一维相对论性量子力学中的局域化
Localization in one-dimensional relativistic quantum mechanics
摘要：
我们给出了一维安德森局域化的相对论模拟。本文利用狄拉克方程计算了自旋$\frac{1}{2}$粒子入射到矩形势垒上的透射几率。使用传输矩阵的形式主义，我们数值计算的情况下，大量的相同的障碍随机分布在一维的传输概率。还考虑了入射粒子具有三分量动量并表现自旋翻转现象的特殊情况。我们的计算表明，入射的相对论粒子显示出类似于安德森局域化的局域化行为。也得到了非相对论情形的一些推广结果。
英文摘要：
We present the relativistic analogue of Anderson localization in one dimension. We use Dirac equation to calculate the transmission probability for a spin-$\frac{1}{2}$ particle incident upon a rectangular barrier. Using the transfer matrix formalism, we numerically compute the transmission probability for the case of a large number of identical barriers spread randomly in one dimension. The particular case when the incident particle has three component momentum and shows spin-flip phenomena is also considered. Our calculations suggest that the incident relativistic particle shows localization behaviour similar to that of Anderson localization. A number of results which are generalizations of the non-relativistic case are also obtained.
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