论文标题
在一个维度中进行定位的散射扩展
Scattering Expansion for Localization in One Dimension
论文作者
论文摘要
我们在一个空间维度中提出了一种用于无序系统的扰动方法，该方法访问了各种相位障碍，并阐明了本地化与相信息之间的联系。我们考虑了一系列相同无序的散射器链，并在任何个体散射器的反射强度方面扩展。作为一个示例应用，我们从分析上表明，在离散的量子步行中，定位长度可以非单调地取决于相位障碍的强度（而在弱混乱中扩展会产生单调降低）。更普遍地，我们在扩展中获得了所有订单，一种特定的不可分割的形式，用于传输系数对数和反射阶段的联合概率分布。此外，我们表明，对于较弱的局部反射强度，定位理论的一种版本具有：关节分布仅由三个参数确定。
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of identically disordered scatterers and expand in the reflection strength of any individual scatterer. As an example application, we show analytically that in a discrete-time quantum walk, the localization length can depend non-monotonically on the strength of phase disorder (whereas expanding in weak disorder yields monotonic decrease). More generally, we obtain to all orders in the expansion a particular non-separable form for the joint probability distribution of the transmission coefficient logarithm and reflection phase. Furthermore, we show that for weak local reflection strength, a version of the scaling theory of localization holds: the joint distribution is determined by just three parameters.
