describe the vanishing of diffusion at this transition. We find that the low-energy asymptotics of the electron-hole correlation function undergoes a crossover with a disorder-dependent time scale separating the two regimes. This scale determines how long the propagating particle remains captured within a finite volume. It is critical and diverges at the localization transition. According to our analysis, the diffusionless phase consists of quantum bound states that cannot be described in the space of Bloch waves and with the diffusion equation. We identify the necessary amendments to the existing approaches to reach a consistent microscopic picture of the emergence of Anderson localization.