论文标题
障碍，路径积分和本地化
Disorder, Path Integrals and Localization
论文作者
论文摘要
在存在随机势能函数的情况下，安德森定位直接来自量子力学的路径积分表示。势能的概率分布被认为是具有给定自相关函数的功能空间中的高斯。 Averaging the path integral itself we find that the localization length, in one-dimension, is given by (E_{ξ}/σ)(KE_{cl}/σ)ξ where E_{ξ} is the "correlation energy", KE_{cl} the average classical kinetic energy, σ the root-mean-square variation of the potential energy and ξ the autocorrelation length.平均路径积分的正方形明确表示路径中的闭合环在时间前进和向后穿越时会导致指数衰减，从而导致定位。我们还展示了如何使用Schwinger正确的时间，路径积分可以与通常用于研究定位的绿色功能直接相关。
Anderson localization is derived directly from the path integral representation of quantum mechanics in the presence of a random potential energy function. The probability distribution of the potential energy is taken to be a Gaussian in function space with a given autocorrelation function. Averaging the path integral itself we find that the localization length, in one-dimension, is given by (E_{ξ}/σ)(KE_{cl}/σ)ξ where E_{ξ} is the "correlation energy", KE_{cl} the average classical kinetic energy, σ the root-mean-square variation of the potential energy and ξ the autocorrelation length. Averaging the square of the path integral shows explicitly that closed loops in the path when traversed forward and backward in time lead to exponential decay, and hence localization. We also show how, using Schwinger proper time, the path integral result can be directly related to the Greens function commonly used to study localization.
